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Synthetic and spectroscopic studies of metal carboxylate dimers

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Title:
Synthetic and spectroscopic studies of metal carboxylate dimers
Creator:
Telser, Joshua A., 1958- ( Dissertant )
Drago, Russell S. ( Thesis advisor )
Ryschkewitsch, George ( Reviewer )
Weltner, William ( Reviewer )
Stoufer, R. Carl ( Reviewer )
Maddala, G. S. ( Reviewer )
Place of Publication:
Gainesville, Fla.
Publisher:
University of Florida
Publication Date:
Copyright Date:
1984
Language:
English
Physical Description:
vi, 308 leaves : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Adducts ( jstor )
Carboxylates ( jstor )
Dimers ( jstor )
Ligands ( jstor )
Pyridines ( jstor )
Rhodium ( jstor )
Solvents ( jstor )
Spectral bands ( jstor )
Spectral methods ( jstor )
Subroutines ( jstor )
Chemistry thesis Ph. D
Dissertations, Academic -- Chemistry -- UF
Molybdenum ( lcsh )
Rhodium ( lcsh )
Ruthenium ( lcsh )
Transition metal compounds -- Spectra ( lcsh )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Abstract:
Synthetic and spectroscopic studies on several complexes in the metal carboxylate series are described. These complexes are of general formula M 2 (02CR) 4 where M is a transition metal and "0 2 CR is a bridging carboxylate ligand. The metals used in this study are molybdenum, rhodium, and ruthenium. The studies were undertaken to help understand the nature of the metal -metal interaction in these complexes and to see what effect this interaction has on the reactivity of these complexes. To effect removal of the bridging carboxylate ligands, acetonitrile solutions of Rh2(0 2 CCH 2 CH 2 CH3) 4 and Mo 2 (0 2 CCH 3 ) 4 were reacted with stoichiometric amounts of the strong non-complexing acids CF3SO3H and (CH 3 CH 2 ) 20.HBF4 . This generated Rh2 (02 CH 2 CH 2 CH 3 ) 2 2+ and Mo 2 (02CCH 3 )? 2+ species in solution. The former was not isolated, but characterized in solution by NMR and UV-visible spectroscopy. Two derivatives of Mo 2 (02 CCH 3 ) 2 2+ were isolated: CMo 2 (0 2 CCH3) 2 (CH 3 CN) 4 ](CF 3 S03) 2 and [Mo 2 (0 2 CCH3) 2 (CH3CN) 5 ](BF 3 0H) 2 . The reactivity of the former complex towards oxidative addition was investigated. The complex was found to be quite stable towards oxidation in contrast to other Mo(II) complexes. Rhodium trifluoroacetate was reacted with various Lewis bases to give adducts of general formula Rh2 ( 02^3)482 as had been previously reported for Rh 2 (0 2 CR)4. However, with pyridine and £-butyl Isonitrile, complexes of general formula Rh2(0 2CCF3)4B4 were isolated constituting a new class of adduct. With phosphorus donors, Rh-Rh bond cleavage occurred to give monomeric Rh(I) and Rh(III) complexes. This demonstrates enhanced reactivity for Rh2(02CCF3)4 compared to rhodium alkyl carboxylate dimers. The chemical and electrochemical generation of Rh2(02CCH 2 CH 2CH3)4B2 + is described. These results and EPR spectra of these species are explained using a molecular orbital model. The strength of the rhodium Lewis base interaction determines the chemical and spectroscopic properties of these species. The formally mixed oxidation state complex Ru2(02CCH2CH2CH3)4Cl was studied by powder magnetic susceptibility measurements over the temperature range 5-300 K, by EPR spectroscopy In various glasses at 4 K and by Far IR spectroscopy at room temperature. In agreement with previous reports, the complex has a quartet ground state with unpaired electron spin density delocalized over both Ru atoms. Reactivity studies of this compound with Lewis bases are described. A bispyridine adduct of ruthenium butyrate chloride is reported.
Thesis:
Thesis (Ph. D.)--University of Florida, 1984.
Bibliography:
Includes bibliographic references (leaves 298-307).
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Joshua A. Telser.

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SYNTHETIC AND SPECTROSCOPIC STUDIES OF METAL CARBOXYLATE DIMERS


BY

JOSHUA A. TELSER


























A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR CF PHILOSOPHY

UNIVERSITY OF FLORIDA

1984















ACKNOWLEDGEMENTS


There are many people and things responsible for a successful

graduate career and I would like to take this opportunity to mention

them.

First of all, I would like to thank my research director, Professor

Russell S. Drago, for his continuous help from near and from afar. It

was a privilege to be part of a research group that has accomplished so

much in so many areas over so long.

Since a group is not one man, I would also like to thank the many

members of the Drago group who have helped me out: Charlotte Owens,

Rich Cosmano, Barry Corden, Pete Doan, Dave Pribich, Carl Bilgrien, Andy

Griffis, and Ernie Stine.

Since a group is not alone, I would also like to thank the faculty

and students of other groups at both Illinois and Florida. In

particular, thanks are due to Professor R. Linn Belford and Jeff

Cornelius and to Professor William Weltner, Jr., and Richard Van Zee.

Since faculty and students cannot do everything themselves, I would

also like to thank the many support personnel who made my work a lot

easier. In particular, I greatly appreciate the help of the glass shop

and NMR and Elemental Analysis Labs at both Illinois and Florida.















TABLE OF CONTENTS


PAGE

ACKNOWLOGEMENTS....................... ........................ ii

ABSTRACT...................... ................................ v

CHAPTER I. GENERAL INFORMATION................................ 1

CHAPTER II. THE ACTION OF STRONG ACIDS ON M2(O2CR)4 SPECIES.... 15
Introduction ............................................. 15
Results and Discussion.................................... 19
Conclusion................................................ 57
Experimental Section...................................... 58

CHAPTER III. THE REACTIONS OF RHODIUM TRIFLUORACETATE WITH
VARIOUS LEWIS BASES............................... 65
Introduction................. ............................ 65
Results and Discussion.................................... 68
Conclusion............................................... 113
Experimental Section..................................... 114

CHAPTER IV. SPECTROSCOPIC AND BONDING STUDIES OF RHODIUM
CARBOXYLATE DIMER CATION RADICALS.................. 123
Introduction............................................. 123
Results and Discussion................................... 128
Conclusion............................................... 144
Experimental Section..................................... 145

CHAPTER V. SPECTROSCOPIC AND REACTIVITY STUDIES OF RUTHENIUM
BUTYRATE CHLORIDE.................................. 147
Introduction............................................. 147
Results and Discussion................................... 153
Conclusion............................................... 190
Experimental Section..................................... 191

CHAPTER VI. GENERAL CONCLUSIONS............................... 197

APPENDIX A. EXPERIMENTAL AND CALCULATED MAGNETIC
SUSCEPTIBILITY DATA ............................... 199

APPENDIX B. UPPER RIGHT HAND NON-ZERO MATRIX ELEMENTS FOR
SPIN HAMILTONIAN USED IN METHOD 1.................. 200










PAGE

APPENDIX C. COUPLED BASIS SET FOR S = S + S2 WHERE
S = 2 = 3/2, USED IN METHOD 5.................... 201

APPENDIX D. UPPER RIGHT HAND NON-ZERO MATRIX ELEMENTS FOR
SPIN HAMILTONIAN USED IN METHOD 5.................. 202

APPENDIX E. COMPUTER PROGRAMS USED FOR EPR SPECTRAL
SIMULATIONS...................................... 203

APPENDIX F. COMPUTER PROGRAMS USED FOR MAGNETIC
SUSCEPTIBILITY DATA SIMULATIONS.................... 255

APPENDIX G. COMPUTER PROGRAMS USED FOR MOSSBAUER AND MMR
SPECTRAL SIMULATIONS.............................. 273

REFERENCES.................................................... 298

BIOGRAPHICAL SKETCH........................................... 308














Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

SYNTHETIC AND SPECTROSCOPIC STUDIES OF METAL CARBOXYLATE DIMERS

By

Joshua A. Telser

December 1984
Chairman: Professor Russell S. Drago
Major Department: Chemistry
Synthetic and spectroscopic studies on several complexes in the

metal carboxylate series are described. These complexes are of general

formula M2(O2CR)4 where M is a transition metal and -02CR is a bridging

carboxylate ligand. The metals used in this study are molybdenum,

rhodium, and ruthenium. The studies were undertaken to help understand

the nature of the metal-metal interaction in these complexes and to see

what effect this interaction has on the reactivity of these complexes.

To effect removal of the bridging carboxylate ligands, acetonitrile

solutions of Rh2(02CCHCH22CH3)4 and Mo2(02CCH3)4 were reacted with

stoichiometric amounts of the strong non-complexing acids CF3SO3H and

(CH3CH2)20.HBF4. This generated Rh2(02CH2CH2CH3)22+ and Mo2(02CCH3)22+
species in solution. The former was not isolated, but characterized in

solution by NMR and UV-visible spectroscopy. Two derivatives of

Mo2(02CCH3)22+ were isolated: [Mo2(O2CCH3)2(CH3CN)4](CF3SO3)2 and

[Mo2(02CCH3)2(CH3CN)5](BF3OH)2. The reactivity of the former complex
towards oxidative addition was investigated. The complex was found to









be quite stable towards oxidation in contrast to other Mo(II)

complexes. Rhodium trifluoroacetate was reacted with various Lewis

bases to give adducts of general formula Rh2(02CCF3)4B2 as had been

previously reported for Rh2(02CR)4. However, with pyridine and t-butyl

isonitrile, complexes of general formula Rh2(02CCF3)4B4 were isolated

constituting a new class of adduct. With phosphorus donors, Rh-Rh bond

cleavage occurred to give monomeric Rh(I) and Rh(III) complexes. This

demonstrates enhanced reactivity for Rh2(O2CCF3)4 compared to rhodium

alkyl carboxylate dimers. The chemical and electrochemical generation

of Rh2(02CCH2CH2CH3)4B2+ is described. These results and EPR spectra of

these species are explained using a molecular orbital model. The

strength of the rhodium Lewis base interaction determines the chemical

and spectroscopic properties of these species. The formally mixed-

oxidation state complex Ru2(O2CCH2CH2CH3)4C1 was studied by powder

magnetic susceptibility measurements over the temperature range 5-300 K,

by EPR spectroscopy in various glasses at 4 K and by Far IR spectroscopy

at room temperature. In agreement with previous reports, the complex

has a quartet ground state with unpaired electron spin density

delocalized over both Ru atoms. Reactivity studies of this compound

with Lewis bases are described. A bispyridine adduct of ruthenium

butyrate chloride is reported.















CHAPTER I
GENERAL INFORMATION


The discovery of transition metal complexes containing metal-metal

bonds is a relatively recent one. This discovery and much of the

subsequent progress towards understanding metal-metal bonded complexes

have been discussed in detail by Cotton and Walton in their book

"Multiple Bonds Between Metal Atoms"' as well as in various review

articles by others.2-6 Nevertheless, a brief summary of the historical

background of this class of complexes is in order.

For the first half of the 20th century, transition metal chemistry

was dominated by the concepts developed by Alfred Werner.7 That is,

most complexes were thought of as what are now referred to as classical

coordination compounds, a central transition metal ion surrounded by

electron donating ligands usually in an octahedral orientation. Square

planar, tetrahedral and other geometries were known, but the concept

that a compound could exist in which there were several metals

interacting in various ways had not been suggested. Metal-metal

interactions were something thought to occur in bulk metals and not in

complexes with oxidized metals. This idea was so firmly held that

compounds that were synthesized during that time that contained metal-

metal bonds were not investigated further. Notable examples are

chromium acetate, first prepared in 1844,8 and various tantalum9 and

molybdenuml0 halides synthesized during the early part of the 20th

century.









With the advent of improved methods of crystal structure

determination by x-ray diffraction, the discovery of metal-metal bonds

in dimeric and cluster compounds became inevitable. It was in the metal

carbonyl complexes that metal-metal bonding was first demonstrated. The

reason for this may be a practical one in that these compounds were

relatively easy to study, but it may also be a philosophical one. Metal

carbonyls and other organometallic compounds are newer and quite

different from classical coordination compounds and thus understanding

them was not hampered by older ideas that would be invariably applied to

complexes such as metal halides and carboxylates. In Fe2(CO)g in 1938

and with greater certainty in Mn2(CO)10 in 195711 metal-metal single

bonds were first proposed. The existence of metal-metal single bonds in

carbonyl complexes containing two to twelve or more metal atoms is

widely accepted.

The existence of multiple bonds between metal atoms was not

originally found in carbonyl complexes, but in some rhenium halides.

The stoichiometry and the structure, when it was eventually

determined,12 of [Re2Clg]2- could not be explained by classical

theories. It was necessary to invoke a multiple metal-metal bonding

scheme.13 A qualitative diagram of this molecular orbital (MO) scheme

is shown in Figure 1-1. In a compound such as Mn2(CO)10 it is not

surprising that the odd d electron on each manganese pairs up to give a

single a bond. However, it is surprising that in a Re(III) compound all

four d electrons pair up to give a quadruple bond. The evidence for

this quadruple bond comes primarily from the crystal structure. The Re-

Re distance is extremely short, 2.222 A in (n-Bu)4NRe2Cl8, and there is

no twist angle between the ReCI4 subunits so that the chlorides are
































Figure 1-1. Formation of metal-metal bond molecular orbitals
from individual metal d atomic orbitals.











antibonding
combinations


dxy


+ a !

2 2
dx -y




dxz






dyz




dz2


y


Sz


T*


= 77


dxy





22
dxy 2




dxz






dyz




dz2


7T








CT


__ c


:9-









fully eclipsed.14 This sterically unfavorable structure is the result

of the fourth bond, the 6 bond between the Re atoms which arises

primarily from the in-phase addition of the dxy orbitals. The in-phase

addition of the two dx2_y2 orbitals could give another 6 bond; however

these orbitals are usually primarily involved in forming metal-ligand

bonds and are thus rarely considered in MO schemes for metal-metal

bonded complexes. The other three Re-Re bonds are derived in a more

conventional manner, analogous to the triple bond well known for

alkynes. The in-phase addition of the two dz2 orbitals gives the a bond

and the in-phase addition of the four dxz and dyz orbitals gives a

degenerate pair of r orbitals. The out-of-phase addition of these Re d

orbitals gives a corresponding set of higher energy anti-bonding 6*, a*,

and r* orbitals. In the Re(III) dimer the eight d electrons just fill

all the bonding orbitals giving a diamagnetic compound with a total bond

order of four. Subsequent to this work on the rhenium dimer, other

dimeric metal-metal bonded complexes were studied and their properties

explained using this MO scheme. The previously known complex

Cr2(O2CCH3)4(H20)2 was reinvestigated and proposed15 to have a quadruple

bond resulting from the pairing up of the four d electrons on each

Cr(II) in the same manner as described above for Re(III). Chromium is

the only first row transition metal proposed to form a multiply bonded

dimer. The small size of first as opposed to second and third row

transition metals makes it less convincing that enough orbital overlap

occurs to give a quadruply bonded complex. It has even been suggested

that no Cr-Cr bond exists at all in the chromium dimers.16 Copper forms

the well known complex Cu2(O2CCH3)4(H20)2 which is isostructural with

chromium acetate. This general structure is shown in Figure 1-2. This































Figure 1-2. General structure for metal carboxylate dimer with
idealized D4h symmetry. Axial ligands, L, need not
be present.











C


o /R


0


L


0


~ --~-0


0'









copper complex was studied by Bleaney and Bowers17 a number of years

ago, before the multiple metal-metal bond theory was proposed. They

found that the two copper atoms were strongly antiferromagnetically

coupled, but there was no true Cu-Cu bond. Thus it is possible, by

analogy between the two first row transition metal dimers, that chromium

acetate has a bond order of less than four with the remaining d

electrons antiferromagnetically coupled.

A large number of second and third row transition metal dimers have

been reported and in these there is little doubt that the metal-metal

bond MO scheme is valid. In addition to crystal structure

determinations of many metal-metal bonded complexes, other spectroscopic

and theoretical studies have been performed to confirm the generality of

this MO scheme. Metal-metal bonded complexes are known for molybdenum,

tungsten, technetium, rhenium, ruthenium, osmium, rhodium, and

platinum. The compounds are far too numerous to list; however some

examples of each will be given. The first studied was the rehnium

chloride and a variety of multiple metal-metal bonded rhenium,

technetium, and molybdenum halides are known.1-4 However, carboxylate

complexes were also among the first known as with the chromium and

copper acetates mentioned above. This thesis is concerned with the

metal carboxylate dimers and thus to show the generality of this type of

ligand in forming metal-metal bonded complexes, one should note the

following compounds: Re2(02C(CH3)3)4C12, Tc2(O2C(CH3)3)4C12,

Ho2(O2CCH3)4, W2(02CCF3)4, Ru2(02CCH3)4CI and Rh2(02CCH3)4 In these

complexes the bond orders range from four in Re, Tc, Mo and W to 2.5 in

Ru to one in Rh. These bond orders can be easily determined using the

MO scheme in Figure 1-1 and adding the appropriate number of d electrons
for both metals.









Given that a great variety of metal-metal bonded complexes exist

and that a qualitative MO scheme exists which can explain their overall

properties, the question then arises as to why would one wish to study

them further. There are several reasons to do so. First, as was

indicated specifically with the chromium carboxylate, the exact nature

of the metal-metal bonding in these complexes is not yet completely

resolved. Second, the wide range in bond orders in metal-metal bonded

complexes such as the carboxylate dimers means that there is a wide

range in strength of metal-metal interaction. Thus, what exists here is

an isostructural series for which comparison of the reactivity and

spectroscopic properties of members of the series affords a direct means

of understanding the effect different metal-metal interactions have on

the chemistry of transition metal complexes. One can also compare the

reactivity and spectroscopic properties of a metal-metal bonded complex

to that of a monomeric complex of the same metal. The presence of two

or more metals in close proximity leads to the possibility of metal

synergism.18 This means that one metal can influence the chemistry and

the other metal site leading to different reactivity than would be

expected for noninteracting multi-metal or monomeric metal systems.

Synergism from metal clusters is proposed in a number of biological

systems such as the ferredoxins, nitrogenase, cytochrome oxidase, and

copper type 3 proteins.19'20 Synergism in metal carboxylate clusters

has also been used to model surface reactions.21 The variety of metals

and their oxidation states that form metal carboxylate dimers makes this

class of complexes a good model system to study synergistic effects.

The nature of the synergistic effect in metal carboxylate dimers has

been previously examined by Richman and co-workers.22-26 The enthalpies









of Lewis base binding to the vacant coordination sites along the M-M

axis in several complexes of general type M2(02CR)4 were measured.

These sites will hereafter be referred to as axial sites since they are

along the metal-metal bond axis. Enthalpies of formation of both 1:1

and 2:1 Lewis base axial adducts were obtained for metal carboxylate

dimers such as Rh2(O2CCH2CH2CH3)4, Rh2(02CCCF2CFC3)4 and

Mo2(02CCF2CF2CF3)4 These will be abbreviated as Rh2(but)4, Rh2(hfb)4
and Mo2(hfb)4, respectively. Comparison of the enthalpies for 1:1 and

2:1 axial adduct formation clearly showed significant changes in the

acidic properties of the second metal as a result of base coordination

to the first. Significant differences between rhodium and molybdenum

systems were also found. Use of the E and C equation27-29 and

modifications thereof allowed quantitative understanding of these

effects. It was found that inductive transfer of electrostatic

properties of the base was more effective through the shorter Mo-Mo

quadruple bond than through the longer Rh-Rh single bond. Inductive

transfer of the covalent properties of the base was more effective

through the more polarizable Rh-Rh bond than the Mo-Mo bond.

Differences in the type of Lewis acid-base interactions were also found

for the two metals. Using the MO scheme in Figure 1-1, disregarding the

second S bond, it can be seen that the molydenum carboxylate dimer with

the total of eight d electrons from the two Mo(II) subunits has no 7*

electron density. In contrast, the rhodium carboxylate dimers with a

total of 14 d electrons from the two Rh(II) subunits have filled v*

orbitals. This r* electron density can interact with empty n* orbitals

on bases with these orbitals of the right energy. Thus, a higher than

expected enthalpy of adduct formation was found for the rhodium









carboxylate dimers with Lewis bases such as pyridine and acetonitrile.

These bases can function as w-acceptors as well as o-donors. No such w-

backbonding stabilization was found for the molybdenum carboxylate dimer

since it has vacant n* orbitals.

A final reason for studying metal-metal bonded complexes, in

addition to understanding synergistic effects where one metal influences

the reactivity of the other, is to understand reactions where both

metals are directly involved. An example would be the reaction of M-M

with some X-Y species to give M-X and M-Y. This can be considered an

oxidative addition and would be analogous to many reactions of organic

compounds, particularly those with carbon-carbon multiple bonds. The

reactivity of metal-metal bonded complexes has been recently reviewed30

and there are many examples of this type of reaction. However, most

involve organometallic complexes such as metal carbonyl clusters. It is

not clear that this reactivity would occur to as great an extent in

carboxylate or halide complexes wherein the metals are generally in a

higher oxidation state.

One means of enhancing the reactivity of and understanding the

metal-metal interaction in metal carboxylate dimers is to achieve varied

ligand coordination to other than just the axial sites. As can be seen

in Figure 1-2, the sites perpendicular to the metal-metal axis are fully

occupied by the bridging carboxylate ligands. These sites will be

referred to hereafter as equatorial sites. If these ligands could be

wholly or partly removed, then the reactivity of the metal-metal b"nd

could be better investigated. It was reported a number of years ago by

Legdzins and co-workers31'32 that strong, non-complexing aqueous acids

could protonate the bridging carboxylates generating in solution species









with available equatorial coordination sites. The effect of strong,

non-complexing acids on metal carboxylate dimers of rhodium and

molybdenum in organic solvents, chiefly acetonitrile, is the subject of

the second chapter of this thesis.

Another approach to achieving ligand coordination to the equatorial

sites is to use a more poorly coordinating bridging carboxylate to begin

with. Recently, Girolami and co-workers33 obtained unusual products

from the reaction of Mo2(02CCF3)4 with various Lewis bases, primarily

phosphorus donors. In some of the products, equatorial rather than

axial Lewis base coordination was observed. This was found for

phosphines that were sterically small and good a-donors. Thus, use of a

fluorocarboxylate rather than an alkylcarboxylate can lead to equatorial

coordination without the need for protonation of the carboxylate by

strong acid. The reactivity of Rh2(02CCF3)4 towards Lewis bases was

systematically investigated and is the subject of the third chapter of

this thesis.

Another interesting aspect of multi-metal systems, besides their

variety of ligand coordination sites, is the variety of oxidation states

available to them. A monomeric complex might have two accessible

oxidation states, an oxidized and a reduced state. In contrast, a

dimeric complex of this metal could well have more since the two metals

could be both oxidized or both reduced or one of each to give a wider

range of electrochemical behavior. This ability is one reason why metal

clusters are proposed to play an important role in biological redox

processes such as the photochemical oxidation of water in

photosynthesis.34 Thus one would expect metal-metal bonded complexes to

exhibit a wide range of oxidation states. For metal-metal bonded dimers









this is only partly true. Some variety of oxidation state does exist.

For Mo, W, Tc and Re stable complexes with bond orders of 3, 3.5, and 4

are known1 and they can be electrochemically interconverted. In these

the metals are in the (III,III), (II,III) and (II,II) oxidation states

respectively for Mo and W with the order reversed for Re and Tc. Only

the (II,II) oxidation state for Rh and the (II,III) state for Ru give

stable metal-metal bonded complexes that have been well characterized.

Thus, the range of oxidation states in some metal-metal bonded dimeric

systems is no greater than in monomeric complexes. Nevertheless, the

redox behavior of metal carboxylate dimers is of interest and the use of

electrochemical methods and EPR spectroscopy is helpful in understanding

this behavior. A number of studies of this nature have been made on
metal carboxylate dimers and related complexes by Cotton and Pedersen35-

39 and by other workers40,41 and show that the redox and EPR properties
of these complexes can be explained by the qualitative MO scheme

described above. In a study by Drago and co-workers23 the effect of

both axial Lewis base coordination and different caboxylate ligands was

quantitatively examined. Oxidation of the dimer is easier when the base

is strongly donating and the carboxylate is not electron with-drawing.

This oxidation converts the diamagnetic dimers to paramagnetic complexes

which can subsequently studied by EPR spectroscopy. This technique

gives information on the electronic properties of the complex that can

be directly compared to theoretical studies. In addition to the

qualitative MO scheme described earlier, a number of quantitative
studies using a variety of calculational methods have been performed.42-
47 However, these results are not always in full agreement with

experimental data. The generation of paramagnetic rhodium carboxylate









dimer species and comparison between these experimental and various

theoretical results is the subject of the fourth chapter of this thesis.

In contrast to the normally diamagnetic metal carboxylate dimers of

rhenium, molybdenum, rhodium, and others mentioned above, there exists a

normally paramagnetic dimer. Ruthenium does not form a doubly bonded

d12 (II,II) or a triply bonded d10 (III,III) dimer. Rather, a d11

(II,III) dimer of formal bond order 2.5 is formed upon reaction of

ruthenium salts with carboxylic acids.48 This complex, of general

formula Ru2(02CR)4X, is quite stable compared to the rhodium (II,III)

species described above. Thus, it can be easily studied using EPR and

magnetic susceptibility. These techniques were applied to Ru2(but)4C1 a

number of years ago by Cotton and Pedersen.36 However, due to

experimental difficulties their results on the electronic and magnetic

nature of the complex were not conclusive. Thanks to improved

technology in EPR and magnetic susceptibility instrumentation, it was

now possible to perform detailed studies on this ruthenium carboxylate

dimer. These studies are the subject of the fifth chapter of this

thesis. In addition, since in contrast to the rhodium and molybdenum

systems the reactivity of the ruthenium dimer towards Lewis bases has

not been widely investigated, some reactivity studies were performed and

are also described in this chapter.















CHAPTER II
THE ACTION OF STRONG ACIDS ON M2(O2CR)4


Introduction


When dissolved in a coordinating solvent, the counter anions bound

to a transition metal cation often dissociate. For example, most first

row transition metal salts dissolve in water to give M(H20)6n+

species.49 In contrast, metal carboxylate dimers do not readily give

M2n+ and RC02". The bridging carboxylate ligands remain coordinated to

give neutral species in solution of general structure as shown in Figure

1-2 where L could be solvent. To further understand the coordination

chemistry of metal-metal bonded systems, it would be desirable to

achieve ligand coordination to a variety of sites such as those

equatorial as well as axial to the metal-metal bond. Furthermore, it is

well known that generation of coordinative unsaturation about a metal

center is crucial for the generation of a catalytic cycle.50 This often

occurs by reversible ligand binding. Thus, it would be desirable to

prepare metal-metal bonded dimers with labile ligands so that they could

be used in catalytic studies and be more effective than analogous

complexes with more strongly bound ligands. These catalytic processes

could involve thermally or photochemically activated ligand

dissociation. In this way any synergistic advantages to using such a

system as opposed to one with monomeric complexes could be determined.

A metal-metal bonded complex analogous to the M(H20)6n+ species has

been reported. Maspero and Taube51 prepared Rh24+(aq) by the reduction

1 rz









of RhCl2+(aq) by Cr2+(aq). This species was identified by conversion to

Rh2(02CCH3)4(H20)2 by addition of sodium acetate. This conversion

from the solvated cationic species does not appear to be completely

reversible. Legdzins and co-workers31,32 treated various metal

carboxylate dimers with strong, non-complexing aqueous acids such as

HBF4(aq). They claim to have generated Rh24+ in this manner. This

claim was subsequently refuted by Wilson and Taube52 who proposed that

the treatment of Rh2(02CCH3)4 with, for example, hot 1 M aqueous CF3SO3

generated Rh2(02CCH3)33+(aq) and Rh2(02CCH3)22+(aq) but no Rh24+(aq).

The formulation of these species was based on UV-visible spectroscopy

and column chromatography. Neither group reported the isolation of any

stable rhodium dimer containing zero, two or three bridging acetates.

The action of strong acids does lead to carboxylate protonation which

allows generation of equatorial coordination sites on the rhodium

dimer. The use of this general method in wholly organic solvent systems

was investigated here. It was hoped that in such solvents more complete

ligand protonation of Rh2(02CR)4 would occur since there would be no

leveling effect from water. Furthermore, the species generated this way

might prove easier to isolate. Very recently, Ford and co-workers53,54

were able to prepare a series of complexes of formula Rh2(02CCH3)3L+,

Rh2(02CCH3)22+, and Rh2L44+ where L = 1,8=naphthyridine or derivatives

thereof such as 2,7-bis(2-pyridyl)-l,8-naphthyridine. These were

prepared by addition of stoichiometric amounts of the ligand and aqueous

1 M HC1 to methanol solutions of rhodium acetate. Similar results using

pyridine are discussed below and were carried out at roughly the same

time. Thus, use of a strongly donating, preferably chelating ligand

does allow isolation of cationic rhodium dimer species. However, these









are not complexes with the type of labile ligand one would desire so

that catalytic activity would result. Isolation of this type of rhodium

dimer has not yet been achieved.

The analogous Mo2(02CR)4 system has proven somewhat more amenable

to study. A very large number of complexes containing the Mo-Mo

quadruple bond are known. Most have bridging carboxylate ligands,

halides or a variety of other anionic groups. Complexes with neutral

ligands are far fewer. Species such as Mo2X4L4 are known where X =

halide or alkyl and L = phosphine such as P(CH3)354-57 Fewer still are

complexes which contain the Mo-Mo quadruple bond coordinated by neutral,

weakly donating ligands. A number of years ago, Bowen and Taube58

reported the Mo24+(aq) species. This was not isolated as solid, but

prepared in solution in the following manner. First, K4Mo2C18 was

reacted with K2S04 in 0.2 M CF3SO3H(aq) to give K4Mo2(S04)4 a stable

salt. This sulfate was reacted with Ba(CF3S03)2 to precipitate BaSO4

and give the red aquo molybdenum dimer in solution. This species was

identified by UV-visible spectroscopy and could be converted back to the

acetate. This work and the corresponding study with rhodium described

above showed that these metal-metal bonded dimers could exist in

solution without the presence of bridging or even anionic ligands. As

was found much later with rhodium,53,54 Bowen and Taube58 were able to

isolate salts of the molybdenum dimer by using strongly donating

chelating neutral ligands. Addition of ethylendiamine (en) and 2,2'-

dipyridyl (dipy) to solutions of Mo2C184- led to isolation

of Mo2(en)4Cl4 and Mo2(dipy)2Cl4 Although these complexes have not

been structurally characterized, the former species presumably has no C1

coordinated to the molybdenum atoms. The Mo24+(aq) species and related









complexes such as Mo2C184- have been used in a photochemical study by

Trogler and co-workers.59 Ultraviolet irradiation of aqueous solutions

of these complexes produced dihydrogen. This reaction was proposed to

proceed via Mo2(v-OH)24+(aq) which was generated directly from Mo24+(aq)

and via Mo2(u-Cl)2Cl4(u-H)3- with the halides. This indicates a

potential application for molydenum dimer species. Analogous complexes

that would be soluble in organic solvents might also show interesting

photochemical behavior.

Another approach towards generating molybdenum dimers with weakly

coordinating ligands was taken by Abbott and co-workers.60 Molybdenum

acetate was reacted with neat CF3SO3H at 100 C. Removal of solvent and

drying at 100 C under vacuum yielded a tan solid formulated as

Mo2(CF3S03)4. This product was frequently contaminated by Mo2(02CCH3)1_3

impurities which were very difficult to remove. Furthermore, the

complex was extremely prone to decomposition making it difficult to use

for subsequent reactions. Very recently, Mayer and Abbott61 achieved

greater success using Mo2(02CH)4 rather than the acetate as starting

material. Molybdenum format was reacted with CF3SO3H and (CF3SO2)20

for six days to yield CO and a tan product formulated as [Mo2(H20)4

(CF3S03)2](CF3SO3)2. This complex reacts with acetronile to yield blue

[Mo2(CH3CN)8](CF3S03)4. These very air and water sensitive complexes
were characterized by IR and UV-visible spectroscopy and elemental

analysis. This represents the first reported example of a quadruply

bonded molybdenum dimer coordinated only by monodentate, weakly

donating, natural ligands. The reaction of Mo2(O2CCH3)4 with CF3SO3H

and other strong nonaqueous acids in acetonitrile and other organic

solvents is described here. These studies were carried out at roughly









the same time as those of Mayer and Abbott61 and gave similar results.

The reactivity of the resulting complexes was also investigated.


Results and Discussion


Rhodium

Treatment of the purple solution of Rh2(but)4 in acetonitrile with

CF3SO3H leads to an immediate, although slight, color change to dark

red. The n-butyrate ligand was chosen for increased solubility; similar

results were obtained with acetate. Trifluoromethanesulfonic acid was

chosen since it is a very strong, poorly coordinating acid that is

somewhat soluble in organic solvents. The effect of different amounts

of CF3SO3H on the UV-visible absorption spectrum of Rh2(but)4 is shown

in Figure 2-1. Rhodium butyrate with no acid showed absorption bands at

552 (e=202) and 438 nm (E=101). These are virtually identical to the

results reported for rhodium acetate in acetronitrile, bands at 552

(e=235) and 437 nm (e=125).62 Single crystal polarized electronic

absorption spectra of rhodium acetate led to a proposal that these bands

correpond to (Rh-Rh)i* + (Rh-Rh)a* and (Rh-Rh)r* + (Rh-O)o* transitions,

respectively.63 Some controversy has recently arisen as to this

assignment and will be discussed in Chapter IV. Addition of two

equivalents of CF3SO3H leads to a very little change in the UV-visible

spectrum. However, addition to four equivalents of acid leads to a

dramatic change. The primarily metal-metal bond trnasition at 552 nm is

relatively unaffected, but the metal-liga~d transition is strongly

affected, shifting to 380 nm. This shift to lower wavelength may result

from a strengthening of the Rh-0 bonds of the remaining butyrates caused

by the higher relative charge on the metal dimer. This would lower the























-1 E

4Nm 4- S-
C -,
o u

a






0-
'O a















0 I0 0
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*- -o















*M
'a
C) W}









s- C








0. O *-
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4-- *a *








h-0
S1C C-

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.3 0
/ C C0
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.0 VO
U >

a- O- a
t/ C-
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N










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CD CO C C


c o
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energy of the Rh-O a bonding orbitals and raise the energy of the Rh-

0 a* antibonding orbitals leading to the observed shift to higher

energy. Addition of excess CF3SO3H (-10 equivalents) and allowing the

solution to sit for one hour does not greatly change the spectrum. The

main transitions are observed at roughly the same wavelengths. A large

band extending into the ultraviolet region is observed which may result

from rhodium dimer or solvent decomposition. Solvent decomposition is a

definite problem when trifluoromethanesulfonic acid is used with organic

solvents. For example, it catalyzes the decomposition of THF.64 With

acetonitrile, trimerization probably occurs to give 2,4,6-trimethyl-

1,3,5-triazine. This compound was not isolated, but when benzonitrile

was used as a solvent in the above procedure, the analogous compound

kyaphenine (2,4,6-triphenyl-1,3,5-triazine) was isolated and easily

identified by elemental analysis, melting point and mass spectroscopy.

Kyaphenine is normally synthesized by the addition of excess CC13CO2H to

benzonitrile.65 Thus, the use of excess CF3SO3H should be avoided.

Nevertheless, the UV-visible spectrum suggests that protonation of the

bridging carboxylates is occurring with four equivalents of acid. The

species generated in this manner can be identified by NMR

spectroscopy. NMR data are summarized in Table 2-I. The 13C{1H} NMR

spectra of n-butyric acid and Rh2(but)4, both in acetonitrile-d3, are

shown in Figures 2-2 and 2-3, respectively. Of particular importance is

the signal for the carboxyl carbon which has a very different chemical

shift in the two compounds. Addition to four equivalents of CF3SO3H

leads to a spectrum as shown in Figure 2-4. The four peaks at 139.47,

126.87, 114.85, and 102.46 ppm relative to internal TMS correspond to

the carbon in CF3SO3(H) split by three equivalent fluorine nuclei (19F,



























4c 4- 4-'


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I=1/2). The other signals correspond to free and Rh coordinated butyric

acid, with the carboxyl carbon peaks occurring in the expected places,

by analogy with Figures 2-3 and 2-3. Proton NMR spectroscopy gave

similar results. Figure 2-5A shows the 1H NMR spectrum of Rh2(but)4

with the expected splitting patterns for an n-propyl group. Figure 2-5B

shows the spectrum after addition of four equivalents of CF3SO3H.

Signals are observed for coordinated and free butyric acid. The poor

resolution of some of these peaks may be due to the presence of acid,

causing proton exchange and perhaps decomposition. Based on the peak

intensities, the dominant species in solution has an average composition

of Rh2(but)22+. The area ratio of peaks corresponding to free and

coordinated butyrate was 1:1 in several separately prepared solutions.

The ratio of peak areas for the protons for both free and coordinated

butyrate was 2:2:3 for H :HB:HY as expected. This solution gave no EPR

signal at 77 K indicating that a Rh(II) monomer was not present. This

does not prove that the dimer remains intact since disproportionation to

diagmetic Rh(III) and Rh(I) may have occurred. However, the NMR data

suggest that the solution contains the dimer since the signals for

coordinated butyrate, particularly C1, occur near those for Rh2(but)4.

Also Rh(III) and Rh(I) complexes are generally orange or yellow. The

NMR data, in conjunction with the UV-visible results, indicate that four

equivalents of CF3SO3H generate Rh2(but)22+ in acetonitrile solution.

Attempts to isolate a solvated Rh2(but)22+ salt were unsuccessful.

Evaporation of the acetonitrile solution left a dark red, water soluble

oil. Previous workers32,52 reported that evaporation of the solution

obtained by the titration of Rh2(02CCH3)4 with aqueous CF3SO3H led to a

deliquescent green oil which was similarly intractable. Attempts to


























tC
-

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S-
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0 =
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isolate a product using BPh4 and PFg" as counterions were

unsuccessful. Some solids were obtained, but the results were not

repeatable and the products could not be well characterized.

Another approach that was taken to isolate a Rh2(but)42+ species

involved using a bridging dianionic ligand, Y2-, to form a neutral

compound Rh2(but)2Y. This type of compound has precedent in the A-frame

series of complexes, which have been found to coordinate a wide variety

of molecules to their exposed side.66-69 The sulfide ligand was chosen

since it is used in the A-frame complexes,69 is readily available, has a

high affinity for transition metals, and bridges easily. Anhydrous

sulfide was generated directly in THF by addition of "Super-Hydride"

(LiBH(CH2CH3)2) to elemental sulfur. This solution was added to the

Rh2(but)22+ solution leading to immediate formation of a black

precipitate. The black compound was insoluble in all solvents so it

could only be characterized by elemental analysis. Elemental analysis

indicated a complex with 1-2 sulfurs and two butyrate groups. Mass

spectroscopy was used to little avail. No molecular ion peaks were

detected at m/e=412 for Rh2(but)2S or m/e=446 for Rh2(but)2(SH)2.

Intense peaks corresponding to H2S and HS fragments were observed. The

compound is possibly a sulfide or hydrosulfide bridged rhodium polymer

which contains two butyrates per rhodium dimer. A similarly intractable

compound was prepared using selenide. Rakowski Dubois and co-workers70

successfully converted the molybdenum sulfide polymer [(CSH5)MoSx]y to

the soluble binuclear complex [(C5H5)MoS(SH)232 by stirring the polymer

for 5-7 days under 1 atm of H2. This was attempted with the rhodium

sulfide polymer, but no dissolution was observed. The solid was also

treated with 1-iodoheptane in the hope of alkylating any bridging SH









groups to solubilize the complex. However, no reaction or dissolution

was observed and the solid recovered should no increase in carbon or

hydrogen content. The anion of 1,3-dithiopropane, generated in the same

manner as the sulfide, was used in the hope of obtaining more soluble

products, but gave only an oil. Other Y2- type ligands that could be

considered are cis-1,2-dicyanoethene-1,2-dithiolate (mnt) which forms

complexes with many transition metals71 and (HOPO)202- (pop) which forms

binuclear complexes with platinum.72,73 However, mnt reacts with

Rh2(O2CCH3)4 to give a monomeric Rh(II) complex,71 and would doubtless
do the same with Rh2(02CR)2+. In contrast to the results with

platinum,72,73 rhodium as both RhC13 and Rh2(02CCH3)4 does not appear to

react readily with pop or H3PO3 to give analogous P-bonded dimeric

complexes.

A final attempt at isolating a cationic rhodium carboxylate dimer

involved the use of pyridine, a Lewis base far stronger than

acetonitrile. Addition of excess pyridine to the acetonitrile solution

of Rh2(but)42+ led to an immediate color change to orange. The UV-

visible absorption spectrum of this solution showed a band at 465 nm

(F=481) presumably corresponding to the (Rh-Rh)r* + (Rh-Rh) a*

transition and a very large band extending into the UV region. This

latter band may involve rhodium to pyridine w* transitions. The order

of addition of pyridine and acid is important. When pyridine (10

equivalents) is added to rhodium butyrate in acetonitrile, the purple

Rh2(but)4(CH3CN)2 solution immediately turns red, indicative of

Rh2(but)4(pyr)2. The equilibrium constants for axial coordination of

various Lewis bases to rhodium butyrate have been determined,23-25 and

Keq for pyridine binding is several orders of magnitude larger than that









for acetonitrile. However, when CF3SO3H (10 equivalents) is added, the

purple color is restored indicating that the pyridine is completely

protonated by the strong acid. This occurs even though some pyridine is

coordinated to the Lewis acid Rh2(but)4. Adding more pyridine

neutralizes the acid present and the red color of the axial pyridine

adduct eventually develops. When excess acid is added to this, as with

any acetonitrile solution of rhodium butyrate, the Rh2(but)42+ species

results and subsequent addition of pyridine leads to the orange color of

what is presumably a pyridine adduct of Rh2(but)4 with equatorial base

coordination. Addition of excess acid to the orange solution restores

the purple color indicating that the equatorially coordinated pyridines

can also be protonated. Attempts were made to isolate solids from the

orange solution by evaporation, cooling, and the use of various solvents

such as water and methanol and various counter anions such as BPh4- and

PF6-. Oils were usually obtained; however a solid was isolated which

analyzed approximately for Rh2(but)2(pyr)4(PF6)2. With Rh2(O2CCH3)4,

less oiling occurred and what is presumably [Rh2(02CCH3)2(pyr)4]

(CF3SO3)2 was isolated. Based on this result and those from Ford's

laboratory,53,54 use of butyrate, while helpful in solution studies, is

not recommended for isolation of solids.

Some other reactivity studies were undertaken on the Rh2(but)42+

solution. This solution showed no visible change upon exposure to air

and the 1H NMR spectrum was unchanged. On the basis of kinetic data,

HRh2(02CCH3)3 has been proposed as an intermediate in the hydrogenation

of olefins catalyzed by rhodium acetate.74 Rhodium acetate itself shows

no reactivity towards H2 (1 atm) at temperatures up to 80 C. It was

hoped that such a hydride species might be observed in the reaction of









H2 with the cationic rhodium dimer solution. This solution was sealed

in an NMR tube under 1 atm of H2, but showed no visible or 1H NMR

spectral change. Furthermore, the solution shows no reaction with one

or two equivalents of 1-hexene or CH302CC=CCO2CH3, both of which might

be expected to add oxidatively to the Rh-Rh bond. Thus, reactivity with

organic molecules has not been enhanced by exposing the metal-metal

bond.

Molybdenum

In contrast to the work with rhodium described above, it was

possible to isolate stable, cationic acetonitrile coordinated

derivatives of the molybdenum carboxylate dimer. Molybdenum acetate is

completely insoluble in organic solvents, but when suspended in

acetonitrile, addition of two equivalents of CF3SO3H leads to immediate

formation of an intensely colored purple solution. Removal of solvent

and recrystallization of the resulting solid from 1:1 acetonitrile/

toluene allows isolation in good yield of a purple crystalline

complex. Elemental analysis suggests its formulation as

[Mo2(02CCH3)2(CH3CN)4] (CF3S03)2, (1). Use of more acid, up to 10
equivalents, leads to essentially the same product with greater solvent

decomposition. The use of neat acid will be discussed below. This

compound is air sensitive and very hygroscopic but is indefinitely

stable under an inert atmosphere. Various methods were used to confirm

that I is an acetonitrile coordinated Mo-Mo quadruply bonded species as

formulated above. The oxidation state of molybdenum was found to be 2+

using Fe3+ as oxidant using a reported method.58 However, metal-metal

bond cleavage can occur without oxidation state change. Examples

include the photolysis of Re2Cl82- in acetonitrile to give









Re(CH3CN)3C1375 and the reaction of Mo2(02CCH3)4 with t-BuNC to give

Mo(t-BuNC)5(02CCH3)2.76 The conditions required were more strenuous

than those used here. Irradiation at 366 nm for 24-48 hours was needed

for photolysis and in the second case, t-BuNC is a far stronger ligand

than acetonitrile.

The UV-visible absorption spectrum of I is of interest and provides

conclusive evidence that the Mo-Mo quadruple bond remains intact. In

acetonitrile solution bands are observed at 535 (E=864), 390 (e=117) and

255 nm (E=7383). This resembles the results of Bowen and Taube58 who

found for Mo24+(aq) and Mo2(en)44+ absorption bands at 504 (E=337) and

478 nm (e=483), respectively and weaker bands at 370 (E=40) and 360

(E=36.4), respectively. A band at 235 nm (e=966) was also observed for

Mo2(en)42+. Some controversy exists as to the assignment of the
electronic transitions in the Mo-Mo quadruply bonded system. However, a

very detailed single crystal polarized electronic absorption spectrum

study by Martin and co-workers77 indicated that the band observed at 435

nm corresponds to a (Mo-Mo)6 + (Mo-Mo)6* transition. The second band at

377 nm was more tentatively assigned to a (Mo-Mo)6* + (Mo-Mo) r*

transition. A recent study by Manning and Trogler78 of the electronic

spectrum of matrix isolated Mo2(02CCH3)4 confirmed the assignment of the

6+6* transition although suggested that other, probably Mo-0 states,

contribute to the observed band. At any rate, these two transitions are

observed for 1. The UV-visible spectrum of I was also obtained in THF

solution and gave qualitatively the same results. Bands at 490 (E=321),

335 (E=461), and 277 nm (E=3066) were observed. Dissociation of

coordinated acetonitrile probably occurs which changes the absorption

bands. The shift to shorter wavelengths may result from the replacement








of the r-acceptor CH3CN by the a-only ligand THF. Thus i in THF shows

absorptions closest in wavelength and intensity to those of Mo24+(aq)

and Mo2(en)44+. In addition, I in THF is far more air sensitive than 1

in acetonitrile, changing color almost immediately upon air exposure,

perhaps indicating poorer stabilization of the Mo24+ unit.

The IR spectrum of I (Nujol mull) is shown in Figure 2-6. Most of

the absorption bands can be readily assigned. Very sharp bands

corresponding to v(CN) of coordinated acetonitrile are observed at 2300

and 2285 cm-1. This shift to higher frequency, compared to 2266 cm-1

for free acetonitrile, is indicative of end-on nitrile coordination with

little i-backbond stabilization.79 Two v(CN) bands are seen because in

addition to the v(CN) fundamental, there is a combination of the

symmetrical CH3 deformation and the C-C stretch. These two bands are

subject to Fermi resonance coupling which affects their frequencies and

intensities. Unfortunately, no assignment can be made as to Mo-N

stretches. Very few metal organonitrile complex M-N stretches have been

conclusively identified and they usually are weak and of widely varying

frequency.80 Absorption bands corresponding to the acetate ligand are

of interest. For 1 no band corresponding to vasy(CO2) was observed.

This is seen at 1578 cm"1 in Na02CCH3.81 However, a strong band at 685

cm-1 is observed which is most likely 6(C02). This occurs at 675 cm-1

in Mo2(02CCH3)460 and at 646 cm-1 in Na02CCH380 and indicates the

presence of bridging acetate in 1. Finally, a weak band is observed at

410 cm-1 which may correspond to a Mo-Mo stretch. In centrosynm=tric

metal carboxylate dimers this band is IR inactive. However, Raman

spectroscopy studies56 on a number of derivatives of the quadruply

bonded Mo dimer show v(Mo2) occurring at 383 to 404 cm-1 with weak to

























Q.


r 0










CD
U,



01
cu



1--

C)

























0
C O


































4-
U, r















-? 0
-4-)




co
u
























I



C ,
.





















OO
S" O










Uu
m VI
















1/1 s

S-



0; 0
l -i

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33lOlHIISNyil %









medium intensities. It is possible that non-centrosymmetric isomers of

I are present allowing observation of v(Mo2) in the IR spectrum. Known

molybdenum dimer complexes with this geometry in which the acetates are

cis are Mo2(02CCH3)2((Pz)3BH)282 and Mo2(02CCH3)2(CH3COCHCOCH3)2.83

Infrared studies on these complexes were not reported; however these and

an analogous isomer of 1, all with C2v symmetry, would have an IR active
Mo-Mo stretch. This would most likely be of low intensity due to the

small dipole moment change involved. This possible structure and that

of a centrosymmetric isomer are shown in Figure 2-7. The remaining IR

bands can be assigned to the counterion, non-coordinated CF3S03". Bands

are observed at 1285, 1245, 1160, 1030, 755, 720, 635, 575, and 520

cm-1. The IR and Raman spectra of solid Na03SCF3 have been carefully

analyzed by Miles and co-workers.84 The vibrations they observed and

their assignments are as follows: 1280 (vasy(CH3)), 1232 (vs(CF3)),

1168 (vasy(S03)), 1036 (vs(S03)), 766 (6s(CF3)), 630 (6asy(S03)), and

531 and 515 cm-1 both asy(CF3)). These bands can be directly compared

to those observed for 1. When CF3S03- is coordinated, the IR bands for

v(S03) change greatly. For example, Mo2(03SCF3)4 has S-0 stretches at
1350, 1110, and 990 cm-1.60 The band observed in I at 720 cm-1 cannot

be assigned to the CF3S03- and is probably an acetate or acetonitrile
vibration.

Proton NMR spectroscopy was performed on 1, but did not provide

much insight into its structure. Signals were observed at 4.3 and 2.0

ppm relative to internal TMS in nitromethane-d3. The upfield signal is

probably coordinated CH3CN since in CD3CN solution it broadened and

decreased in intensity over time, disappearing after about one hour,

indicating exchange with the solvent. The downfield signal is probably












V0




















OO
o
























0---
0




















n I
I c
O
+2
O--


o Z



Z I

\ 0
Z I
0 0
U


zO
C-

0 /
--0









CH3C02- although it is rather far downfield for metal coordinated

acetate. Paramagnetic impurities initially present or arising from

complex decomposition would cause line broadening and unusual chemical

shifts.85 However, I does not show an EPR signal in 1:1

acetonitrile/toluene at 77K.

A different synthetic approach was used to study the

interconvertability of the Mo24+ derivatives. What is presumably the
reported60 Mo2(03SCF3)4 complex was prepared but not characterized. To

this was added acetonitrile to give an intensely colored blue

solution. Addition of toluene led to formation of a bright blue

precipitate. This complex did not give a satisfactory elemental

analysis. The IR spectrum indicated coordinated CH3CN, non-coordinated

CF3SO3- and some residual bridging acetate as well as a strong v(OH)

band. Slow evaporation of the filtrate led to formation of purple

crystals. The IR spectrum and elemental analysis of these crystals

coresponded to that of 1. The initially isolated blue complex is most

likely one with less than two acetates giving a more highly charged

species which is less soluble in organic solvents. Subsequent to this

work, Mayer and Abbott61 reported the synthesis of [Mo2(H20)4(03SCF3)2]

(CF3S03)2. This complex was synthesized from Mo2(02CH)4 and thus, in

contrast to the previously reported Mo2(O3SCF3)4, could be reproducibly
prepared free from any carboxylate contamination since the format

decomposes to CO and H20. Addition of acetonitrile to this complex led

to isolation of blue [Mo2(CH3CN)8](CF3S03)2. The blue complex reported

here is most likely impure [Mo2(CH3CN)8](CF3SO3)2, indicating that the

acetonitrile solvate of Mo24+ can also be prepared from molybdenum

acetate, but much less successfully than by the method using molybdenum









format as starting material. What is interesting is that as found with

the rhodium systems, the M2(02CR)22+ species is very stable. Even

following the extreme conditions of Abbott and co-workers,60 a

considerable amount of the Mo2(02CCH3)22+ species is isolated.

Some reactivity studies on I were performed. As stated previously,

the complex is air sensitive and quite hygroscopic as a solid. However,

in acetonitrile solution, the complex is relatively stable. Dioxygen

can be bubbled through this solution for at least 30 minutes without any

visible change. Exposure to air does eventually decompose the dimer.

This decomposition was monitored by UV-visible spectroscopy and is shown

in Figure 2-8. The characteristic Mo-Mo quadruple bond absorption bands

disappear and most likely a variety of monomeric molybdenum species

result. Prolonged exposure to air gives a blue-green solution

characteristic of high oxidation state Mo. It is likely that this

decomposition is assisted by replacement of coordinated acetonitrile by

water. Complex 1 dissolves in water to give a red solution similar to

that of Mo24+(aq). This solution is very air sensitive, as is

Mo24+(aq), in contrast to I in acetonitrile. Complex 1 reacts
immediately with Et4NO2CCH3 in acetonitrile to give a yellow solution

from which yellow crystals of Mo2(02CCH3)4 precipitate. Complex 1

reacts readily in acetonitrile solution with stronger Lewis bases.

Addition of excess (-10 equivalents) of nitrogen donors such as pyridine

or N-methylimidazole gave red solutions and phosphorus donors such as

tricyclohexylphosphine gave blue solutions. These reactions were not

investigated further; however, it is likely that a variety of derivatives







































350 400 450 500 550 600

X (nm)



Figure 2-8. UV-visible absorption spectrum of 1 in acetonitrile
(6.0 x 10- M) showing changes on exposure to air.








of the Mo2(02CCH3)22+ unit with various ligands stronger than

acetonitrile could easily be prepared.
The electrochemistry of 1 was Investigated to determine if stable

Mo2(II,III) or other species could be generated. Previous
electrochemical studies by Cotton and Pedersen38 on Mo2CIS4- and
Mo2(but)4 indicated that these complexes could be quasireversibly

oxidized at -0.4 V vs. sce to short-lived Mo2(II,III) species that were

not isolated. The Mo2(but)4+ species was observed by EPR
spectroscopy. Complex 1 in acetonitrile with 0.1 M (n-Bu)4NBF4 as the

supporting electrolyte showed no reversible redox waves over the range

+2.0 to -2.0 V vs. Ag/AgC1,KC1(sat'd). A weak irreversible oxidation

occurred at +1.5 V. Acetonitrile coordination may stablize the dimer

towards oxidation, but does not facilitate isolation of oxidized

species.

Another form of oxidation of the Mo2(II,III) unit could involve
oxidative addition to the Mo-Mo quadruple bond. Such reactions are well

known for carbon-carbon multiply bonded compounds. For example, Br2
oxidatively adds to olefins to give dibromo compounds. Of more

relevance here are the studies by Chisholm and co-workers86-88 who have
achieved oxidative addition to the Mo-Mo triple bond in Mo2(OR)6

complexes. For example, Mo2(i-PrO)6 reacts with (i-PrO)2 to give

Mo2(u-i-PrO)2(i_-PrO)6,86 with various alkynes in the presence of
pyridine to give Mo2(u-i-PrO)2(i-PrO)4(pyr)2(u-C2R)87 and with
dimethylcyanamide to give Mo2(i-PrO)6(u-NCMNe2).88 Such reactions might
be expected for Mo2(02CR)4 complexes if the ilo-Mo bond were more

exposed. Thus, complex 1 is a likely candidate. Unfortunately, no
reaction was observed between 1 and CH3I, (CH3CH2S)2 and 1-hexene, all









of which could oxidatively add across the Mo-Mo quadruple bond. Complex

1 did react readily with dimethylcyanamide (~10 equivalents) in

acetonitrile to give a blue solution. From this a bright blue solid was

isolated. The IR spectrum of this solid showed a very strong v(CN) band

at 2260 cm-1 (Nujol mull) with no bands in the 1600 to 2200 cm-1

range. This can be compared to free (CH3)2NCN, with v(CN) at 2205 cm-1

and to complexes with side-on dimethylcyanamide coordination such as

[Ni(CO)(NCN(CH3)2)]2 with v(CN) at 2008 cm-1 89 and the above Mo(III)

alkoxide dimer with u(CN) at 1582 cm-1.88 The shift to higher frequency

seen here indicates end-on nitrile coordination as seen with

acetonitrile, with no evidence for side-on coordination involving the

Mo-Mo bond. Complex I also showed no reaction with SnC12 or Vaska's

compound (Ir(CO)(PPh3)2C1). These complexes were hoped to add

reductivity to 1 replacing acetonitrile to give clusters containing 4-

coordinate Sn or 6-coordinate Ir, respectively.

A final approach towards investigating the reactivity of I was to

use anionic metal fragments to generate clusters resembling the

reactions attempted above to generate Sn or Ir containing clusters. The

reaction of monomeric metal fragments to form clusters has been widely

studied.90 Of particular use is the reaction of anionic metal complexes

with species containing a weakly bound ligand. An example is the

reaction of Fe5C(CO)142- with W(CO)3(CH3CI)3 to give WFe5C(CO)172-.91

An important point regarding the complexes synthesized in this manner is

that the reactants ar" generally both metal carbonyl complexes or at

least compounds containing metals in similar, low oxidation states with

similar ligands. If 1 would react with these anionic species to form

clusters, the result would be a cluster in which two of the metals, the








molybdenum atoms, would be in a relatively high oxidation state with

relatively electron-withdrawing ligands, carboxylates, while the other

metal would be in a relatively low oxidation state with electron-

donating ligands such as carbonyls.

Complex I was reacted with Mn(CO)5- (C5H5)Mo(CO)3- and Fe(CO)42-

The first two can be easily prepared by reduction of the dimeric species

Mn2(CO)10 and (C5H5)2Mo2(CO)6 by Na/K alloy.92 The iron complex is

available commercially and is often referred to as Collman's

reagent.93 Unfortunately, these reduced species reacted with 1 via

redox reactions. The metal carbonyl starting material was regenerated

and could be identified by IR. Uncharacterized species from

decomposition of the Mo dimer were also produced. Apparently, these

anionic carbonyl complexes are too strongly reducing to form clusters.

This problem often occurs in the reaction of anionic complexes even with

other low oxidation state carbonyl compounds. For example,

(C5H5)Fe(CO)2- and V(CO)6- are not usable in these reactions because

they are such strong reducing agents.90 Furthermore, some clusters are,

like 1, easily reduced. For example, Fe3(C0)12, Fe2Ru(CO)12 and

FeRu2(CO)12 are easily reduced and fragmented.90 Thus, it appears that

the reaction of higher oxidation state metal-metal bonded dimers with

reduced organometallic species is not a facile means of synthesizing

metal custers.

In addition to 1, [Mo2(02CCH3)2(CH3CN)4](CF3SO3)2, the synthesis of

other complexes containing the Mo-Mo quadruple bond was iv-estigated.

One approach would be to use a solvent other than acetonitrile. As

discussed previously, the strong acid needed for carboxylate protonation

precludes the use of many solvents. The problems with THF








(polymerization) and nitriles (oligomerization) have already been

mentioned. Solvents that would solvate the cationic species generated

by carboxylate protonation but be only weakly coordinating are

nitromethane, propylene carbonate and sulfolane (tetrahydrothiophene-

1,1-dioxide). The first two decompose readily upon addition of CF3SO3H;

however sulfolane appears not to decompose. Addition of CF3SO3H (~4

equivalents) to suspensions of Mo2(02CCH3)4 in these three solvents

leads to a faint red color indicative of aquo-coordinated Mo dimer

species. However, the bulk of the molybdenum acetate does not dissolve

and addition of more acid does not lead to more dissolution, only to

solvent decomposition. Clearly, the only reaction occurred because of

the presence of water in these solvents. A reasonably good donor

solvent, such as acetonitrile, is needed to stabilize any cationic

molydenum complexes produced and so drive the carboxylate protonation

reaction to completion.

Another parameter that can be varied besides solvent is the acid

used. It was desired in this work to avoid the use of aqueous solvent

systems since those had been studied previously58 and cationic Mo dimer

complexes were not isolated except with strong ligands such as

ethylenediamine. This solvent choice limits the variety of acids

usable. Furthermore, acids containing halide ions are to be avoided

since the Mo dimer readily coordinates halides. For example,

Mo2(02CCH3)4 reacts with Ph4AsCl in dilute HC1 to give [Mo2(02CCH3)2C14]
(Ph4As)2.83 Other completing acids would produce similar species,

resulting in a Mo dimer coordinatively saturated by strong, anionic

ligands. A non-complexing, nonaqueous acid that is readily available,

besides CF3SO3H, is fluoroboric acid as the diethylether adduct,









C(CH3CH2)20]HBF4. This acid is very difficult to handle since it is

very viscous and hygroscopic. Furthermore, it is difficult to purify

and may be of varying composition, as will be shown below. Addition of

approximately four equivalents of [(Et20)]HBF4 to an acetonitrile

suspension of Mo2(02CCH3)4 leads to formation of an intensely colored

magenta solution. From this solution an air sensitive, hygroscopic

magenta compound can be isolated that is best formulated as

[Mo2(O2CCH3)2(CH3CN)5](BF3OH)2, (2). This complex was characterized in
the same manner as 1. The oxidation state of Mo was found to be 2+.

The UV-visible absorption spectrum of 2 in acetonitrile shows bands at

527 (E=890), 370 (=205), and 269 nm (e=7000). This indicates that the

Mo-Mo quadruple bond is present. Exposure to air leads to

decomposition, as with 1, only it occurs more rapidly with 1. This

process is shown in Figure 2-9.

The IR spectrum of 2 is of interest and supports the above

formulation based on elemental analysis. The spectrum (Nujol mull) is

shown in Figure 2-10. Three strong bands corresponding to v(CN) of

coordinated acetonitrile are observed at 2308, 2282, and 2258 cm1.

Elemental analysis indicated that there were five acetonitriles in 2 as

opposed to four in 1. In 1 there are two v(CN) bands whereas in 2 a

third band results from CH3CN in either a different coordination

environment or from different isomers. Two possible isomeric structures

for 2 are shown in Figure 2-11. As can be seen by comparison with

Figure 2-8, in I the acetonitriles are equivalent while in 2 they are

not. Comparison of the IR absorption bands corresponding to the acetate

demonstrates again the difference between I and 2. Complex 1 showed no

band corresponding to vasy(C02). By contrast, 2 shows bands at 1647,










































350 400 450 500 550 600

X (nm)


Figure 2-9. UV-visible absorption spectrum of 2 in
acetonitrile (6.5 x 10-4 M) showing changes
on exposure to air.



























































































































33NVlHIASNlai %








1540, and 1500 cm-1. The first is most likely Vasy(CO2) for monodentate

acetate, the latter two for bridging acetate. Comparison with known

compounds with bridging acetate, such as Cr2(02CCH3)4(H20)2 which has

vasy(C02) at 1575 cm-1 94 and those with monodentate acetate, such as

Ru(02CCH3)2(CO)2(PPh3)2 which has vasy(CO2) at 1613 cm-1,95 shows that a

band at this high frequency is characteristic of monodentate acetate.

Very sharp, intense bands are observed at 680 and 685 cm-1 corresponding

to S(C02). If one of the acetates is monodentate this would allow
coordination of an additional acetonitrile as shown in Figure 2-11. It

is possible that the fifth acetonitrile is axially coordinated; however

this site in Mo carboxylate dimers is only weakly coordinating. Even a

strong Lewis base such as pyridine only weakly binds to this position in

Mo2(02CCF3)4,96 which is a stronger Lewis acid than Mo2(02CCH3)4. A
weak, but distinct, band at 405 cm-1 may correspond to the Mo-Mo

stretch. This would be IR allowed in 2 since no centrosymmetric isomers

are possible as can be seen in Figure 2-11. A band is observed at 720

cm-1 corresponding to an acetate or acetonitrile vibration as in 1.

The remaining bands correspond to the counterion and support its

formulation as BF3OH-. A strong band is seen at 1060 cm-1 with weak,

but distinct, bands at 950, 765, 520, 378, and 360 cm-1. Vibrational

absorptions for BF4- are at 1070 (v3, vasy(BF)), 777 (vl, vs(BF)), 533

(v4, 6asy(FBF)), and 360 cm-1 (v2, 5asy(FBF)).97 These same bands for
B(OH)4- are at 945, 754, 533, and 379 cm1.98 All of these modes are

Raman allowed, but only '3 and v4 are IR allowed in these tetrahedral

complexes. The bands observed in 2 at 1060 and 520 cm-1 correspond to

these two IR allowed vibrations. The band at 950 cm-1 may be v3 for 8-0.

The bands at 378 and 360 cm-1 may correspond to v2 for 8-0 and B-F





53

+

I
O

\ 0

0- -0 0O "


\ o

O --- Z
z


lo o
ZI u
O O
S4-
0
O





CM 1
0-0 -
Io








z I-
0 0







I -
o-









bonds, respectively. In BF30H-, a complex with C3v symmetry, all

vibrations are IR allowed so these would be observed. Finally, two

strong bands assigned to v(OH) are seen at 3600 and 3530 cm-1. Thus,

the IR spectrum of 2 supports the formulation of the counterion as

BF30H- presumably resulting from an impurity in the [(Et20)]HBF4 used.

Support for this counterion formulation is also obtained by anion

exchange. Complex 2 can be dissolved in an acetonitrile solution of

excess (n-Bu)4NBF4 or (n-Bu)4PF6 and addition of toluene leads to

precipitation of primarily the BF4- or PF6- salt. This process can be

repeated to effect complete exchange.

The 1H NMR spectrum of 2 resembles that of I with signals observed

at 3.0 and 2.1 ppm in CD3CN. Thus, NMR does not distinguish between

different types of acetonitrile coordination.

Due to the more difficult synthetic procedure for 2 compared to 1,

as well as more uncertainty as to the exact structure of 2, reactivity

studies were not performed.

Interestingly, a complex analogous to 2 can be obtained using

CF3SO3H. After recrystallization of 1, the filtrate is often magenta

rather than purple. Addition of a small amount of toluene and allowing

the solution to sit overnight leads to formation of a. crystalline

magenta precipitate, (3). The amount of 3 varies greatly from one

preparation of i to the next. It is not clear as to the procedure for

selectively preparing one or the other, although use of freshly

distilled CF3SO3H leads to better yields of I over 3. A formula that

can be proposed for 3 is [Mo2(02CCH4)2(CH3CN)4X](CF3S03)2 where X=CH3CN

or H20. The oxidation state of Mo in 3 is 2+. The elemental analysis

of 3 favors X=H20. This is also supported by the fact that 3 is more
































33NllIMSNVai %


- t









likely to be obtained with less pure, presumably water contaminated

CF3SO3H. However, the IR spectrum of 3, shown in Figure 2-12 (Nujol

mull), has no band corresponding to v(OH). A shoulder on the Nujol band

at 3250 cm-1 might be from this vibration. The bands assignable to

v(CN) at 2310, 2285, and 2255 cm-1 are virtually identical in frequency

and intensity pattern to those observed for 2. Furthermore, the bands

assignable to the CO2 vibrations are similar for 2 and 3. A weak band

is seen at 1640 with stronger bands at 1530 and 1508 cm-1. The first

can be assigned to vasy(C02) for monodentate acetate, the latter two to
bridging acetate. Well resolved bands at 680 and 690 cm-1 correspond to

6(C02). Strong, well resolved bands corresponding to all the vibrations
of non-coordinated CF3S03" are observed at 1280, 1230, 1150, 1030, 755,

635, 575, and 515 cm-1. The assignment of these bands has been

discussed previously and are the same as those found in 1. Without a

structure determination by single crystal x-ray diffraction, the

differences between complexes 1, 2, and 3 cannot be definitively

determined. Assuming that 2 and 3 contain monodentate and I bidentate

acetate, it is remarkable that these two types of carboxylate

coordination lead to such different colors. The exact orientation of

the monodentate acetate might give some clue to this. It is clear that

different anions do not lead to different properties.

In addition to the Mo2(O2CR)4 system, the Mo2(S2CR)4 system was
investigated. The facile synthesis of Mo2(S2CCH3)4 has been reported.99

Unfortunately, it shows no reaction with two to four equivalents of

CF3SO3H in acetonitrile. Overnight stirring of Mo2(S2CCH3)4 in neat

CF3SO3H leads to recovery of the starting material along with a small

amount of decomposition products. The CH3CS2 species binds very









strongly to Mo and is not readily protonated. Mo2(S2CR)4 complexes

could be used in calorimetric studies of Lewis base binding for

comparison with RCO2- complexes. Mo2(02CCH3)4 is soluble in THF and a

complex such as Mo2(S2CCH2CH2CH3)4 might be soluble in more poorly

coordinating solvents suitable for use in calorimetric work.


Conclusion

The addition of stoichiometric amounts of strong, non-complexing

acids to metal-metal bonded carboxylate dimers leads to protonation of

the bridging carboxylate and generation in solution of M2(02CR)22+

species. Spectroscopic evidence confirms that the metal-metal bond

remains intact and that two carboxylates are retained. The choice of

solvent is crucial since it must stabilize the resulting coordinatively

unsaturated cationic complex, but withstand the strong acid.

Acetonitrile fits these requirements and several acetonitrile

coordinated complexes of the molybdenum dimer are reported here and

elsewhere.61 With rhodium it was not possible to isolate such a complex

as was previously found by workers using aqueous solvents.32,52 Using

strong donors such as pyridine as described here, and related ligands as

reported elsewhere,53,54 it is possible to isolate a cationic rhodium

carboxylate dimer. However, these ligands may not be sufficiently

labile for subsequent reactivity studies on the rhodium system. It may

be that even acetonitrile coordinates too strongly to the Mo dimer,

since the complex reported here does not show reactivity towards

oxidative addition in contrast to various organometallic metal-metal

bonded complexes. Another interesting possibility is that only

organometallic dimers, containing relatively electron donating ligands









and with metals in a low oxidation state, can undergo these reactions

which resemble those found in organic chemistry. The metal carboxylate

dimer with acetonitrile coordination differs from organometallic

complexes and undergoes reactions such as Lewis base coordination and

ligand substitution resembling those found in classical coordination

chemistry. Nevertheless, the photochemical and photophysical properties

of the complexes described here may be of interest. Analogous systems

studied by Gray and co-workers such as Mo24+(aq)59, the metal-metal

bonded diphosphite bridged Pt(II)/(III) dimers72 and the non-metal-metal

bonded isonitrile bridged Rh(I) dimers100 have shown interesting

photochemical behavior. Furthermore, the ligand substitution reactions

of the metal-metal bonded complexes described here which contain

accessible equatorial sites could be investigated in a quantitative

manner as was previously done for systems containing only axial

coordination sites.


Experimental Section

Operations were carried out under nitrogen using Schlenk techniques

or an inert atmosphere box except as otherwise noted. Solvents were

distilled before use. Trifluoromethanesulfonic acid was distilled under

reduced pressure. Tetrafluoroboric acid diethyletherate (Pfaltz and

Bauer) was used without further purification. Rhodium acetate was

synthesized from RhCI3(H20)3 by literature methods.101

Tetrakis(n-butyrato)dirhodium(II)

{h2(02CCH3)4 (0.5 g, 1.1 mmol) was refluxed for 6 h in n-butyric

acid (14 mL) and n-butyric anhydride (1 mL). The solution was

concentrated to 3 mL and cooled at -20 C overnight. The resulting crude









Rh2(but)4 was recrystallized from hot toluene, washed with cold hexane

and dried over P205 overnight to yield 0.5 g (0.9 mmol, 80%). Anal.

Calcd. for Rh2C16H2808: C, 34.68; H, 5.09. Found: C, 34.74; H, 4.99.


Rh7(but)?2+ Solution

Rh2(but)4 (0.328 g, 0.59 mmol) was dissolved in CH3CN (5.00 mL) to

give a purple solution. To this was added CF3SO3H (0.21 mL, 2.37 mmol)

leading to an immediate slight color change towards dark red. Similar

solutions using CD3CN were used for the NMR work.

Sulfide Complex

Elemental sulfur (0.0236 g, 0.74 mmol) was suspended in THF (1

mL). To this Super-Hydride (LiBH(CH2CH3)3, 1.5 mL, 1 M in THF, Aldrich)

was added dropwise. Gas evolution was vigorous and a pale yellow

solution resulted. This solution was added to the above Rh2(but)22+

solution (2 mL, 0.092 M in rhodium dimer). A black precipitate formed

immediately. Filtration, washing with THF and drying under vacuum at

100 C afforded 0.8 g of a black, completely insoluble solid. Anal.

Calcd. for Rh2(02CCH2CH2CH3)2S: C, 23.32; H, 3.43; S, 7.78; C:H,

6.80. Found: C, 24.39; H, 3.70; S, 12.53; C:H, 6.81. The high sulfur

analysis results from SH units and bridging polysulfide. The selenium

compound was prepared in the same manner and gave an even less

satisfactory elemental analysis.

Pyridine Complex

To the above Rh2(but)22+ solution (3 mL, 0.03 M in rhodium dimer)

was added pyridine (0.16 mL, 2.0 mmol). An orange color immediately

resulted. Attempts to obtain a solid by cooling and evaporation yielded

only an oil. Addition of NH4PF6 (0.16 g, 1.0 mmol) dissolved in water









(1 mL) and subsequent evaporation and cooling led to formation of an

orange-red precipitate. This procedure was not always repeatable; oils
often resulted. Furthermore, IR indicated the presence of CF3S03- as

well as PF"6. Anal. Calcd. for [Rh2(02CCH2CH2CH3)2(C5H5N)4](PF6)2: C,
34.09; H, 3.47; N, 5.68. Found: C, 33.99; H, 3.87; N, 6.18. The above

procedure using Rh2(02CCH3)4 allowed isolation of an orange solid

without addition of PF6-. Anal. Calcd. for [Rh2(O2CCH3)2(C5H5N)4]

(CF3S03)2: C, 33.27; H, 2.79; N, 5.97. Found: C, 32.73; H, 2.98; N,
6.03.

Tetrakis(acetato)dimolybdenum(II)

This complex was synthesized following the procedure of Martin and
co-workers77 which gives much higher yields than the original

method.102 Mo(CO)6 (1 g, 3.8 mmol) was added to o-dichlorobenzene (30

mL). Acetic acid (8 mL) and acetic anhydride (1 mL) were added and the

solution refluxed overnight during which time the solution turned almost

black. The heating was stopped and the solution allowed to cool without

removal of the heating mantle for 8 h. Filtration and washing with

ethanol followed by diethylether led to isolation of beautiful yellow

needle crystals of Mo2(02CCH3)4 (0.65 g, 1.5 mmol, 80%). Anal. Calcd.

for Mo2C8H1208: C, 22.45; H, 2.83. Found: C, 22.45; H. 2.90.

Molybdenum acetate should be used as soon as possible since it

decomposes even under inert atmosphere or vacuum over a period of days
to green and eventually black products.

Tetrakis(acetonitrile)bis(acetato)dimolybdenum(II)
Bis(trifluoromethylsulfonate), (U)

Mo2(02CCH3)4 (0.40 g, 0.93 mnol) was suspended in acetonitrile (4
mL). It is important that the acetonitrile be degassed using freeze-









pump-thaw cycles with the final vacuum broken by nitrogen, otherwise

decomposition of molybdenum acetate often occurs giving a brown

solution. To this was added CF3SO3H (0.17 mL, 1.92 mmol). An intensely

colored purple solution formed immediately and was stirred for 10 min.

Removal of solvent by pumping left a dark purple solid which was

dissolved in a minimum amount of acetonitrile (~2 mL) and filtered.

Addition of toluene (~3 mL) led to formation of a purple precipitate

after 1 h. The solid was recrystallized from 1:1 acetonitrile/toluene

and washed with toluene followed by hexane to yield 0.5 g. Anal. Calcd.

for [Mo2(02CCH3)2(CH3CN)4](CF3S03)2: C, 21.77; H, 2.35; N, 7.25; S,

8.30; F, 14.76; Mo, 24.84; 0, 20.72. Found: C, 21.83; H, 2.38; N,

7.56; S, 8.28; F, 15.10; Mo, 24.00; 0 (by diff.), 20.85. From the

filtrate obtained in the above recrystallization a magenta, rather than

a purple, solution is often obtained. Addition of toluene (~1 mL) to

this leads to formation of a magenta precipitate, 3. Anal. Calcd. for

[Mo2(02CCH3)2(CH3CN)4(H20)](CF3S03)2: C, 21.27; H, 2.55; N, 7.09; S,
8.11; F, 14.42; Mo, 24.48; 0, 22.27. Found: C, 22.00; H, 2.65; N,

7.06; S, 8.08; F, 12.7; Mo, 22.59; 0 (by diff.), 24.92.


Pentakis(acetonitrile)bis(acetato)dimolybdenum(II)
Bis(trifluorohydroxyborate), (2)

Mo2(02CCH3)4 (0.71 g, 1.66 mmol) was suspended in acetonitrile as
above. To this was added (Et20).HBF4 (0.8 mL, approx. 6 mmol). An

intensely colored magenta solution immediately resulted. Removal of

solvent by pumping left a magenta solid which was dissolved in

acetonitrile (~4 mL) and filtered. A small amount of yellow needle

crystals of unreacted Mo2(02CCH3)4 remained. When less acid is used,

more unreacted molybdenum acetate is recovered. To the filtrate was









added diethylether (5 mL) which caused rapid formation of a magenta

precipitate. The compound was recrystallized from 1:1

acetonitrile/toluene and washed with toluene followed by hexane to yield

0.9 g. Anal. Calcd. for [Mo2(02CCH3)2(CH2CN)5](BF30H)2: C, 24.55; H,

3.38; N, 10.23; F, 16.65; Mo. 28.02. Found: C, 23.79; H, 3.32; N,

10.02; F, 17.03; Mo, 26.36.


Anion Exchange

Complex 2 (0.3 g, 0.44 mmol) and (n-Bu)4NBF4 (1 g, 3.0 mmol) were

dissolved in acetonitrile (5 mL). To this was added toluene (5 mL)

leading to formation of a magenta precipitate. After two cycles of this

procedure, IR of the magenta precipitate showed a greatly diminished

v(OH) band and the other bands unchanged. Anal. Calcd. for

[Mo2(O2CCH3)2(CH2CN)5](BF4)2: C, 24.41; H, 3.07; N, 10.17; F, 22.06;
Mo, 27.86. Found: C, 24.49; H, 3.29; N, 11.77; F, 19.16; Mo, 38.13.


Molybdenum Trifluoromethylsulfate Complex

To Mo2(02CCH3)4 (0.2 g, 0.47 mmol) was added to CF3SO3H (10 mL).

The suspension was heated at 100 C with stirring for 1 h, by which time

all the solid dissolved. The acid was removed by pumping leaving a red

solid which presumably corresponds to the Mo2(03SCF3)4(CF3SO3H) complex

described by Abbott and co-workers.60 Further pumping with heating at

160 C led to formation of a tan solid which is presumably the

Mo2(03SCF3)4 complex.60 These intermediates were not isolated or
characterized. Addition of acetonitrile (10 mL) to the tan solid led to

formation of a bright blue solution. Addition of toluene (-7 mL) caused

formation of a blue precipitate. Elemental analysis of this compound

was not satisfactory, although it appeared to be an acetonitrile









coordinated Mo(II) dimer. IR spectroscopy indicated strong v(CN) and

v(OH) bands as well as bands corresponding to non-coordinated CF3SOg".

Bands corresponding to residual acetate were observed at 1615 cm-1

(vasy(C02)) and 675 cm-1 (6(C02)). A band at 415 cm-1 may be v(Mo2).

Slow evaporation of the filtrate obtained above resulted in formation of

purple cyrstals of what is most likely Complex 1. The IR

spectrumcorresponded to I as did the elemental analysis although the

precipitate may have been contaminated with species such as

[Mo2(02CCH3)(CH3CN)x](CF3S03)3 giving higher %S, %F, and %0. Anal.
Calcd. for [Mo2(02CCH3)2(CH3CN)4](CF3SO3)2: See above. Found: C,

21.33; H, 2.10; N, 6.23; S, 9.48; F, 15.48; Mo, 21.47; 0 (by diff.),

23.91.

Tetrakis(dithioacetato)dimolybdenum(II)

This complex was synthesized following the procedure of Cotton and

co-workers.99 CS2 (0.77 mL, 0.013 mol) was added to CH3MgBr (5.63 mmol,

as THF solution, Aldrich) in THF (10 mL). A pale yellow solution

resulted which was stirred for 45 min. To this was added Mo2(02CCH3)4

(0.60 g, 1.4 mmol). A dark red-brown solution formed immediately.

After stirring 15 min, methanol (20 mL, N2 purged) was added leading to

formation of an orange-red precipitate. Filtration and washing with

methanol afforded 0.44 g (56%). This complex, in contrast to

Mo2(02CCH3)4, is indefinitely stable and can be recrystallized in air
from THF. Anal. Calcd. for Mo2C8H12S8: C, 17.26, H, 2.17; S, 46.09;

Mo, 34.48. Found: C, 17.46; H, 2.43; S, 45.93; Mo (by diff.), 34.18.









Experimental Methods

Elemental analyses were performed by the Microanalytical Laboratory

of the University of Illinois, Urbana, IL, or by Galbraith Laboratories,

Knoxville, TN. Ultraviolet-visible spectra were recorded on a Cary 14

spectrometer using matched quartz 1.0 cm cells. Infrared spectra were

recorded on a Perkin-Elmer 5998 instrument using KBr cells. Fourier

transform 13C{1H} NMR spectra were recorded on a Varian Associates XL-

100 FT spectrometer operating at 25.2 MHz. The 13C chemical shifts were

measured with respect to the nitrile carbon of CD3CN (118.2 ppm relative

to TMS). Proton NMR spectra were recorded using a Varian HR-220 NMR

spectrometer equipped with a Nicolet Technology Corp. TT-220 Fourier

transform accessory. Precision-grade tubes were used for the 220 MHz

spectra so as to reduce spinning sidebands. The 1H chemical shifts were

measured with respect to internal TMS.














CHAPTER III
THE REACTIONS OF RHODIUM TRIFLUOROACETATE WITH VARIOUS LEWIS BASES


Introduction


As discussed in the previous chapter, it is possible to effect

removal of the removal of the bridging carboxylate ligands in metal

carboxylate dimers by reaction with stoichiometric amounts of strong

non-complexing acids. This reaction allows Lewis bases and potentially,

substrates for catalytic processes, to coordinate to equatorial as well

as axial sites on the metal carboxylate dimer. An alternative approach

to achieving this type of coordination is to use a carboxylate ligand

with an electron-withdrawing group. This type of carboxylate would

donate less electron density to the metal dimer subunit rendering the

carboxylates more prone to displacement and the metals more susceptible

to attack by Lewis bases. The effect of an electron-withdrawing

carboxylate ligand, CF3CF2CF2CnO- (hfb), has been quantitatively shown

in earlier studies by Drago and co-workers.25 The erthalpies of axial

Lewis base adduct formation by Rh2(hfb)4 versus Rh2(but)4 were

examined. The hfb ligand greatly enhanced the Lewis acidity of the

rhodium system towards electrostatic interactions and increased the

acidity towards covalent interactions by almost as much. In addition to

this greater reactivity towards Lewis bases, the metal fluorocarboxylate

dimers have much greater solubility in non-coordinating organic solvents

than do the corresponding alkylcarboxylate systems. This facilitates

study of their solution chemistry. For example, since io"2(02CCH3)a is









completely insoluble in organic solvents and Rh2(02CCH3)4 only sparingly

so, a direct comparison of their solution properties is impossible. Use

of the trifluoroacetate ligand makes such a study possible. The

interest in a comparison of the solution chemistry of the rhodium and

molybdenum carboxylate dimers stems from the large difference in their

metal-metal interactions. As discussed earlier, the d8 Mo system has a

strong, short, relatively unpolarizable quadruple bond. The d14 Rh

system has a longer, weaker, more polarizable single bond. Furthermore,

since rhodium is more electronegative than molybdenum, the Rh-Rh

molecular orbitals are overall lower in energy than the Mo-Mo bond

orbitals. The result of all this is that in the rhodium dimer, the

frontier MO's are the 7* HOMO and the o* LUMO while for molybdenum those

metal-metal orbitals are vacant and high in energy while the 6 HOMO and

the 6* LUMO are of main importance. This implies that the covalent

interaction with axial bases should be strong for the rhodium

carboxylate dimer and much less for molybdenum. This has been

quantitatively confirmed by Drago and co-workers25 in a comparison of

the enthalpies of axial Lewis base adduct formation by Rh2(hfb)4 versus

Mo2(hfb)4. In addition, a r-backbonding interaction was observed

between the filled 7* orbitals on the rhodium dimer and vacant r*

orbitals on bases such as pyridine and acetonitrile. This interaction

was not seen for the molybdenum dimer as expected from the MO scheme

described above.

Another implication of the MO scheme is that given the opportunity,

Lewis bases should coordinate more readily to equatorial than to axial

sites on molybdenum, while this would be less likely for rhodium. This

type of reactivity has indeed been found with Mo when the








trifluoroacetate dimer is used, since this ligand allows access to the

equatorial sites. Girolami and co-workers33,103 synthesized and

characterized a number of adducts of molybdenum trifluoroacetate with

phosphines and other Lewis bases. They found that Mo2(02CCF3)4 not only

formed adducts in which there was coordination along the Mo-Mo axis, but

also some in which there was coordination in sites perpendicular to the

Mo-Mo axis. All of these complexes were of general formula

Mo2(02CCF3)4L2. Those with axial coordination were called Class I
adducts, those with equatorial coordination, Class II. Only Lewis bases

that are sterically small and good o-donors were reported to give

isolable equatorial adducts. Examples are trimethylphosphine (PMe3),

triethylphosphine (PEt3), and dimethylphenylphosphine (PMe2Ph).

Andersen estimated steric bulk by cone angle and o-donor strength by

v(CO) values as described by Tolman.104 The assignment of complexes

into the two classes was made on the basis of 19F and 31P NMR

spectroscopy which showed different signals resulting from phosphines in

different coordination sites. Infrared spectroscopy also showed

different CO2 stretches for the two types of CF3CO2" ligands. However

some controversy exists over the assignment of IR and NMR peaks for

these complexes. Cotton and Lay105 also prepared phosphine complexes of

Mo2(O2CCF3)4 and obtained spectra at variance with those of Girolami and
Andersen and co-workers.33,103 In addition, these two groups reported

different structures for the complex Mo2(02CCF3)4(PMePh2)2. Cotton and
Lay105 obtained a Class II (equatorial) adduct and Girolami and

Andersen103 a Class I (axial) adduct. Slight variations in synthetic

procedure led to this difference since PMePh2 is a phosphine inter-

mediate on the size and donor strength scales.








Other solution studies106,107 have been performed on Mo2(02CCF3)4
as well as a number of crystallographic studies.96,103,104,108 In

contrast, the analogous rhodium system has not been as extensively
investigated, particularly in solution.5,6 Crystal structures have been

determined for Rh2(02CCF3)4L2 where L=(CH3)2S02,109 (CD3)2SO,110

PPh3,111 P(OPh)3,111 CH3CH2OH,112 H20113, 2,2,6,6-tetramethylpiper-
idinolyl-1-oxyll3 and (CH3)2S0.114 In all these cases, as in those with

alkylcarboxylates, only Class I (axial) adducts were formed. However, a

systematic study of the Lewis base reactivitiy of Rh2(02CCF3)4 had not

been performed. For the reasons discussed above, that is ligand effects
and metal-metal bond effects, such a study was performed and is
described below. Furthermore, it was hoped that this study would shed

some light on the discrepancies in the interpretation of the
spectroscopy properties of the molybdenum systems described above.

Results and Discussion

The 19F NMR spectrum of Rh2(02CCF3)4 was obtained in both

nitromethane-d3 and toluene-d All of the 19F NMR data are summarized
in Table 3-1. A sharp singlet was found in both room and low

temperatures in both solvents which corresponds to the CF3 groups on the
four equivalent bridging trifluoroacetates. Nitromethane and toluene

are very weak bases and thus should coordinate weakly, if at all, to the
rhodium dimer. What is significant is that these signals occurred in

the -73 to -75 ppm range (relative to internal CFC13). The signals were
somewhat solvent and temperature dependent. Earlier workers33,106,107
have assigned peaks in the -72 to -74 ppm range to monodentate CF3CO2
and peaks at -70 ppm to bidentate CF3C02" in Mo2(02CCF3)4 complexes.








The IR spectrum of Rh2(02CCF3)4 shows a single vasy(CO2) band in
solution and in the solid state. All the major IR data are summarized

in Table 3-11 and the IR spectrum of Rh2(O2CCF3)4 is shown in Figure 3-

1. However, this stretch occurs at a higher frequency (1650 to 1670

cm-1) than vasy(C02) for bidentate CF3CO2" in Mo2(02CCF3)4 complexes

(-1600 cm-1). Thus, there is no direct correspondence between the

location of the 19F NMR and IR signals for the rhodium and molybdenum

systems. Nevertheless, mono- and bidentate CF3CO2 give significantly

different spectra in the rhodium complexes as will be shown below.

Oxygen Donors

Emerald green Rh2(O2CCF3)4 forms blue 2:1 complexes with oxygen

donor bases such as tetrahydrofuran (THF), dimethylsulfoxide (DMSO),

N,N-dimethylformamide (DMF), and trimethylphosphine oxide (OPMe3). The

THF adduct is quite stable but heating at 100 C under vacuum effects

quantitative removal of THF to give base-free starting material.

The 19F NMR and IR spectra are characteristic of a Class I adduct. A

singlet is observed in the 19F NMR spectrum at -75 ppm and vasy(C02)

occurs at about 1660 cm-1 in both the solid adduct and in solution. The

IR spectrum of Rh2(02CCF3)4(THF)2 is shown in Figure 3-2. These results

are similar to those for the free Lewis acid, Rh2(02CCF3)4.

The crystal structure of Rh2(02CCF3)4(DMSO)2 showed a Class I
adduct, with 0-bonded DMSO.109 There was nothing to indicate otherwise

in solution since a single peak was observed in the 19F NMR spectrum.

Both axial S-coordination and equatorial 0- or S-bonding would most

likely lead to additional signals. The equivalence of the solution and

solid state structures was confirmed by IR, which showed a single

Vasy(C02) band at 1662 cm-1 (Nujol mull) and at 1655 cm-1 (CHC13








Table 3-1. 19F NMR Data for Rh2(02CCF2)4 Complexesa


Complex


Rh2(02CCF3)4




Rh2(02CCF3)4(THF)2


Rh2(02CCF3)4(Me2SO)2


Rh2(02CCF3)4(DMF)2


Rh2(O2CCF3)4(Et3N)2


Rh2(02CCF3)4(py)4




Rh2(02CCF3)4(t-BuNC)4




Rh2(02CCF3)4(PPh3)3


19F Chemical Shiftb

-73.28

-74.29

-75.04

-74.65

-75.19
-74.17

-76.41
-74.18

-74.86

-75.31
-75.92

-74.69, -75.44

-74.08, -74.87

-74.73, -75.34

-73.0, -73.2

-73.4, -73.8

-74.2, -74.6

-73.98, -74.90

(-75.23)c,-75.72
-74.41, -74.75

(-75.32)c,-75.88


Area
Ratios


1:1
1:1

1:1

2:1:1.5:

4:1.5:1


1:1:1.3
1:1:2.0


Solvent Temperature(oC)


CD3NO2

tol uene-d

tol uene-d.

CDC13

CDC13
CDC13

CDC13

CDC13

CDC13

CDC13

CDC13

CDC13

toluene-,d
tol uene-d8

CDC13


CDC13


CDC13







Table 3-I. continued


1F Chemical Shiftb


Area
Ratios


Solvent Temperature(oC)


Rh2(02CCF3)4(P(c-Hx)3)2


Rh2(O2CCF3)4(P(OPh)3)2


Rh2(O2CCF3)2(P(OMe)3)3


-72,73, -74.51

-75.42, -75.92

-75.08

-74.68, -74.83

(-75.10, -75.45

-76.20)c

-73.40, -73.88

-74.65, -75.25


1:1:2:1 CDC13

CDC13

2.5:1 CDC13


3:2 CDC13

3:2 CDC13


a. Data are reported for those complexes that were obtainable as
and the P(OMe)3 complex. Solution studies were undertaken on
and are described in the text.


genuine adducts
other systems


b. All chemical shifts are with respect to internal CFC13.

c. These signals are of very low intensity and may indicate the beginning of
complex decomposition.


Complex







Table 3-11. Infrared Data for Rh2(02CCF3)4 Complexes


Complex


Rh2(02CCF3)4
Rh2(02CCF3)4
Rh2(02CCF3)4(Me2SO)2
Rh2(02CCF3)4(DMF)2
Rh2(02CCF3)(Et3N)2
Rh2(02CCF3)4(py)4
Rh2(O2CCF3)4(t-BuNC)4
Rh2(02CCF3)4(PPh3)2

Rh2(O2CCF3)4(P(c-Hx)3)2
Rh2(O2CCF3)4(P(OPh)3)2
Rh2(02CCH2CH2CH3)4(PPh3)2c
Rh2(02CCF3)4(CH3CN)2


asy(C02) (cm-1)a
CHC13 Solution


1670
1658
1655
1662
1670 s, 1660 s
1705 s, 1642 m
1693 s br, 1658 s
1715 w, 1654 m, 1652 m
1715 w, 1660 m
1665
1587
1658 m, 1648 w


Nujol mull


1650
1668
1662
1650
1660
1705
1720
1665
1663
1670


brb

s, 1650 s
s, 1655 s
m br, 1660 m br


1663 m, 1653 w


a. s = strong, m = medium, w = weak, br = broad
b. includes amide v(CO), resolved in solution
c. included to contrast with Rh2(O2CCF3)4(PPh3)2




























=


In


C,















4..
0

L
U










0

r-













U
+--












SO
C-












































E
O




































.-a
U-
-'-}

Z




























LL.
14 U


























a,

Ll-


33NV111HSW"1 h










































8
E

rO






rc
C1_

4-
L)







0
u



IC-
t0
C-



E





Ct







0=
L

C-








solution) in agreement with the assignment as an axial adduct. The IR

spectrum of Rh2(02CCF3)4(DMSO)2 is shown in Figure 3-3. The DMSO bands

are also of interest. In the solid state, two doublets were observed at

1005 (s) and 995 cm-1 (s) and at 945 (s) and 937 cm-1 (s). In CHC13

solution these occurred at 1020 (m) and 1000 cm-1 (m) and at 948 (m) and

931 cm-1 (w). Free DMSO in CHC13 solution has v(SO) at 1055 cm-1 and a

6(CH3) band at 946 cm-1. Oxygen coordination lowers v(SO) and sulfur

coordination raises the frequency of this band. No bands were observed

for Rh2(02CCF3)4 in the 1050 to 1150 cm-1 region where S-coordinated

DMSO would obsorb. It should be noted that Rh2(02CCH3)4 binds DMSO via

the sulfur atom (v(SO) at ~1090 cm-1),62'115 further evidence of ligand

effects on Lewis acidity of the rhodium carboxylate dimer.115 Cotton

and Felthouse114 have reported bands for this complex at 943 and 939

cm-1 (Nujol mull) which they assigned to v(SO) of 0-coordinated DMSO,

while the higher frequency doublet was not mentioned. Their assignment

was based on earlier work by Cotton and co-workers,116 who proposed that

the band at ~950 cm-1 in DMSO complexes corresponds to v(SO) while that
at ~1000 cm-1 to 6(CH3). However, Drago and Meek117 reversed this

assignment since the band at ~1000 cm-1 is more sensitive to the type of

metal coordinated. The IR spectrum of Rh2(02CCF3)4(DMSO-6 )2 was
obtained here in the hope of clarifying the assignment of these two

bands. The IR spectrum of this deuterated complex was identical to the

original complex with respect to the bands related to CF3C02-.

Unfortunately, in the area of interest, there was also little change.

Fairly strong, broad bands were seen at 1020 and 950 cm-1, with the

latter more intense. A new band occurred at 825 cm-1 which may































































































































MNVIfIMSNv %.








correspond to a 6(CD3) band at 811 cm-1 in free DMSO-d. Thus, a

definitive assignment of these two bands cannot be made.

When DMF was added to Rh2(02CCF3)4, a purple color initially
appeared, but the solution then rapidly turned blue. The 19F NMR

spectrum of this complex showed a single peak at -74 ppm at room and low

temperature. The IR spectrum was also characteristic of a Class I

adduct (vasy(C02) at 1662 cm'1 in CHC13 solution). In solution the

amide v(CO) could be resolved from the vasy(C02) band (this was not

possible in the solid) and was shifted from 1685 cm-1 in free DMF (CC14
solution) to 1643 cm-1, indicative of 0-coordination.118 The IR

spectrum of Rh2(02CCF3)2(DMF)2 is shown in Figure 3-4. Addition of
excess DM1F did not change the 19F NMR spectrum. Rh2(02CCF3)4 was

indefinitely stable in excess DMF. This is in contrast to DMSO.

Kitchens and Bear119 reported that addition of excess DMSO to

Rh2(02CCF3)4 led to formation of a yellow decomposition product, which

was also observed here. This is probably due to eventual sulfur

coordination.

The reaction of Rh2(02CCF3)4 with 10 equivalents of OPMe3 in 1:1

toluene/dichloromethane afforded a blue solid contaminated with

crystalline, white, unreacted OPMe3. The IR spectrum of this blue solid

(Nujol mull) showed a strong, broad vasy(CO2) band at 1650 cm-1 and a
band assignable to 6(C02) at 725 cm-1. A very strong, broad band at
-1200 cm-1 included vasy(CF3) and v(PO). Thus, a Class I adduct is most

likely formed as with the above oxygen donors. This is to be expected
since using the E and C parameters,27-29 OPMe3 is a Lewis base roughly

comparable to DMSO. Due to limited availability of OPMe3, further

studies were not performed.





















0
UJ

v>




O





.C-















a
U,











4-
=-














0.. 0
uc





O

















0- 0
Cr r
















o u


OC
r 0



1- 3







I
0.)

C,
5-
0 -


33NVlllH NSUy *I.








Nitrogen Donors

A variety of nitrogen donor bases were reacted with Rh2(02CCF3)4

with varying results. Isolable analytically pure complexes could not be

obtained with piperidine and N-methylimidazole (N-MeIm). When these

bases were added to toluene solutions of Rh2(02CCF3)4, a red color

immediately resulted indicative of nitrogen base coordination. However,

after several hours the solutions turned yellow and evaporation gave an

intractable yellow tar in both cases. This indicates dimer

decomposition forming Rh(I) and/or Rh(III) as was described with DMSO.

Some 19F NMR studies were performed on solutions of Rh2(02CCF3)4 with

these bases. A freshly prepared solution containing 10:1 N-

MeIm/Rh2(02CCF3)4 showed single peaks at -74.6 ppm at 27 C and at -74.1

ppm at -61 C in CDC13. Thus, a 2:1 Class I adduct was initially present

and remained for a few hours. The spectrum became complex as the yellow

color appeared. A freshly prepared solution of 10:1

piperldine/Rh2(02CCF3)4 showed a major signal at -74.2 ppm and smaller

peaks at -68.4 and -80.3 ppm indicating that rapid decomposition

occurred. The major peak is presumably from axially coordinated dimer,

the other two from decomposition products. It might be possible to

prepare adducts with these two bases if only stoichiometric amounts were

used. By contrast, use of excess triethylamine led to facile isolation

of Rh2(O2CCF3)4(Et3N)2. This complex had a singlet in the 19F NMR

spectrum, even with excess base, at -75 ppm at both room and low

temperatures. This complex had an IR spectrum characteristic of

bidentate CF3CO2- in solution and in the solid state. The latter is

shown in Figure 3-5.






80













2 a8
























CL,






-,
aa




4 -




0
o




CL




0
fe'-1
^^"^ '

''~^


















4-





- ^
~

Q-


53flNYJi5MVELbA








With pyridine an interesting product was formed that is

intermediate between the Class I adduct formed with Et3N and the

decomposition products formed with piperidine and N-MeIm. This complex

is a stable red 4:1 adduct containing both axially (Class I) and

equatorially (Class II) coordinated Lewis base and thus may be
considered a new type of complex which will be called Class III. These

three structures are shown in Figure 3-6. Only one of six isomers of

Class II and III adducts are depicted. This behavior can be contrasted

with the reaction of pyridine with Mo2(02CCF3)496 and Rh2(O2CCH3)4120 in

which Class I adducts form. A precedent for this Class III compound

exists. Webb and Dong106 have performed solution studies on

Mo2(O2CCF3)4 with varying amounts of pyridine and found 19F NMR signals
in the places predicted33 for mono- and bidentate CF3CO2- (-70.5, -75.3

ppm, respectively) and IR adsorption bands at 1713, 1617, and 1611 cm-1

corresponding to vasy(CD2) of mono- and bidentate CF3CO2". Only one Mo-

Mo stretch was observed in the Raman spectrum (343 cm-1) indicating the

presence of only one centrosymmetric isomer. The 19F NMR spectrum of

Rh2(O2CCF3)4(pyr)4 prepared here showed signals at -74.1 and -74.9 ppm
in toluene-dg and at -74.7 and -75.4 ppm in CDC13, both at -60 C. In

both solvents the peak ratio was 1:1. Here mono- and bidentate CF3CO2

are separated by less than 1 ppm, whereas in the molybdenum work they

were separated by about 3 ppm. However, there are examples of mono- and
bidentate CF3CO2- with all resonances in the -74 to -76 ppm range. King
and Kapoor121 have synthesized a large number of complexes such as

(CsH5)Fe(CO)2(CF3CO2) which has monodentate CF3C02- and gives a 19F NMR
signal at -74.2 ppm in CDC13. Creswell and co-workers122 have prepared

compounds such as Os(CO)(PPh3)2(CF3C02)2 which has two 19F NMR signals





























Figure 3-6. Possible structures for Lewis base adducts of
Rh2(02CCF3)4. Only one of the six isomers of
both Class II and Class III adducts are shown.




83





I I
CF3 CF'
C C
0 0 CF3 0 -
/0 \3
-C, c \ 0C-OCF
L- -h 0 L 0
0RRh Rh C Rh C h
0 \ CF, L

CF3 0 0 o 0
I I
CF3 CF,





Il
CF3


\o %
0 C-CF
LL

CF3 o L/
0 0

CF3








at -75.44 and -75.22 ppm in CDC13 assigned to mono- and bidentate

CF3CO2-. Thus, not only do the locations of resonances in the rhodium

dimer differ from molybdenum, but the chemical shift differences between

CF3CO2-'s in different environments do not correspond. The IR data for

the pyridine complex are also in agreement with the Class III

formulation. Absorption bands for vasy(C02) were observed at 1705 and
1642 cm-1 (CHCl3 solution) and at 1705 and 1655 cm-1 (Nujol mull)

corresponding to mono- and bidentate CF3C02-. Another characteristic IR
band is 6(C02) which occurs at 740 cm-1 in Rh2(02CCF3)4. Free pyridine

has bands at 740 and 693 cm-1. In the pyridine complex bands were

observed at 760, 750, 738, 725, and 690 cm-1. It is likely that at

least two of the first three bands correspond to 6(C02) for mono- and

bidentate CF3C02-. The other absorption bands could be assigned to

either pyridine or Rh2(02CCF3)4 and the latter showed little change from

the base-free rhodium dimer. The IR spectrum of Rh2(O2CCF3)4(pyr)4 is

shown in Figure 3-7. Addition of excess pyridine, up to 20 equivalents,

caused no change in the 19F NMR spectrum. Two sharp signals of equal

intensity were still observed at -74.7 and -75.3 ppm in the toluene-d_

at 27 C. By contrast, in the molybdenum case106 the two peaks coalecse

at 30 C, indicating fast exchange. However, the slower exchange

observed here is not unusual since in the M(CO)(PPh3)2(CF3C02)2
complexes studied by Creswell and co-workers,122 separate resonances

corresponding to mono- and bidentate CF3CO2- were observed at room

temperature. As a final note, it should be mentioned that the synthesis
of "Rh2(02CCF3)4(pyr)2" was reported123 a number of years ago, but the

complex characterized only by C and H analysis. This procedure was

repeated here and a compound was isolated that was most likely a mixture






























































































































3Ol I INSNfl I%








of pyridine adducts. This was the result of using ethanol as solvent

rather than toluene, used here to obtain the pure 4:1 adduct. (See

Experimental Section.)

It is difficult to draw general conclusions from the above results

based on criteria such as steric size, a-donor, and n-acceptor abilities

of the bases. Triethylamine was the strongest a-donor used; it is bulky

and has no i-acceptor ability. It formed axial adducts. Similarly,

quinuclidine (a Lewis base very comparable to Et3N) formed a Class I

(axial) adduct with Mo2(02CCF3)4 although its size and a-basicity would

favor Class II. Pyridine, a base with less a-donor ability than Et3N,

has i-acceptor ability and formed a stable Class III (axial and

equatorial) adduct. N-methylimidazole, a stronger a-donor but a poorer

n-acceptor than pyridine caused dimer cleavage although via a Class I

adduct. Piperidine is a strong a-donor, but reactivity is most likely

due to the protonic nature of the base.

A final nitrogen donor base, acetonitrile, was used. It is a weak

a-donor, but a i-acceptor. Bear and co-workers40 were unable to isolate

a stable acetonitrile adduct of Rh2(02CCH3)4. These workers claimed

that evaporation of a CH3CN solution of rhodium acetate gave only

starting material.40 It was found here, by contrast, that stable purple

Rh2(02CCH3)4(CH3CN)2 was formed upon evaporation of an acetonitrile

solution of the rhodium dimer. (See Experimental Section.) However,

although Rh2(02CCF3)4(CH3CN)2 can be similarly prepared, it readily

loses acetonitrile and is hydrated to a blue-green material upon

standing in air. The freshly prepared complex 19F NMR showed a singlet

at -74.1 ppm and a doublet at -74.5 ppm in CDC13 at -60 C. The area

ratios were 2:1:1. Addition of excess CH3CN (-10 equivalents) led to








signals at -74.7 and -75.4 ppm in equal area ratios. IR data showed

Class I bridging CF3CO2- bands. The solution structure of Rh2(02CCF3)4

in the presence of acetonitrile is thus uncertain. However, the weaker

coordination of CH3CN to the fluorocarboxylate as opposed to the

alkylcarboxylate rhodium dimer is to be expected. This is due to r-

backbonding interactions as discussed earlier and shown by Drago and co-

workers.22-26

Carbon Donors

Reactions with the isoelectronic carbon donors t-butylisonitrile

and carbon monoxide were investigated. The reaction of t-BuNC with a

variety of metal carboxylate dimers was studied by Girolami and

Andersen.76 They found that only monomeric complexes were obtained with

Mo2(02CCH3)4, Mo2(02CCF4)4, Re2(02CCH3)4C12, and Ru2(02CCH3)4C1.
However, with Rh2(02CCH3)4 only the Class I adduct Rh2(O2CCH3)4(t-BuNC)2

was produced. It was of interest to determine what effect replacement

of CH3CO2- by CF3CO2- would have in the dirhodium system. It was found

here that reaction of Rh2(03CCF3)4 with t-BuNC (~10 equivalents) led to

isolation of an air stable orange-brown complex best formulated as

Rh2(02CCF3)4(t-BuNC)4. Unfortunately, in contrast to the pyridine

complex which had the same stoichiometry and easily interpretable NMR

and IR spectra, t-BuNC gave complicated results, as will be discussed

below. This is most likely due to the presence in solution of a variety

of species including more than one isomer of a Class III adduct and

possibly monomeric species. Although t-BuNC and pyridine have similar

a-donor properties, the isonitrile is a better T-acceptor and somehow

this may lead to a variety of isomers of comparable stability. The 19F

NMR spectrum of this compound showed six peaks occurring between -73.0








and -74.6 ppm in CDC13 at -60 C. The1H NMR spectrum showed signals at

1.61 and 1.43 ppm in CDC13 at -50 C. All NMR data for nuclei other

than 19F are summarized in Table 3-III. At room temperature the peaks

occurred at 1.60 and 1.40 ppm, but instead of a 3:2 area ratio the ratio

was 2:1. Thus, at different temperatures different isomers

predominated, but specific assignment of the signals was not possible.

The IR spectrum of this complex showed bands assignable to vasy(C02) at

1693 and 1658 cm-1 in CHC13 solution and at 1720 and 1660 cm-1 in the

solid state. A single strong 6(C02) band was observed at 725-730 cm-1

(Nujol mull). There may have been more than one 6(C02) band, but
resolution was not possible. Very strong absorption bands corresponding
to v(NC) occurred at 2234 and 2167 cm-1 (CHC13 solution) and at 2212 and

2132 cm-1 (Nujol mull) as opposed to 2127 cm-1 for free t-BuNC. This

shift to higher frequency is expected for end-on isonitrile

coordination. The other absorption bands were assignable to either t-

BuNC or Rh2(02CCF3)4. The IR spectrum of Rh2(02CCF3)4(t-BuNC)4 is shown

in Figure 3-8. Although the solution and solid state IR spectra were

qualitatively the same, the fairly large difference for a given band

such as vasy(CO2) or v(NC) may indicate a different structure in

solution. Further studies with this complex would be needed to

unequivocally determine its structure. However, it seems clear that a

Class I adduct is not formed in contrast to Rh2(02CCH3)4.76 It is not
surprising that a 4:1 complex is formed since t-BuNC is a good o-donor

and an excellent 7-acceptor. As found with pyridine, the CF3CO2- ligand
was needed to allow coordination to the equatorial sites.

The complex Rh2(02CCH3)4(CO)2 has been isolated and structurally
characterized by x-ray crystallography.124 The v(CO) band occurs at






89



- o ___ j_ ,

































co
C,

i- 4
0 0












U-

u
- / I








C-,
s <. -s i



i ^ c,


^ ~ ~" ----


3N3111-SNVYi %







Table 3-111. 1H and 31p 1H} NMR Data for Rh2(O2CR)4 Complexes


Complex


Rh2(O2CCF3)4(t-BuNC)4


Rh2(02CCF3)4(PPh3)2

100 MHz






100 MHz, CCl4 solution






300 MHz






Rh2(O2CCF3)4(P(c-Hx)3)2

300 MHz


Nucleus Chemical Shift (ppm)b

1H 1.61 s, 1.43 s (3:2)
1.60 s, 1.40 s (2:1)

31p

+32.81 d

-14.25 (very weak)

-24.42 d

(major signals 1:1)

+34.78 d

-14.8 t (weak)

-23.66 d

(major signals 1:1)

+34.25 d of d

-15.1 d of d

-23.18 d of quart

(3:1:3)
31p


+32.22

- 7.80

-13.68


d of d

d of d

d of quart


Coupling
Constant
(Hz)


Temp-
erature


-50

27


J=166.0 27


J= 92.7


J=153.0 27

J= 37

J=104.5
1J=164.2

2j= 11.65 -50
1J= 47.4
2J= 33.8
J= 91.9
2= 11.7 (outer peaks)

15.1 (inner peaks)
J=165.2 27
J= 12.0

2J= 49.3
J= 34.8

J2= 88.9
2J= 12.0 (all peaks)


(2:1:2)







Table 3-III. continued


Nucleus Chemical Shift (ppm)b


Rh2(O2CCF3)4(P(OPh)3)2


100 MHz

300 MHz

300 MHz

300 MHz

Rh2(02CCH2CHHCH3)4(PPh3)2

Rh(02CCF3)2(P(OMe)3)3

(empircal formula)


eight peaks in +161 to

+75 ppm range, -18.2

+70.00 d of d

+69.72 d of d

+69.53 t

-18.91 br n

+58 m

+20 m

-72 t


J= 50 27


one observed

J 20
avg
Javg 20
J= 50


a. All complexes are in CDC13 solution except as otherwise noted.

b. 3P chemical shifts relative to external 85% H3PO4. 1H chemical shifts
relative to internal TMS.

c. Decomposition occurring during data collection. Chemical shift of
OP(OPh)3 is ca. -18 ppm.


Complex2
Complex


Coupling
Constant
(Hz)


Temp-
erature
(0C)








2105 cm-1, below that of free CO (2143 cm-1), indicative of ir-

backbonding. The mechanism. of this was discussed earlier. Rh2(O2CCF3)4
also forms a 2:1 adduct with CO although the CO is much more weakly

bound. Indeed, it was not possible to isolate a CO adduct of

Rh2(O2CCF3)4, CO was too readily lost. However, other workers125
reported isolation of this adduct as a light brown solid. The IR

spectrum of this complex prepared as a KBr pellet under 1 atm of CO
showed v(CO) at 2150 cm-1 and vasy(C02) at 1644 cm-1'125 It was found

here that bubbling CO through a solution of Rh2(O2CCF3)4 in CH2C12 led

to appearance of a purplish blue color, resembling that formed with

similar weak donors such as acetonitrile. The brown solid is surprising

since this resembles complexes formed with strong donors such as
phosphines and phosphites. The IR spectrum of this CH2C12 solution
showed bands assignable to v(CO) at 2160 cm-1 (m) and to vasy(CO2) at

1660 (s) and 1760 cm-1 (m). The former vasy(CO2) band may correspond to

CO free Rh2(O2CCF3)4. This positive shift in v(CO) from free CO was
taken as evidence of no r-backbonding in Rh2(O2CCF3)4.125 However, this

is not a definitive argument. If there were no r-backbonding it is
unlikely that CO would coordinate at all. As shown by Drago,26 BF3,
which using the E and C analysis,27-29 is a stronger Lewis acid than

Rh2(02CCF3)4, but does not bind CO since BF3 cannot provide any T-
backdonation. The perturbation from o effects could cause an increase
in v(CO) in Rh2(02CCF3)4(CO)2 comparable to the decrease cause by n

effects since both effects are small.








Phosphorus Donors

As mentioned previously, a large number of phosphine derivatives of

Mo2(02CCF3)4 have been reported.33,105 However, phosphites do not form
adducts with Mo2(02CCF3)4 presumably since they are not strong enough o-
donors. They do form axial complexes with Rh2(02CCH3)4 since in
contrast to the molybdenum system there is a significant r-backbonding

stabilization. It was of interest to extend this work to Rh2(02CCF3)4
since only triphenylphosphine and triphenyl phosphite adducts of

Rh2(02CCF3)4 have been reported.111 These complexes were studied by x-
ray crystallography and found to be Class I adducts. However, their

solution properties have not been investigated. The phosphorus donors
used here were dimethylphenylphosphine (PMe2Ph), triphenylphosphine

(PPh3), tricyclohexylphosphine (P(c-Hx)3), triphenyl phosphite (P(OPh)3)
and trimethyl phosphite (P(OMe)3).

PMe2Ph forms a Class II adduct with Mo2(02CCF3)4 due to its small
size and strong basicity.33 Thus, it would be a good candidate to form

a Class III adduct with Rh2(02CCF3)4, Unfortunately, the reaction of

Rh2(02CCF3)4 with four equivalents of PMe2Ph yielded only an intractable
orange oil indicating dimer decomposition.

PPh3 lies far outside the size and basicity range described by
Andersen33 for Class II adduct formation. Furthermore, in the solid

state Rh2(02CCF3)4(PPh3)2 is a typical Class I adduct.111 Thus, this
complex would be unlikely to show unusual solution behavior and one
would expect a simple 19F NMR spectrum such as that found for the THF

adduct. This was not the case. A freshly prepared solution of

Rh2(02CCF3)4(PPh3)2 showed sharp 19F NMR resonances at -74.4, -74.9, and
-75.9 ppm in CDC13 at 27 C in area ratios of 1:1:2. There was also a









small peak at -75.3 ppm. At -50 C there were still three sharp, major

peaks only in an area ratio of 1:1:1.3. That there was little change

over this temperature range indicates that the same species were

present, although perhaps in differing amounts. Assignment of these

peaks is difficult, presumably they corresond to mono- and bidentate

CF3CO2-. However, the situation differs from that observed with the

pyridine adduct and from the solution studies on Mo2(02CCF3)4 with

pyridine.106 In those cases there were two peaks representing one Class

III isomer with 1:1 mono- and bidentate CF3CO2. The more complex

spectrum observed here could be the result of a mixture of iscmers

containing axially and equatorially coordinated PPh3. That there would

be anything other than axial coordination in solution is surprising.

However, it is possible that in solution the dimer may dissociate to

some extent. The molecular weight of Rh2(02CCF3)4(PPh3)2 in CH2C12 was

found to be 590, half the expected value of 1183. This value could

result from the existence of Rh2(02CCF3)4(PPh3) and free PPh3 in

solution. However, if these were the major solution species, then only

one 19F NMR resonance would be observed, although perhaps weak signals

corresponding to 2:1 and base free species would be seen with similar

chemical shifts. Furthermore, a singlet corresponding to free PPh3

would be observed in the 31p{1H} NMR spectrum or a single broad peak

corresponding to fast exchange between free and coordinated PPh3. Such

behavior was found by Boyar and Robinsonl26 who very recently reported

the 31p{lH} NMR spectrum of Rn2(u2CCH3)4(P(OMe)3)2 in dichloromethane-d~

solution. These workers126 observed a single broad peak at room

temperature. The 31P{1H} NMR spectrum of Rh2(but)4(PPh3)2 in CDC13 at

room temperature was obtained here and it also exhibited a single broad




Full Text
SYNTHETIC AND SPECTROSCOPIC STUDIES OF METAL CAR30XYLATE DIMERS
BY
JOSHUA A. TELSER
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR CF PHILOSOPHY
UNIVERSITY OF FLORIDA
1584

ACKNOWLEDGEMENTS
There are many people and things responsible for a successful
graduate career and I would like to take this opportunity to mention
them.
First of all, I would like to thank my research director, Professor
Russell S. Drago, for his continuous help from near and from afar. It
was a privilege to be part of a research group that has accomplished so
much in so many areas over so long.
Since a group is not one man, I would also like to thank the many
members of the Drago group who have helped me out: Charlotte Owens,
Rich Cosmano, Barry Corden, Pete Doan, Dave Pribich, Carl Bilgrien, Andy
Griffis, and Ernie Stine.
Since a group is not alone, I would also like to thank the faculty
and students of other groups at both Illinois and Florida. In
particular, thanks are due to Professor R. Linn Belford and Jeff
Cornelius and to Professor William Weltner, Jr., and Richard Van Zee.
Since faculty and students cannot do everything themselves, I would
also like to thank the many support personnel who made my work a lot
easier. In particular, I greatly appreciate the help of the glass shop
and NMR and Elemental Analysis Labs at both Illinois and Florida.
n

TABLE OF CONTENTS
PAGE
ACKNOWLDGEMENTS 11
ABSTRACT v
CHAPTER I. GENERAL INFORMATION 1
CHAPTER II. THE ACTION OF STRONG ACIDS ON M2(02CR)4 SPECIES.... 15
Introduction 15
Results and Discussion 19
Conclusion 57
Experimental Section 58
CHAPTER III. THE REACTIONS OF RHODIUM TRIFLUORACETATE WITH
VARIOUS LEWIS BASES 65
Introduction 65
Results and Discussion 68
Conclusion 113
Experimental Section 114
CHAPTER IV. SPECTROSCOPIC AND BONDING STUDIES OF RHODIUM
CARBOXYLATE DIMER CATION RADICALS 123
Introduction 123
Results and Discussion 128
Conclusion 144
Experimental Section 145
CHAPTER V. SPECTROSCOPIC AND REACTIVITY STUDIES OF RUTHENIUM
BUTYRATE CHLORIDE 147
Introduction 147
Results and Discussion 153
Conclusion 190
Experimental Section 191
CHAPTER VI. GENERAL CONCLUSIONS 197
APPENDIX A. EXPERIMENTAL AND CALCULATED MAGNETIC
SUSCEPTIBILITY DATA 199
APPENDIX B. UPPER RIGHT HAND NON-ZERO MATRIX ELEMENTS FOR
SPIN HAMILTONIAN USED IN METHOD 1 200

PAGE
APPENDIX C. COUPLED BASIS SET FOR S = S, + So WHERE
Sj = S2 = 3/2, USED IN METHOD 5 201
APPENDIX D. UPPER RIGHT HAND NON-ZERO MATRIX ELEMENTS FOR
SPIN HAMILTONIAN USED IN METHOD 5 202
APPENDIX E. COMPUTER PROGRAMS USED FOR EPR SPECTRAL
SIMULATIONS 203
APPENDIX F. COMPUTER PROGRAMS USED FOR MAGNETIC
SUSCEPTIBILITY DATA SIMULATIONS 255
APPENDIX G. COMPUTER PROGRAMS USED FOR MOSSBAUER AND MMR
SPECTRAL SIMULATIONS 273
REFERENCES 298
BIOGRAPHICAL SKETCH 308
iv

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
SYNTHETIC AND SPECTROSCOPIC STUDIES OF METAL CAR80XYLATE DIMERS
By
Joshua A. Telser
December 1984
Chairman: Professor Russell S. Drago
Major Department: Chemistry
Synthetic and spectroscopic studies on several complexes in the
metal carboxylate series are described. These complexes are of general
formula M2(02CR)4 where M is a transition metal and '02CR is a bridging
carboxylate ligand. The metals used in this study are molybdenum,
rhodium, and ruthenium. The studies were undertaken to help understand
the nature of the metal-metal interaction in these complexes and to see
what effect this interaction has on the reactivity of these complexes.
To effect removal of the bridging carboxylate ligands, acetonitrile
solutions of Rh2(02CCH2CH2CH2)4 and Mo2(02CCH2)4 were reacted with
stoichiometric amounts of the strong non-complexing acids CF3SO3H and
(CH3CH2)20.HBF4. This generated Rh2(02CH2CH2CH3)22+ and Mo2(02CCH3)22+
species in solution. The former was not isolated, but characterised in
solution by NMR and UV-vi sib1e spectroscopy. Two derivatives of
Mo2(02CCH3)22+ were isolated: [Mo2(0j>CCH3) 2 (CH3CN )4] (CF3SO3 )2 and
[Mo2(02CCH3)2(CH3CN)g](BF3OH)2. The reactivity of the former complex
towards oxidative addition was investigated. The complex was found to
v

be quite stable towards oxidation in contrast to other Mo(II)
complexes. Rhodium trifluoroacetate was reacted with various Lewis
bases to give adducts of general formula Rh2(O2CCF3)4B2 as had been
previously reported for Rh2(02CR)4. However, with pyridine and _t_-butyl
Isonitrile, complexes of general formula Rh2(02CCF3)484 were isolated
constituting a new class of adduct. With phosphorus donors, Rh-Rh bond
cleavage occurred to give monomeric Rh(I) and Rh(III) complexes. This
demonstrates enhanced reactivity for Rh2(02CCF3)^ compared to rhodium
alkyl carboxylate dimers. The chemical and electrochemical generation
of Rh2(02CCH2CH2CH3)4_B2+ 1s described. These results and EPR spectra of
these species are explained using a molecular orbital model. The
strength of the rhodium Lewis base interaction determines the chemical
and spectroscopic properties of these species. The formally mixed-
oxidation state complex Ru2(02CCH2CH2CH3)4C1 was studied by powder
magnetic susceptibility measurements over the temperature range 5-300 K,
by EPR spectroscopy in various glasses at 4 K and by Far IR spectroscopy
at room temperature. In agreement with previous reports, the complex
has a quartet ground state with unpaired electron spin density
delocalized over both Ru atoms. Reactivity studies of this compound
with Lewis bases are described. A bispyridine adduct of ruthenium
butyrate chloride is reported.
vi

CHAPTER I
GENERAL INFORMATION
The discovery of transition metal complexes containing metal-metal
bonds is a relatively recent one. This discovery and much of the
subsequent progress towards understanding metal-metal bonded complexes
have been discussed in detail by Cotton and Walton in their book
"Multiple Bonds Between Metal Atoms"1 as well as in various review
articles by others.2-6 Nevertheless, a brief summary of the historical
background of this class of complexes is in order.
For the first half of the 20th century, transition metal chemistry
was dominated by the concepts developed by Alfred Werner.^ That is,
most complexes were thought of as what are now referred to as classical
coordination compounds, a central transition metal ion surrounded by
electron donating ligands usually in an octahedral orientation. Square
planar, tetrahedral and other geometries were known, but the concept
that a compound could exist in which there were several metals
interacting in various ways had not been suggested. Metal-metal
interactions were something thought to occur in bulk metals and not in
complexes with oxidized metals. This idea was so firmly held that
compounds that were synthesized during that time that contained metal-
metal bonds were not investigated further. Notable examples are
chromium acetate, first prepared in 1844,3 and various tantalum9 and
molybdenum10 halides synthesized during the early part of the 20th
century.
1

2
With the advent of Improved methods of crystal structure
determination by x-ray diffraction, the discovery of metal-metal bonds
in dimeric and cluster compounds became inevitable. It was in the metal
carbonyl complexes that metal-metal bonding was first demonstrated. The
reason for this may be a practical one in that these compounds were
relatively easy to study, but it may also be a philosophical one. Metal
carbonyls and other organometallic compounds are newer and quite
different from classical coordination compounds and thus understanding
them was not hampered by older ideas that would be invariably applied to
complexes such as metal halides and carboxylates. In Fe2(C0)g in 1938
and with greater certainty in Mn2(C0)ig in 195711 metal-metal single
bonds were first proposed. The existence of metal-metal single bonds in
carbonyl complexes containing two to twelve or more metal atoms is
widely accepted.
The existence of multiple bonds between metal atoms was not
originally found in carbonyl complexes, but in some rhenium halides.
The stoichiometry and the structure, when it was eventually
determined,^ of [Re2Clg]^- could not be explained by classical
theories. It was necessary to invoke a multiple metal-metal bonding
scheme.^ A qualitative diagram of this molecular orbital (MO) scheme
is shown in Figure 1-1. In a compound such as Mn2(C0)iQ it is not
surprising that the odd d electron on each manganese pairs up to give a
single a bond. However, it is surprising that in a Re{111) compound all
four d electrons pair up to give a quadruple bond. The evidence for
this quadruple bond comes primarily from the crystal structure. The Re-
Re distance is exremely short, 2.222 A in (^-Bu)4NRe2Clg, and there is
no twist angle between the ReCl4 subunits so that the chlorides are

Figure 1-1. Formation of metal-metal bond molecular orbitals
from individual metal d atomic orbitals.

4
antibonding
combinations
cr
*
IT
x
s
dz
4-
y
t
dz
CT

5
fully eclipsed.14 This sterically unfavorable structure is the result
of the fourth bond, the 5 bond between the Re atoms which arises
primarily from the in-phase addition of the dxy orbitals. The in-phase
addition of the two dx2_y2 orbitals could give another 6 bond; however
these orbitals are usually primarily involved 1n forming metal-ligand
bonds and are thus rarely considered in MO schemes for metal-metal
bonded complexes. The other three Re-Re bonds are derived in a more
conventional manner, analogous to the triple bond well known for
alkynes. The in-phase addition of the two dz2 orbitals gives the a bond
and the in-phase addition of the four dxz and dyz orbitals gives a
degenerate pair of it orbitals. The out-of-phase addition of these Re d
orbitals gives a corresponding set of higher energy anti-bonding <5*, and ** orbitals. In the Re (III) dimer the eight d electrons just fill
all the bonding orbitals giving a diamagnetic compound with a total bond
order of four. Subsequent to this work on the rhenium dimer, other
dimeric metal-metal bonded complexes were studied and their properties
explained using this MO scheme. The previously known complex
Cr2i02CCH3)4(H20)2 was reinvestigated and proposed15 to have a quadruple
bond resulting from the pairing up of the four d electrons on each
Cr(II) in the same manner as described above for Re(III). Chromium is
the only first row transition metal proposed to form a multiply bonded
dimer. The small size of first as opposed to second and third row
transition metals makes it less convincing that enough orbital overlap
occurs to give a quadruply bonded complex. It has even been suggested
that no Cr-Cr bond exists at all in the chromium dimers.15 Copper forms
the well known complex which is isostructural with
chromium acetate. This general structure is shown in Figure 1-2. This

Figure 1-2. General structure for metal carboxylate dimer with
idealized D,, symmetry. Axial ligands, L, need not
be present.

7
R
R

8
copper complex was studied by Bleaney and Bowers17 a number of years
ago, before the multiple metal-metal bond theory was proposed. They
found that the two copper atoms were strongly antiferromagnetically
coupled, but there was no true Cu-Cu bond. Thus it is possible, by
analogy between the two first row transition metal dimers, that chromium
acetate has a bond order of less than four with the remaining d
electrons antiferromagnetically coupled.
A large number of second and third row transition metal dimers have
been reported and in these there is little doubt that the metal-metal
bond MO scheme is valid. In addition to crystal structure
determinations of many metal-metal bonded complexes, other spectroscopic
and theoretical studies have been performed to confirm the generality of
this MO scheme. Metal-metal bonded complexes are known for molybdenum,
tungsten, technetium, rhenium, ruthenium, osmium, rhodium, and
platinum. The compounds are far too numerous to list; however some
examples of each will be given. The first studied was the rehnium
chloride and a variety of multiple metal-metal bonded rhenium,
technetium, and molybdenum halides are known.1-4 However, carboxylate
complexes were also among the first known as with the chromium and
copper acetates mentioned above. This thesis is concerned with the
metal carboxylate dimers and thus to show the generality of this type of
ligand in forming metal-metal bonded complexes, one should note the
following compounds: Re2(02C(CH3)3 )4C12, Tc2(02C(CH3)3)4C12,
Mo2(02CCH3)4, W2(02CCF3)4, Ru2(02CCH3)4C1 and RhgtOgCCH^ . In these
complexes the bond orders range from four in Re, Tc, Mo and VI to 2.5 in
Ru to one in Rh. These bond orders can be easily determined using the
MO scheme in Figure 1-1 and adding the appropriate number of d electrons
for both metals.

9
Given that a great variety of metal-metal bonded complexes exist
and that a qualitative MO scheme exists which can explain their overall
properties, the question then arises as to why would one wish to study
them further. There are several reasons to do so. First, as was
indicated specifically with the chromium carboxylate, the exact nature
of the metal-metal bonding in these complexes is not yet completely
resolved. Second, the wide range in bond orders in metal-metal bonded
complexes such as the carboxylate dimers means that there is a wide
range in strength of metal-metal interaction. Thus, what exists here is
an isostructural series for which comparison of the reactivity and
spectroscopic properties of members of the series affords a direct means
of understanding the effect different metal-metal Interactions have on
the chemistry of transition metal complexes. One can also compare the
reactivity and spectroscopic properties of a metal-metal bonded complex
to that of a monomeric complex of the same metal. The presence of two
or more metals in close proximity leads to the possibility of metal
synergism.*® This means that one metal can influence the chemistry and
the other metal site leading to different reactivity than would be
expected for noninteracting multi-metal or monomeric metal systems.
Synergism from metal clusters is proposed in a number of biological
systems such as the ferredoxins, nitrogenase, cytochrome oxidase, and
copper type 3 proteins.19,20 Synergism 1n metal carboxylate clusters
has also been used to model surface reactions.21 The variety of metals
and their oxidation states that form metal carboxylate dimers makes this
class of complexes a good model system to study synergistic effects.
The nature of the synergistic effect in metal carboxylate dimers has
been previously examined by Richman and co-workers.22-2® The enthalpies

10
of Lewis base binding to the vacant coordination sites along the M-M
axis in several complexes of general type M2(02CR)4 were measured.
These sites will hereafter be referred to as axial sites since they are
along the metal-metal bond axis. Enthalpies of formation of both 1:1
and 2:1 Lewis base axial adducts were obtained for metal carboxylate
dimers such as Rh2(02CCH2CH2CH3)4, Rh2(02CCF2CF2CF3)4 and
Mo2(02CCF2CF2CF3)4 . These will be abbreviated as Rh2(but)4, Rh2(hfb)4
and Mo2(hfb)4, respectively. Comparison of the enthalpies for 1:1 and
2:1 axial adduct formation clearly showed significant changes in the
acidic properties of the second metal as a result of base coordination
to the first. Significant differences between rhodium and molybdenum
systems were also found. Use of the E and C equation27-2® and
modifications thereof allowed quantitative understanding of these
effects. It was found that inductive transfer of electrostatic
properties of the base was more effective through the shorter Mo-Mo
quadruple bond than through the longer Rh-Rh single bond. Inductive
transfer of the covalent properties of the base was more effective
through the more polarizable Rh-Rh bond than the Mo-Mo bond.
Differences in the type of Lewis acid-base interactions were also found
for the two metals. Using the MO scheme in Figure 1-1, disregarding the
second 5 bond, it can be seen that the molydenum carboxylate dimer with
the total of eight d electrons from the two Mo(II) subunits has no tt*
electron density. In contrast, the rhodium carboxylate dimers with a
total of 14 d electrons from the two Rh(II) subunits have filled n*
orbitals. This tt* electron density can interact with empty it* orbitals
on bases with these orbitals of the right energy. Thus, a higher than
expected enthalpy of adduct formation was found for the rhodium

11
carboxylate dimers with Lewis bases such as pyridine and acetonitrile.
These bases can function as ir-acceptors as well as a-donors. No such n-
backbonding stabilization was found for the molybdenum carboxylate dimer
since it has vacant u* orbitals.
A final reason for studying metal-metal bonded complexes, in
addition to understanding synergistic effects where one metal influences
the reactivity of the other, is to understand reactions where both
metals are directly involved. An example would be the reaction of M-M
with some X-Y species to give M-X and M-Y. This can be considered an
oxidative addition and would be analogous to many reactions of organic
compounds, particularly those with carbon-carbon multiple bonds. The
reactivity of metal-metal bonded complexes has been recently reviewed30
and there are many examples of this type of reaction. However, most
involve organometalUc complexes such as metal carbonyl clusters. It is
not clear that this reactivity would occur to as great an extent in
carboxylate or halide complexes wherein the metals are generally in a
higher oxidation state.
One means of enhancing the reactivity of and understanding the
metal-metal interaction in metal carboxylate dimers is to achieve varied
ligand coordination to other than just the axial sites. As can be seen
In Figure 1-2, the sites perpendicular to the metal-metal axis are fully
occupied by the bridging carboxylate ligands. These sites will be
referred to hereafter as equatorial sites. If these ligands could be
wholly or partly removed, then the reactivity of the metal-metal bend
could be better investigated. It was reported a number of years ago by
Legdzins and co-workers31,32 that strong, non-complexing aqueous acids
could protonate the bridging carboxylates generating in solution species

12
with available equatorial coordination sites. The effect of strong,
non-complexing acids on metal carboxylate dimers of rhodium and
molybdenum in organic solvents, chiefly acetonitrile, is the subject of
the second chapter of this thesis.
Another approach to achieving ligand coordination to the equatorial
sites is to use a more poorly coordinating bridging carboxylate to begin
with. Recently, Girolami and co-workers^ obtained unusual products
from the reaction of Mo2(02CCF3)4 with various Lewis bases, primarily
phosphorus donors. In some of the products, equatorial rather than
axial Lewis base coordination was observed. This was found for
phosphines that were sterically small and good a-donors. Thus, use of a
fluorocarboxylate rather than an alkyl carboxyl ate can lead to equatorial
coordination without the need for protonation of the carboxylate by
strong acid. The reactivity of RhgiC^CCFj^ towards Lewis bases was
systematically investigated and is the subject of the third chapter of
this thesis.
Another interesting aspect of multi-metal systems, besides their
variety of ligand coordination sites, is the variety of oxidation states
available to them. A monomeric complex might have two accessible
oxidation states, an oxidized and a reduced state. In contrast, a
dimeric complex of this metal could well have more since the two metals
could be both oxidized or both reduced or one of each to give a wider
range of electrochemical behavior. This ability is one reason why metal
clusters are proposed to play an important role in biological redox
processes such as the photochemical oxidation of water in
photosynthesis.^ Thus one would expect metal-metal bonded complexes to
exhibit a wide range of oxidation states. For metal-metal bonded dimers

13
this is only partly true. Some variety of oxidation state does exist.
For Mo, W, Tc and Re stable complexes with bond orders of 3, 3.5, and 4
are known1 and they can be electrochemically interconverted. In these
the metals are in the (111,111), (II,III) and (II,II) oxidation states
respectively for Mo and W with the order reversed for Re and Tc. Only
the (II,II) oxidation state for Rh and the (II.III) state for Ru give
stable metal-metal bonded complexes that have been well characterized.
Thus, the range of oxidation states in some metal-metal bonded dimeric
systems is no greater than in monomeric complexes. Nevertheless, the
redox behavior of metal carboxylate dimers is of interest and the use of
electrochemical methods and EPR spectroscopy is helpful in understanding
this behavior. A number of studies of this nature have been made on
metal carboxylate dimers and related complexes by Cotton and Pedersen33-
39 and by other workers40,41 and show that the redox and EPR properties
of these complexes can be explained by the qualitative MO scheme
described above. In a study by Drago and co-workers33 the effect of
both axial Lewis base coordination and different caboxylate ligands was
quantitatively examined. Oxidation of the dimer is easier when the base
is strongly donating and the carboxylate is not electron with-drawing.
This oxidation converts the diamagnetic dimers to paramagnetic complexes
which can subsequently studied by EPR spectroscopy. This technique
gives information on the electronic properties of the complex that can
be directly compared to theoretical studies. In addition to the
qualitative MO scheme described earlier, a number of quantitative
studies using a variety of calculational methods have been performed.43-
4^ However, these results are not always in full agreement with
experimental data. The generation of paramagnetic rhodium carboxylate

14
dimer species and comparison between these experimental and various
theoretical results is the subject of the fourth chapter of this thesis.
In contrast to the normally diamagnetic metal carboxylate dimers of
rhenium, molybdenum, rhodium, and others mentioned above, there exists a
normally paramagnetic dimer. Ruthenium does not form a doubly bonded
d12 (II,II) or a triply bonded d10 (III,III) dimer. Rather, a d11
(11,111) dimer of formal bond order 2.5 is formed upon reaction of
ruthenium salts with carboxylic acids.48 This complex, of general
formula Ru2(02CR)4X, is quite stable compared to the rhodium (II,III)
species described above. Thus, it can be easily studied using EPR and
magnetic susceptibility. These techniques were applied to Ru2(but)^Cl a
number of years ago by Cotton and Pedersen.36 However, due to
experimental difficulties their results on the electronic and magnetic
nature of the complex were not conclusive. Thanks to improved
technology in EPR and magnetic susceptibility Instrumentation, it was
now possible to perform detailed studies on this ruthenium carboxylate
dimer. These studies are the subject of the fifth chapter of this
thesis. In addition, since in contrast to the rhodium and molybdenum
systems the reactivity of the ruthenium dimer towards Lewis bases has
not been widely investigated, some reactivity studies were performed and
are also described in this chapter.

CHAPTER II
THE ACTION OF STRONG ACIDS ON M2(02CR)4
Introduction
When dissolved in a coordinating solvent, the counter anions bound
to a transition metal cation often dissociate. For example, most first
row transition metal salts dissolve in water to give M(H20)gn+
species.^ in contrast, metal carboxylate dimers do not readily give
M2n+ and RC02". The bridging carboxylate ligands remain coordinated to
give neutral species in solution of general structure as shown in Figure
1-2 where L could be solvent. To further understand the coordination
chemistry of metal-metal bonded systems, it would be desirable to
achieve ligand coordination to a variety of sites such as those
equatorial as well as axial to the metal-metal bond. Furthermore, it is
well known that generation of coordinative unsaturation about a metal
center 1s crucial for the generation of a catalytic cycle.50 This often
occurs by reversible ligand binding. Thus, it would be desirable to
prepare metal-metal bonded dimers with labile ligands so that they could
be used in catalytic studies and be more effective than analogous
complexes with more strongly bound ligands. These catalytic processes
could involve thermally or photochemically activated ligand
dissociation. In this way any synergistic advantages to using such a
system as opposed to one with monomeric complexes couid be determined.
A metal-metal bonded complex analogous to the M(H20)gn+ species has
been reported. Maspero and Taube51 prepared Rh24+(aq) by the reduction

16
of RhC1(aq) by Cr2+(aq). This species was Identified by conversion to
by addition of sodium acetate. This conversion
from the solvated cationic species does not appear to be completely
reversible. Legdzins and co-workers21,22 treated various metal
carboxylate dimers with strong, non-complexing aqueous acids such as
HBF4(aq). They claim to have generated Rh24+ in this manner. This
claim was subsequently refuted by Wilson and Taube22 who proposed that
the treatment of Rh2(02CCH3)4 with, for example, hot 1 M_ aqueous CF3SO3
generated Rh2(O^CCH^ )32+(aq) and RhgiO^CCH^)22+(aq) but no Rh24+(aq).
The formulation of these species was based on UV-visible spectroscopy
and column chromatography. Neither group reported the isolation of any
stable rhodium dimer containing zero, two or three bridging acetates.
The action of strong acids does lead to carboxylate protonation which
allows generation of equatorial coordination sites on the rhodium
dimer. The use of this general method 1n wholly organic solvent systems
was investigated here. It was hoped that in such solvents more complete
ligand protonation of Rh2(02CR)4 would occur since there would be no
leveling effect from water. Furthermore, the species generated this way
might prove easier to isolate. Very recently, Ford and co-workers22,5*1
were able to prepare a series of complexes of formula Rh2(02CCH-j)3L+,
Rh2(02CCHj)22+, and Rh2L44+ where L = l,8=naphthyridine or derivatives
thereof such as 2,7-bis(2-pyridyl)-l,8-naphthyridine. These were
prepared by addition of stoichiometric amounts of the ligand and aqueous
1 M HC1 to methanol solutions of rhodium acetate. Similar results using
pyridine are discussed below and were carried out at roughly the same
time. Thus, use of a strongly donating, preferably chelating ligand
does allow isolation of cationic rhodium dimer species. However, these

17
are not complexes with the type of labile ligand one would desire so
that catalytic activity would result. Isolation of this type of rhodium
dimer has not yet been achieved.
The analogous Mo2(O2CR)4 system has proven somewhat more amenable
to study. A very large number of complexes containing the Mo-Mo
quadruple bond are known. Most have bridging carboxylate ligands,
halides or a variety of other anionic groups. Complexes with neutral
ligands are far fewer. Species such as Mo2X4L4 are known where X =
halide or alkyl and L = phosphine such as P£CH3}3.54-57 pewer still are
complexes which contain the Mo-Mo quadruple bond coordinated by neutral,
weakly donating ligands. A number of years ago, Bowen and Taube58
reported the Mo24+(aq) species. This was not isolated as solid, but
prepared in solution in the following manner. First, K4Mo2Clg was
reacted with K2S04 in 0.2 M CF3S02H(aq) to give K4Mo2(S04)4 , a stable
salt. This sulfate was reacted with Ba(CF3SO3)2 to precipitate BaS04
and give the red aquo molybdenum dimer in solution. This species was
identified by UV-visible spectroscopy and could be converted back to the
acetate. This work and the corresponding study with rhodium described
above showed that these metal-metal bonded dimers could exist in
solution without the presence of bridging or even anionic ligands. As
was found much later with rhodium,53,54 Bowen and Taube58 were able to
Isolate salts of the molybdenum dimer by using strongly donating
chelating neutral ligands. Addition of ethylendiamine (en) and 2,2'-
dipyridyl (dipy) to solutions of Mc2Clg4- led to isolation
of Mo2(en)4Cl^ and Mo2(dipy)2Cl^ . Although these complexes have not
been structurally characterized, the former species presumably has no Cl
coordinated to the molybdenum atoms. The Mo24+(aq) species and related

13
complexes such as Mo^jClg4- have been used in a photochemical study by
Trogler and co-workers.Ultraviolet irradiation of aqueous solutions
of these complexes produced dihydrogen. This reaction was proposed to
proceed via Mo2{v-0H)24+(aq) which was generated directly from Mo24+(aq)
and via Mog(u-ClIgCl^im-H)^— with the halides. This indicates a
potential application for molydenum dimer species. Analogous complexes
that would be soluble in organic solvents might also show interesting
photochemical behavior.
Another approach towards generating molybdenum dimers with weakly
coordinating ligands was taken by Abbott and co-workers.6(1 Molybdenum
acetate was reacted with neat CF3S03H at 100 C. Removal of solvent and
drying at 100 C under vacuum yielded a tan solid formulated as
Mo2(CF3S03)4. This product was frequently contaminated by Mo2(02CCH3)3_3
impurities which were very difficult to remove. Furthermore, the
complex was extremely prone to decomposition making it difficult to use
for subsequent reactions. Very recently, Mayer and Abbott61 achieved
greater success using Mo2(02CH)4 rather than the acetate as starting
material. Molybdenum formate was reacted with CF3S03H and (CF3S02)20
for six days to yield CO and a tan product formulated as [Mo2(H20)4
(CF3S03)2](CF3S03)2. This complex reacts with acetronile to yield blue
[Mo2(CH3CN)g](CF3S03)4. These very air and water sensitive complexes
were characterized by IR and UV-visible spectroscopy and elemental
analysis. This represents the first reported example of a quadruply
bonded molybdenum dimer coordinated only by monodentate, weakly
donating, netural ligands. The reaction of Mo2(02CCK3)4 with CF3S03H
and other strong nonaqueous acids in acetonitrile and other organic
solvents is described here. These studies were carried out at roughly

19
the same time as those of Mayer and Abbott®1 and gave similar results.
The reactivity of the resulting complexes was also investigated.
Results and Discussion
Rhodium
Treatment of the purple solution of Rh2(but)4 in acetonitrile with
CF3SO3H leads to an immediate, although slight, color change to dark
red. The _n_-butyrate ligand was chosen for increased solubility; similar
results were obtained with acetate. Trifluoromethanesulfonic acid was
chosen since it is a very strong, poorly coordinating acid that is
somewhat soluble in organic solvents. The effect of different amounts
of CF3SO3H on the UV-v1s1ble absorption spectrum of Rh2(but)4 1s shown
in Figure 2-1. Rhodium butyrate with no acid showed absorption bands at
552 (e=202) and 438 nm (e=101). These are virtually identical to the
results reported for rhodium acetate in acetronitrlle, bands at 552
(e=235) and 437 nm (e=125).®2 Single crystal polarized electronic
absorption spectra of rhodium acetate led to a proposal that these bands
correpond to (Rh-Rh)ir* + (Rh-Rh)a* and (Rh-Rh)ir* + (Rh-O)a* transitions,
respectively.®3 Some controversy has recently arisen as to this
assignment and will be discussed in Chapter IV. Addition of two
equivalents of CF3SO3H leads to a very little change in the UV-visible
spectrum. However, addition to four equivalents of acid leads to a
dramatic change. The primarily metal-metal bond trnasition at 552 nm is
relatively unaffected, but the metal-ligand transition is strongly
affected, shifting to 380 nm. This shift to lower wavelength may result
from a strengthening of the Rh-0 bonds of the remaining butyrates caused
by the higher relative charge on the metal dimer. This would lower the

_ q
Figure 2-1. UV-visible absorption spectra for RhgCbut)^ in acetonitrile (1.98 x 10" M)
using 1.0 cm quartz cells with: (A) no acid added; (B) 2 equivalents of
CF^SO^H added; (C) 4 equivalents added; (D) 10 equivalents added, spectrum
after 1 h.

60
21
350 400 450 500 550 600

22
energy of the Rh-0 a bonding orbitals and raise the energy of the Rh-
0 a* antibonding orbitals leading to the observed shift to higher
energy. Addition of excess CF3SO3H (~10 equivalents) and allowing the
solution to sit for one hour does not greatly change the spectrum. The
main transitions are observed at roughly the same wavelengths. A large
band extending into the ultraviolet region is observed which may result
from rhodium dimer or solvent decomposition. Solvent decomposition is a
definite problem when trifluoromethanesulfonic acid is used with organic
solvents. For example, 1t catalyzes the decomposition of THF.64 With
acetonitrile, trimerization probably occurs to give 2,4,6-trimethyl-
1,3,5-triazine. This compound was not isolated, but when benzonitrile
was used as a solvent in the above procedure, the analogous compound
kyaphenine (2,4,6-triphenyl-l,3,5-triazine) was isolated and easily
Identified by elemental analysis, melting point and mass spectroscopy.
Kyaphenine is normally synthesized by the addition of excess CCI3CO2H to
benzonitrile.65 Thus, the use of excess CF3SO3H should be avoided.
Nevertheless, the UV-visible spectrum suggests that protonation of the
bridging carboxylates is occurring with four equivalents of acid. The
species generated in this manner can be identified by NMR
spectroscopy. NMR data are summarized in Table 2-1. The *5C{*H} NMR
spectra of n_-butyric acid and Rt^tbut)^, both in acetonitrile-^, are
shown in Figures 2-2 and 2-3, respectively. Of particular importance is
the signal for the carboxyl carbon which has a very different chemical
shift in the two compounds. Addition to four equivalents of CF3SO3H
leads to a spectrum as shown in Figure 2-4. The four peaks at 139.47,
126.87, 114.85, and 102.46 ppm relative to internal TMS correspond to
the carbon in CF3SO3(H) split by three equivalent fluorine nuclei (19F,

Table 2-1. NMR Data on Rh2(but)^ Systems3
13C{1H}b
Co
Co
C.
H
H0
H
1
2
3
4
a
&
Y
Rh2(but)^
194.5
39.6
19.7
13.7
1.97 m
1.38 hex
0.69 t
Rh2(but)^ + 4 equiv
CF3S03H: Rh2(but)22+
196.8
39.6
19.5
13.7d
2.28 t
1.46 m
0.83 t
Free Butyric
182.1
36.3
18.6
13.7d
2.67 t
1.69 m
1.0 in
Acid
Butyric Acid
178.2
37.0
19.2
13.9
2.4 t
1.7 m
1.0 t
aAll spectra run at 25°C and in CD^CN solution.
bIn units relative to TMS, calibrated using nitrile C of CD^CN
(118.20 ppm relative to TMS).
cppm relative to TMS.
d0nly one signal resolved due to small chemical shift difference.

13 1
Figure 2-2. C{ H) NMR spectrum of n-butyric acid in acetonitrile-d3 at room temperature
using 500 scans at 25.161 MHz with an external D20 lock. The peak labelled
"-CN" and the upfield heptet (CD^, 2H, 1=1) are due to solvent.

25

13 1
C{ H} NMR spectrum of [^(but)^ in acetonitrile-^ at room temperature
using 3000 scans.
Figure 2-3.

27

13C{} NMR spectrum of Rh2(but)^
with 4 equivalents of CF^SO^H in acetonitrile-^
at room temperature using 3000 scans. The quartet at -120 ppm is from the acid
(CF3, 19F, 1=1/2).
Figure 2-4.

29

30
1=1/2). The other signals correspond to free and Rh coordinated butyric
acid, with the carboxyl carbon peaks occurring in the expected places,
by analogy with Figures 2-3 and 2-3. Proton NMR spectroscopy gave
similar results. Figure 2-5A shows the 1H NMR spectrum of Rh2(but)4
with the expected splitting patterns for an n-propyl group. Figure 2-5B
shows the spectrum after addition of four equivalents of CF3SO3H.
Signals are observed for coordinated and free butyric acid. The poor
resolution of some of these peaks may be due to the presence of acid,
causing proton exchange and perhaps decomposition. Based on the peak
intensities, the dominant species in solution has an average composition
of Rh2(but)22+. The area ratio of peaks corresponding to free and
coordinated butyrate was 1:1 in several separately prepared solutions.
The ratio of peak areas for the protons for both free and coordinated
butyrate was 2:2:3 for Ha:Hg:HY as expected. This solution gave no EPR
signal at 77 K indicating that a Rh(II) monomer was not present. This
does not prove that the dimer remains intact since disproportionation to
diagmetic Rh(III) and Rh(I) may have occurred. However, the NMR data
suggest that the solution contains the dimer since the signals for
coordinated butyrate, particularly C^, occur near those for Rh2(but)4.
Also Rh(III) and Rh(I) complexes are generally orange or yellow. The
NMR data, in conjunction with the UV-visible results, indicate that four
equivalents of CF3SO3H generate Rh2(but)22+ in acetonitrile solution.
Attempts to isolate a solvated Rh2(but)22+ salt were unsuccessful.
Evaporation of the acetonitrile solution left a dark red, water soluble
oil. Previous workers32*52 reported that evaporation of the solution
obtained by the titration of Rh2(02CCH3)4 with aqueous CF3SO3H led to a
deliquescent green oil which was similarly intractable. Attempts to

*H NMR spectra of Rh2(but)^ in acetonitrile-d3 at room temperature with:
(A) no CF^SO^H present; (B) 4 equivalents of CF^SO^H added.
Figure 2-5.

2
PPM
2
O

33
isolate a product using BPh^" and PFg" as counterions were
unsuccessful. Some solids were obtained, but the results were not
repeatable and the products could not be well characterized.
Another approach that was taken to isolate a Rh2(but)42+ species
involved using a bridging dianionic ligand, Y2-, to form a neutral
compound Rh2(but)2Y. This type of compound has precedent in the A-frame
series of complexes, which have been found to coordinate a wide variety
of molecules to their exposed side.®®-69 The sulfide ligand was chosen
since it is used in the A-frame complexes,69 is readily available, has a
high affinity for transition metals, and bridges easily. Anhydrous
sulfide was generated directly in THF by addition of "Super-Hydride"
(LiBH(CH2CH3)2) to elemental sulfur. This solution was added to the
Rh2(but)2 solution leading to immediate formation of a black
precipitate. The black compound was insoluble in all solvents so it
could only be characterized by elemental analysis. Elemental analysis
indicated a complex with 1-2 sulfurs and two butyrate groups. Mass
spectroscopy was used to little avail. No molecular ion peaks were
detected at m/e=412 for Rh2(but)2S or m/e=446 for Rh2(but)2(SH)2.
Intense peaks corresponding to H2S and HS fragments were observed. The
compound is possibly a sulfide or hydrosulfide bridged rhodium polymer
which contains two butyrates per rhodium dimer. A similarly intractable
compound was prepared using selenide. Rakowski Dubois and co-workers79
successfully converted the molybdenum sulfide polymer [(CgHg)MoSx]y to
the soluble binuclear complex [(CgHg)MoS(SH)2]2 by stirring the polymer
for 5-7 days under 1 atm of H2. This was attempted with the rhodium
sulfide polymer, but no dissolution was observed. The solid was also
treated with 1-iodoheptane in the hope of alkylating any bridging SH

34
groups to solubilize the complex. However, no reaction or dissolution
was observed and the solid recovered should no increase in carbon or
hydrogen content. The anion of 1,3-dithiopropane, generated in the same
manner as the sulfide, was used in the hope of obtaining more soluble
products, but gave only an oil. Other Y2- type ligands that could be
considered are cis-l,2-dicyanoethene-l,2-dithiolate (mnt) which forms
complexes with many transition metals71 and (H0P0)202- (pop) which forms
binuclear complexes with platinum.72,72 However, mnt reacts with
Rh2(02CCH3)4 to give a monomeric Rh(II) complex,71 and would doubtless
do the same with Rh2(02CR)22+. In contrast to the results with
platinum,72,73 rhodium as both RhCl3 and Rh2(02CCH3)4 does not appear to
react readily with pop or H3PO3 to give analogous P-bonded dimeric
complexes.
A final attempt at isolating a cationic rhodium carboxylate dimer
involved the use of pyridine, a Lewis base far stronger than
acetonitrile. Addition of excess pyridine to the acetonitrile solution
of Rh2(but)42+ led to an immediate color change to orange. The In¬
visible absorption spectrum of this solution showed a band at 465 nm
U=481) presumably corresponding to the (Rh-Rh)ir* + (Rh-Rh) transition and a very large band extending into the UV region. This
latter band may involve rhodium to pyridine v* transitions. The order
of addition of pyridine and acid is important. When pyridine (10
equivalents) is added to rhodium butyrate in acetonitrile, the purple
Rh2(but)4(CH3CN)2 solution immediately turns red, indicative of
Rh2(but)4(pyr)2. The equilibrium constants for axial coordination of
various Lewis bases to rhodium butyrate have been determined,23-23 and
Keq for pyridine binding is several orders of magnitude larger than that

35
for acetonitrile. However, when CF3SO3H (10 equivalents) is added, the
purple color is restored indicating that the pyridine is completely
protonated by the strong acid. This occurs even though some pyridine is
coordinated to the Lewis acid R h2(but >4. Adding more pyridine
neutralizes the acid present and the red color of the axial pyridine
adduct eventually develops. When excess acid is added to this, as with
any acetonitrile solution of rhodium butyrate, the Rh2(but)42+ species
results and subsequent addition of pyridine leads to the orange color of
what is presumably a pyridine adduct of Rh2(but>4 with equatorial base
coordination. Addition of excess acid to the orange solution restores
the purple color indicating that the equatorially coordinated pyridines
can also be protonated. Attempts were made to isolate solids from the
orange solution by evaporation, cooling, and the use of various solvents
such as water and methanol and various counter anions such as BPI14' and
PFg”. Oils were usually obtained; however a solid was isolated which
analyzed approximately for Rh2(but)2(pyr)4(PFg)2. With Rh2(02CCH3)4,
less oiling occurred and what is presumably [Rh2(02CCH3)2(pyr)4]
(053503)3 was isolated. Based on this result and those from Ford's
laboratory,53,54 use 0f putyrate, while helpful in solution studies, is
not recommended for isolation of solids.
Some other reactivity studies were undertaken on the Rh2(but>42+
solution. This solution showed no visible change upon exposure to air
and the 1H NMR spectrum was unchanged. On the basis of kinetic data,
HRh2(92CCH3)3 has been proposed as an intermediate in the hydrogenation
of olefins catalyzed by rhodium acetate.^ Rhodium acetate itself shows
no reactivity towards H2 (1 atm) at temperatures up to 80 C. It was
hoped that such a hydride species might be observed in the reaction of

36
H2 with the cationic rhodium dimer solution. This solution was sealed
in an NMR tube under 1 atm of H2, but showed no visible or *H NMR
spectral change. Furthermore, the solution shows no reaction with one
or two equivalents of 1-hexene or Cl^C^CCsCCC^CHj, both of which might
be expected to add oxidatively to the Rh-Rh bond. Thus, reactivity with
organic molecules has not been enhanced by exposing the metal-metal
bond.
Molybdenum
In contrast to the work with rhodium described above, it was
possible to isolate stable, cationic acetonitrile coordinated
derivatives of the molybdenum carboxyl ate dimer. Molybdenum acetate is
completely insoluble in organic solvents, but when suspended in
acetonitrile, addition of two equivalents of CF^SOgH leads to immediate
formation of an intensely colored purple solution. Removal of solvent
and recrystallization of the resulting solid from 1:1 acetonitrile/
toluene allows isolation in good yield of a purple crystalline
complex. Elemental analysis suggests its formulation as
[Mo2(02CCH3)2(CH3CN)(CF3S03)2, (1). Use of more acid, up to 10
equivalents, leads to essentially the same product with greater solvent
decomposition. The use of neat acid will be discussed below. This
compound is air sensitive and very hygroscopic but is indefinitely
stable under an inert atmosphere. Various methods were used to confirm
that 1 is an acetonitrile coordinated Mo-Mo quadruply bonded species as
formulated above. The oxidation state of molybdenum was found to be 2+
using Fe3+ as oxidant using a reported method.58 However, metal-metal
bond cleavage can occur without oxidation state change. Examples
include the photolysis of Re2C1g in acetonitrile to give

37
Re(CH3CN)3Cl375 and the reaction of Mo2(02CCH3)4 with t_-BuNC to give
Mo(_t-BuNC)5(02CCH3)2.76 The conditions required were more strenuous
than those used here. Irradiation at 366 nm for 24-48 hours was needed
for photolysis and in the second case, _t-BuNC is a far stronger ligand
than acetonitrile.
The UV-visible absorption spectrum of 1 is of interest and provides
conclusive evidence that the Mo-Mo quadruple bond remains intact. In
acetonitrile solution bands are observed at 535 (c=864), 390 (e=117) and
255 nm {e=7383). This resembles the results of Bowen and Taube88 who
found for Mo2^+(aq) and Mo2(en)4^+ absorption bands at 504 {e=337) and
478 nm (e=483), respectively and weaker bands at 370 (e=40) and 360
(e=36.4), respectively. A band at 235 nm (e=966) was also observed for
Mo2(en)42+. Some controversy exists as to the assignment of the
electronic transitions in the Mo-Mo quadruply bonded system. However, a
very detailed single crystal polarized electronic absorption spectrum
study by Martin and co-workers77 indicated that the band observed at 435
nm corresponds to a (Mo-Mo)5 + (Mo-Mo)S* transition. The second band at
377 nm was more tentatively assigned to a (Mo-Mo)5* + (Mo-Mo) tt*
transition. A recent study by Manning and Trogler78 of the electronic
spectrum of matrix isolated Mo2(02CCH3)4 confirmed the assignment of the
6+5* transition although suggested that other, probably Mo-0 states,
contribute to the observed band. At any rate, these two transitions are
observed for 1. The UV-visible spectrum of l was also obtained in THF
solution and gave qualitatively the same results. Bands at 490 (e=321),
335 (£=461), and 277 nm (e=3066) were observed. Dissociation of
coordinated acetonitrile probably occurs which changes the absorption
bands. The shift to shorter wavelengths may result from the replacement

38
of the ir-acceptor CH3CN by the a-only ligand THF. Thus 1 in THF snows
absorptions closest in wavelength and intensity to those of Mo2^+(aq)
and Mo2(en)44+. In addition, i in THF is far more air sensitive than 1
in acetonitrile, changing color almost immediately upon air exposure,
perhaps indicating poorer stabilization of the Mo24+ unit.
The IR spectrum of 1 (Nujol mull) is shown in Figure 2-6. Most of
the absorption bands can be readily assigned. Very sharp bands
corresponding to v{CN) of coordinated acetonitrile are observed at 2300
and 2285 cm-1. This shift to higher frequency, compared to 2266 cm-*
for free acetonitrile, is indicative of end-on nitrile coordination with
little ir-backbond stabilization.7® Two v(CN) bands are seen because in
addition to the v{CN) fundamental, there is a combination of the
symmetrical CH3 deformation and the C-C stretch. These two bands are
subject to Fermi resonance coupling which affects their frequencies and
intensities. Unfortunately, no assignment can be made as to Mo-N
stretches. Very few metal organonitrile complex M-N stretches have been
conclusively identified and they usually are weak and of widely varying
frequency.80 Absorption bands corresponding to the acetate ligand are
of interest. For 1 no band corresponding to vasy(C02) was observed.
This is seen at 1578 cm--*' in Na02CCH3.8* However, a strong band at 685
cm-* is observed which is most likely <5(C02). This occurs at 675 cm-*
in Mo2(02CCH3)460 and at 646 cm-1 in Na02CCH380 and indicates the
presence of bridging acetate in 1. Finally, a weak band is observed at
410 cm-* which may correspond to a Mo-Mo stretch. In centrosymmctric
metal carboxylate dimers this band is IR inactive. However, Raman
spectroscopy studies88 on a number of derivatives of the quadruply
bonded Mo dimer show v(Mo2) occurring at 383 to 404 cm-* with weak to

MICRONS
Figure 2-6. IR spectrum of 1 as a Nujol mull using KBr cells. The bands labelled "P"
correspond to polystyrene calibration peaks at 1601 and 907 cm"1.

40
medium Intensities. It is possible that non-centrosymmetric isomers of
1 are present allowing observation of v(Mo2) in the IR spectrum. Known
molybdenum dimer complexes with this geometry in which the acetates are
cis are Mo2(02CCH3)2((Pz)3BH)282 and Mo2(02CCH3)2(CH3C0CHC0CH3)2.83
Infrared studies on these complexes were not reported; however these and
an analogous isomer of 1, all with C2v symmetry, would have an IR active
Mo-Mo stretch. This would most likely be of low intensity due to the
small dipole moment change involved. This possible structure and that
of a centrosyrnmetric isomer are shown in Figure 2-7. The remaining IR
bands can be assigned to the counterion, non-coordinated CF3SO3'. Bands
are observed at 1285, 1245, 1160, 1030, 755, 720, 635, 575, and 520
cm'1. The IR and Raman spectra of solid Na03SCF3 have been carefully
analyzed by Miles and co-workers.8¿1 The vibrations they observed and
their assignments are as follows: 1280 (vasy(CH3)), 1232 (vs{CF3)),
1168 (vasy(S03)), 1036 (v$(S03)), 766 {ós(CF3)), 630 (6asy(S03>), and
531 and 515 cm'1 both 5asy{CF3)). These bands can be directly compared
to those observed for 1. When CF3S03_ is coordinated, the IR bands for
v{SO3) change greatly. For example, Mo2(03SCF3)4 has S-0 stretches at
1350, 1110, and 990 cm'1.80 The band observed in J, at 720 cm"1 cannot
be assigned to the CF3SO3' and is probably an acetate or acetonitrile
vibration.
Proton NMR spectroscopy was performed on 1, but did not provide
much insight into its structure. Signals were observed at 4.3 and 2.0
ppm relative to internal TMS in nitromethane^d-. The upfield signal is
probably coordinated CH3CN since in CD3CN solution it broadened and
decreased in intensity over time, disappearing after about one hour,
indicating exchange with the solvent. The downfield signal is probably

ch3
ch3
2 +
/NCCH3
Figure 2-7. Proposed structure for 1.
ch3cn
ch3cn
somer on left has D2h symmetry, isomer on right C2v-

42
CH3CO2" although ft is rather far downfield for metal coordinated
acetate. Paramagnetic impurities initially present or arising from
complex decomposition would cause line broadening and unusual chemical
shifts.85 However, 1 does not show an EPR signal in 1:1
acetonitrile/toluene at 77K.
A different synthetic approach was used to study the
interconvertability of the Mo24+ derivatives. What is presumably the
reported50 MogiOjSCFj)^ complex was prepared but not characterized. To
this was added acetonitrile to give an intensely colored blue
solution. Addition of toluene led to formation of a bright blue
precipitate. This complex did not give a satisfactory elemental
analysis. The IR spectrum indicated coordinated CH3CN, non-coordinated
CF3SO3" and some residual bridging acetate as well as a strong v(0H)
band. Slow evaporation of the filtrate led to formation of purple
crystals. The IR spectrum and elemental analysis of these crystals
coresponded to that of 1. The initially isolated blue complex is most
likely one with less than two acetates giving a more highly charged
species which is less soluble in organic solvents. Subsequent to this
work, Mayer and Abbott51 reported the synthesis of [Mo2(H20)4(O3SCF3)2]
(CF3SO3)2. This complex was synthesized from and thus, in
contrast to the previously reported MO2(03SCF3)4, could be reprodudbly
prepared free from any carboxylate contamination since the formate
decomposes to CO and H20. Addition of acetonitrile to this complex led
to isolation of blue [Mo2(CH3CN)0](CF3SO3)2. The blue complex reported
here is most likely impure [Mo2(CH3CN)g](CF3S03)2, indicating that the
acetonitrile solvate of Mo24+ can also be prepared from molybdenum
acetate, but much less successfully than by the method using molybdenum

43
formate as starting material. What is interesting is that as found with
the rhodium systems, the M2(O2CR)2^+ species is very stable. Even
following the extreme conditions of Abbott and co-workers,6^ a
considerable amount of the Mo2(02CCH3)22+ species is isolated.
Some reactivity studies on 1 were performed. As stated previously,
the complex is air sensitive and quite hygroscopic as a solid. However,
in acetonitrile solution, the complex is relatively stable. Dioxygen
can be bubbled through this solution for at least 30 minutes without any
visible change. Exposure to air does eventually decompose the dimer.
This decomposition was monitored by UV-visible spectroscopy and is shown
in Figure 2-8. The characteristic Mo-Mo quadruple bond absorption bands
disappear and most likely a variety of monomeric molybdenum species
result. Prolonged exposure to air gives a blue-green solution
characteristic of high oxidation state Mo. It is likely that this
decomposition is assisted by replacement of coordinated acetonitrile by
water. Complex 1 dissolves
in
water to give a red
solution similar
to
that of Mo24+(aq). This
solution is very air
sensitive,
as
is
Mo24+(aq), in contrast to
1
in acetonitrile.
Complex 1
reacts
immediately with Et4N02CCH3 in acetonitrile to give a yellow solution
from which yellow crystals of M02(O2CCH3precipitate. Complex 1
reacts readily in acetonitrile solution with stronger Lewis bases.
Addition of excess (-10 equivalents) of nitrogen donors such as pyridine
or N-methylimidazole gave red solutions and phosphorus donors such as
tricyclohexylphosphine gave blue solutions. These reactions were not
investgated further; however, it is likely that a variety of derivatives

44
X (nm)
Figure 2-8. UV-visible absorption spectrum of 1 in acetonitrile
(6.0 x 10~4 M) showing changes on exposure to air.

45
of the Mo2(02CCH3)22+ unit with various ligands stronger than
acetonitrile could easily be prepared.
The electrochemistry of 1 was investigated to determine if stable
fdo2 (II.III) or other species could be generated. Previous
electrochemical studies by Cotton and Pedersen38 on Mo2Clg4- and
Mo2(but)4 indicated that these complexes could be quasireversibly
oxidized at ~0.4 V vs. see to short-lived Mo2(II.III) species that were
not isolated. The Mo2(but)4+ species was observed by EPR
spectroscopy. Complex 1 in acetonitrile with 0.1 M_ (n_-Bu)4NBF4 as the
supporting electrolyte showed no reversible redox waves over the range
+2.0 to -2.0 V vs. Ag/AgCl ,KC1 (sat'd). A weak irreversible oxidation
occurred at +1.5 V. Acetonitrile coordination may stablize the dimer
towards oxidation, but does not facilitate isolation of oxidized
species.
Another form of oxidation of the Mo2(II,III) unit could involve
oxidative addition to the Mo-Mo quadruple bond. Such reactions are well
known for carbon-carbon multiply bonded compounds. For example, Br2
oxidatively adds to olefins to give di bromo compounds. Of more
relevance here are the studies by Chisholm and co-workers86-88 who have
achieved oxidative addition to the Mo-Mo triple bond in Mo2(0R)6
complexes. For example, Mo2(v-Pr0)6 reacts with (v-PrO)2 to give
Mo2(u-v-PrO)2(v-PrO)g,86 with various alkynes in the presence of
pyridine to give Mo2(u-v-PrO)2(2_-PrO)4(pyr)2(u-C2R)87 and with
dimethylcyanamide to give Mo2(v-PrO)g(u-HCMNe2).88 Such reactions might
be expected for Mo2(02CR)4 complexes if the Mo-Mo bond were more
exposed. Thus, complex i is a likely candidate. Unfortunately, no
reaction was observed between 1 and CH3I, (CH3CH2S)2 and 1-hexene, all

46
of which could oxidatively add across the Mo-Mo quadruple hand. Complex
1 did react readily with dimethylcyanamide (~10 equivalents) in
acetonitrile to give a blue solution. From this a bright blue solid was
isolated. The IR spectrum of this solid showed a very strong v(CN) band
at 2260 cm-1 (Nujol mull) with no bands in the 1600 to 2200 cm-1
range. This can be compared to free (CH3)2NCH, with v(CN) at 2205 cm-1
and to complexes with side-on dimethylcyanamide coordination such as
[Ni(C0)(NCN(CH3)2)]2 with v(CN) at 2008 cm-1 89 and the above Mo (111)
alkoxlde dimer with v(CN) at 1582 cm-1.88 The shift to higher frequency
seen here indicates end-on nitrile coordination as seen with
acetonitrile, with no evidence for side-on coordination involving the
Mo-Mo bond. Complex 1 also showed no reaction with SnCl2 or Vaska's
compound (Ir(C0)(PPh3)2Cl). These complexes were hoped to add
reductivity to 1 replacing acetonitrile to give clusters containing 4-
coordinate Sn or 6-coordinate Ir, respectively.
A final approach towards investigating the reactivity of X was to
use anionic metal fragments to generate clusters resembling the
reactions attempted above to generate Sn or Ir containing clusters. The
reaction of monomeric metal fragments to form clusters has been widely
studied.90 Of particular use is the reaction of anionic metal complexes
with species containing a weakly bound ligand. An example is the
reaction of FegCtCO)^2- with W(CO)3(CH3CN)3 to give WFe5C(C0)372-.91
An important point regarding the complexes synthesized in this manner is
that the reactants arc generally both metal carbonyl complexes or at
least compounds containing metals in similar, low oxidation states with
similar ligands. If 1 would react with these anionic species to form
clusters, the result would be a cluster in which two of the metals, the

47
molybdenum atoms, would be in a relatively high oxidation state with
relatively electron-withdrawing ligands, carboxylates, while the other
metal would be in a relatively low oxidation state with electron-
donating ligands such as carbonyls.
Complex 1 was reacted with Mn(C0)g' (CgHgjMolCO^- and FeiCO)^2-.
The first two can be easily prepared by reduction of the dimeric species
Mn2(CO) and (CgHg^Mo^COjg by Na/K alloy.92 The iron complex is
available commercially and is often referred to as Collman's
reagent.93 Unfortunately, these reduced species reacted with J, via
redox reactions. The metal carbonyl starting material was regenerated
and could be identified by IR. Uncharacterized species from
decomposition of the Mo dimer were also produced. Apparently, these
anionic carbonyl complexes are too strongly reducing to form clusters.
This problem often occurs in the reaction of anionic complexes even with
other low oxidation state carbonyl compounds. For example,
(C5H5)Fe(CO)2- and V(C0)6_ are not usable in these reactions because
they are such strong reducing agents.90 Furthermore, some clusters are,
like 1, easily reduced. For example, Fe3{C0)12, Fe2Ru(C0)12 and
FeRu2{C0)12 are easily reduced and fragmented.90 Thus, it appears that
the reaction of higher oxidation state metal-metal bonded dimers with
reduced organometallic species is not a facile means of synthesizing
metal custers.
In addition to 1, [Mo2(02CCH3)2(CH3CN)4](CF3S03)2, the synthesis of
other complexes containing the Mo-Mo quadruple bond was investigated.
One approach would be to use a solvent other than acetonitrile. As
discussed previously, the strong acid needed for carboxylate protonation
precludes the use of many solvents. The problems with THF

48
(polymerization) and nitriles (oligomerization) have already been
mentioned. Solvents that would solvate the cationic species generated
by carboxylate protonation but be only weakly coordinating are
nitromethane, propylene carbonate and sulfolane (tetrahydrothiophene-
1,1-dioxide). The first two decompose readily upon addition of CF3SO3H;
however sulfolane appears not to decompose. Addition of CF3SO3H (~4
equivalents) to suspensions of h^tOgCC^)^ in these three solvents
leads to a faint red color indicative of aquo-coordinated Mo dimer
species. However, the bulk of the molybdenum acetate does not dissolve
and addition of more acid does not lead to more dissolution, only to
solvent decomposition. Clearly, the only reaction occurred because of
the presence of water in these solvents. A reasonably good donor
solvent, such as acetonitrile, is needed to stabilize any cationic
molydenum complexes produced and so drive the carboxylate protonation
reaction to completion.
Another parameter that can be varied besides solvent is the acid
used. It was desired in this work to avoid the use of aqueous solvent
systems since those had been studied previously58 and cationic Mo dimer
complexes were not isolated except with strong ligands such as
ethylenediamine. This solvent choice limits the variety of acids
usable. Furthermore, acids containing halide ions are to be avoided
since the Mo dimer readily coordinates halides. For example,
Mo2(02CCH3)4 reacts with Ph^AsCl in dilute HC1 to give CM02(O2CCH3}2d4]
(Ph^As>2-33 Other complexing acids would produce similar species,
resulting in a Mo dimer coordinatively saturated by strong, anionic
ligands. A non-complexing, nonaqueous acid that is readily available,
besides CF3SO3H, is fluoroboric acid as the diethylether adduct,

49
[(CH3CH2)20]HBF4. This acid is very difficult to handle since it is
very viscous and hygroscopic. Furthermore, it is difficult to purify
and may be of varying composition, as will be shown below. Addition of
approximately four equivalents of [(Et20)]HBF^ to an acetonitrile
suspension of Mo2(02CCH3)4 leads to formation of an intensely colored
magenta solution. From this solution an air sensitive, hygroscopic
magenta compound can be isolated that is best formulated as
[Mo2(02CCH3)2(CH3CN)5](BF30H)2, (2). This complex was characterized in
the same manner as 1. The oxidation state of Mo was found to be 2+.
The UV-visible absorption spectrum of 2 in acetonitrile shows bands at
527 (e=890), 370 (c=205), and 269 nm (e=7000). This indicates that the
Mo-Mo quadruple bond is present. Exposure to air leads to
decomposition, as with 1, only it occurs more rapidly with 1. This
process 1s shown in Figure 2-9.
The IR spectrum of 2 is of interest and supports the above
formulation based on elemental analysis. The spectrum (Nujol mull) is
shown in Figure 2-10. Three strong bands corresponding to v(CN) of
coordinated acetonitrile are observed at 2308, 2282, and 2258 cm-1.
Elemental analysis indicated that there were five acetonitriles in 2 as
opposed to four in 1. In 1 there are two v(CN) bands whereas in 2 a
third band results from CH3CN in either a different coordination
environment or from different isomers. Two possible isomeric structures
for 2 are shown in Figure 2-11. As can be seen by comparison with
Figure 2-8, in 1 the acetonitriles are equivalent while in 2 they are
not. Comparison of the IR absorption bands corresponding to the acetate
demonstrates again the difference between 1 and 2. Complex 1 showed no
band corresponding to vaSy(C02). By contrast, 2 shows bands at 1647,

50
350 400 450 500 550 600
X (nm)
Figure 2-9. UV-visible absorption spectrum of 2 in
acetonitrile (6.5 x 10~4 M) showing changes
on exposure to air.

MtCHOMS
Figure 2-10.
IR spectrum of 2 as a Nujol mull.

52
1540, and 1500 cm'1. The first Is most likely vasy(C02) for monodentate
acetate, the latter two for bridging acetate. Comparison with known
compounds with bridging acetate, such as Crg^CCHj^iHjOlg which has
VasyiCOj) at 1575 cm'1 94 and those with monodentate acetate, such as
Ru^CC^^tCO^tPPf^^ which has vasyico21 at 1613 dm'1,95 shows that a
band at this high frequency is characteristic of monodentate acetate.
Very sharp, intense bands are observed at 680 and 685 cm"1 corresponding
to S(C02). IT one of the acetates is monodentate this would allow
coordination of an additional acetonitrile as shown in Figure 2-11. It
is possible that the fifth acetonitrile is axially coordinated; however
this site in Mo carboxylate dimers is only weakly coordinating. Even a
strong Lewis base such as pyridine only weakly binds to this position in
Mo2(02CCF3)4,9® which is a stronger Lewis acid than Mo2(02CCH3)4. A
weak, but distinct, band at 405 cm'1 may correspond to the Mo-Mo
stretch. This would be IR allowed in 2 since no centrosymmetric isomers
are possible as can be seen in Figure 2-11. A band is observed at 720
cm'1 corresponding to an acetate or acetonitrile vibration as in X.
The remaining bands correspond to the counterion and support its
formulation as 3F30H'. A strong band is seen at 1060 cm'1 with weak,
but distinct, bands at 950, 765, 520, 378, and 360 cm'1. Vibrational
absorptions for BF4' are at 1070 (v3, vasy (BF)), 777 (vj, vs(BF)), 533
(v4, 6asy(FBF)}, and 360 cm'1 (v2, SasyCFSF))These same bands for
B(0H)4' are at 945, 754, 533, and 379 cm'1.98 All of these modes are
Raman allowed, but only \>3 and v4 are IR allowed in these tetrahedral
complexes. The bands observed in Z at 1060 and 520 cm'1 correspond to
these two IR allowed vibrations. The band at 950 cm'1 may be V3 for 3-0.
The bands at 378 and 360 cm"1 may correspond to vj for 8-0 and B-F

CH.
2 +
CH.
2 +
0'
0
0 >
Mo
/NCCH3
0
/
C~CK
CH3CN'
Mo
CH3CN
CH3CN CH3CN
0'
ch3cn
0
Mol
,NCCH.
CH3CN
ch3cn
,Mo
0
-NCCH:
C H 3 <
3 ^
0
Figure 2-11. Proposed structures for 2. Isomer on left has Cj symmetry, on right Cs

54
bonds, respectively. In 8F30H“, a complex with C3v symmetry, all
vibrations are IR allowed so these would be observed. Finally, two
strong bands assigned to v{0H) are seen at 3600 and 3530 cm-1. Thus,
the IR spectrum of 2 supports the formulation of the counterion as
BF30H- presumably resulting from an impurity in the [(Et20)]HBF^ used.
Support for this counterion formulation is also obtained by anion
exchange. Complex 2 can be dissolved in an acetonitrile solution of
excess (rr-Bu^NBF^ or (n_-Bu)^PFg and addition of toluene leads to
precipitation of primarily the BF4" or PF6" salt. This process can be
repeated to effect complete exchange.
The NMR spectrum of 2 resembles that of 1 with signals observed
at 3.0 and 2.1 ppm in CD3CN. Thus, NMR does not distinguish between
different types of acetonitrile coordination.
Oue to the more difficult synthetic procedure for 2 compared to X,
as well as more uncertainty as to the exact structure of 2, reactivity
studies were not performed.
Interestingly, a complex analogous to 2 can be obtained using
CF3SO3H. After recrystallization of X, the filtrate is often magenta
rather than purple. Addition of a small amount of toluene and allowing
the solution to sit overnight leads to formation of a. crystalline
magenta precipitate, (X). The amount of 2 varies greatly from one
preparation of X to the next. It is not clear as to the procedure for
selectively preparing one or the other, although use of freshly
distilled CF3S03H leads to better yields of X over 3. A formula that
can be proposed for X is [Mo2(02CCH4)2(CH3CN)4X](CF3S03)2 where X=CH3CN
or H20. The oxidation state of Mo in X is 2+. The elemental analysis
of X favors X=H20. This is also supported by the fact that X is more

MICRONS
2.5 JO 40 50 60
100
Figure 2-12. IR spectrum of 3 as a Nujol mull.
_9Q
if. IS ?0
25 JO 4Q 50

56
likely to be obtained with less pure, presumably water contaiminated
CF3SO3H. However, the IR spectrum of 3, shown in Figure 2-12 (Nujol
mull), has no band corresponding to v(0H). A shoulder on the Nujol band
at 3250 cm'1 might be from this vibration. The bands assignable to
v(CN) at 2310, 2285, and 2255 cm'1 are virtually identical in frequency
and intensity pattern to those observed for £. Furthermore, the bands
assignable to the C02 vibrations are similar for Z and 3. A weak band
is seen at 1640 with stronger bands at 1530 and 1508 cm'1. The first
can be assigned to vaSy{C02) for monodentate acetate, the latter two to
bridging acetate. Well resolved bands at 680 and 690 cm'1 correspond to
5(C02). Strong, well resolved bands corresponding to all the vibrations
of non-coordinated CF3SO3" are observed at 1280, 1230, 1150, 1030, 755,
635, 575, and 515 cm'1. The assignment of these bands has been
discussed previously and are the same as those found in 1. Without a
structure determination by single crystal x-ray diffraction, the
differences between complexes 1, Z, and 3 cannot be definitively
determined. Assuming that Z and 3 contain monodentate and 1 bidentate
acetate, it is remarkable that these two types of carboxylate
coordination lead to such different colors. The exact orientation of
the monodentate acetate might give some clue to this. It is clear that
different anions do not lead to different properties.
In addition to the M02ÍO2CR)4 system, the Mo2(S2CR)4 system was
investigated. The facile synthesis of Mo2(S2CCH3)4 has been reported."
Unfortunately, it shows no reaction with two to four equivalents of
CF3SO3H in acetonitrile. Overnight stirring of Mo2(S2CCH2)4 in neat
CF3SO3H leads to recovery of the starting material along with a small
amount of decomposition products. The CH3CS2' species binds very

57
strongly to Mo and is not readily protonated. M02{SgCR)4 complexes
could be used in calorimetric studies of Lewis base binding for
comparison with RC02" complexes. Mo2{02CCH3)4 is soluble in THF and a
complex such as Mo2(S2CCH2CH2CH3)4 might be soluble in more poorly
coordinating solvents suitable for use in calorimetric work.
Conclusion
The addition of stoichiometric amounts of strong, non-complexing
acids to metal-metal bonded carboxylate dimers leads to protonation of
the bridging carboxylate and generation in solution of M2(02CR)22+
species. Spectroscopic evidence confirms that the metal-metal bond
remains intact and that two carboxylates are retained. The choice of
solvent is crucial since It must stabilize the resulting coordinatively
unsaturated cationic complex, but withstand the strong acid.
Acetonitrile fits these requirements and several acetonitrile
coordinated complexes of the molybdenum dimer are reported here and
elsewhere.61 With rhodium it was not possible to isolate such a complex
as was previously found by workers using aqueous solvents.22*62 Using
strong donors such as pyridine as described here, and related ligands as
reported elsewhere,53*64 it is possible to isolate a cationic rhodium
carboxylate dimer. However, these ligands may not be sufficiently
labile for subsequent reactivity studies on the rhodium system. It may
be that even acetonitrile coordinates too strongly to the Mo dimer,
since the complex reported here does not show reactivity towards
oxidative addition in contrast to various organometallic metal-metal
bonded complexes. Another interesting possibility is that only
organometallic dimers, containing relatively electron donating ligands

58
and with metals In a low oxidation state, can undergo these reactions
which resemble those found in organic chemistry. The metal carboxylate
dimer with acetonitrile coordination differs from organometallic
complexes and undergoes reactions such as Lewis base coordination and
ligand substitution resembling those found in classical coordination
chemistry. Nevertheless, the photochemical and photophysical properties
of the complexes described here may be of interest. Analogous systems
studied by Gray and co-workers such as Mo24+(aq)59, the metal-metal
bonded diphosphite bridged Pt(II)/(III) dimers72 and the non-metal-metal
bonded isonitrile bridged Rh(I) dimers^® have shown interesting
photochemical behavior. Furthermore, the ligand substitution reactions
of the metal-metal bonded complexes described here which contain
accessible equatorial sites could be investigated in a quantitative
manner as was previously done for systems containing only axial
coordination sites.
Experimental Section
Operations were carried out under nitrogen using Schlenk techniques
or an inert atmosphere box except as otherwise noted. Solvents were
distilled before use. Trifluoromethanesulfonic acid was distilled under
reduced pressure. Tetrafluoroboric acid diethyletherate (Pfaltz and
Bauer) was used without further purification. Rhodium acetate was
synthesized from RhC 13{H2O)3 by literature methods.^7
Tetrakis(n-butyrato)dirhodium(II)
R^«2(O2CCH3)4 (0.5 g, 1.1 mmol) was refluxed for 6 h in n-butyric
acid (14 mL) and jv-butyric anhydride (1 mL). The solution was
concentrated to 3 mL and cooled at -20 C overnight. The resulting crude

59
Rh2(but)4 was recry stall ized from hot toluene, washed with cold hexane
and dried over P205 overnight to yield 0.5 g (0.9 mmol, 80%). Anal.
Caled, for Rh2C16H2808: C, 34.68; H, 5.09. Found: C, 34.74; H, 4.99.
Rh?(but)?‘^'l~ Solution
Rh2(but)4 (0.328 g, 0.59 mmol) was dissolved in CH3CN (5.00 mL) to
give a purple solution. To this was added CF3SO3H (0.21 mL, 2.37 mmol)
leading to an Immediate slight color change towards dark red. Similar
solutions using CD3CN were used for the NMR work.
Sulfide Complex
Elemental sulfur (0.0236 g, 0.74 nmol) was suspended in THF (1
mL). To this Super-Hydride (LiBH(CH2CH3)3, 1.5 mL, 1 M_in THF, Aldrich)
was added dropwise. Gas evolution was vigorous and a pale yellow
solution resulted. This solution was added to the above Rh2(but)22+
solution (2 mL, 0.092 in rhodium dimer). A black precipitate formed
immediately. Filtration, washing with THF and drying under vacuum at
100 C afforded 0.8 g of a black, completely insoluble solid. Anal.
Caled, for Rh2(02CCH2CH2CH3)2S: C, 23.32; H, 3.43; S, 7.78; C:H,
6.80. Found: C, 24.39; H, 3.70; S, 12.53; C:H, 6.81. The high sulfur
analysis results from SH units and bridging polysulfide. The selenium
compound was prepared in the same manner and gave an even less
satisfactory elemental analysis.
Pyridine Complex
To the above Rh2(but)22+ solution (3 mL, 0.03 M in rhodium dimer)
was added pyridine (0.16 mL, 2.0 mmol). Ari orange color immediately
resulted. Attempts to obtain a solid by cooling and evaporation yielded
only an oil. Addition of NH4PF6 (0.16 g. 1.0 mmol) dissolved in water

60
(1 mL) and subsequent evaporation and cooling led to formation of an
orange-red precipitate. This procedure was not always repeatable; oils
often resulted. Furthermore, IR indicated the presence of CF3S03" as
well as PF6“. Anal. Caled, for [Rh2(02CCH2CH2CH3)2(C5H5N)4](PFg)2: C,
34.09; H, 3.47; N, 5.68. Found; C, 33.99; H, 3.87; N, 6.18. The above
procedure using Rh2(02CCH3)4 allowed Isolation of an orange solid
without addition of PFg". Anal. Caled, for [Rh2(02CCH3)2(CsH5N)4]
(CF3S03)2: C, 33.27; H, 2.79; N, 5.97. Found: C, 32.73; H, 2.98; N,
6.03.
Tetrakis(acetato)dimolybdenum(II)
This complex was synthesized following the procedure of Martin and
co-workers^ which gives much higher yields than the original
method.Mo(C0)g {1 g, 3.8 mmol) was added to _o_-dichlorobenzene (30
ml). Acetic acid (8 mL) and acetic anhydride (1 mL) were added and the
solution refluxed overnight during which time the solution turned almost
black. The heating was stopped and the solution allowed to cool without
removal of the heating mantle for 8 h. Filtration and washing with
ethanol followed by diethylether led to isolation of beautiful yellow
needle crystals of Mo2(02CCH3)4 (0.65 g, 1.5 mmol, 80%). Anal. Caled,
for Mo2C8H1208: C, 22.45; H, 2.83. Found; C, 22.45; H. 2.90.
Molybdenum acetate should be used as soon as possible since it
decomposes even under inert atmosphere or vacuum over a period of days
to green and eventually black products.
Tetrakis(acetonitrile)bis(acetato)dimo1ybdenum(II)
Bis(trifluoromethylsulfonate), (XT'
Mo2(02CCH3)4 (0.40 g, 0.93 ranol) was suspended in acetonitrile (4
mL). It is important that the acetonitrile be degassed using freeze-

61
pump-thaw cycles with the final vacuum broken by nitrogen, otherwise
decomposition of molybdenum acetate often occurs giving a brown
solution. To this was added CF3SO3H (0.17 mL, 1.92 mmol). An intensely
colored purple solution formed immediately and was stirred for 10 min.
Removal of solvent by pumping left a dark purple solid which was
dissolved in a minimum amount of acetonitrile (~2 mL) and filtered.
Addition of toluene (~3 mL) led to formation of a purple precipitate
after 1 h. The solid was recrystallized from 1:1 acetonitrile/toluene
and washed with toluene followed by hexane to yield 0.5 g. Anal. Caled,
for [Mo2(02CCH3)2(CH3CM)4J(CF3SO3)2: C, 21.77; H, 2.35; N, 7.25; S,
8.30; F, 14.76; Mo, 24.84; 0, 20.72. Found: C, 21.83; H, 2.38; N,
7.56; S, 8.28; F, 15.10; Mo, 24.00; 0 (by diff.), 20.85. From the
filtrate obtained in the above recrystallization a magenta, rather than
a purple, solution 1s often obtained. Addition of toluene (~1 mL) to
this leads to formation of a magenta precipitate, 3. Anal. Caled, for
[Mo2(02CCH3)2(CH3CN)4(H20)](CF3S03)2: C, 21.27; H, 2.55; N, 7.09; S,
8.11; F, 14.42; Mo, 24.48; 0, 22.27. Found: C, 22.00; H, 2.65; N,
7.06; S, 8.08; F, 12.7; Mo, 22.59; 0 (by diff.), 24.92.
Pentakis(acetonitri1e)bis(acetato)dimolybdenum(II)
Bisttrifluorohydroxyborate), (2)
Mo2(02CCH3)4 (0.71 g, 1.66 mmol) was suspended in acetonitrile as
above. To this was added (Et20).HBF4 (0.8 mL, approx. 6 mmol). An
intensely colored magenta solution immediately resulted. Removal of
solvent by pumping left a magenta solid which was dissolved in
acetonitrile (~4 mL) and filtered. A small amount of yellow needle
crystals of unreacted Mo2(02CCÜ3)4 remained. When less acid is used,
more unreacted molybdenum acetate is recovered. To the filtrate was

62
added diethylether (5 mL) which caused rapid formation of a magenta
precipitate. The compound was recrystallized from 1:1
acetonitrile/toluene and washed with toluene followed by hexane to yield
0.9 g. Anal. Caled, for [Mo2(02CCH3)2(CH2CN)53(BF30H)2: C, 24.55; H,
3.38; N, 10.23; F, 16.65; Mo. 28.02. Found: C, 23.79; H, 3.32; N,
10.02; F. 17.03; Mo, 26.36.
Anion Exchange
Complex 2 (0.3 g, 0.44 mmol) and (jv-Bu)4NBF4 (1 g, 3.0 mmol) were
dissolved in acetonitrile (5 mL). To this was added toluene (5 mL)
leading to formation of a magenta precipitate. After two cycles of this
procedure, IR of the magenta precipitate showed a greatly diminished
v(0H) band and the other bands unchanged. Anal. Caled, for
[Mo2(02CCH3)2(CH2CN)5](BF4)2: C, 24.41; H, 3.07; N, 10.17; F, 22.06;
Mo, 27.86. Found: C, 24.49; H, 3.29; N, 11.77; F, 19.16; Mo, 38.13.
Molybdenum Trifluoromethylsulfate Complex
To Mo2(02CCH3)4 (0.2 g, 0.47 mmol) was added to CF3SO3H (10 mL).
The suspension was heated at 100 C with stirring for 1 h, by which time
all the solid dissolved. The acid was removed by pumping leaving a red
solid which presumably corresponds to the Mo2(03SCF3)4(CF3S03H) complex
described by Abbott and co-workers.60 Further pumping with heating at
160 C led to formation of a tan solid which is presumably the
Mo2(03SCF3)4 complex.60 These intermediates were not isolated or
characterized. Addition of acetonitrile (10 mL) to the tan solid led to
formation of a bright blue solution. Addition of toluene (~7 mL) caused
formation of a blue precipitate. Elemental analysis of this compound
was not satisfactory, although it appeared to be an acetonitrile

63
coordinated Mo(II) dimer. IR spectroscopy indicated strong v(CN) and
v(0H) bands as well as bands corresponding to non-coordinated CF3SO3-.
Bands corresponding to residual acetate were observed at 1615 cm-*
{vgsylCOg)) and 675 cm-* (5{COg))- A band at 415 cm-* may be v(Mo2).
Slow evaporation of the filtrate obtained above resulted in formation of
purple cyrstals of what is most likely Complex 1. The IR
spectrumcorresponded to X as did the elemental analysis although the
precipitate may have been contaminated with species such as
[Mo2(02CCH3)(CH3CN)x](CF3S03)3 giving higher ZS, ZF, and ZO. Anal.
Caled, for [MogtOgCCHgJ^CHgCNj^iCFgSOgJg: See above. Found: C,
21.33; H, 2.10; N, 6.23; S, 9.48; F, 15.48; Mo, 21.47; 0 (by diff.),
23.91.
Tetrakis(dithioacetato)dimolybdenum(II)
This complex was synthesized following the procedure of Cotton and
co-workers.®® CS2 (0.77 mL, 0.013 mol) was added to CHgMgBr (5.63 mmol,
as THF solution, Aldrich) in THF (10 mL). A pale yellow solution
resulted which was stirred for 45 min. To this was added Mo2(02CCH3)4
(0.60 g, 1.4 mmol). A dark red-brown solution formed immediately.
After stirring 15 min, methanol (20 mL, N2 purged) was added leading to
formation of an orange-red precipitate. Filtration and washing with
methanol afforded 0.44 g (56Z). This complex, In contrast to
Mo2(02CCH3)4, is indefinitely stable and can be recrystallized in air
from THF. Anal. Caled, for Mo2CgH12Sg: C, 17.26, H, 2.17; S, 46.09;
Mo, 34.48. Found: C, 17.46; H, 2.43; S, 45.93; Mo (by diff.), 34.18.

64
Experimental Methods
Elemental analyses were performed by the Microanalytical Laboratory
of the University of Illinois, Urbana, IL, or by Galbraith Laboratories,
Knoxville, TN. Ultraviolet-visible spectra were recorded on a Cary 14
spectrometer using matched quartz 1.0 cm cells. Infrared spectra were
recorded on a Perkin-Elmer 599B instrument using KBr cells. Fourier
transform 13C{*H} NMR spectra were recorded on a Varían Associates XL-
100 FT spectrometer operating at 25.2 MHz. The 13C chemical shifts were
measured with respect to the nitrile carbon of CO3CN (118.2 ppm relative
to TMS). Proton NMR spectra were recorded using a Varían HR-220 NMR
spectrometer equipped with a Nlcolet Technology Corp. TT-220 Fourier
transform accessory. Precision-grade tubes were used for the 220 MHz
spectra so as to reduce spinning sidebands. The 3H chemical shifts were
measured with respect to internal TMS.

CHAPTER III
THE REACTIONS OF RHODIUM TRIFLUOROACETATE WITH VARIOUS LEWIS BASES
Introduction
As discussed in the previous chapter, it is possible to effect
removal of the removal of the bridging carboxylate ligands in metal
carboxyl ate dimers by reaction with stoichiometric amounts of strong
non-complexing acids. This reaction allows Lewis bases and potentially,
substrates for catalytic processes, to coordinate to equatorial as well
as axial sites on the metal carboxylate dimer. An alternative approach
to achieving this type of coordination is to use a carboxylate ligand
with an electron-withdrawing group. This type of carboxylate would
donate less electron density to the metal dimer subunit rendering the
carboxylates more prone to displacement and the metals more susceptible
to attack by Lewis bases. The effect of an electron-withdrawing
carboxylate ligand, CF^CF^CF^Cru" (hfb), has been quantitatively shown
in earlier studies by Drago and co-workers.2® The enthalpies of axial
Lewis base adduct formation by Rl^thfbJa versus Rhjtbut)^ were
examined. The hfb ligand greatly enhanced the Lewis acidity of the
rhodium system towards electrostatic interactions and increased the
acidity towards covalent interactions by almost as much. In addition to
this greater reactivity towards Lewis bases, the metal fluorocarboxylate
dimers have much greater solubility in non-coordinating organic solvents
than do the corresponding alkylcarboxylate systems. This facilitates
study of their solution chemistry. For example, since Mo2(02CCH3)d is

66
completely insoluble in organic solvents and Rh¿(O2CCH3only sparingly
so, a direct compari.'-on of their solution properties is impossible. Use
of the trifluoroacetate ligand makes such a study possible. The
interest in a comparison of the solution chemistry of the rhodium and
molybdenum carboxylate dimers stems from the large difference in their
metal-metal interactions. As discussed earlier, the d8 Mo system has a
strong, short, relatively unpolarizable quadruple bond. The d14 Rh
system has a longer, weaker, more polarizable single bond. Furthermore,
since rhodium is more electronegative than molybdenum, the Rh-Rh
molecular orbitals are overall lower in energy than the Mo-Mo bond
orbitals. The result of all this is that in the rhodium dimer, the
frontier MO's are the r* HOMO and the a* LUMO while for molybdenum those
metal-metal orbitals are vacant and high in energy while the <$ HOMO and
the 6* LUMO are of main importance. This implies that the covalent
interaction with axial bases should be strong for the rhodium
carboxylate dimer and much less for molybdenum. This has been
quantitatively confirmed by Drago and co-workers25 in a comparison of
the enthalpies of axial Lewis base adduct formation by Rh2(hfb)4 versus
Mo2(hfb)4. In addition, a r-backbonding interaction was observed
between the filled v* orbitals on the rhodium dimer and vacant r*
orbitals on bases such as pyridine and acetonitrile. This interaction
was not seen for the molybdenum dimer as expected from the MO scheme
described above.
Another implication of the MO scheme is that given the opportunity,
Lewis bases should coordinate more readily to equatorial than to axial
sites on molybdenum, while this would be less likely for rhodium. This
type of reactivity has indeed been found with Mo when the

67
trifluoroacetate dimer is used, since this ligand allows access to the
equatorial sites. Girolami and co-workers33»103 synthesized and
characterized a number of adducts of molybdenum trifluoroacetate with
phosphines and other Lewis bases. They found that MogiC^CCFj)^ not only
formed adducts in which there was coordination along the Mo-Mo axis, but
also some in which there was coordination in sites perpendicular to the
Mo-Mo axis. All of these complexes were of general formula
Mo2(02CCF3)4L2. Those with axial coordination were called Class I
adducts, those with equatorial coordination, Class II. Only Lewis bases
that are sterically small and good o-donors were reported to give
isolable equatorial adducts. Examples are trimethylphosphine (PMe3),
triethylphosphine (PEt3), and dimethylphenylphosphine (PMe2Ph).
Andersen estimated steric bulk by cone angle and a-donor strength by
v(C0) values as described by Tolman.10^ The assignment of complexes
into the two classes was made on the basis of and 31P NMR
spectroscopy which showed different signals resulting from phosphines in
different coordination sites. Infrared spectroscopy also showed
different C02 stretches for the two types of CF3C02~ ligands. However
some controversy exists over the assignment of IR and NMR peaks for
these complexes. Cotton and Lay103 also prepared phosphine complexes of
Mog(O2CCF3)4 and obtained spectra at variance with those of Girolami and
Andersen and co-workers.33»103 In addition, these two groups reported
different structures for the complex Mo2(02CCF3)4(PMePh2)2. Cotton and
Lay105 obtained a Class II (equatorial) adduct and Girolami and
Andersen103 a Class I (axial) adduct. Slight variations in synthetic
procedure led to this difference since PMePh2 is a phosphine inter¬
mediate on the size and donor strength scales.

68
Other solution studies106,107 have been performed on Mo2(02CCF3)4
as well as a number of crystallographic studies.96,103,104,Í08 jn
contrast, the analogous rhodium system has not been as extensively
investigated, particularly in solution.5,6 Crystal structures have been
determined for Rh2(02CCF3)4L2 where L=(CH3)2S02,109 (CD3)2S0,110
PPhs,111 P(OP h)3,111 CH3CH20H,112 H20113, 2,2,6,6-tetramethylpiper-
idinolyl-l-oxy113 and (CH3)2S0.114 In all these cases, as in those with
alkylcarboxylates, only Class I (axial) adducts were formed. However, a
systematic study of the Lewis base reactivitiy of Rh2(02CCF3)4 had not
been performed. For the reasons discussed above, that is ligand effects
and metal-metal bond effects, such a study was performed and is
described below. Furthermore, it was hoped that this study would shed
some light on the discrepancies in the interpretation of the
spectroscopy properties of the molybdenum systems described above.
Results and Discussion
The 19F NMR spectrum of Rh2(02CCF3)4 was obtained in both
nitromethane-jfj and toluene-jig. All of the 19F NMR data are summarized
in Table 3-1. A sharp singlet was found in both room and low
temperatures in both solvents which corresponds to the CF3 groups on the
four equivalent bridging trifluoroacetates. Nitromethane and toluene
are very weak bases and thus should coordinate weakly, if at all, to the
rhodium dimer. What is significant is that these signals occurred in
the -73 to -75 ppm range (relative to internal CFC13). The signals were
somewhat solvent and temperature dependent. Earlier workers33,106,107
have assigned peaks in the -72 to -74 ppm range to monodentate CF3C02"
and peaks at -70 ppm to bidentate CF3C02” in Mo2(02CCF3)4 complexes.

69
The IR spectrum of Rh2(02CCF3)4 shows a single vasy^co2^ band *n
solution and in the solid state. All the major IR data are summarized
in Table 3-II and the IR spectrum of Rh2(02CCF3)4 is shown in Figure 3-
1. However, this stretch occurs at a higher frequency (1650 to 1670
cm-1) than vaSy^C02> for bidentate CF3C02" in Mo2(02CCF3)4 complexes
(~1600 cm-*). Thus, there is no direct correspondence between the
location of the *®F NMR and IR signals for the rhodium and molybdenum
systems. Nevertheless, mono- and bidentate CF3C02" give significantly
different spectra in the rhodium complexes as will be shown below.
Oxygen Donors
Emerald green Rh2(O2CCF3)4 forms blue 2:1 complexes with oxygen
donor bases such as tetrahydrofuran (THF), dlmethylsulfoxide (DMSO),
N,N-dimethylformamide (DMF), and trimethylphosphine oxide (0PMe3). The
THF adduct is quite stable but heating at 100 C under vacuum effects
quantitative removal of THF to give base-free starting material.
The *®F NMR and IR spectra are characteristic of a Class I adduct. A
singlet is observed in the *®F NMR spectrum at -75 ppm and \>aSy(C02)
occurs at about 1660 cm-1 in both the solid adduct and in solution. The
IR spectrum of Rh2(02CCF3>4(THF)2 is shown in Figure 3-2. These results
are similar to those for the free Lewis acid, Rh2(02CCF3)4.
The crystal structure of Rh2(02CCF3)4(DMS0)2 showed a Class I
adduct, with 0-bonded DMSO.*®® There was nothing to indicate otherwise
in solution since a single peak was observed in the *®F NMR spectrum.
Both axial S-coordination and equatorial 0- or S-bonding would most
likely lead to additional signals. The equivalence of the solution and
solid state structures was confirmed by IR, which showed a single
vasy(C02) band at 1662 cm-1 (Nujol mull) and at 1655 cm-1 (CHC13

70
Table 3-1. 19F NMR Data for Rh2(02CCF2)4 Complexes3
Complex
Rh2(02CCF3)4
Rh2(02CCF3)4(THF)2
Rh2(02CCF3)4(Me2S0)2
Rh2(02CCF3)4(DMF)2
Rh2(02CCF3)4(Et3N)2
Rh2(02CCF3)4(py)4
Rh2(02CCF3)4(jt-BuNC)4
1 q . Area
iaF Chemical Shift0 Ratios Sol vent Temperature(°C)
-73.28
cd3no2
-35
-74.29
toluene-dg
-60
-75.04
toluene-dg
+27
-74.65
CDC13
-50
-75.19
CDC13
+27
-74.17
CDC13
-60
-76.41
CDC13
+27
-74.18
CDC13
-60
-74.86
cdci3
+27
-75.31
cdci3
-40
-75.92
cdci3
+27
-74.69, -75.44
1:1
cdci3
-60
-74.08, -74.87
1:1
toluene-dg
-60
-74.73, -75.34
1:1
toluene-dg
+27
-73.0, -73.2
2:1:1.5:
cdci3
-60
-73.4, -73.8
4:1.5:1
-74.2, -74.6
-73.98, -74.90
CDC13
-50
-75.23)c,-75.72
1:1:1.3
-74.41, -74.75
1:1:2.0
CDC13
+27
(-75.32)c,-75.88
Rh2(02CCF3)4(PPh3)3

71
Table 3-1. continued
Complex
19F Chemical Shift5
Area
Ratios
Solvent
Temperature(°C)
Rh2(02CCF3)4(P(c-Hx)3)2
-72,73, -74.51
-75.42, -75.92
1:1:2:1
CDC13
+27
Rh2(02CCF3)4(P(0Ph)3)2
-75.08
CDC13
+27
-74.68, -74.83
2.5:1
CDC13
-50
(-75.10, -75.45
-76.20)c
Rh2(02CCF3)2(P(0Me)3)3
-73.40, -73.88
3:2
CDC13
-50
-74.65, -75.25
3:2
CDC13
+27
a. Data are reported for those complexes that were obtainable as genuine adducts
and the P(0Me)3 complex. Solution studies were undertaken on other systems
and are described in the text.
b. All chemical shifts are with respect to internal CFC13-
c. These signals are of very low intensity and may indicate the beginning of
complex decomposition.

72
Table 3—II. Infrared Data
for Rh2(02CCF3)4 Complexes
Complex
vasy(c°2) (cm'1)3
CHC1^ Solution
Nujol mull
Rh2(02CCF3)4
1670
1650
Rh2(02CCF3)4
1658
1668
Rh2(02CCF3)4(Me2S0)2
1655
1662
Rh2(02CCF3)4(DMF)2
1662
1650 brb
Rh2(02CCF3)(Et3N)2
1670 s, 1660 s
1660 s, 1650 s
Rh2(02CCF3)4(py)4
1705 s, 1642 m
1705 s, 1655 s
Rh2(02CCF3)4(t-BuMC)4
1693 s br, 1658 s
1720 m br, 1660 m br
Rh2(02CCF3)4(PPh3)2
1715 w, 1654 m, 1652 m
1665
Rh2(02CCF3)4(P(c-Hx)3)2
1715 w, 1660 m
1663
Rh2(02CCF3)4(P(0Ph)3)2
1665
1670
Rh2(02CCH2CH2CH3)4(PPh3)2c
1587
Rh2(02CCF3)4(CH3CN)2
1658 m, 1648 w
1663 m, 1653 w
a. s = strong, m = medium,
w = weak, br = broad
b. includes amide v(CO), resolved in solution
c. included to contrast with Rh2(02CCF3)4(PPh3)2

Figure 3-1. IR spectrum of Rh2(02CCF3)4 as a Nujol mull. The bands labelled "N" correspond
to Nujol peaks.

2 5 50 40 50 MICRONS 60 8 0 90 iO 12 |4 16 18 20 25 30 35 40
Figure 3-2. IR spectrum of RhgCOgCCFg^CTHF^ as a Nujol mull.

75
solution) in agreement with the assignment as an axial adduct. The IR
spectrum of Rh2(02CCF3)4(DMS0)2 is shown in Figure 3-3. The DMSO bands
are also of interest. In the solid state, two doublets were observed at
1005 (s) and 995 cm-1 (s) and at 945 (s) and 937 cm'1 (s). In CHC13
solution these occurred at 1020 (m) and 1000 cm-1 (m) and at 948 (m) and
931 cm-1 (w). Free DMSO in CHCI3 solution has v(SO) at 1055 cm-1 and a
<5(CH3) band at 946 cm'1. Oxygen coordination lowers v(S0) and sulfur
coordination raises the frequency of this band. No bands were observed
for Rh2(02CCF3)^ in the 1050 to 1150 cm"1 region where S-coordinated
DMSO would obsorb. It should be noted that Rhg(O2CCH3binds DMSO via
the sulfur atom (vCSO) at ~1090 cm'1),52,115 further evidence of ligand
effects on Lewis acidity of the rhodium carboxylate dimer.115 Cotton
and Felthouse114 have reported bands for this complex at 943 and 939
cm-1 (Nujol mull) which they assigned to v(SO) of 0-coordinated DMSO,
while the higher frequency doublet was not mentioned. Their assignment
was based on earlier work by Cotton and co-workers,115 who proposed that
the band at ~950 cm'1 in DMSO complexes corresponds to v(S0) while that
at -1000 cm'1 to 6(CH3). However, Drago and Meek11^ reversed this
assignment since the band at -1000 cm'1 is more sensitive to the type of
metal coordinated. The IR spectrum of Rh2(02CCF3)4(DMS0-d£)2 was
obtained here in the hope of clarifying the assignment of these two
bands. The IR spectrum of this deuterated complex was identical to the
original complex with respect to the bands related to CF3CO2".
Unfortunately, in the area of interest, there was also little change.
Fairly strong, broad bands were seen at 1020 and 950 cm'1, with the
latter more intense. A new band occurred at 825 cm'1 which may

Figure 3-3. IR spectrum of Rh^OgCCF^ÍDMSO^ as a Nujol mull.

77
correspond to a S(CD3) band at 811 cm'1 in free DMS0-d¿. Thus, a
definitive assignment of these two bands cannot be made.
When DMF was added to Rh2(02CCF3)4, a purple color initially
appeared, but the solution then rapidly turned blue. The 19F NMR
spectrum of this complex showed a single peak at -74 ppm at room and low
temperature. The IR spectrum was also characteristic of a Class I
adduct (vaSy(C02) at 1662 cm'1 in CHC13 solution). In solution the
amide v(C0) could be resolved from the vaSy(C02) band (this was not
possible in the solid) and was shifted from 1685 cm'1 in free DMF (CC14
solution) to 1643 cm'1, indicative of O-coordination.118 The IR
spectrum of Rh2(02CCF3)2{DMF)2 is shown in Figure 3-4. Addition of
excess DMF did not change the 19F NMR spectrum. Rh2(02CCF3)4 was
indefinitely stable in excess DMF. This is in contrast to DMSO.
Kitchens and Bear119 reported that addition of excess DMSO to
Rh2(02CCF3)4 led to formation of a yellow decomposition product, which
was also observed here. This is probably due to eventual sulfur
coordination.
The reaction of Rh2(02CCF3)4 with 10 equivalents of 0PMe3 in 1:1
toluene/dichloromethane afforded a blue solid contaminated with
crystalline, white, unreacted 0PMe3. The IR spectrum of this blue solid
(Nujol mull) showed a strong, broad vaSy(C02) band at 1650 cm'1 and a
band assignable to 6(C02) at 725 cm'1. A very strong, broad band at
-1200 cm'1 included vaSy(CF3) and v{P0). Thus, a Class I adduct is most
likely formed as with the above oxygen donors. This is to be expected
since using the E and C parameters,27"29 0PMe3 is a Lewis base roughly
comparable to DMSO. Due to limited availability of 0PMe3, further
studies were not performed.

Figure 3-4. IR spectrum of Rh2(02CCF3)4(DMF)2 as a Nujol mull. Inset shows the o (CO,,)
region of a chloroform solution.

79
Nitrogen Donors
A variety of nitrogen donor bases were reacted with Rh2(O2CCF3)4
with varying results. Isolable analytically pure complexes could not be
obtained with piperidine and N-methylimidazole (N-Melm). When these
bases were added to toluene solutions of Rh2(02CCF3)4» a red color
immediately resulted indicative of nitrogen base coordination. However,
after several hours the solutions turned yellow and evaporation gave an
intractable yellow tar in both cases. This indicates dimer
decomposition forming Rh(I) and/or Rh(III) as was described with DMSO.
Some ^F NMR studies were performed on solutions of Rh2(02CCF3)4 with
these bases. A freshly prepared solution containing 10:1 N-
MeIm/Rh2(02CCF3)4 showed single peaks at -74.6 ppm at 27 C and at -74.1
ppm at -61 C in CDC13. Thus, a 2:1 Class 1 adduct was initially present
and remained for a few hours. The spectrum became complex as the yellow
color appeared. A freshly prepared solution of 10:1
piper1dine/Rh2(02CCF3)4 showed a major signal at -74.2 ppm and smaller
peaks at -68.4 and -80.3 ppm indicating that rapid decomposition
occurred. The major peak is presumably from axially coordinated dimer,
the other two from decomposition products. It might be possible to
prepare adducts with these two bases if only stoichiometric amounts were
used. By contrast, use of excess triethylamine led to facile isolation
of Rh2(02CCF3)^(Et3N)2. This complex had a singlet in the 19F NMR
spectrum, even with excess base, at -75 ppm at both room and low
temperatures. This complex had an IR spectrum characteristic of
bidentate CF3C02“ in solution and in the solid state. The latter is
shown in Figure 3-5.

Figure 3-5. IR spectrum of RhgíO^CCFj^CEtgN^ as a Nujol mull.

81
With pyridine an interesting product was formed that is
intermediate between the Class I adduct formed with EtjN and the
decomposition products formed with piperidine and N-Melm. This complex
is a stable red 4:1 adduct containing both axially (Class I) and
equatori ally (Class II) coordinated Lewis base and thus may be
considered a new type of complex which will be called Class III. These
three structures are shown in Figure 3-6. Only one of six isomers of
Class II and III adducts are depicted. This behavior can be contrasted
with the reaction of pyridine with Mog^CCFj^96 and Rh2(O2CCH3)4120 in
which Class I adducts form. A precedent for this Class III compound
exists. Webb and Dong106 have performed solution studies on
Mo2(02CCF3)4 with varying amounts of pyridine and found 19F NMR signals
in the places predicted33 for mono- and bidentate CF3C02- (-70.5, -75.3
ppm, respectively) and IR adsorption bands at 1713, 1617, and 1611 cm-1
corresponding to vaSy(C02) of mono- and bidentate CF3C02~. Only one Mo-
Mo stretch was observed in the Raman spectrum (343 cm-1) indicating the
presence of only one centrosymmetric isomer. The 19F NMR spectrum of
Rh2(02CCF3¡4(pyr)4 prepared here showed signals at -74.1 and -74.9 ppm
in toluene-_dg and at -74.7 and -75.4 ppm in CDC13, both at -60 C. In
both solvents the peak ratio was 1:1. Here mono- and bidentate CF3C02~
are separated by less than 1 ppm, whereas in the molybdenum work they
were separated by about 3 ppm. However, there are examples of mono- and
bidentate CF3C02~ with all resonances in the -74 to -76 ppm range. King
and Kapoor133 have synthesized a large number of complexes such as
(Cc;H5)Fe(C0)2(CF3C02) which has monodentate CF3C02- and gives a 19F NMR
signal at -74.2 ppm in CDC13. Creswell and co-workers122 have prepared
compounds such as 0s(C0)(PPh3)2(CF3C02)2 which has two 19F NMR signals

Figure 3-6. Possible structures for Lewis base adducts of
Rh2(02CCF3)^. Only one of the six isomers of
both Class II and Class III adducts are shown.

83
CFS
I 3
C
;Rh-
VCF=
No
0
\
/C '
cF,o ,
I
CF,
Rh'
n
CF,
//
cv
CF3
I 3
c
"o %
Rh:
C-CF,
/ 3
: Rh
°\ /°
c
CF,
m
CF,
CF, 0
0 \
C-CF,
/ 3
•Rh
°\ /°
XC^
CF,

84
at -75.44 and -IS.22 ppm in CDClj assigned to mono- and bidentate
CF3CO2-. Thus, not only do the locations of resonances in the rhodium
dimer differ from molybdenum, but the chemical shift differences between
CF3CC>2-,s in different environments do not correspond. The IR data for
the pyridine complex are also in agreement with the Class III
formulation. Absorption bands for vaSy(CC>2) were observed at 1705 and
1642 cm-1 (CHC13 solution) and at 1705 and 1655 cm-1 (Nujol mull)
corresponding to mono- and bidentate CF3C02~. Another characterise IR
band is 6(C02) which occurs at 740 cm-1 in Rh2(O2CCF3)4. Free pyridine
has bands at 740 and 693 cm-1. In the pyridine complex bands were
observed at 760, 750, 738, 725, and 690 cm-1. It is likely that at
least two of the first three bands correspond to 6(CO2) for mono- and
bidentate CFjCC^"- The other absorption bands could be assigned to
either pyridine or Rh2(O2CCF3)4 and the latter showed little change from
the base-free rhodium dimer. The IR spectrum of Rh2(02CCF3)^(pyr)4 is
shown in Figure 3-7. Addition of excess pyridine, up to 20 equivalents,
caused no change in the *®F NMR spectrum. Two sharp signals of equal
intensity were still observed at -74.7 and -75.3 ppm in the toluene-jdg
at 27 C. By contrast, in the molybdenum case106 the two peaks coalecse
at 30 C, indicating fast exchange. However, the slower exchange
observed here is not unusual since in the H(C0)(PPh3)2(CF3C02)2
complexes studied by Creswell and co-workers,^2 separate resonances
corresponding to mono- and bidentate CF3CO2- were observed at room
temperature. As a final note, it should be mentioned that the synthesis
of "Rh2(02CCF3)4(pyr)2" was reported123 a number of years ago, but the
complex characterized only by C and H analysis. This procedure was
repeated here and a compound was isolated that was most likely a mixture

Figure 3-7. IR spectrum of Rh2(02CCF3)4(pyr)4 as a Nujol mull.

86
of pyridine adducts. This was the result of using ethanol as solvent
rather than toluene, used here to obtain the pure 4:1 adduct. (See
Experimental Section.)
It is difficult to draw general conclusions from the above results
based on criteria such as steric size, c-donor, and u-acceptor abilities
of the bases. Triethylamine was the strongest a-donor used; it is bulky
and has no u-acceptor ability. It formed axial adducts. Similarly,
quinuclidine (a Lewis base very comparable to Et-jN) formed a Class I
(axial) adduct with Mo2(02CCF3)4 although its size and o-basicity would
favor Class II. Pyridine, a base with less a-donor ability than Et3N,
has n-acceptor ability and formed a stable Class III (axial and
equatorial) adduct. N-methylimidazole, a stronger a-donor but a poorer
n-acceptor than pyridine caused dimer cleavage although via a Class I
adduct. Piperidine is a strong a-donor, but reactivity is most likely
due to the protonic nature of the base.
A final nitrogen donor base, acetonitrile, was used. It is a weak
a-donor, but a n-acceptor. Bear and co-workers40 were unable to isolate
a stable acetonitrile adduct of Rh2(02CCH3)4. These workers claimed
that evaporation of a CH3CN solution of rhodium acetate gave only
starting material.40 It was found here, by contrast, that stable purple
Rh2(02CCH3)4(CH3CN)2 was formed upon evaporation of an acetonitrile
solution of the rhodium dimer. (See Experimental Section.) However,
although Rh2(02CCF3)4(CH3CN)2 can be similarly prepared, it readily
loses acetonitrile and is hydrated to a blue-green material upon
standing in air. The freshly prepared complex ^9F NMR showed a singlet
at -74.1 ppm and a doublet at -74.5 ppm in CDC13 at -60 C. The area
ratios were 2:1:1. Addition of excess CH3CN (~10 equivalents) led to

87
signals at -74.7 and -75.4 ppm in equal area ratios. IR data showed
Class I bridging CF3CO2- bands. The solution structure of Rh2{O2CCF3)^
in the presence of acetonitrile is thus uncertain. However, the weaker
coordination of CH3CN to the fluorocarboxylate as opposed to the
alkylcarboxylate rhodium dimer is to be expected. This is due to ir-
backbonding Interactions as discussed earlier and shown by Drago and co¬
workers.22-26
Carbon Donors
Reactions with the isoelectronic carbon donors _t-butylisonitrile
and carbon monoxide were investigated. The reaction of t-BuNC with a
variety of metal carboxyl ate dimers was studied by Giro!ami and
Andersen.?6 They found that only monomeric complexes were obtained with
Mo2(02CCH3)4, Mo2(02CCF4)4, Re2(02CCH3)4Cl2, and Ru2(02CCH3)4Cl.
However, with Rh2(02CCH2)4 only the Class I adduct Rh2{02CCH3)4(t_-BuNC)2
was produced. It was of interest to determine what effect replacement
of CH3CO21- by CF3C02- would have in the dirhodium system. It was found
here that reaction of Rh2(03CCF3)4 with _t-BuNC (~10 equivalents) led to
isolation of an air stable orange-brown complex best formulated as
Rh2(02CCF3)4(_t-BuNC)4. Unfortunately, in contrast to the pyridine
complex which had the same stoichiometry and easily interpretable NMR
and IR spectra, _t-BuNC gave complicated results, as will be discussed
below. This Is most likely due to the presence in solution of a variety
of species including more than one isomer of a Class III adduct and
possibly monomeric species. Although t_-BuNC and pyridine have similar
c-donor properties, the isonitrile is a better ir-acceptor and somehow
this may lead to a variety of isomers of comparable stability. The 19F
NMR spectrum of this compound showed six peaks occurring between -73.0

88
and -74.6 ppm in CDCI3 at -60 C. The *H NMR spectrum showed signals at
1.61 and 1.43 ppm in CDC13 at -50 C. All NMR data for nuclei other
than are summarized in Table 3—III. At room temperature the peaks
occurred at 1.60 and 1.40 ppm, but instead of a 3:2 area ratio the ratio
was 2:1. Thus, at different temperatures different isomers
predominated, but specific assignment of the signals was not possible.
The IR spectrum of this complex showed bands assignable to vaSy(C02) at
1693 and 1658 cm-* in CHCI3 solution and at 1720 and 1660 cm'1 in the
solid state. A single strong S(C02) band was observed at 725-730 cm-1
(Nujol mull). There may have been more than one 6(C02) band, but
resolution was not possible. Very strong absorption bands corresponding
to v(NC) occurred at 2234 and 2167 cm-1 (CHC13 solution) and at 2212 and
2132 cm-1 (Nujol mull) as opposed to 2127 cm-* for free _t-BuNC. This
shift to higher frequency is expected for end-on isonitrile
coordination. The other absorption bands were assignable to either _t-
BuNC or Rh2(O2CCF3)4. The IR spectrum of Rh2(02CCF3)4(^-BuNC)4 is shown
in Figure 3-8. Although the solution and solid state IR spectra were
qualitatively the same, the fairly large difference for a given band
such as vasy(C02) or v(NC) may indicate a different structure in
solution. Further studies with this complex would be needed to
unequivocally determine its structure. However, it seems clear that a
Class I adduct is not formed in contrast to Rh2(02CCH3)4.76 It is not
surprising that a 4:1 complex is formed since _t-BuNC is a good o-donor
and an excellent n-acceptor. As found with pyridine, the CF3C02” ligand
was needed to allow coordination to the equatorial sites.
The complex Rh2(02CCH3)4(C0)2 has been isolated and structurally
characterized by x-ray crystallography.124 The v(C0) band occurs at

Figure 3-8. IR spectrum of Rh^O^CCF^Ct-BuNC)^ as a Nujol mull.

90
Table 3-III. *H and 31P{1H} NMR Data for Rh2(02CR)4 Complexes
Complex3
Nucleus
Chemical Shift (ppm)'3
Coupling
Constant
Rh2(02CCF3)4(t-BuNC)4
JH
1.61 s, 1.43 s (3:2)
1.60 s, 1.40 s (2:1)
(Hz)
Rh2(02CCF3)4(PPh3)2
31p
100 MHz
+32.81 d
J=166.0
-14.25 (very weak)
-24.42 d
J= 92.7
(major
signals 1:1)
100 MHz, CCT4 solution
+34.78 d
J=153.0
-14.8 t (weak)
J= 37
-23.66 d
J=104.5
(major
signals 1:1)
1J=164.2
300 MHz
+34.25 d of d
-15.1 d of d
-23.18 d of quart
?J= 11.6E
ÍJ= 47.4
TJ= 33.8
,J= 91.9
¿J= 11.7
(3:1:3)
15.1
Rh2(02CCF3)4(P(c-Hx)3)2
300 MHz
31P
+32.22 d of d
- 7.80 d of d
¿J=165.2
¿J= 12.0
h= 49.3
J= 34.8
-13.68 d of quart
h= 88.9
¿J= 12.0
Temp¬
erature
(°C?
-50
27
27
27
-50
(outer peaks)
(inner peaks)
27
(all peaks)
(2:1:2)

91
Table 3-III. continued
„ , 2
K
Coup!ing
Temp-
Complex
Nucleus
Chemical Shift (pom)
Constant
erature
(Hz)
(°C)
Rh2(02CCF3)4(P(0Ph)3)2
31P
eight peaks in
+161 to
J= 50
27
100 MHz
+75 ppm range,
-18.2
*J= 73.1
300 MHz
+70.00 d of d
fj= 61.6
ÍJ= 71.8
-50
300 MHz
+69.72 d of d
¿J= 61.9
-20
300 MHz
+69.53 t
J= 66.6
0
Rh2(02CCH2CH2CH3)4(PPh3)2
3!p
-18.91 br
none observed
27
Rh(02CCF3)2(P(0Me)3)3
3!p
+58 m
J =20
avg
(empircal formula)
+20 m
J =20
avg
-72 t
J= 50
a. All complexes are in CDClg solution except as otherwise noted.
b. 3*P chemical shifts relative to external 85% H^PO^. *H chemical shifts
relative to internal TMS.
c. Decomposition occurring during data collection. Chemical shift of
0P(0Ph)j is ca. -18 ppm.

92
2105 cm”1, below that of free CO (2143 cm”1), indicative of x-
backbonding. The mechanise of this was discussed earlier. Rhg^CCF^
also forms a 2:1 adduct with CO although the CO is much more weakly
bound. Indeed, it was not possible to isolate a CO adduct of
Rh2(O2CCF3)CO was too readily lost. However, other workers125
reported isolation of this adduct as a light brown solid. The IR
spectrum of this complex prepared as a KBr pellet under 1 atm of CO
showed v(CO) at 2150 cm-1 and vaSy(C02) at 1644 cm-1.125 It was found
here that bubbling CO through a solution of Rh2(O2CCF3)4 in CH2C12 led
to appearance of a purplish blue color, resembling that formed with
similar weak donors such as acetonitrile. The brown solid is surprising
since this resembles complexes formed with strong donors such as
phosphines and phosphites. The IR spectrum of this CH2C12 solution
showed bands assignable to v(C0) at 2160 cm-1 (m) and to vaSy(C02) at
1660 (s) and 1760 cm”1 (m). The former vasy(C02) band may correspond to
CO free Rh2(02CCF3)^. This positive shift in v(CO) from free CO was
taken as evidence of no x-backbonding in Rh2(02CCF3>4.125 However, this
is not a definitive argument. If there were no x-backbonding it is
unlikely that CO would coordinate at all. As shown by Drago,26 BF3,
which using the E and C analysis,27”29 is a stronger Lewis acid than
Rh2(02CCF3)4, but does not bind CO since BF3 cannot provide any x-
backdonation. The perturbation from o effects could cause an increase
in v(C0) in Rh2(02CCF3>4(00)2 comparable to the decrease cause by x
effects since both effects are small.

93
Phosphorus Donors
As mentioned previously, a large number of phosphine derivatives of
Mo2(02CCF3)4 have been reported.33,105 However, phosphites do not form
adducts with Mo2(02CCF3)4 presumably since they are not strong enough o-
donors. They do form axial complexes with Rh2(02CCH3)4 since in
contrast to the molybdenum system there is a significant ir-backbonding
stabilization. It was of interest to extend this work to Rh2(O2CCF3)4
since only triphenylphosphine and triphenyl phosphite adducts of
Rh2(02CCF3)4 have been reported.111 These complexes were studied by x-
ray crystallography and found to be Class 1 adducts. However, their
solution properties have not been investigated. The phosphorus donors
used here were dimethylphenylphosphine (PMe2Ph), triphenylphosphine
(PPhj), tricyclohexylphosphine (P(c—Hx)3)» triphenyl phosphite (P(0Ph)3)
and trimethyl phosphite (P(OMe)3).
PMe2Ph forms a Class II adduct with Mo2(02CCF3)4 due to its small
size and strong basicity.33 Thus, it would be a good candidate to form
a Class III adduct with Rh2(02CCF3)4. Unfortunately, the reaction of
Rh2(02CCF3)4 with four equivalents of PMe2Ph yielded only an intractable
orange oil indicating dimer decomposition.
PPh3 lies far outside the size and basicity range described by
Andersen33 for Class II adduct formation. Furthermore, in the solid
state Rh2(02CCF3)4(PPh3)2 is a typical Class I adduct.111 Thus, this
complex would be unlikely to show unusual solution behavior and one
would expect a simple 19F NMR spectrum such as that found for the THF
adduct. This was not the case. A freshly prepared solution of
Rh2(02CCF3)4(PPh3)2 showed sharp 19F NMR resonances at -74.4, -74.9, and
-75.9 ppm in CDC13 at 27 C in area ratios of 1:1:2. There was also a

94
small peak at -75.3 ppm. At -50 C there were still three sharp, major
peaks only in an area ratio of 1:1:1.3. That there was little change
over this temperature range indicates that the same species were
present, although perhaps in differing amounts. Assignment of these
peaks is difficult, presumably they corresond to mono- and bidentate
However, the situation differs from that observed with the
pyridine adduct and from the solution studies on Mo2{O2CCF3)4 with
pyridine.106 In those cases there were two peaks representing one Class
III isomer with 1:1 mono- and bidentate CF3CO2. The more complex
spectrum observed here could be the result of a mixture of isomers
containing axially and equatorially coordinated PPh3. That there would
be anything other than axial coordination in solution Is surprising.
However, it is possible that 1n solution the dimer may dissociate to
some extent. The molecular weight of Rt^tl^CCFj^iPPhj^ in CH2Cl2 was
found to be 590, half the expected value of 1183. This value could
result from the existence of Rl^^CCFjl^PPhj) and free PPh3 in
solution. However, if these were the major solution species, then only
one 10F NMR resonance would be observed, although perhaps weak signals
corresponding to 2:1 and base free species would be seen with similar
chemical shifts. Furthermore, a singlet corresponding to free PPI13
would be observed in the ^P^H} NMR spectrum or a single broad peak
coresponding to fast exchange between free and coordinated PPh3. Such
behavior was found by Boyar and Robinson126 who very recently reported
the 01P{1H} NMR spectrum of Rn2(U2CCH3)^(P(OMe73)3 ln dichloromethane-d?
solution. These workers126 observed a single broad peak at room
temperature. The 31P{1H} NMR spectrum of Rh2(but)4(PPh3)2 in CDC13 at
room temperature was obtained here and it also exhibited a single broad

95
resonance. Thus, in both phosphine and phosphite coordinated rhodium
alkyl carboxyl ate dimers rapid exchange occurs at room temperature
between free and coordinated phosphorus ligands. However, Boyar and
Robinson126 found that at 213 K exchange was slow enough to give an
informative spectrum. Signals were observed that were assigned to
Rh2(02CCH)3)4(P(0Me3)2, Rh2(02CCH3)4(P(OMe)3) and free P(0Me)3. The 1:1
adduct showed an AMX pattern and the 2:1 an AA'XX' pattern (A, A',
M=103Rh; X, X'=31P). The AMX system was analyzed by a first-order
approach, the AA'XX’ by iterative computer simulation. Presumably,
effective spin polarization occurs through the Rh-Rh bond (100* 103Rh,
1=1/2) that allows extensive rhodium-phosphorus and phosphorus-
phosphorus coupling. By contrast, in the Mo2(02CCF3)4 systems33,1(16 no
molybdenum-phosphorus (25* Mo, 1=5/2) or phosphorus-phosphorus coupling
was seen for either Class 1 or Class II adducts. However, the 31P{1H}
NMR spectra obtained here for Rh2(03CCF3)4(PPh3)2 were far more complex
than those for the alkylcarboxylate systems. Using a 100 MHz
instrument, two strong, sharp signals were observed in both CDC13 and
CC14 solution. These signals had the same chemical shifts and coupling
constants in the two solvents, indicating no effect of a hydrogen
bonding solvent. A third, very weak signal was also observed and
appeared to be a triplet in CC14. However, use of a 300 MHz instrument
which gave better resolution and required fewer scans revealed the true
nature of the splitting. In addition, the 300 MHz spectrum was obtained
at -50 C on a solution that had been frozen in an acetone/C02 bath
immediately after preparation. When this precaution was not taken, the
NMR spectra, both 19F and 31P{1H}, showed some signs of decomposition
since additional, very weak signals were observed. Three 31P signals

96
were observed for this freshly frozen solution at -50 C. Two consisted
of a doublet of doublets, and the third was a doublet of quartets.
These signals were in an area ratio of 3:1:3. Since 3J=2J for the
second (weak) doublet of doublets, it closely resembled a triplet. True
coupling constants cannot easily be obtained for spectra this complex.
The two doublets of doublets could be either AMX or AA'XX1 systems and
the other signal could be something more complex, such as ABMX (or
ABXY). Without definite knowledge of the solution species, it would be
of little utility to attempt a computer simulation of the spectrum.
Even 1f a set of coupling constants could be determined that would fit
an observed signal, it might not be a unique solution. It should be
noted that the descriptions "doublet of doublets" and "doublet of
quartets" only roughly describe the observed signals since the
splittings and intensities do not exactly correspond to what would be
expected for first-order AMX, AMX2, A3MX, or ABMX systems. The X
portion of both AMX and AMX2 systems would show four peaks in 1:1:1; 1
area ratios. The X portion of both A3MX and ABMX systems would have a
doublet of four peaks in 1:3:3:1 area ratios for the former and 1:1:1:1
for the latter system. In the A3MX sysem, the four peaks would be
equally separated, in the ABMX system that would be true only if
JBX=23AX* Ttle latter system more accurately describes the observed
signal since the peaks were roughly equal in inetnsity and were not
equally spaced. The inner two peaks were nearer the outer peaks than to
each other. Nevertheless, the 31P{1H} NMR spectrum of
Rh2(02CCF3)4(PPh3)2 does allow some proposals to be made as to the
solution behavior of this complex through a process of elimination.
Although any interconversion between species was slow enough to give

97
well resolved and fjMR spectra at room as well as low
temperature, no signal for free PPh3 was seen. This indicates that all
PPh3 present was coordinated to rhodium and most likely no 1:1 adducts
were present, in contrast to the results with the acetate and butyrate
dimers. This is not surprising, since as will be shown below,
Rh2(02CCF3)4 has a great affinity for phosphorus donors and of course is
a much stronger Lewis acid than rhodium alkylcarboxylate dimers.
Possible solution species are therefore those in which the rhodium dimer
remains intact, but existing as more than one isomer, and monomeric
rhodium complexes. A simple cleavage of the Rh-Rh bond would give
Rh(02CCF3)2(PPh3)2- Rhodium(II) complexes are uncommon, although
species such as Rh(P(c-Hx)3)2Cl2 are known.127 These Rh(II) monomers
are EPR active as would be expected for a square planar d7 complex.
However, a Rh(II) monomer does not exist in the system described here
since the NMR spectra showed no evidence of paramagnetic species (no
line broadening or large isotropic shifts) and Rh(02CCF3)4(PPh3)2 gave
no EPR signal in CH2CT2 solution at 77 K. The possibility of species
containing one Rh and one PPh3 such as weakly associated
[Rh(02CCF3)2(PPh3)]“ and the Rh(III) cation of the same formulation can
also be ruled out. Species containing one Rh and one PPh3 would
necessarily give AX signals. Although the 100 MHz 31P{1H} NMR spectrum
gave support to this, the higher field spectrum clearly showed more
complex splitting patterns and no simple doublets were observed. It is
possible that in solution such complexes as Rh(02CCF3)3 and
Rh(02CCF3)(PPh3)2 are present. The latter complex has been previously
reported.128 The reaction of 'RhCl(PPh3)3 with CF3C02H was reported to
yield a yellow, very air-sensitive complex characterized only by

98
elemental analysis and IR which showed bidentate CF3C02' (vasy(C02) at
1660 cm-1).128 Thus, Rh(02CCF3)(PPh3)2 is most likely a square planar,
symmetrical complex. It would be an AX2 system since it is difficult to
imagine that the two PPh3 ligands would be chemically or magnetically
inequivalent. Furthermore, the solution would be expected to change
color, which was not seen. Although the solution molecular weight
favored monomeric species, the lower than expected value may have been
the result of decomposition over the time period required for the
procedure mainly due to oxidation. Previous workers95,128,12® also
often obtained lower than expected molecular weights for analogous
monomeric rhodium complexes. This leaves dimeric 2:1 adducts as
possible solution species. Both axial (Class I) and equatorial (Class
II) adducts as well as species containing both axially and equatorially
coordinated PPh3 (Class III) could exist. There are a total of nine
possible isomers, one Class I, six Class II33 and two Class III. These
last two have either both PPh3 ligands coordinated to one Rh, one
axially the other equatorially, or one PPh3 coordinated to each Rh, one
axially the other equatorially. The relative amounts of these isomers
is uncertain, but the presence of several of them would give rise to a
variety of 19F NMR signals as well as the complex 31P{1H} spectrum. The
Class I and Class II isomers would most likely be AA’XX1 systems since
the two phosphine ligands are symmetry related. However, the Class III
(axial and equatorial) isomers would probably be ABMX systems (A,
B=103Rh; M, X=31P). This allows a tentative interpretation of
the 31P{1H} NMR spectrum of Rh2(02CCF3)4(PR3)2 complexes which will be
made after discussion of the other phosphorus donor adducts. As a final
note, the coupling constants seen here are comparable to those

99
previously reported for rhodium-phosphorus coupling in monomeric Rh(I)
and Rh(III) complexes such as trans-RhCl(CO)(PPH^)? for which
Jrh_P=129 Hz130 and mer-Rh(PMePh?)^Cl-j for which JRh-pi=36.0 Hz and
Jr,1_P2=114.5 Hz.131 Of course, the values obtained here (see Table 3-
III) are only first order approximations and do not accurately represent
the true rhodium-phosphorus (or P-P and Rh-Rh) coupling constants.
The IR spectrum of Ri^iC^CCF-j^fPPh^ differed between solution
and the solid state. In a Nujol mull a single vaSy(C02) bancl was
observed at 1665 cm'1 consistent with the bridging carboxylate
structure. The other absorption bands were assignable to PPh3 or
Rh2(O2CCF3)4. The IR spectrum is shown in Figure 3-9. However, in
CHC13 solution vasy(C02) bands were observed at 1717 cm'1 and at 1658
and 1648 cm'1. Thus, in solution some monodentate CFjCC^' coordination
occurs which would be expected as a result of equatorial PPh3
coordination in dimeric complexes. Some preliminary studies of the
reaction of excess PPh3 with Rt^d^CCF^ were undertaken. Details are
given in the Experimental Section. Two main products were isolated, an
orange compound which was most likely the known129 complex
Rh(O2CCF 3)(PPh3)3 and a yellow compound best formulated as
Rh(02CCF3)3(PPh3)2- The latter complex has not been previously
reported, although yellow Rh(PR3)3C13 (where R=Me, Et, etc., but not Ph)
is well known.139,131 In addition, a small amount of an orange, fairly
insoluble complex was obtained which was best formulated as
Rh2(02CCF3)4(PPh3)4. It is important that air be excluded from the
reactin or else triphenylphosphine oxide is produced. This was isolated
as a crystalline compound, but it can also coordinate and complicate
analysis of the products. Detailed investigation of these monomeric

Figure 3-9. IR spectrum of RhgíC^CCF^ÍPPh.^ as a Nujol mull. Inset shows the
vasy(C02) region of a chloroform solution.

101
rhodium complexes is beyond the scope of this work. It appears that
given enough phosphine, cleavage of the Rh-Rh bond is possible, even by
a bulky and relatively poor a-donor such as PPh3. Furthermore, there is
strong evidence that in solution the Class I solid state structure does
not remain intact. Both Class II and III complexes are also present and
over time, monomeric Rh(I) and Rh(III) species may result.
Interesting results were also found with tricyclohexylphosphine.
The hope was that if any Rh-Rh bond cleavage occurred, Rh(II) species
might be stabilized since, as described above, the only known Rh(II)
phosphine complexes are those with P(c-Hx)3-This ligand was reacted
in excess (~10 equivalents) with Rh2(02CCH3)4 in toluene and with
Rfi2(02CCF3)4 in toluene and dichloromethane. In all cases, complexes of
stiochiometry Rh2(02CR)4(P(c-Hz)3)2 were isolated. The rhodium
trifluoroacetate complex was brown and that for acetate was orange, as
was found for the PPh3 adducts. The IR spectrum of Rh2(02CCF3)4(P(c-
Hx)3)2 is shown in Figure 3-10. However, use of 1:1 toluene/
acetonitrile and heating led to a yellow solution from which a pale
yellow, presumably Rh(I) and/or Rh(III) complex was isolated. These
results may be explained by the very large steric size of P(c-Hx)3 (cone
angle=170‘). Although this phosphine is a good a-donor, its large size
makes Rh-Rh bond cleavage reactions more difficult. The solution
behavior of Rh2(02CCF3)4(P(c-Hx)3)2 greatly resembled that of the PPh3
adduct. Complex 19F and 31P{1H} NMR spectra were observed indicating
the Class I structure was not maintained in solution. There was no
evidence of Rh(II) species being present in solution since no EPR signal
was observed for either the acetate or fluoroacetate adducts in toluene
at both room temperature and 77 K. For Rh2(02CCF3)4(P(c-Hx)3)2, four

transmittance
MICRONS
Figure 3-10. IR spectrum of Rhg^CCFg^Ptc-Hx)^^ as a Nujol mull.

103
signals were observed in the 1!3F NMR spectrum over a 3 ppm range,
indicating mono- and bidentate CF3C02~. The 31P{^H} NMR spectrum showed
three signals, two doublets of doublets and a doublet of quartets, in a
2:1:2 area ratio. The chemical shifts and estimated coupling constants
for these signals were very similar to those seen for
Rh2(02CCF3)4(PPh3)2 (see Table 3-1II), although the chemical shift
similarity may be coincidental since 31P chemical shifts vary greatly.
No signal for free P(c-Hx)3 was seen. With the P(c-Hx)3 adduct, it was
not necessary to freeze the solution to obtain good NMR spectra. The
greater stability of the tri cyclohexyl phosphine complex is also
suggested by the value of 1060 obtained for the molecular weight in
CH2C12 solution. This was lower than the expected value of 1219, but is
much closer to the dimer molecular weight than found with PPh3. As with
the PPh3 adduct, an accurate analysis of this spectrum is not possible,
however the signals observed most likely resulted from isomers with
axial and equatorial P(c-Hx)3 coordination. The solution IR spectrum
supported this, since bands for vaSy(C02) were seen at 1710 and 1660
cm-1 indicating mono- and bidentate CF3C02” in solution in contrast to
the solid state IR spectrum.
With P(0Ph)3 less unusual results were obtained. Triphenyl
phosphite is a poor o-donor although it has better Tt-acceptor properties
than PPh3. No complex of this ligand with Mo2(02CCF3)4 exists and
Rh2(02CCF3)4(P(0Ph)3)2m as well as Rh2 (02CCH3 )4 (P (DPh )3 )2132 are
typical Class I adducts in the solid state. Thus, it would seem very
unlikely that this Rh2(02CCF3)4 complex would show unusual solution
behavior. This was found to be the case with one important proviso.
Even in a sealed tube under a nitrogen atmostphere, a CHC13 solution of

104
Rh2(02CCF3)4ÍP(0Ph)3)2 changed color over a period of days from orange-
yellow to emerald green, characteristic of base free Rh2(O2CCF3)4
Addition of excess P(0Ph)3 to a sample of this green solution restored
the original orange color. Apparently, ligand oxidation occurred,
similar to the 0PPh3 formation discussed above. The mechanism for this
phosphite decomposition is unknown. Presumably, if the reaction
proceeds stoichiometrically only trace amounts of 02 or H20 would be
needed to effect complete oxidation with apparently little, if any,
dimer decomposition. It should be noted that Kawamura and co-workers*^
have reported the frozen solution EPR spectrum of Rh2{02CCF3 )4
(P(0Ph)2)2+ generated from the neutral dimer by y-ray irradiation. In
addition to the expected signal, a weak signal was detected but not
discussed. It is possible that this arose from Rh2(02CCF3)4+ or some
other species in which the phosphite had decomposed. The solid state IR
spectrum showed a single vaSy(C02) at 1670 cm-1 and a fresh CHCI3
solution showed this band at 1665 cm“*. There were no differences
between the two and all bands were assignable to P(OP h)3 and
Rh2{02CCF3)4. The IR spectrum of Rh2(02CCF3)4(P(0Ph)3)2 is shown in
Figure 3-11. P(OPh)3 is too poor a a-donor and too good a ir-acceptor to
cause other than axial coordination. The Class I solution structure of
the P(0Ph)3 adduct was confirmed with NMR. A freshly prepared solution
of this complex showed a single sharp *9F NMR resonance at -75.1 ppm in
CDC13 at room temperature. However, by the time the low temperature
spectrum was obtained, decomposition had occurred giving two major
signals and several minor ones in the -74.5 to -75.5 ppm range. This
rapid decomposition made ^lp NMR studies difficult. Using a 100 MHz
instrument, which required a long data acquisition time and large NMR

Figure 3-11. IR spectrum of Rh^íOgCCF^)^(P(OPh)3)2 as a Nujol mull.

106
tubes (12 mm), the 31P{*H} NMR spectra that were obtained showed several
signals presumably corresponding to coordinated phosphite and a sharp
signal assignable to triphenyl phosphate. The OP(OPh)3 signal increased
over time. However, using a 300 MHz instrument (using 5 mm NMR tubes),
and freezing the solution immediately after preparation prevented
phosphate formation. The 31P{1H} NMR spectrum of Rh2(02CCF3)4 obtained in this manner showed only one signal. At -50 C it was a
doublet of doublets, but upon wanning, the center two peaks collapsed so
that by 0 C, a 1:2:1 triplet was seen. This indicates that the second,
weak doublet of doublets observed in the 31P{^H} NMR spectra of the PPh3
and P(c-Hz)3 complexes was most likely due to the Class I axial
adduct. At higher temperatures the Class I adduct is an A2X2 system
(A=103Rh; x=3^P) so that a triplet is seen. This suggests that the
triplet seen in the room temperature spectrum of the PPh3 adduct in CC14
was probably real, and not an artifact of poor resolution. The
separation between the outer peaks is 2At low temperatures, the
Class I adduct is an AA'XX' system. The separation of the outer peaks
is then |0AX + and ttie separation of the inner peaks is either
£((JAA' " JXX,)2 + (JAX ■ jax')2)1/2 * lJAA' ■ Jxx‘|] C( Jxx’)2 + ' JAX')2^2 * lJAA' + JXX1)AA-XX1 system has a
total of ten lines, however very often they are not all observed since
many are very broad and/or of low intensity. As A' becomes equivalent
to A and X' to X, the inner peak separation becomes zero in all four
possible combinations. All that can be determined here is that the
rhodium-rhodium and phosphorus-phosphorus couplings are small compared
to the rhodium-phosphorus coupling. Two signals are left to be
accounted for in the PPh3 and P(c-Hx)3 spectra, the doublet of doublets

107
and the doublets of quartets. These two signals were in equal area
ratios in both spectra, suggesting they arose from two chemically
different phosphine ligands on the same molecule. Using a first-order
analysis, these signals correspond to an ABMX system (A, B=^03Rh; M,
X=3^P). The doublet of quartets would be due to an axially coordinated
phosphine coupled strongly to one rhodium Í^AX=1JUh-P^90 Hz) and 1ess
strongly to the other rhodium (JBX=2jRh-P^25 Hz) and the ottler phosphine
{JMX=3Jp_p=12 Hz), which would be equatorially coordinated. The
doublets would then be due to the equatorially coordinated phosphine
coupled strongly to one rhodium (JBM=1JRfl_p=165 Hz) and weakly to the
other phosphine (JMX=3Jp_p=12 Hz, as above) with the coupling to the
other rhodium not observable (JAH=2JRtl_p=0). It is not unreasonable to
assume that the axially coordinated phosphine would have a larger 2JRtl_p
value than the equatorial phosphine, since the axial phosphine is along
the Rh-Rh bond, allowing strong through-bond coupling. In the Class I
P{0Ph3) adduct and the signals assigned to the Class I complex in the
phosphine spectra, 2JRh_p almost equals ^p-p. The above discussion
fits the data reasonably well, although there are several
difficulties. It is not clear why the Class I AA'XX' system becomes an
ArX2 system at higher temperature, this may have to do with easier
rotation. Also, the 19F NMR spectra are more complex than would be
expected in the phosphine complexes, but this may be due to slight
changes in CFjCOp” coordination that do not affect the 31P signals.
Finally, a higher order computer-assisted analysis is needed to fully
analyze the 31P{3H} spectra and possibly obtain accurate coupling
constants.

108
Quite different results were obtained with P(OMe)3 although
Rh£(O2CCH3)4.(P(OMe>3)2 has been reported and is a Class I adduct.124
With this very small phosphorus donor the Rh-Rh bond was cleaved much
more readily than with PPh3. Reaction of excess (10 equivalents)
P(OMe)3 with Rh2(OgCCF3)4 in toluene led to isolation of a pale yellow,
air-sensitive, hygroscopic compound best formulated as
Rh(02CCF 3)2(P(OMe)3)3. Elemental analysis and molecular weight
determination in CH2C12 supported this formula (see Experimental
Section). However, since no EPR signal was observed for the complex in
CH2C12 at 77 K and it gave a normal, diamagnetic NMR spectrum, monomeric
Rh(II) was not present. Rather, the complex is most likely a mixture of
equal amounts of Rh(I) and Rh(III) species. The pale yellow color is
characteristic of Rh(I) and Rh(II) phosphite complexes such as
HRh(P(0Et)3)3Cl2,134 HRh(P(0Et}3)4,134 Rh(0P(0Me)2)(P(0Me)3)4135 and
[Rh(P(OMe)3)5] BPh4.136
The 19F NMR spectrum of the reaction product showed two sharp
resonances in a 3:2 area ratio at both room temperature and at -50 C.
The simplicity of the 19F NMR spectrum is surprising since a variety of
complexes could be present. One would expect an area ratio of 1:3 if
the species present were Rh (02CCF3)(P(OMe)3)3 and Rh(02CCF3)3
(P(0Me)3)3. The signals would then rise from monodentate CF3C02“ in
either the square planar Rh(I) or octahedral Rh(III) complex. The
observed area ratio most likely arises from different isomers. The
principal species likely to be present in this case are [Rh(P(DMe)3)4]+
and [Rh(02CCF3)4(P(0Me)3)2]'. These would also be square planar Rh(I)
and octahedral Rh(II) complexes, respectively. The latter compound
would have only monodentate CF3C02~ and could exist as both cis or trans

109
isomers. These isomers could be present in virtually any ratio, such as
3:2, since steric constraints are minimal with this small posphite.
Interconversion between the two Isomers would not be expected and this
accounts for the temperature independence of the 39F NMR spectrum. As
shown by Muetterties,137 octahedral low oxidation state transition metal
phosphite complexes are generally stereochemically rigid.
The 31P{3H} NMR spectrum of the PlOMelg reaction product was more
complex than would be expected for the two ions given above. Multiplets
were observed at +58 and +20 ppm and a smaller triplet at -72 ppm
relative to external phosphoric acid in CDCI3 at room temperature.
The 31P{1H) NMR spectrum is shown in Figure 3-12. Since the 19F NMR
spectrum is simple, the complexity of the 31P{1H} NMR spectrum must
arise from species without CF3C02- ligands. In addition to
[Rh(P(OMe)3)4]+, other Rh(I) phosphite complexes could exist in
solution. In contrast to the octahedral complexes, lower coordination
number phosphite complexes are generally stereochemically
nonrigid.13^-137 Compounds such as Rh {OP(OMe)2)(P(OMe)3)4135 and
[Rh(P(OMe)3)5]+ 136 have complex, fluxional 31P{3H} NMR spectra which
nevertheless have been thoroughly analyzed. However, uncertainty about
the exact products of the P(OMe)3 reaction studied here and lack of
variable temperature spectra makes such an analysis difficult. Most
likely, the observed room temperature 31P{1H) NMR spectrum arises from a
variety of Rh(I) phosphite complexes that are not stereochemically rigid
combined with the two isomers of the Rh(III) trifluoroacetate phosphite
complex. As a final note, the complex Rh(0P(0Me)2)(P(OMe)3)4 was
originally reported as Rh2(P(OMe)3)q. Subsequent work led to the new
formulation but indicated that Rh2(P(OMe)3)g could indeed be

^P{*H} NMR spectrum of "Rh^CCF-^ÍPlOMe).^" in chloroform-id using
8916 scans at 40.5 MHz with an external D.,0 lock.
Figure 3-IE.

Ill

112
prepared.135 It is possible that OP(OMe)2 is present in the complex
reported here, although it is not supported by the analytical data.
The IR spectrum of the P(OMe)3 reaction product confirmed that only
mondentate CF3CO2- was present. No bands were observed between 1600 and
1700 cm-1, only a single broad band at 1710 cm-1 in CHC13 solution and
at 1725 cm-1 in the solid state. Although further work is needed to
characterize the reaction products, it is clear that P(OMe)3 readily
cleaves the Rh-Rh bond causing disproportionation Into monomeric Rh{I)
and Rh(III) complexes. This is in contrast to Rh2(O2CCH3)4 in which the
acetates do not allow phosphite access to the equatorial coordination
sites and dimer break up does not result.
It appears that the action of phosphorus donors on Rh2(02CCF3)4
leads to unusual reactivity. The normal air stable compounds PPh3 and
P(0Ph)3 are easily oxidized. The rhodium dimer itself, which remains
intact when reacted with strong a-donors such as Et3N or pyridine, the
latter also having iv-acceptor abilities, cannot stand up to reaction
with phosphorus donors of comparable o-donor strength that are often
sterically bulky. However, the failure of P(OPh)3 to effect Rh-Rh bond
cleavage indicates that there are limits on donor ability beyond which
only Class I adducts are formed. Nevertheless, the reason for the
strong overall affinity of rhodium for phosphorus donors is not clear.
Criteria such as ir-backbonding and certainly o-donor strength and ligand
size are not enough to fully classify the Lewis base reactivity of
Rh2(02CCF3 54.

113
Conclusion
The reactivity of Rn2(02CCF3)4 with Lewis bases shows significant
differences from the analogous ^102(02^3)4 and Rh2(O2CCH3)4 systems.
Differences in the frontier MO’s between the rhodium and molybdenum
dimers can be used to explain the propensity for rhodium as opposed to
molybdenum to form Class I adducts. For example, the poor o-donors but
good n-acceptors P(OPh)3 and CO form Class I adducts with Rh2(02CCF3
and Rt^^CCHg^, but not with any molybdenum dimer. This 1s due to the
strong ?r-backbonding interaction between the filled n* orbitals on Rh-Rh
and empty it* orbitals on these ligands. This interaction cannot occur
in Mo-Mo which has empty u* orbitals. The a-bonding interaction between
the ligand lone pair and the empty a* orbital on the metal carboxylate
dimers is also important, but with weaker o-donors such as PfOPhlj and
CO it is not enough to allow isolation of molybdenum adducts with these
ligands. Differences in electronegativity between CF3CO2- and CH3CO2-
can be used to explain the ability to isolate Class III (4:1, axial and
equatorial) adducts of Rh2(02CCF3)4 with pyridine and t_-BuNC, but only
Class I adducts of Rh2(02CCH3)4 with these Lewis bases. The electron-
withdrawing CF3 group causes CF3CO2- to coordinate less strongly to the
rhodium dimer than does acetate. This allows Lewis bases access to
equatorial sites as well as the always available axial sites. When the
Lewis base has the right combination of o-donor and n-acceptor
properties, such as in pyridine and _t-BuNC, the base is not labile, it
binds permanently and Class III adducts can be easily isolated.
When phosphorus donors are used, except when they are very poor cr-
donors (P(OPh>3)» cleavage of the Rh-Rh bond can occur to give monomeric
Rh(I) and Rh(III) products. The reason for this instability of the

114
usually robust Rh-Rh bond towards phosphorus donors is not certain.
Clearly, the CF3CO2" ligand is necessary to allow the P donor to attack
at a kinetically viable rate. Then, perhaps, the thermodynamic
stability of Rh(I) and Rh(III) phosphine and phosphite complexes drives
these reactions to completion. Further work could involve the
structural characterization of some of the complexes mentioned here.
This would fully confirm the Class III structure. Another spectroscopic
method that could prove useful is 103Rh NMR, which has very recently
been applied to Rh(II) dimers with bridging hydroxypyridine
ligands.138 This would assist in confirming the solution structure of
many of the species described above, whether they are Class I, Class II
or monomeric species. In addition, in 1:1 Lewis base adducts, the
chemical shift of and coupling between the non-equivalent Rh nuclei
could be used to understand electron polarization within the Rh-Rh bond
as a result of coordination of a single base. It is also important that
kinetic studies should be undertaken on the reactions of phosphorus
donors with metal carboxylate dimers and analogous metal-metal bonded
and monomeric complexes. This might shed some light on the unusual
reactivity described here. These sorts of studies have been performed
extensively on transition metal carbonyl complexes, often containing
metal-metal bonds139 and perhaps should be extended to other systems.
Experimental Section
All solvents were of reagent grade and were distilled from the
appropriate drying agents before use. Bases were purified following
established procedure.140 Pyridine, N-methylImidazole, piperidine,
trithylamine, N,N-dimethylformamide, dimethylsulfoxide, tetrahydrofuran,

115
and acetonitrile were distilled from the appropriate drying agents
before use. Trimethyl phosphite, triphenyl phosphite,
dimethylphenylphosphine and _t-butylisonitrile were used as purchased
without further purification. However, their purity was checked by
IR. Triphenylphosphine was recrystallized from toluene before use.
Operations were performed under nitrogen except as otherwise noted.
Rhodium acetate was synthesized from RhCl3(H20)3 by literature
methods.101
Tetrakis(trifluororacetato)dirhodium(II)
This compound was synthesized using a modification of the procedure
of Cotton and Norman108 for Mo2(02CCF3)4. Rh2(02CCH3)4 (0.5 g, 1.13
mmol) was suspended in CF3C02H (10 mL) and (CF3C0)20 (1 mL). The
mixture was refluxed for 2 h. The solvent was then removed by pumping
and the procedure repeated with fresh acid. After removal of solvent
the crude product, which was often a bluish green color, was
recrystallized from 1:1 dichloromethane/toluene to give the bright green
Rh2(02CCF3)4 (0.60 g, 0.91 mmol, 81%). Anal. Caled, for Rh2CgF120g: C,
14.61; H, none; F, 34.65. Found: C, 14.65; H, none; F, 34.12, The
compound decomposes under nitrogen in a sealed tube at 265 C.
Bis(tetrahydrofuran)tetrakis(trif1uoroacetato)dirhodium(II)
Rh2(02CCF3)4 (0.10 g, 0.15 nmol) was dissolved in THF (2 mL) to
give a dark blue solution. Removal of solvent by pumping and
recrystallization from boiling hexane in air afforded medium blue
Rh2(02CCF3)4(THF)2 (0.11 g, 0.14 mmol, 91S). Anal. Caled, for
Rh2ci6Hi6Fi2°io: c> 23.92; H, 2.01; F, 28.39. Found: C, 23.61; H,
2.02; F, 28.22. The adduct loses THF quantitatively upon heating at 100

116
C under vacuum. This makes it a convenient form for storing
Rh2(02CCF3)4 since the base-free rhodium dimer is rather hygroscopic.
Also the above procedure of THF adduct formation and hexane
recrystallizati on is a convenient method for obtaining pure
Rh2(02CCF3)4.
Bis(diroethylsulfoxide)tetrakis(trifluoroacetato)dirhodium(II)
This compound was synthesized following the procedure of Cotton and
Felthouse.114 Rh2(02CCF3)4 (0.050 g, 0.076 mmol) was dissolved in 1:1
benzene/chloroform (5 mL). DMS0 (0.2 mL) was added and a blue solution
resulted. The solvent was removed by pumping and the resultant solid
was washed twice each with toluene and hexane leaving a blue
microcry stalline solid (0.059 g, 0.07 mmol, 955). Anal. Caled, for
Rh2c12H12F12s2°10: c* 17>7°: H, 1.49; F, 28.00; S, 7.88. Found: C,
19.05; H, 1.88; F, 28.32; S, 8.00.
Bis(N,N-diroethylformamide)tetrakis(trifluoroacetato)dirhodium(II)
Rh2(02CCF3)4 (0.030 g, 0.046 mmol) was dissolved in 1:1
dichloromethane/toluene (5 mL) in air. Addition of DMF (0.2 mL) led to
an initial purple color which rapidly changed to blue. Evaporation led
to formation of dark blue platelike crystals of Rh2(02CCF3)4(DMF)2
(0.033 g, 0.041 ironol, B9%). Anal. Caled, for Rh2('14H14N2F12°10: c>
21.30; H, 1.76; N, 3.48; F, 28.35. Found: C, 21.30; H, 1.82; N, 3.30;
F, 28.02.
Bis(tri ethyl ami ne)tetrakis(trif! uoroacetato)dirhodium(II)
Rh2(02CCF3)4 (0.050 g, 0.076 mol) was dissolved in toluene (4
mL). Addition of Et3N (0.1 mL) caused an immediate color change to
red. Concentration to 1 mL led to formation of a red precipitate.

117
Filtration and washing with hexane afforded red, microcrystalline
Rh2(O2CCF3)4(Et3N)2 (0.050 g, 0.058 mmol, lt%). Anal. Caled, for
Rh2c20H30N2F12°8: c> 27-92l H» 3-52í N» 3-26: p> 26.50. Found: C,
28.33; H, 3.56; N, 3.12; F, 25.60.
Tetrakis(pyridine)tetrakis1trif 1 uoroacetato)dirhodi um(11)
Rh2{02CCF3(0.10 g, 0.15 nmol) was dissolved in toluene (5 mL).
Addition of 2 mL of a 10:1 toluene/pyridine solution caused an immediate
color change to red. Concentration to 2 mL and cooling led to formation
of a red precipitate. Filtration and washing with hexane afforded
pinkish red microcrystalline Rh2(02CCF3)4(pyr)4 (0.13 g, 0.13 mmol,
885). Anal. Caled, for Rh2C28H2QN4F1208: C, 34.52; H, 2.07; N, 5.75;
F, 23.40. Found: C, 34.98; H, 2.14; N, 5.64; F, 22.22. The compound
melts in a sealed tube under nitrogen at 169-170 C. The synthesis of
Rh2(02CCF3)4(pyr)2 was attempted by following the procedure of
Stephenson and co-workers.123 Rh2(02CCF3)4 (0.03 g, 0.045 mmol) was
dissolved in cold ethanol (2 mL). To this pyridine (~0.2 tti) was added
dropwise. A red solution resulted and with further cooling a red
precipitate formed. Filtration and washing with hexane afforded a red
solid (0.025 g). Anal. Caled, for Rh2C18H^gN2F1208: C, 26.49; H, 1.24;
N, 3.43. Found: C, 30.67; H, 2.05; N, 4.16. IR (CHCI3 solution)
vasy(C02), 1705 (m)’ 1688 1660 (s)« 1650 cm’1 (ra)- 19p NMR (CDC13,
27 C) -75.0 (complex m), -75.8 (5). The reaction is most likely a
mixture of 2:1, 3:1, and 4:1 pyridine adducts of Rh2(02CCF3)4.
Tetrakis(tert-butylisonitri1e)tetrakis(trifluoroacetato)dirhodium(II)
Rh2(02CCF3)4 (0.10 g, 0.15 mmol) was dissolved in toluene (4 mL).
To this solution was added t-BuNC (0.10 mL, 0.89 mmol, Strem

118
Chemicals). An orange solution immediately resulted. After 1 h, the
solution was concentrated to 1 mL. Filtration of the resulting
precipitate and washing with hexane afforded an orange-brown solid (0.12
g, 0.12 mmol, 80Í). Anal. Caled, for RhgCggHgg^FigOg: C* 33.92; H,
3.66; N, 5.65; F, 23.00. Found: C, 33.67, H, 3.80; N, 5.39; F, 23.24.
Bis(acetonitri le)tetrakis(trif1uoracetato)dirhodium(II)
RhgiOgCCFj^ (0.10 g, 0.15 mmol) was dissolved in air in acetronile
(2 mL) to give a purple solution. Addition of water (3 mL) led to
immediate precipitation of a purple solid. Filtration and drying under
vacuum afforded ¡*(12(02^3)4(0(130^) (0.09 g, 0.12 mmol, 802). Anal.
Caled, for RhgC^HgNgF^Og: C, 1945; H, 0.82; N, 3.78; F, 30.77. Found
C, 25.18; H, 1.95; N, 3.79; F, 22.65. Synthesis of this compound using
only organic solvents failed to give any purer a product. Furthermore,
the compound is not indefinitely stable. It loses CH3CN even under
inert atmosphere. In air, CH3CN is replaced over a period of 1 h by H20
to give a blue-green solid. By contrast, evaporation in air of an
acetonitrile solution of RI^OgCCHg^ afforded a stable purple solid
that is most likely the 2:1 acetonitrile adduct. Anal. Caled, for
Rh2C12H18N2°8: C* 27.50; H, 3.46; N, 5.34. Found: C, 27.54; H, 3.53;
N, 5.02.
Bis(triphenylphosphine)tetrakis(trif1uoroacetato)dirhodium(II)
This complex was synthesized following the procedure of Cotton and
co-workers.m Rh2(0gCCF3)4 (0.050 g, 0.076 mmol) was dissolved in
methanol (5 mL). Triphenylphosphine (0.040 g, 0.15 mmol) was dissolved
in hot methanol (~5 mL). This solution was added to the blue
Rf^tOgCCFg^fCHgOH^ solution to give an immediate dark brown color.

119
The solution quickly became colorless and purplish brown needle crystals
were deposited. Filtration and washing with methanol afforded 0.085 g
(0.075 mmol, 94%), Anal. Caled. for Rh2C44H3QP2Fj20g: C, 44.66; H,
2.56; P, 5.23. Found: C, 44.18; H, 2.67; P, 5.18. Orange
Rl^ibut^fPPhjJg was synthesized in the same manner in 82% yield. Anal.
Caled, for Rh2Cg2H5gF2®8: C» 57.89; H, 5.43; P, 5.74. Found: C,
58.07; H, 5.40; P, 5.88.
Bis(triphenyl phosphite)tetrakis(trif1uoroacetato)dirhodium(11)
Rh2(02CCF3)4 (0.178 g, 0.286 mmol) was dissolved in methanol (10
mL). Triphenyl phosphite (0.150 ml, 0.572 mmol) was added dropwise to
give a red-brown solution. The solution quickly became colorless and an
orange-brown microcrystalline solid precipitated. Filtration, washing
with methanol and drying under vaccum afforded 0.32 g (0.25 mmol,
87.5*). Anal. Caled, for R^2^44R30P2F12®14* C, 41.31; H, 2.35; P,
4.84. Found: C, 40.93; H, 2.25; P, 4.28.
Bis(tricyclohexylphosphine)tetrakis(trif1uoroacetato)dirhodium(11)
Rh2(02CCF3)4 (0.053 g, 0.080 mmol) was dissolved in toluene (2.5
ml). Tricyclohexylphosphine (0.045 g, 0.160 mmol, Aldrich) was
dissolved in toluene (2 mL) and added dropwise to the Ri^^CCFg^
solution. A dark brown color immediately resulted. The solvent was
removed by pumping to give a brown solid. Recrystallization from hot
toluene afforded 0.08 g (0.07 mmol, 87.5%). Anal. Caled, for
Rh2C44H66p2F12°8: C* 43-36: 5.46; p. 5.08. Found: C, 45.53; H,
5.49; P, 5.23. Use of the above procedure with 10 equivalents of P(c-
Hx)3 in CH2C12 solvent gave the same product as shown by IR and
elemental analysis. Use of the above procedure with Rh2(O2CCH3)4 and 10

120
equivalents of P(c-Hx)3 and recrystallization from heptane afforded
orange-brown Rh2(02CCH3)4(P(c-Hx)3)2. Anal. Caled, for Rh2C44H73P20g:
C, 52.70; H, 7.84; P, 6.18. Found: C, 52.54; H, 7.82; P. 5.00.
Reaction of Rh?(0-?CCF-^)a with excess PPh-¡
Rh2(02CCF3)4 (0.162 g, 0.246 mmol) was dissolved in toluene (5
mL). Triphenylphosphine (0.640 g, 2.44 mmol) was dissolved in toluene
(3 mL) and added dropwise to the Rh2(02CCF3)4 solution. A dark brown
color characteristic of Rh2(02CCF3)4(PPh3)2 immediately resulted. The
reaction mixture was stirred with heating for 1 h. During this time an
orange precipitate formed. Filtration of the hot solution afforded 0.24
g. Thin layer chromatography using 2:1 chloroform/toluene indicated two
components. Extraction of the orange product with hot 1:1
dichloromethane/toluene left behind a small amount (~0.05 g) of an
orange solid which may be a 4:1 PPh3 adduct of Rh2(02CCF3)4 which
precipitated before Rh-Rh bond cleavage could occur. Anal. Caled, for
Rh2c80H60p4F12°8: c> 56.29; H, 3.54. Found: C, 56.12; H, 3.87.
Evaporation of the dichloromethane/toluene extract afforded an orange
solid (0.15 g). This compound is most likely Rh(02CCF3)(PPh3)3. Anal.
Caled, for RhC56H45P3F302: C, 67.07; H, 4.52; P, 9.27. Found: C,
67.86; H, 4.71; P, 9.58. IR (Nujol mull) single vasy(C02) 1678 cm-1
(lit.130 1670 cm-1). Addition of hexane (5 mL) to the filtrate from the
original reaction mixture with cooling led to formation of a yellow
precipitate. Filtration and washing with hexane afforded 0.12 g. This
compound is most likely Rh(02CCF3)3(PPh3)2. Anal. Caled, for
RhC42H30P2Fg06: C. 52.19; H. 3.13; P, 6.41. Found: C, 51.95; H. 3.10;
P, 6.12. IR (Nujol mull) vasy(C02), 1710 cm-1. When the above
procedure was repeated without rigorous exclusion of air, the reaction

121
proceeded in qualitatively the same manner, but 0PPh3 was isolated
(checked by IR and elemental analysis) and the products gave less
satisfactory analyses presumably due to 0PPh3 coordination or possible
side reactions.
Reaction of Rh^lO^CCF^)^ with excess PtOMe)^
Rh2(02CCF3)4 (0.169 g, 0.256 mmol) was dissolved in toluene (3
mL). Trimethyl phosphite (0.30 mL, 2.54 mmol) was added dropwise to
this solution. A red-brown solution initially resulted, presumably due
to axial adduct formation. The reaction was fairly exothermic. After 1
h the solution had turned yellow with formation of a pure yellow
precipitate. Addition of hexane (2 mL) with cooling followed by
filtration and washing with hexane afforded a pale yellow solid (0.30
g). Anal. Caled, for RhC13K27P3F6013: C, 22.27; H, 3.88; P, 13.25;
mol. wt., 701. Found: C, 22.50; H, 3.98; P, 13.40; mol. wt., 698 (in
ch2ci2).
Experimental Methods
Elemental analyses were performed by the Microanalytical Laboratory
of the University of Illinois, Urbana, IL. Fourier transform NMR
spectra were recorded on a Nicolet Technology Corp. NT-360 spectrometer
operating at 338.6 MHz for 19F and 360.1 MHZ for 3H NMR spectra.
All 19F chemical shifts are with respect to internal CFC13 and all *H
chemical shifts are with respect to internal TMS. 31P{1H} NMR spectra
were recorded either on a Varian Associates XL-100 FT spectrometer
operating at 40.5 MHz or on a Nicolet NT-300 spectrometer at 121.5
MHz. For the former instrument, samples were 1n 12 mm tubes with
O I
the J1P chemical shifts previously set relative to 85" phosphoric

122
acid. For the latter instrument, samples were in 5 mm tubes coaxial in
12 mm tubes containing trimethyl phosphite in chloroform-d_ as a 31P
chemical shift reference. However, all 31P chemical shifts are reported
with respect to 85? phosphoric acid. Phosphorus chemical shifts for
reference were taken from the literature.141 Infrared spectra were
recorded on a Nicolet 7900 FTIR spectrometer for the CHC13 solutions and
on a Perkin-Elmer 5998 instrument for the Nujol mulls. The assistance
of the staff of the Molecular Spectroscopy Laboratory, University of
Illinois and of Professor Wallace Brey and Mr. James Rocca, both of the
Department of Chemistry, University of Florida, is appreciated.

CHAPTER IV
SPECTROSCOPIC AND BONDING STUDIES OF
RHODIUM CARBOXYLATE DIMER CATION RADICALS
Introduction
The qualitative MO scheme used in the previous two chapters was
quite successful at explaining some general results obtained therein.
Furthermore, this MO scheme has been used successfully to interpret
quantitative results obtained from calorimetric studies of Lewis base
binding to metal carboxylate dimers.23-25 jhis scheme has been helpful
in understanding electrochemical data on the rhodium system.
Electrochemical studies by Drago and co-workers23*24 and Bear and co¬
workers40 demonstrated that Rh2(02CR>4 species are easier to oxidize
when strong donors such as pyridine and ÃœMS0 are present. The stronger
the rhodium-Lewis base a-bond, the higher in energy become the metal
non-bondinq electrons. This allows easier oxidation of the metal dimer,
since electrons are removed from these orbitals, lihen there is a *-
backbondinq interaction between the metal and Lewis base, the metal
anti-bonding orbitals are lowered in energy. This stablization
increases the electrochemical potential for oxidation. Carboxylate
ligand effects are also Important. With the electron withdrawing
fluorocarboxvlate ligand the rhodium dimer is virtually impossible to
oxidize. There is some controversy as to the specific orbitals Involved
in this oxidation as will be discussed below. This qualitative MO scheme
has also been used to explain UV-visible absorption125 and EPP,
123

124
spectra133 observed for [Rh2(02CR)4B2]+ species generated either
electrochemical!;/ or by y-ray irridiation. The chemical oxidation of
the rhodium dimer and some UV-visible studies are described here.
A number of theoretical studies have also been made on the metal
carboxyl ate dimer. An MO scheme drawn from the calculations of Norman
and co-workers^ using the SCF-Xa scattered wave method is shown in
Figure 4-1. This is the MO scheme they propose for the rhodium and
ruthenium carboxlate dimers. The scheme differs for the molybdenum and
rhenium (or technetium) dimers in that the 6* orbital is lower in energy
than the degenerate ir* orbitals. It is proposed that this occurs
because the fi* orbital has significant carboxyl ate character while the
it* orbitals are primarily metal based. Thus, for the less
electronegative earlier transition metals such as molybdenum and
rhenium, the metal only orbitals (such as n*) are relatively higher in
energy while for the more electronegative later transition metals such
as ruthenium and rhodium, these metal only orbitals are lower in
energy. However, the 6* orbital remains relatively constant in energy
on going from Mo to Rh since the carboxylate ligands, which make a large
contribution to this orbital, do not change. Naturally, for the ligand
free M2n+ system, 5* is always lower in energy than it*. This change in
the relative energies of 6* and it* most likely occurs, but it is not
clear that a reversal occurs. As will be discussed below, it is
possible that it* is always above 5*. The above discussion of MO schemes
does not include the effect of axial Lewis base coordination. A
qualitative MO scheme which takes into account this effect is shown in
Figure 4-2. The results of interaction between Rh2(02CR)4 and two types
of Lewis bases (B) are shown. The interaction between the two Lewis

big ,b2u,eg
a ,tt
J2U
} dx2y2, dxy
dz2
M - 0
M - M a*
h...
dxv
M -M
s4
p ~
dxz. vz
M- M
77r*
y
b,„
dxy
M - M
s
—
dxz,yz
M-0
77
eu
dxz.yz
M-M
77
aig ia2u,
b?u |b|U . big
—
| dxy,dx2-y2,dz2
M-0
a ,77
n. „
dz2
M- M
a
'y
D4h level
M2(02CR)4
M d orbital
orbital
type
basis function
Figure 4-1. MO scheme for metal carboxylate dimers based on calculations by Norman
44
and co-workers. Energy spacings are not to scale.

126
major
04hlev/el contribution abbreviation
°2U i
f Rh -
Rha‘,1
cr* (Rh)
- a*
[Rh-
Bo-* J
eg
Rh-
Rhv*
M
IT*
1
=»=
- cr3
: 7r*
^2U
Rh-
RhS"
-Ml—
S'
Mi-
- 8*
a,n J
^Rh-
Rhcr]
—H—
a, (Rh,B)
19 1
.Rh -
Bcr’J
t>ig
Rh-
Rh 8
MM
s
M-
- 8
eu
Rh-
Rh 77"
7T
_ IT
°2U |
rRh-
LRh -
Rh cr*A
B a J
—4V—
a2 (B)
Oig -j
f Rh -
iRh -
Rhcr,].
Bcr J
MM
a] (Rh)
11
Mt-
1 1
[Rh2(but)4B2] +
[Rh2(but)4B^+
B = 0-
donor
I
Q_
II
GO
donor
Figure 4-2.
. MO
1 scheme
for Rhgibut)^
+ with two types
of
axially coordinated Lewis bases: an oxygen
(weak) donor and a phosphorus (strong) donor.

127
base lone pair orbitals and the Rh-Rh o and o* orbitals leads to four
molecular orbitals. These are represented as cr^ which is lowest in
energy and is Rh-Rh and Rh-B a in character, c>2 which is Rh-Rh a* and
Rh-B, 03 which is Rh-Rh a and Rh-B a* in character and the a* anti¬
bonding orbital which is Rh-Rh and Rh-B a* in character. With weaker
donor bases such as oxygen donors, the base lone pair orbital is lower
in energy, so the rhodium-Lewis base Interaction is not as strong and o2
and c3 are relatively close in energy with 03 well below S* and it*.
With strong donors with higher energy lone pairs, such as phosphorus
bases, the rhodium-Lewis base interaction is strong. The result is that
o2 is low In energy and its anti-bonding counterpart, o3, is high in
energy, above 6* and tt*. This gives a different HOMO for Rh2(02CR)4
with strong donors than with weak or no axial bases. The LUMO in all of
these neutral complexes is a*, but the HOMO is 03 in the former case and
5* or ti in the latter cases. When these species are oxidized, the
resulting unpaired electron is in these different HOMO'S (or SOMO's for
semi-occupied molecular orbitals). Thus, with strong donors the
electronic ground state is and w-jth weak donors
al2a22'J^s^s*^a3^1’*^' This 1eacls quite different EPR behavior as will
be shown below.
More recent calculations have lead to conclusions at variance with
above MO scheme. Using ab_ initi0 methods, Nakatsuji and co-workers47
proposed that [Rh2(02CH)4B2]+ where B=H20 or PH3 both have an electronic
ground state represented by (o2)0252Tt4Tr*46*2a1 , while [Rh2(02CH)4
2 2 4 4 1
with no axial Lewis bases has a a J 1 1* S* ground state. Using this
proposal, the complexes represented as [Rh2(02CR)4(0-donor )2]+ and
[Rh2(02CR)4
128
with the unpaired electron in o3 in both cases. This is somewhat
surprising and is in conflict with experimental results.
Results and Discussion
Chemical and UV-Visible Spectroscopic Studies
As originally reported by Wilson and Taube,52 it is possible to
chemically oxidize the rhodium carboxylate dimer. Chlorine gas, lead
dioxide or Ce(IV)(aq) all convert blue-green aqueous solutions of
Rh2(02CCH3)4 to orange solutions of Rh2(O2CCH3)4+. Magnetic
susceptibility by the Evans method gave ueff=2.1 ± 0.4 per mole of Rh
dimer, indicating one unpaired electron. The workers also isolated a
solid from the oxidation product, but it was found to be unstable,
reverting to Rh2(02CCH3)4 and a Rh(III) product. The chemical oxidation
of Rh2(02CR)4 where R=CH3 and CH3CH2CH2 was investigated here in organic
solvents for comparison to the aqueous solution work and 1n the hope
that it would be possible to isolate a more stable Rh2(II,III) species
in this manner. Solutions of Rh2(02CCH3)4 and Rh2(but)4 in both ethanol
and acetonitrile were oxidized by Cl2 and Ce(IV). These orange
solutions of Rh2(02CR)4+ were generated by bubbling through chlorine gas
or by addition of one equivalent of (NH4)Ce(N03)g and are stable for
about one hour. Unfortunately, a stable Rh2(02CR)4+ complex could not
be obtained using ethanol or acetonitrile with either the acetate or _n_-
butyrate. Some orange-brown solids similar to that described by Wilson
and Taube52 were obtained from these solutions, but they were not
indefinitely stable. Nevertheless, the Rh2(II,III) species can be
generated in solution relatively easily and used in spectroscopic
studies. These workers also reported52 the UY-visible spectrum of

129
Rr^tC^CCHj^ and its cation radical, both in aqueous solution. Bands
were seen at 585 (e=106) for the neutral complex. The UV-visible
spectra of this complex in ethanol and acetonitrile were obtained here
and are shown in Figures 4-3A and 4-4A, respectively. Bands were
observed at 580 (e=l56) and 430 nm (e=75) in ethanol and at 543 (e=233)
and 430 nm (e=129) in acetonitrile. As discussed in Chapter II, these
bands have been assigned to (Rh-Rh)** + (Rh-Rh)a* and (Rh-Rh)it* + (Rh—
0)o* transitions, respectively.63 The band at longer wavelength is more
strongly affected by solvent since it involves a transition to an
orbital that contributes greatly to axial Lewis base bonding, while the
shorter wavelength band involves orbitals that are relatively less
affected by axial base coordination. The band at -580 nm in ethanol and
water is at much lower wavelength in acetonitrile. This is due to ir-
backbonding from the Rh-Rh tt* orbitals lowering their energy. These
effects have been discussed 1n detail elsewhere.23-26 Wilson and
Taube52 reported that oxidation of rhodium acetate by Ce(IV) in 1 M
CF3SO3H gave bands at 758 (e=330), 515 (e=316) and 217 nm (e=1.19 x
104). The results obtained here in ethanol solvent are in good
agreement with those in aqueous solution. As shown in Figure 4-3B,
bands were observed at 785 (e=191) and 510 nm (e=120). A large band at
-300 nm includes Ce(III). In acetonitrile, as shown in Figure 4-4B,
bands were seen at 815 (e=25) and 530 nm (e=180) as well as the large
band extending into the UV region. It is proposed44 that the band in
[Rh2(02CR)4l+ at -500 nm corresponds to the (Rh-Rh)ir* (Rh-Rh)o*
transition and the band extending into the ultraviolet region is due to
the (Rh-Rh)ir* + (Rh-O)o* transition. This shift to higher energy is the
result of oxidation. What is of interest is that the shift observed in

Figure 4-3. UV-visible absorption spectra of Rh2(02CCH3)4 in ethanol (1.99 x 10'3 M) with:
(A) no oxidizing agent; (B) 1 equivalent of Ce(IV).

Figure 4-
UV-visibie absorption spectrum of Rh2(OgCCHg)^
(2.17 x 10 ^ m) with: (A) no oxidizing agent;
of Ce(IV).
in acetonitrile
(B) 1 equivalent

132
400 4 50 500 550 600 650 700 7 50 800

133
acetonitrile solvent is very small compared to the other solvents. This
may be the result of m-backbonding effects. Neutral
Rh2(O2CCH3)4(CH3CN)2 has more n-backbonding than the corresponding
cation since in the latter there is less n* electron density to
backbond. This decrease in backbonding raises it* narrowing the energy
gap between n* and 0* in the cation relative to the neutral complex.
This compensates to some extent for the shift to higher energy
transitions caused by oxidation. The last transition seen, that at the
longest wavelength, does not occur in the neutral complex and based on
MO calculations has been assigned to a {Rh-Rh) 6 + (Rh-Rh) 5*
transition. This is a z-dipole allowed transition in D4h symmetry. It
could occur if the unpaired electron were in a 6* orbital. This would
be the case if 6* were higher in energy than u*. The opposite ordering
may exist. Then the unpaired electron would be in it* and the transition
could be (Rh-Rh)u -*■ (Rn—Rh)tt*. This is an x,y-dipole allowed transition
in D^f,. The energy of this transition would be affected by axial base
coordination since these orbitals are involved in base binding. In
contrast, i + s* would be completely unaffected by the axial base since
these orbitals are not at all involved in base binding. This could
explain why in acetonitrile the transition occurs at lower energy and
lesser intensity than in ethanol or water. Backbonding with
acetonitrile lowers the n* orbital energy relative to that in solvents
incapable of this interaction. The above discussion is based on an
earlier study®2 of the UV-visible spectrum of rhodium acetate. Gray and
co-workers142 have very recently reinvestigated the polarized electronic
spectrum of this compound and disagree with the previous study. These
workers have reassigned the band at -580 nm to a (Rh-Rh)ir* + (Rh-O)a*

134
transition and that at ~450 nm to a (Rh-O)r + (Rn-O)o* transition.142
This is surprising since the band at -530 nm is very sensitive to axial
and not to equatorial ligation while the band at -450 nm is sensitive to
equatorial and not axial coordination. As discussed in Chapter II,
these results would be expected based on the earlier62 assignment.
Since the Rh-Rh n* M0‘s are involved in axial base binding, it 1s
possible that the 580 nm band would be sensitive to axial base even
though it might not Involve a transition to a Rh-Rh a* orbital.
Furthermore, the u-backbonding argument given above to explain the shift
of this band upon oxidation would still be valid. Nevertheless, it
appears that assignment of the electronic transitions of the rhodium
carboxylate dimer is not yet certain. If single crystal polarized
electronic absorption spectra could be obtained for a Rh2(02CR)4+
species and for various Ri^iOgCR)^ complexes, then perhaps the
transitions could be assigned with greater certainty.
EPR Studies
EPR spectra for several metal carboxylate dimers have been
observed.35-39,133 In some cases the diamagnetic dimer can be converted
to an S=l/2 system electrochemically or by chemical oxidation as
discussed in the previous section. The EPR spectra of these
paramagnetic dimers provide much information regarding their electronic
structure. Of relevance here are the studies by Kawamura and co¬
workers133 on [Rh2(02CR)4B2]+ species where B=various phosphorus
donors. These workers generated cationic rhodium dimers using
electrochemical and y-ray irradiation methods. It was attempted here to
study the EPR spectra of these species generated by simpler, chemical
means such as chlorine oxidation. Unfortunately, EPR spectra could not

135
be observed for any [Rt^^CR^]4 systems although the UV-visible
absorption spectra indicated oxidation had occurred. Thus, all EPR
spectra had to be obtained by electrochemical methods. Furthermore,
spectra were only obtained when the electrochemical cell was active.
Possible reasons for this difficulty of obtaining spectra are
aggregation of the cation radicals or O2 binding to the rhodium
complexes. Dioxygen binding to Rh24+(aq) has been proposed51 to give
C(H20)gRh-O-O-Rh(H20)534+ although no dioxygen bridged rhodium dimer has
been isolated. Such complexes are known for cobalt.145 Although
attempts were made to keep out 02, some was not doubt inevitably
present.
EPR spectra were observed for [Ri^fbut^E^^ only when
B=triphenylphosphine (PPhj), pyridine (pyr) and N-methylimidazole (N-
Melm). The spectra observed for the first two complexes are shown in
Figures 4-5 and 4-6, respectively. These particular spectra were
obtained by Mr. Richard Cosmano using an electrochemical cell designed
by him. The complexes were in CH2C12 solution with (n^-Bul^NBF^ as the
supporting electrolyte. Computer simulations using a program for powder
pattern spectra144 are given below the experimental spectra. The
simulations were performed by treating the Rh25+ unit as an S=l/2, 1=1
system since there are two equivalent rhodium nuclei with one isotope
(105Rh, 1=1/2, un=0.0884, 1002 natural abundance). Superhyperfine
interactions from two equivalent phosphorus nuclei were included (51P,
1=1/2, 1002 natural abundance). In the pyridine adduct, nitrogen
superhyperfine was not resolved and was not included in the
simulations. The parameters obtained from these simulations are given
in Table 4-1. The parameters obtained for the PPh3 adduct, assuming

Table 4-1. Parameters Obtained from Computer Simulation of Frozen Solution EPR Spectra of RhgiOgCR^B,,
Systems
Reference
133
-CH2CH3 PPh3 1.996
ftRh3 A6" A03
2.148 13
205
152
This Work
-CH2CH2CH3 PPh3 1.998
2.147
202
150
This Work
-CH2CH2CH3 pyr 2.095 1.990 2.027
avalues in x 10 ^ cm *
not resolved
co

Figure 4-5. Upper trace: EPR spectrum of Rh2(but)4(PPh3)2+ in CHgCi2 (~1 x 10~3 M) in
active electrochemical cell at 77 K. Instrumental parameters are as follows:
Frequency, 9.10494 GHz; Power, 2 mW; Gain, 4.0 x 103; Modulation Amplitude,
5 G; Time Constant, 0.30 sec; Scan Time, 8 min.
Lower trace: Computer simulation of the above using S=l/2, I,=l (Rh9), I„=l Í2P),
g|(=1.998, gi=2.147, k-SQ =20 MHz, A„ =605 MHz, A^=450 MHz. Single molecule
spectra with Lorentzian linewidths (half-width at half-height) of 40 MHz were
added for every step of 4.0 degrees in the polar angle 0.


Figure 4-6. Upper trace: EPR spectrum of Rl^but^tpyr^ in CH^Cl^ (~1 x 10"3 M)
in active electrochemical cell at 77 K. Instrumental parameters are as
in Figure 4-5 except: Frequency, 9.10554 GHz-, Gain, 2.0 x 103.
Lower trace: Computer simulation of the above using S=l/2, 1=0, gx=1.990,
gy=2.027, gz=2.095. Single molecule spectra with Lorentzian linewidths
(hwhh) of 35 MHz in the x and y directions and 45 MHz in the z direction
were added for every step of 6.0 degrees in the polar angle 0.

2800.0G
3200. OG
3500. OG

141
perfect axial symmetry, are g)( =1.998, g^=2.147, Afíp=202 x 10"4 cm"1,
Aj_ p=150 x 10"4 cm-1 and A^S0Rfl=7 x 10"4 cm"1. The value obtained for
the rhodium hyperfine is very approximate. It is an upper limit based
on the observed linewidths {40 MHz, hwhh). The EPR parameters obtained
here are identical, within experimental error, to those reported by
Kawamura and co-workers133 for Rh2(02CCH2CH3)4(PPh3)4+. Their values
were g(( =1.996, g¿=2.148, A Rfl=13 x 10"4 cm"1 and was not resolved.
The MO scheme given in Figure 4-2 can be used to explain the EPR
spectra observed for the PPh3 adduct. In this complex, since the axial
base is a strong donor, the a3 orbital is high in energy and lies
above 6* and it*. Thus, the unpaired electron generated by oxidation is
in this orbital. Since o3 is a non-degenerate orbital, g values close
to the free electron value (ge=2.0023) are expected. However,
contributions from excited electronic states can mix in orbital momentum
effects which would give deviations from the free electron g value.
Only states of the proper symmetry can contribute. Assuming idealized
D4tl symmetry in the dimer, only electronic states with a2g symmetry can
contribute to g^ since a3 has a3g symmetry and the z angular momentum
operator, Lz, transforms as a a2g in D4tl (only alg x a2g x a2g contains
aig), Only electronic states with eg symmetry can contribute to g^
since the x,y angular momentum operator, Lx>y, transforms as eg in 04h
(only a^g x eg x eg contains a^g). Using Figure 4-1, it can be seen
that no electronic states have a2g symmetry so g)( =gft. However, states
involving electron promotion from the degenerate â– ** orbitals which have
eg symmetry can contribute to shift g^ from ge. Since the tt* orbitals
are filled, a positive shift is observed. The phosphorus hyperfine

142
coupling constants support this assignment of the unpaired electron
being in a a type orbital. Values of A1-S0=(A^+2A_¿) (1/3)=502 MHz and
Ad1-p=(Ay/-Aj_)(l/3)=52 MHz were observed. These can be compared to the
values that would result in a system in which all the spin were
localized on two equivalent sp3 hybridized phosphorus orbitals. Using
the tabulated145*146 atomic parameters, A1-SO=(13306)(l/2)=6653 MHz and
Adip=(áp)(P)(1/2)=(2/5)(917.0)(l/2)=183.4 MHz. Thus, a phosphorus s
orbital contribution of (502/6653)=7.54% and a p orbital contribution of
(52/183.4)=28.17% is indicated. The ratio of these is 3.74:1 (p:s)
versus 3:1 for true sp3 hybridization. The above calculations indicate
a substantial spin density on the phosphorus ligands, specifically on a
phosphorus orbital which is largely of sp3 hybridization. The
additional p spin density, manifested by the large anisotropy in Ap,
most likely arises from phosphorus-rhodium ¥ interactions. Thus, the
EPR parameters for [Rh2(but)4(PPh3)2]+ as well as those of related
complexes133 are in agreement with the MO scheme shown in Figure 4-2.
However, the EPR results for the adducts with the strong nitrogen
donors pyridine and M-methylimidazole cannot be easily explained since
rhombic spectra were observed. Values of gx=1.990, gy=2.027, and
gz=2.095 were obtained for the pyridine adduct. No rhodium or nitrogen
hyperfine could be detected. However, the different linewidths
(Wx=Wy=35 Hz and Vlz=45 Hz, hwhh) may indicate unresolved anisotropic
hyperfine interactions. The positive shift of gz from ge and large
difference between gx and gy indicate that the pyridine adduct is very
different from the phosphine complexes. This deviation from axial
symmetry is most likely the result of Lewis base coordination to

143
equatorial sites on the rhodium dimer as was observed with Rh2 (02CCF-j )4
as discussed in the previous chapter.
No EPR spectra were observed at 77 K for Rh2(but)4+ alone or with
any weak donors such as methanol or acetonitrile. This can be easily
explained using the MO scheme in Figure 4-2. In Rh2(but)4+ or
[Rh2(but)4B2]+ where B 1s a weak donor, the Rh-B Interaction 1s low in
energy and lies below the 5* and n* orbitals. Thus, the unpaired
electron is in a degenerate pair of tt* orbitals. This leads to a great
deal of spin orbit coupling which causes fast electron spin relaxation,
preventing observation of an EPR spectrum. In contrast, the
theorectical results of Nakatsuji and co-workers4^ would predict
similar, and easily observable, EPR spectra for both [Rh2(02CR)4(PR3)2]+
and [Rh2(02CR)4(R0H)2]+ since they claim that both have a tt*^5*2o-1
electronic ground state. This clearly cannot be the case. It is also
unlikely that the unpaired electron is in the 5* orbital. The
theoretical results of Norman and co-workers44 would suggest this.
Their MO scheme, as shown in Figure 4-1, places &* slightly above n* in
energy. Thus, oxidation would lead to a tt*46*^ electronic ground state
for Rh2(but>4+ alone or with weak donors. (Their predictions for the
rhodium dimer with strong donors are the same as in the qualitative
scheme shown in Figure 4-2 in which the unpaired electron is in a o-type
orbital). If the unpaired electron were indeed in the non-degenerate 5*
orbital, then the EPR spectrum would be observed. For example, in
electrochemical ly generated Mo2(but)4+ an EPR spectrum with g(|=g^=1.941
was observed in CH2C12 at 77 K.38 In this complex the unpaired electron
is undoubtedly in a 6 orbital. This g value less than ge is to be
expected since excited states involving transitions to empty (Mo-O)a*

144
and (Mo-Mo) tt* orbitals are of the proper symmetry to affect g and g ,
respectively. These transitions are of b^g and eg symmetry,
respectively and 5 is of b2g symmetry, all in D^. Similarly,
Re2(02CCgH5)4Cl2 was electrochemically reduced to a Re2(II,III) species
whose EPR spectrum in CH2C12 at 77 K gave g^ =1-713 and gJ>=2.136.3® In
this case, with a 5*1 electronic ground state which has b1(J symmetry,
transitions involving empty (Re-O)c* and filled (Re-Re)u orbitals are of
the property symmetry (b2u and eu, respectively) to affect g;/ and g^,
respectively. This leads to a negative shift in gff and a positive shift
in gj^. Based on this extensive evidence, it appears that if the
unpaired electron were indeed in a 5* orbital, an EPR spectrum similar
to that seen for the rhenium complex would be observed. Since this was
not the case, S* must be either below or equal in energy to the m*
orbitals. Further support for this proposal will be given in the
following chapter in discussing the Ru2(02CCR)4+ system.
Conclusion
Rhodium alkyl carboxyl ate dimers can be easily oxidized using
chemical oxidizing agents such as Cl2 or Ce(IV) or by electrochemical
methods to give formally Rh2(II,III) species. The UV-visible absorption
spectrum of the resulting cation can be interpreted using a metal-metal
bonding MO scheme. The effects of different solvents, which can axially
coordinate to the dimer, can be seen in the UV-visible spectrum of the
cation as well as the neutral dimer. These lend support to a ir-
backbonding interaction between rhodium and Lewis bases such as
acetonitrile. EPR spectra for these cations can only be observed in
active electrochemical cells and not in chemically generated species

145
although they have the same UV-visible spectrum. This suggests an
aggregation or dioxygen binding mechanism may be occurring. The EPR
spectra that are observed for the rhodium dimer with phosphorus donors
can be explained using the same MO scheme. No EPR spectra are observed
for Rh2(but)4+ with weak or no donors since the unpaired electron spin
density is 1n degenerate Rh-Rh it* orbitals. Theoretical studies47 that
propose identical electronic configurations for Rh2(02CR)4+ with both
weak and strong donors are not in agreement with the experimental
results. Furthermore, in contrast to other calculations,44 it is
unlikely that the unpaired electron 1s in a 5* rather than n* orbital.
If this were so, then an EPR spectrum for Rh2(but)4+ would be observed
as seen38,39 with other metal carboxylate dimer complexes with unpaired
electrons in 5 or 5* orbitals.
Experimental Section
Synthesis
RhgiC^CCHj^, Rh2(but)4, and Rh2(but)4(PPh3)2 were synthesized as
described in Chapters II and III. The other rhodium species were
generated in solution by addition of stoichiometric amounts of the
appropriate Lewis base to the rhodium dimer. Solvents (all reagent
grade) and bases were distilled before use.
Experimental Methods
UV-v1s1ble spectra were recorded on a Cary 14 spectrometer using
matched quartz 1.0 cm cells. Electrochemical procedures are described
in detail elsewhere.23,25 A PAR Model 173 potentiostat/galvanostat and
a PAR Model 176 current-to-voltage converter were used. An
electrochemical cell designed by Mr. Richard Cosmano was used.

146
Electrochemical solutions for EPR spectroscopy were ~1 x 10“^ M in
rhodium dimer and 0.1 in (jt_-Bu)4NBF4 in CH2C12. The reference cell
consisted of a silver wire in a solution which was 0.42 in (_rr-Bu)4NBF4
and 0.05 1n (jt_—Bu)4NI in CH2C12 saturated with Agl. A potential ~200
mV more positive than the redox couple involved was applied. During
this process, EPR spectra could be observed. EPR spectra were recorded
on a Yarian E-9 X-band instrument. Computer simulations of the EPR
spectra were performed using the program QPOW.144 A copy of the program
is given in Appendix E. In the simulations done here, the frame of
reference was chosen so that the g tensor was diagonal and the A tensor
was held in the same orientation as the g tensor. The nuclear g tensor
was approximated as a Isotropic gN=uN/I.

CHAPTER V
SPECTROSCOPIC AflO REACTIVITY STUDIES
OF RUTHENIUM BUTYRATE CHLORIDE
Introduction
As discussed earlier, almost all of the known metal-metal bonded
complexes have an even number of d electrons. Although, as was shown in
Chapter IV, it is possible to chemically or electrochemically generate
paramagnetic metal-metal bonded complexes, thus containing an odd number
of d electrons, and these species are often reasonably stable in
solution. Nevertheless, normal synthetic procedure leads to even d
electron metal carboxylate dimers for transition metals such as
chromium, copper, molybdenum, tungsten, technetium, and rhenium.
However, as was first discovered a number of years ago by Stephenson and
Wilkinson,48 when RuCl3(H20)x is reacted with carboxylic acids a
paramagnetic, odd d electron dimer of formula Ru2(02CR)4C1 results.
This is formally a Ru2(II.III) complex.
The electronic structure of this complex was originally explained
using the MO scheme applied to other metal-metal bonded dimers. The
eleven d electrons fill the a, 5, and ir bonding orbitals and half fill
the 5* and n* antibonding orbitals. This gives a net Ru-Ru bond order
of 2.5. A simplified version of this MO scheme is shown in Figure 5-1.
Structural studies on Ru2(but)4Cl*4^ and other Ru2(02CR)4+
derivatives*48 indicate that the two Ru atoms are crystallographically
equivalent. Furthermore, a report by Cotton and Pedersen36 of the
147

Figure 5-1. Qualitative MO scheme for metal-metal bonding
in Ru2(02CR)4+.

149
8 —H-
7T

150
magnetic properties and EPR spectra of Ri^ibut^Cl gave no support to a
localized Ru2(11,111) system. Evidence was found to support the
description of Ru2(but)4C1 as an S=3/2 rather than S=l/2 system with the
three unpaired electrons delocalized over both ruthenium atoms.
Scattered-wave Xa calculations have been performed44 on the Ru2(OgCH)4+
species and they support this description of the electronic structure of
the ruthenium carboxylate dimer. Qualitatively, the reason for this
complex being a quartet rather than a doublet system is the stability of
a half filled set of degenerate orbitals relative to other
configurations. This is due to electron exchange interactions. Thus,
the lowest energy configuration is for the 6* and degenerate ** orbitals
to be half filled, since the 6* orbital is very close in energy to
the it* orbitals. In the calculations by Norman and co-workers,44 S*
was proposed to be slightly higher in energy than n*, but as discussed
in the previous chapter, 1t Is difficult to confirm this experimentally.
If the 6* orbital were indeed higher in energy than tt*. it might be
possible to prepare a Ru2(III,III) carboxylate dimer which would then
have a Ru-Ru bond order of three and half filled tt* orbitals. Such a
complex might be even more stable than the Ru2(II,III) dimer since 1t
would have a stronger Ru-Ru bond and have Ru in a higher formal
oxidation state. However, no such species has been reported and it
appears that the RugUI.IH) complex cannot be oxidized without
decomposition. In summary, the Ru-Ru 5* and tt* orbitals are close in
energy with the relative ordering and energy difference uncertain.
Nevertheless, this MO scheme has been used with success to explain
resonance Raman44® and single crystal polarized UV-visible spectra4®*4 of
Ru2(02CR)4+ species. In order to further understanding of this

151
interesting complex it was decided to examine the magnetic properties of
Ru2(but)4Cl over the temperature range from 5 to 300 K. The original
measurements were made only over the 60-300 K range.36 In many cases,
magnetic susceptibility measurements are necessary at low temperature to
observe deviations from normal Curie-Weiss law behavior. It was also
decided to repeat the EPR study since due to a poor signal-to-noise
level 1n the original EPR experiments, a complete spectrum was not
obtained and the conclusions are open to question. Complete solution
EPR spectra of Ru^butJ^Cl and some derivatives thereof were obtained at
4 K. Far IR absorption spectra for the complex in the solid state at
room temperature were also obtained.
Another area of Interest with the ruthenium carboxylate dimer, in
addition to the nature of the Ru-Ru bond, is the extent of electron
delocalization since it is, formally at least, a mixed oxidation state
complex. The well known Creutz-Taube ion,151 [(NHj^RudUtpyrazine)
Ru(III)(NH3)g]6+, and derivatives thereof represent another example of a
formally Ru2(II»IH) complex. This class of compound has been widely
used to study electron transfer for it is possible to greatly vary both
the bridging and non-bridging legands.^ Furthermore, these complexes
can frequently be easily converted to Ru2(11,11) or Ru2(III.III)
species. Thus, there are many different parameters which can be varied
to help in understanding the interaction between the two Ru atoms. By
contrast, much less variation is possible in the ruthenium carboxylate
dimer series. This formally Ru2(II.III) complex has thus far (with one
exception described below) resisted efforts to be either oxidized or
reduced to give stable Ru2(III.III) or Ru2(H,II) species. In addition,
less ligand variation is possible. There is no group between the two Ru

152
atoms and there is less freedom in changing the other ligands so that
the dimer is maintained. In contrast to the large number of rhodium and
molybdenum dimers that are known with other than bridging carboxylate
ligands, there are only two such examples with ruthenium. Mo-Mo bonded
complexes exist with halide and carboxylate ligands and with ligands
such as alkoxides,4,86-88 amides,4 dithiocarboxylates," sulfate,88 and
variously substituted 2-oxy-pridines.158 With rhodium, complexes are
known with 6-methyl-2-oxy pyridine (mhp),8,138 carbonate184 and
HNOCCF3-.42 With ruthenium, a Ru2(11,11) mhp complex has been recently
reported.188 However, it was obtained in only 82 yield. Complexes with
complete trifluoroacetamidate substitution,186 Ru2(HN0CCF3)4C1, and
partial oxalate substitution,187 Ru2(02CCH3)2(C204)2-, have also been
very recently reported. Both complexes have properties which greatly
resemble the carboxylate dimer starting material. Finally, in contrast
to the rhodium or molybdenum carboxylate dimers, the ruthenium dimer is
very prone to decomposition into products no longer having the dimeric
structure. For example, pyridine and triphenylphosphine give adducts of
general formula M2(02CRÍ4B2 with Mo and Rh, but these Lewis bases react
with Ru2 (02CR) ¿J.C1 to give [Ru30{02CR)g(pyr)3]+ and [Ru30(02CR)g
(PPh3)3].188,189 in these trimeric complexes, Ru-Ru bonds exist, but
the complexes in no way resemble the carboxylate dimer starting material
in either structure or type of metal-metal bond. The structure of these
complexes is that of "basic Iron acetate'1 which is well known160 for
Cr(III), Mn(III), Fe(III) and other metals in the 3+ oxidation state.
This trimer also results upon treatment of the dimer with strong acid,32
precluding a study of the type done in Chapter II. Perhaps as a result
of this, the reactivity of the ruthenium carboxylate dimer towards Lewis

153
bases has not been studied as extensively as the analogous rhodium and
molybdenum systems. Some preliminary reactivity studies were performed
on Ru2{but)4C1 and are described below. The work was undertaken in
conjunction with a quantitative calorimetric study161 of the enthalpies
of Lewis base coordination to this representative ruthenium carboxylate
dimer.
Results and Discussion
Magnetic Susceptibility
The magnetic susceptibility of a powder sample of Ru2(but)4Cl was
determined over the temperature range 5-300 K. Most data points were
taken at low temperatures since the magnetic susceptibility of
Ru2(but)4Cl had not been previously reported below 60 K.36 A
diamagnetic correction of -278 x 10-6 cgsu was used, and it is simply
the value obtained from Pascal's constants including the underlying
diamagnetism of Ru(II) and Ru(III).162 Initially, the data were fitted
using a linear least-squares equation to a Curie-Weiss law behavior
curve, l/x=a0+a1T. The points above 35 K fitted well to this
equation. An r2 correlation of 0.99998 was obtained indicating that
more points at high temperatures would not have been needed. The values
obtained form this fit of the high temperature data agree closely with
those reported previously by Cotton and Pedersen.36 These values are
summarized in Table 5-1. The value obtained here for (6.852 x
10-3) is much closer to the solution value obtained from both the Gouy
and Evans methods (6.91 x 10“3) than is the previously reported powder
value (6.74 x 10—3).36 This agreement of the solution and solid state
values is supported by computer simulations that show insignificant

154
Table 5-1.
High Temperature Powder Magnetic Susceptibility
Ru2(but)^Cl
Data on
a a,
o 1
C
0
g
300 ..-3
XM x 10 cgsu
Ref.36
6.6 0.472
2.12
14
2.13
6.74 ±0.03
(60-300K)
This work
(350-300K)
6.984 0.4632
2.16
15.1
2.15
6.91 ±0.05 in solu¬
tions
6.852 ±0.003
Table
5-11.
Parameters obtained from Computer Simulation of
Magnetic Susceptibility Data (Full Temperature
the Models Described in the Text
the Powder
Range) Using
Da
Ja
9fl
9t
q
yavg
, ia ia
zJ// zJx
SEb
Method
lc
76.8
-
2.02
2.14
2.10
. .
.0038
Method
2
57.7
-
3.03
1.96
2.32
-
.13
Method
3
-
â–  .036
-
-
1.93
-
.16
Method
4
65.5
-
2.94
2.01
2.32
1.98 -0.250
.11
Method
5
68.8
.0320
1.50
1.48
1.49
_
.0056
aValues in cm"1 .
bSE, the standard error of estimate, is a measure of the goodness of fit of the
model to the data. (See Reference 181.) SE = (obsd) -
(ue^)1-(calcd)}^/(n-k)]1^ where n is the number of data points and k is the
number of varying parameters.
cThe method of choice (see text). Values are accurate to ±5%.

155
interdimer interactions (vide infra). Thus, at temperatures above 35 K,
Ru2(but}4C1 exhibits normal paramagnetic behavior with a positive Weiss
constant. The data below 35 K did not fit the Curie-Weiss law as well
since high temperature approximations were no longer valid. In order to
correctly explain these data, a full exponential treatment was needed.
Several models are reasonable since in Ru2(but)4Cl there may be both
intramolecular and intermolecular effects. The latter are due to the
polymeric nature of the solid state structure of Ru2(but)4Cl wherein
Ru2(but)4+ units are bridged by chlorides to form approximately an
infinite linear chain.147 Thus, intermolecular antiferromagnetic
exchange between ruthenium dimers is possible. Furthermore, as with all
S > 1/2 systems, zero-field splitting within the S=3/2 ruthenium dimer
is possible, which is an "intramolecular antiferromagnetic" effect.
Therefore, five models were developed in an attempt to separate these
effects and understand the magnetic behavior of Ru2(but)4Cl. These
models (Methods 1-5) are described in detail in the Experimental
Section.
The first two zero-field splitting models (Methods 1 and 2) fit the
data reasonably well. The parameters obtained by computer simulation of
the magnetic data using Method 1 gave the best fit and g values of
g/: =2.02 and g_/_ =2.14 that are in good agreement with those obtained
from the EPR spectra of Ru2(but)4Cl in various solvents (g^ =1.9465 and
g^ =2.200, vide Infra). The experimental and theoretical curves for X[,j
and using Method 1 are shown in Figure 5-2. The parameters
obtained from all the simulations are summarized in Table 5—II. The
value obtained for the zero-field splitting parameter, D, is fairly
large, 77 cm-1. In transition metal complexes, D is dominated by spin-

Figure 5-2. Molar paramagnetic susceptibility and effective magnetic moment per
RugibutJ^Cl molecule versus temperature. The solid line result from
a least-squares fit of the data to the theoretical equation for an
S=3/2 system with axial zero-field splitting (Method 1).

TEMPERATURE (K)
50
40
30
2 0
10
o
2
m
H
o
s
o
2
m
2
—i
Í
zo
c
cn
240
~T“
200
320

158
orbit coupling effects.145 These are expressed as Dsq=£2a where ? is
the spin-orbit coupling constant of the molecule and A is a tensor
containing matrix elements of ground and excited electronic states
connected by the orbital angular momentum operator, L. Using a simple
LCAO-MO approximation, Z depends on z, the atomic spin-orbit coupling
constant which in turn is proportional to Z4, where Z is the atomic
number. In a complex such as ^(but^Cl, one would expect 5 to be
large since there are two ruthenium atoms which have high atomic
numbers. A large value for A would also be expected since ^(but^Cl
has many, closely spaced electronic states. Thus, a large value for D
is not surprising. Few calculations have been performed to
theoretically determine D values145 and [^(but^Cl is no doubt far too
complex. There also are no analogous compounds with which to compare
this value to determine how meaningful it is. Conventional EPR
spectroscopy has been used to measure D for a number of high spin
molecules.145*153 However, commonly used microwave frequencies do not
exceed ~3 cm-1, far too small to determine D in this complex. Magnetic
resonance using far-1nfrared sources which can go up to several hundred
cm”1 would allow an independent measurement of D to compare with the
above value. This method has been used successfully to study
metal!oporphyrins with large zero-field splitting.154 Method 2, the
exponential form for the zero-field susceptibility, fitted the data
well, but gave g)( =3.03, in poor agreement with the EPR data. One would
expect use of the full spin Hamiltonian with the experimental magnetic
field to determine the energy more accurately than the zero-field
exponential model. Thus, Method 2 is qualitatively correct, but Method
1 is quantitatively better.

159
By contrast, use of Method 3, the Ising model, gave a very poor fit
to the data. The experimental and theoretical curves using this model
are shown in Figure 5-3. This model only considers anti ferromagnetic
interactions between S=3/2 units in an infinite linear chain.165 A g^
value of 1.93 was obtained with J=-0.32 cm'1. Since the fit was so
poor, these values have little meaning. In addition, a model was used
which contained the exponential form of the zero-field susceptibility
for an Si=S2=3/2 dimer experiencing magnetic exchange. This dimer
version was less successful than Method 3, giving J=-0,48 cm'1 and
g1-so=1.37 and a poor fit.
Use of Method 4 which contained zJ parameters to include both zero-
field splitting and exchange effects was also unsuccessful. These
parameters did not improve the fit and gave unreasonable values. Method
5, a more exact treatment in which the full spin Hamiltonian for a dimer
of S=3/2 units experiencing both anti ferromagnetic exchange and zero-
field splitting was used. Although the fit was quite good, the
parameters obtained were unrealistic. Values for g^ of 1,50 and g^ of
1.48 were obtained, quite different from the g values determined from
EPR. Values for 0 of 68.8 cm'1 and J of +0.032 cm'1 were also
obtained. This 0 value is not inconsistent with that obtained by Method
1 and the very small, surprisingly positive, J value indicates again
that zero-field splitting and not magnetic exchange interactions are
dominant in Rugibutl^Cl. In an attempt to restrain the fitting
procedure to more reasonable values, Method 5 was repeated holding g
=1.95 and gj_=2.20, the g values obtained from EPR. This gave D=250.0
cm'1 and J=-2.00 cm'1 and a very poor fit. The failure of Method 5 is
not surprising since this model assumes that anti ferromagnetic exchange

Figure 5-3. Molar paramagnetic susceptibility and effective magnetic moment per
Ru2(but)^Cl molecule versus temperature. The solid lines result from
a least-squares fit of the data to the theoretical equation for an
infinite chain of antiferromagnetic exchange coupled S=3/2 units (Ising
model, Method 3).

TEMPERATURE (K)
MAGNETIC SUSCEPTIBILITY (XM)
(2ny/J,3-¡H) 1N3IAI0IAI DI13N9VIAI
191

162
is the dominant term in the spin Hamiltonian, whereas in RugtbutJ^Cl it
is zero-field splitting that is dominant, if not the sole field
independent term in the Hamiltonian. There are of course problems
inherent in applying this dimer model to the polymeric Ru2(but)4Cl.
Also, the validity of the use of the Heisenberg Hamiltonian has recently
been questioned.166 However, it was found that for systems in which the
oxidation states are localized, the Heisenberg Hamiltonian is still
valid. This is most likely the case for Ru2(but)4C1 since the Ru-Ru
units are quite widely separated and the interaction is weak, if it
exists at all.
The conclusion that can be drawn from the magnetic susceptibility
data is that Ru2(but)4Cl, in spite of its polymeric structure, is a
complex in which the Ru2(but)4+ units can be treated as isolated S=3/2
systems. This is in agreement with the crystallographic data. In
Ru2(buHj^Cl the Ru-Cl bond is extremely long, 2.587 A1^ versus 2.35 A
in Ru(III) chloride compelxes,167 indicating a weak interaction. This
is also in agreement with the EPR data as discussed below. The experi¬
mental and calculated values for ^ and ueff are given in Appendix A.
EPR Spectra
The EPR spectrum of Ru2(but)4Cl in various solvent systems was
obtained at liquid helium temperature. Mo spectrum could be observed at
liquid nitrogen temperature, although Cotton and Pedersen36 reported a
broad signal at this temperature. No EPR spectrum was observed for pure
powder Ru2(but)4Cl at 4 K, presumably because of magnetic exchange
interactions leading to fast electron spin relaxation.
The following spin Hamiltonian was used to interpret the EPR
spectra.

163
")/ = SH.g.S + Í.A.S - 3|gH.£N.í + S.D.S
Since the value for D is large (~77 cm-1) only the Ms=±l/2 states are
populated at 4K and the microwave frequency is too small (~0.3 cm-1) to
effect any transitions to the Ms=±3/2 states. Thus, a computer
simulation of the frozen solution spectra could be performed using a
program for powder pattern spectra of S=l/2 systems,144 as was used
in the previous chapter. Ruthenium has five zero-spin nuclei
(96Ru, 98Ru, 100Ru, 102Ru, and 104Ru) and two nuclei with
1=5/2: 99Ru, un=-0.63, 12.72% natural abundance and 101Ru, ^=-0.69,
17.07% natural abundance. The simulations done here treated the 1=5/2
nuclei individually using their own g¡,j values (the same g and A values)
and the two were added in the correct isotopic ratio. The spectrum for
the zero-spin nuclei (including only electronic Zeeman terms) was
determined independently and could then be added to the 1=5/2 spectrum
in the desired ratio. The EPR spectrum of Ru2(but)4Cl in 1:1 toluene/
dichloromethane with 1% v/v acetone is shown in Figure 5-4. The
perpendicular and parallel regions are shown independently on an
expanded scale in Figures 5-5 and 5-6, respectively. The EPR spectrum
of Ru2(but)4Cl in 9:1 methanol/ethanol is shown in Figure 5-7. The
perpendicular and parallel regions are shown on an expanded scale in
Figure 5-8 and 5-9, respectively. Simulations are shown below each
experimental spectrum. The values obtained by computer simulation of
the spectra are given in Table 5-111. The simulations gave g_j_ =4.400
for an S=l/2 system. For an S=3/2 system with D » gSH. one can refer
to effective g values, g^^hv/SH, such that for the H$=±l/2 Kramers
doublet: g({ef^=g¡j and g^eff32gj_[l-(3/16)(g^BH/D)2].145 For D as large

164
Table 5-1II. Parameters Obtained from Computer Simulation of Frozen
Solution EPR Spectra of Ru^but^Cl
9//
9_L
9avg
Aa
Rll
Ai
Ref. 36
2.03
2.18
2.13
9 ± 3 x 10'4
31 x 10'4
(methanol
4.2K, 9.186 GHz)
This work
1.9465
2.200
21.
.7 ±.5 x 10‘4
26.7 ±.5 x 10'4
(1:1 toluene/
CH2C12, 3.4K,
9.4450 GHz)
±.0005
±.001
aValues in cm

o
Figure 5-4. Upper trace: EPR spectrum of (^(butJ^Cl (~1 x 10 M) in 1:1 toluene/
dichloromethane with 1% v/v acetone at 4 K. Instrumental parameters are
as follows: Frequency, 9.4447 GHz; Power, 20 dB; Gain, 6.3 x 103;
Modulation Amplitude, 2 G; Time Constant, 0.2 sec; Scan Time, 200 sec.
Lower trace: Computer simulation of the above using 54.09% S=l/2, 1=0,
=1.9465, g^=4.400 and 45.91% S=l/2, 1=5/2, unchanged g values, A/iRu=65.0
MHz, A_/u=80.0 MHz (43% gN=-0.25, 57% gN=-0.28, A values calculated for
the former). Single molecule spectra with Lorentzian linewidths (hwhh) of
40 MHz in the perpendicular region and 10 MHz in the parallel region were
added for every step of 1.0 degree in the polar angle 0.

1000.0 G
2500.0 G
4000.0 G
/
1
/
r
{

Figure 5-5. Same as Figure 5-4 except showing only the perpendicular region.
Same instrumental parameters except: Frequency, 9.4450 GHz;
3
Gain, 3.2 x 10 . Same computer simulation parameters as in
Figure 5-4.

12 50 O G
17 50.0 G

Figure 5-6. Same as Figure 5-4 except showing only the parallel region. Same
5
instrumental parameters except: Frequency, 9.4516 GHz; Gain, 8 x 10
Time Constant, 2 sec; Seen Time, 500 sec. Same computer simulation
parameters as in Figure 5-4.

3250.0 G
350(j).0 G
3750.0 G
o

Figure 5-7. Upper trace: EPR spectrum of Ru2(but)4Cl (~1 x 10~Z M) in 9:1 methanol/
ethanol at 4 K. Instrumental parameters are as in Figure 5-4 except:
Frequency, 9.4476 GHz; Gain, 5 x 10^.
Lower trace: Computer simulation of the above using the same parameters
as in Figure 5-4 except linewidths are 90 MHz in the perpendicular region.

1000.0G
2500.0 G
4500.0 G
I—*
'-J
ro

Figure 5-8. Same as Figure 5-7 except showing only the perpendicular region. Same
â– 3
instrumental parameters except: Frequency, 9.4477 GHz; Gain, 5 x 10 .
Same computer simulation parameters as in Figure 5-7.

1250.0 G
1750.0 G

Figure 5-9. Same as Figure 5-7 except showing only the parallel region. Same
3
instrumental parameters except: Frequency, 9.4477 GHz; Gain, 4 x 10 .
Same computer simulation parameters as in Figure 5-7.

3250.0 G 3500.0 G 3750.0 G

177
as it is in this complex, g_j_eff=2gj_. Thus, g^=2.200 which is close to
the value of 2.18 obtained by Cotton and Pedersen.36 The value for
of 1.9465 differs from theirs (2.03), but they did not actually observe
the parallel signal at 4 K. The value obtained here for Aj_ was 26.7 x
10-4 cm-1 and for Aj was 21.7 x 10-<* cm-1-. The latter value differs
considerable from the previously reported value of 9 x 10-4 cm-1.
However, the value reported here is based on an observed signal. The
£PR parameters and relative intensities of the zero-spin to 1=5/2
signals were solvent independent. The linewidths did vary somewhat with
solvent. The narrower linewidths in 1:1 toluene/dichloromethane (Wj_=40
MHz and Ww=10 MHz, hwhh) allowed better resolution of the perpendicular
region, but led to extensive noise in the parallel region. The broader
linewidths in 9:1 methanol/ethanol (Wj_=90 MHz and W;/=10 MHz) gave less
noise in the parallel region. The relative intensities of the zero-spin
to 1=5/2 signals in all solvent systems corresponded to 54.09% with 1=0
and 45.91% with 1=5/2. This is the ratio that would be expected for
delocalization over both Ru atoms. For a ruthenium dimer, 42.29% of the
dimers will have two zero-spin nuclei, 41.83% will have one 1=5/2 Ru
nucleus and 8.87% will have two 1=5/2 nuclei. The last type will give a
signal of very low intensity since not only will there be few such
dimers, the transitions will be spread out over 11 lines. The high
nuclear spin species was not considered in the simulations.
Delocalization was proposed36 earlier for Ru2(but)4Cl, but since only a
rather broad signal in the perpendicular region and none in the parallel
region was observed, it could not be claimed with complete certainty.
The observation here of the parallel signal which had much narrower
linewidths and larger hyperfine splittings (in G) than the perpendicular

178
signal allows this delocalization to be unequivocally determined.
Furthermore, in the toluene/dichloromethane glass the perpendicular
linewidths were much narrower than in the previous work. This allowed
the relative intensities in that area of the spectrum to be more clearly
determined. To investigate this delocalization as a function of
solvent, anion and added Lewis bases, other spectra were obtained. A
totally symmetric species, for example, [Ru2(but)4(CH30H)2](CF3S03),
would be expected to contain equivalent Ru atoms, but an asymmetric
species such as Ru2(but)4(B)C1 where B=Lewis base, might not. The
effect of chloride coordination was investigated by generating
[Ru2(but)4(CH30H)2](CF3C03) in solution by addition of one equivalent of
Ag(CF3SO3) to a solution of Ru2(but)4CI in 9:1 methanol/ethanol leading
to precipitation of AgCl. The species in solution is presumably
[Ru2(but)4(CH30H)2](CF3S03) since CF3SO3' is such a poorly coordinating
anion. The EPR spectrum of this species was identical to that obtained
for Ru2(but)4Cl in 9:1 methanol/ethanol Indicating extensive chloride
dissociation in agreement with conductivity results.48,161 The
parameters and relative signal intensities were the same for the CF3SC>3“
species as for Ru2(but)4C1 in 1:1 toluene/dichloromethane with 1% v/v
acetone 1n which the complex exists most likely as Ru2(but)4((CH3)2C0)C1
with axially coordinated acetone and chloride. Acetone, even in excess,
would not be expected to displace chloride in such a low dielectric
constant medium.168 Furthermore, a solution of Ru2(bu't)4C1 in 1:1
toluene/dichloromethane with exactly one equivalent of pyridine present
gave an EPR spectrum similar to that for acetone. In this low
dielectric solvent the predominant species is most likely Ru2(but)4~
(pyr)Cl. The main difference in the EPR spectra occured when the

179
solvent was changed from 1:1 toluene/dichloromethane to 9:1 methanol/
ethanol. The linewidths in the former solvent were narrower because It
forms a better glass and has a lower dielectric constant.
EPR spectroscopy can provide information regarding equivalence of
the Ru atoms. If complete localization of unpaired electron spin
density occurred, one would observe an intensity ratio of 70.21% for the
signal arising from spin on an 1=0 nucleus to 29.79% for that of an
1=5/2 nucleus. As expected, this result was never observed since it is
unreasonable to expect localization to this extent in a strongly metal-
metal bonded complex. Delocalization of unpaired electron spin density
over both metal atoms has been found unequivocally in analogous S=l/2
carboxylate dimers of Mo,37,38 Re,35,3® and Rh,133 as discussed in the
previous chapter. If complete electron delocalization existed, the
relative intensities of the zero-spin to 1=5/2 signals would be 54.09%
to 45.91%. This was the observed result. However, this does not prove
that the two ruthenium atoms are chemically equivalent. For non-
equivalent nuclei, the hyperfine pattern would show different A values
for the chloride-coordinated Ru atom versus the pyridine-coordinated Ru
in Ru^(but)^(pyr)C1. Given the experimental linewidths in the parallel
region of 3.34 x 10”^ cm-3, the difference in A values must be
considerably less than this since only one A value could be resolved.
Thus, the question of the equivalence of electron delocalization over
the Ru atoms cannot be completely answered without the use of
isotopically pure ruthenium. Natural abudance ruthenium is dominated uy
the many zero-spin isotopes which give no information on chemical
equivalence and the low abundance of the two 1=5/2 nuclei makes
resolution of slight changes in A values impossible. In contrast,

130
isotoplcally pure complexes would show either an eleven line spectrum in
a 1:2:3:4:5:6:5:4:3:2:1 pattern if the Ru atoms were exactly equivalent
or a sextet of sextets if they were not. Unfortunately, the high cost
and limited avilability of isotoplcally pure ruthenium makes definitive
work on this matter prohibitive.
Infrared and Raman Spectroscopy
Stephenson and Wilkinson48 reported the Far IR spectrum of
Ru2(02CCH3)4C1. Absorption bands were observed at 403 and 341 cm-1
which they assigned to Ru-0 and Ru-Cl stretching modes, respectively.
The latter is where a metal terminal chloride stretch would normally
occur.169 However, in Ru2(02CR)4C1 the chlorides are bridging with a
very long and thus weak Ru-Cl bond. Therefore, one would expect v(Ru-
C1) to occur at a much lower frequency. For example, the chloride
bridged polymeric complexes N1(pyr)2Cl2170 and Co(pyr)2Cl2171 have v(M-
C1) at 186 and 193 cm'1, respectively. Much later, Clark and Ferris149
performed an extensive resonance Raman study on a series of ruthenium
carboxylate dimers as KC1 pellets. No bands were assigned to a Ru-Cl
stretch. Strong bands assigned to v(Ru-Ru) and v(Ru-O) were observed at
room temperature
at
327.3 and
369.2 cm-1,
respectively
for
Ru2(02CCH2 )4C1 and
at
330.8 and
376.5 cm'1,
respectively
for
Ru2(but) 4C1. These
Ru-
Ru and Ru-0
bands have a^g
symmetry in D4tl
and
are thus Raman allowed and IR forbidden. A large number of progressions
of these bands was also seen. The Far IR spectrum of Ru2(but)4Cl was
obtained here as a Csl pellet and is shown in Figure 5-10. A strong
band at 195 cm"1 was observed. This band is very likely v(Ru-Cl) due to
its intensity and low frequency. A strong band was also seen at 460 cm'
1 which could be the asymmetric Ru-0 stretch with a2u symmetry in D4H.

Figure 5-10. Far IR spectrum of Ru2(but)4Cl as a Csl pellet (1% w/w) using 1024 scans
with the background subtracted.

100
80
60
40
20
0
100 200 300 400 500
cm

183
Medium bands were observed at 342 and 375 cm-1. The assignment of these
bands is uncertain. The former is analogous to the band at 341 cm'*
reported for . It is conceivable that distortions from
idealized D4f) symmetry occur on the fast IR time scale that are averaged
out using the much slower method of x-ray crystallography. These
distortions could lower the symmetry allowing observation of the
normally IR forbidden alg modes. Due to Instrumental difficulties, it
was not possible to obtain a good Raman spectrum of Ru2(but)4C1 for
comparison to previous work. A low resolution Raman spectrum of
Ru2(but)4Cl in methanol solution showed a broad band at 360 cm'* which
presumably arose from the v(Ru-Ru) and v>{Ru—0) vibrations. No band
was observed at ~200 cm'* since Ru2(but)4Cl ionizes in methanol.
MO Schemes and Theoretical Calculations
The short Ru-Ru distance in Ru2(but)4Cl of 2.281 A versus 2.65 A in
Ru metal,*47 implies a strong interaction. Thus, some sort of metal-
metal bonding model is needed and various MO schemes have been proposed.
The MO scheme of Norman and co-workers,44 shown in Figure 4-1, is in
reasonably good agreement with the experimental results. They propose
that in the ruthenium carboxylate dimer system there are singly
occupied 6* and n* orbitals that are very close in energy for both
Ru2(02CH)4+ and Ru2(02CH)4Cl2~- In addition to justifying the quartet
electronic ground state of Ru2(but)4Cl, this MO scheme can successfully
explain the EPR parameters observed. The arguments used to interpret
the EPR spectra of the rhodium systems described in the previous chapter
can be used again here. However, in the ruthenium system, transitions
involving both the 5* orbital (b^u in D^) and the w* orbitals {eg in
) must be considered. In this system, there is no concern over the

184
relative order of these two sets of orbitals, since both are semi-
occupied, Since Lz transforms as a2g, only excited states with eg or
b2u symmetry can contribute to shifts in from ge ( since only blu x
a2g x b2u and eg x a2g x eg contain a^g). There are no excited states
of accessible energy with eg symmetry, however there are several with
b2u. A transition of the unpaired electron in 6* to an empty Ru-0 a*
orbital with b2u symmetry would give a negative shift in g^. Norman and
co-workers44 calculated this contribution to be -0.042. However, since
a g shift of +0.03 was originally reported,36 Norman and co-workers also
included promotion of electrons from filled Ru-0 a and n orbitals with
b2u symmetry to obtain a g/j shift of +0.013 leading to a total of
-0.029. Since an accurate g^ shift of -0.056 was observed here, it
appears that only the former mechanism applies and was perhaps slightly
underestimated. The situation for gj_ is more complicated. Since Lx y
transforms as eg in D4h, excited states of eu, alg, a2g, blg, and b2g
symmetry all can contribute to shifts in g^ from ge (since b^u x eg x eu
and all g x g x g states contain ag_g). Almost all of these states arise
from transitions involving filled orbitals, such as Ru-Ru tt (eu) or Ru-
Ru S (b2g), so a positive shift in g^ is expected. Norman and co¬
workers were able to rouglly calculate g_¿ including ten excited states to
obtain a value of 2.18, in good agreement with the observed value of
2.200.
One can also attempt to obtain information from A values. Values of
A1-so=(A//+2A¿)(l/3)=25xlO'4cm"1 and Ad1p=(A//-AJ_) (1/3)— 1.67xl0“4cm_1 were
observed. A simple method for relating these values to a bonding scheme
is to use atomic hyperfine parameters and disregard the ligand effects.
These methods to relate A values with types of bonding have been used

185
successfully in ligand free, matrix isolated metal dimers.145,163 To do
this for Ru2(but)4Cl, one must approximate the complex as Ru25+ with a
d61(xy )dir2(xz,yz) electronic ground state. This approximation is
inaccurate since it would give Ajso=0 due to the assumption that these
are pure d states and thus with no s electron density at the nucleus.
It would also give Ad^p=[(l/3)(aC|xy)+(2/3)(adxz)](P)(l/2)=0 since 3dxy=
-2/7 and “dxz,yz=+177*145 ls necessary to use a more sophisticated
approach that would take into account the fact that the Ru-Ru bond
orbitals are not pure d states and would include spin polarization
effects. Norman and co-workers44 have performed this sort of
calculation and obtained A values for Ru2(02CH)4+ of A1-so=9 x 10_4cm-1
and Adl-p=-0.6 x 10-4cm-1. As these workers point out, these theoretical
values are very crude. Ideally, inclusion of a very large number of
higher order terms is needed. This would lead to greater electron spin
density at the nucleus. The value reported here for A//f (21.7 x 10~4cm_1)
is much larger than the previously reported36 value (9±3 x 10"4cm-1,
also written as 93, presumably a typographical error) which causes Adl-p
to be in much better agreement with the theoretical value.
A different theoretical approach towards developing an MO scheme
for metal carboxylate dimers was recently proposed by Sowa and co¬
workers.125 They combined the d orbitals of monomeric Rh(02CR)2L units
to obtain a metal-metal bonded system. This method was applied here to
Ru2(02CR)4L2 where L=C1_ as in the chloro-bridged solid or CH30H as in
solution. The results are shown in Figure 5-11. It can be seen that it
is very difficult to use this MO scheme consistently to obtain a
reasonable S=3/2 electronic ground state for the ruthenium carboxylate
dimer. Disregarding the effect of the axial ligand L, it is possible to

Figure 5-11. Formation of metal-metal bond orbitals for
RugiOgCR^l^ using the method of Sowa and
co-workers. ^ (A) Ru^CR^ as basis
set, xy > z(B) as in A, but with > xy;
(C) C4v Ru^CR^ as basis set, xy > z'\
(D) as in C, but with > xy. The ordering
2
xy < z is more likely for alkyl as opposed
to fluorocaboxylates.

b¿o oo h
r*-
co
o
<
2o Mb
IIII it
M
RuO
b ¿Ob OO
b
14111
x
*t
O
CD

188
obtain a quartet ground state, particularly with dx2 > dxy in energy.
This is proposed to be the case with alkylcarboxylate ligands.125
However, when L is included, the very high energy a orbital must be
populated to give an S=3/2 state. This seems unlikely so this MO scheme
would suggest a doublet electronic ground state for Ru2(02CR)4L2. This
is clearly not the case. The problem with the MO scheme of Sowa and co¬
workers125 is that it treats the metal-ligand interactions as being of
primary importance with the metal-metal Interaction included
afterwards. This approach 1s not valid, the metal dimer is a distinct
unit with the metal-metal bond playing a major, if not dominant, role.
The qualitative MO scheme used is much more satisfactory at explaining
the properties of the ruthenium carboxylate dimer and is in agreement
with the sophisticated calculations of Norman and co-workers.*1^ As a
final note, it is possible that deviations from D4h symmetry, which
would remove the degeneracy of the tt* orbitals, would lead to an S=1/2
electronic ground state. The oxalate complex mentioned above,
Ru2(02CCH3)2(C204)2-, fits this requirement, but is nevertheless an
S=3/2 system (ueff=4.22 by the Evans method).157 This is not
surprising, since the oxalate and carboxylate ligands are similar and
the coordination of the Ru25+ core is Og in both casees. If a ruthenium
dimer with two sets of very different ligands could be prepared, then
one u* MO or quite possibly the 5* MO might be low enough in energy to
be filled and give a doublet ground state molecule.
Reactivity
As described previously, 1n contrast to rhodium or molybdenum, no
complexes of general formula Ru2(02CR)4¡!C1 or [Ru2(02CR)4B2]C1 have been
reported. Rather, strong Lewis bases such as pyridine or PPh3 react to

189
form complexes such as [Ru20(02CR)6(pyr)3]+ and
Ru20(02CR)g(PPh3)3.^®’^ It was found here that upon exposure to air
of a solution of Ru2(but)4C1 1n CH2C12 with excess pyridine (~10
equivalents), the dark blue-green color of the oxo-bridged trimer
rapidly developed. Similar dark blue-green decomposition products were
observed with N-methylimidazole, 4-pi coline-N-oxide and triethylamine.
By contrast, a red color was observed with primary amines such as
propylamine which most likely resulted from formation of "ruthenium red'1
species by analogy with the known1^ complex [Ru302 {NH3)i4]Cl6.4H20.
However, when air was rigorously excluded a dark brown hygroscopic solid
could be isolated from the pyridine solution which was best formulated
as Ru2(but)4(pyr )2C1. This complex can be prepared by addition of
excess pyridine (5-10 equivalents) to Ru2(but)4C1 in CH2C12 followed by
removal of solvent and washing with hexane. The EPR spectrum of this
complex in CH2C12 at 4 K showed signals at ge^=4.4 and 1.95 as with
Ru2(but)4Cl Itself, indicating the S=3/2 dimer remained intact. As far
as can be determined, this represents the first Lewis base adduct of the
ruthenium carboxylate dimer to be isolated. It was not possible to
isolate a similar complex with triphenylphosphine. Despite careful
exclusion of air and use of only two equivalents of PPh3, small amounts
of the purple oxo-bridged trimer were obtained along with unreacted
Ru2(but)4C1. In contrast to the formally Ru3(III,II I,III) species
formed with pyridine and water, the PPh3 complex is formally a
Ru3(IIlIII>III) system. Since the complex Is normally synthesized using
a large excess of phosphine, it is possible that some PPh3 reduces a
Ru3(111,111,111) species with the remainder coordinating to form
Ru3(II,III,III)0(02CR)g(PPh3)3. Ligand reactivity would make it very

190
difficult to isolate any ruthenium carobxylate dimer phosphine
product. In reactions with weaker Lewis bases, Rugibut^Cl shows no
tendency to decompose. Solutions of RugibutJ^Cl in acetone,
acetonitrile, DMSO, and tetrahydrothlophene (THTP) in air showed no
visible change over prolonged periods. However, attempts to form
adducts with these Lewis bases let only to recovery of starting
material. Unlike these others, THTP is a strong base towards covalent
interactions (Cg=7.9 vs. 6.4 for pyridine),27-29 but -¡s wea|< towards
electrostatic interactions (Eg=0.341 vs. 1.17 for pyridine).27-29 This
indicates that, as is often the case, a combination of electrostatic and
covalent properties are necessary for a strong Lewis acid-base
interaction.
Conclusion
Rugibut^Cl, a typical example of the ruthenium carboxylate dimer
series was examined by a variety of physical methods. Variable
temperature magnetic susceptibility on a powder sample in conjunction
with frozen solution EPR spectroscopy demonstrated that the complex is
an S=3/2 system as was originally proposed.48 In contrast to earlier
suggestions,36 there are no noticeable interdimer magnetic effects
despite the polymeric solid state structure of the complex. Rugtbut^Cl
does exhibit large zero-field splitting Interactions due to spin-orbit
coupling phenomena. Unpaired electron spin density is delocalized over
both Ru atoms as with other S=l/2 metal carboxylate dimer radicals. It
is possible that the two Ru atoms are not chemically equivalent, but
this difference cannot be resolved without the use of isotopically pure
ruthenium. Far IR spectroscopy of solid Rugibutl^Cl showed a previously

191
unreported band which is assigned to v{Ru-Cl). The results obtained
from experiments here are in good agreement with theoretical studies by
Norman and co-workers,44 In contrast, other MO schemes125 could not be
satisfactorily applied to the ruthenium carboxylate dimer system.
Reactivity studies on Ru2(but)4Cl indicate that although strong Lewis
bases readily decompose the metal-metal bonded dimer system, it is
possible to isolate an axial Lewis base adduct of the type more easily
obtained with the rhodium or molybdenum carboxylate dimers. With fairly
weak bases it was not possible to isolate adducts, but as no
decomposition occurred, studies can be performed on the solution
chemistry of Ru2(but)4Cl in the presence of these bases.
Thus, it appears that although the electronic structure of the
ruthenium carboxylate dimer can be reasonably well explained, the Lewis
base reactivity of this complex is less clear. As was found with
Rh2(02CCF3)4, the metal-metal bonded dimer is generally quite stable,
but often under mild conditions can be converted to greatly different
species. In the case of Rh2(02CCF3)4, monomeric Rh(I) and Rh(III)
complexes were formed. With Ru2(but)4Cl trimeric oxo-bridged species
resulted. In both cases the products are thermodynamically very stable
species to which the metal carboxylate dimer converts when given the
opportunity.
Experimental Section
Magnetic Susceptibility
Magnetic susceptibility measurements were performed on an S.H.E,
Corporation (San Diego, CA) VTS-50 SQUID magnetometer. Ten measurements
were recorded at each temperature at a field of 10.0 kG with the mean

192
and standard deviation at each point directly calculated. Hg[Co(NCS)4]
was used to check the instrument and the susceptibility value obtained
agreed with the literature value. 162,173 jpg assistance of Dr. Michael
Weissman and Dr. Apurba Roy, both Department of Physics, University of
Illinois, Urbana, IL, is appreciated.
EPR Spectroscopy
EPR spectra were recorded on a Bruker ER-200D X-band instrument
equipped with an Oxford liquid helium cryostat. The magnetic field was
previously calibrated and the microwave frequency measured by a Systron
Donnor Model 6245A instrument. Samples were ~1 x 10" 2 M_ in sealed,
degassed quartz tubes. The assistance of Dr. Peter Debrunner and Mr.
Michael Hendrich, both Department of Physics, University of Illinois, is
appreciated.
IR and Raman Spectroscopy
Far IR spectra were recorded on a Digilab Fourier transform IR
spectrometer. Rugibut^Cl was prepared as a Csl pellet (U w/w). The
assistance of Dr. David Tanner and Mr. Richard McCall, both Department
of Physics, University of Florida, Gainesville, Florida, is appreciated.
Raman spectra were recorded on a Spex Raman spectrometer using an argon
ion laser at 488.0 nm. Ru2(but)^Cl was prepared as a methanol solution
(~5 x 10-2 M_). The assistance of Dr. Willis Person and Mr. Luis
Hernandez, both Department of Chemistry, University of Florida, is
appreciated.
Computer Simulations
Computer simulations were performed using a DEC VAX 11/780
computer. For the magnetic susceptibility data the master program

193
DSUSFIT was used.174-177 pr0gram uses tne non-linear least-squares
fitting program DSTEPIT.178 Copies of the programs are given in
Appendix F. The assistance of Or. David Hendrickson and Mr. Mark
Timken, both Department of Chemistry, University of Illinois, is
appreciated. For the EPR data the program QPOW was used.144 Copies of
the EPR programs are given in Appendix E. In the simulations done here,
the frame of reference was chosen so that the g tensor was diagonal
(with gx=gy=gj.) and the A tensor was held 1n the same orientation as the
g tensor. The nuclear g tensor was approximated as an isotropic
gN=uN/I. The assistance of Dr. R. Linn Belford and Mr. Jeffrey
Cornelius, both Department of Chemistry, University of Illinois, is
appreciated.
Synthesis
Tetrakis(n-butyrato)diruthenium(II,III) Chloride
Rujibut^Cl was synthesized following the procedure of Stephenson
and Wilkinson.48 An alternative method179 which uses LiCl as an
additional chloride source was not as successful. RuCl3(H20)x (1 g,
Aldrich) was refluxed in a solution of _n_-butyric acid (35 mL) and n-
butyric anhydride (7 mL) for 6 h. The reaction was run under an oxygen
atmosphere. It is important that 02 be bubbled vigorously through the
reaction mixture and not just passed over the solution. Unless this is
done, large amount of black, insoluble reduced Ru carbonyl species are
produced. These complexes were observed by the original workers.48
After 6 h (and no more), the solution was filtered while hot and cooled
at 10 C overnight. Filtration and washing with diethylether yielded
crude Ru2(but)4C1 which was then recrystallized twice from hot butyric
acid. It is important that the recrystallizations be done fairly

194
quickly since Ru£(but)1 is converted to the oxo-bridged trimer in hot
butyric acid. Anal. Caled, for RujC^gt^gOgCl: C, 32.79; H, 4.82; Cl,
6.05. Found: C, 32.65; H, 4.80; Cl, 5.98.
Bis(pyridine)tetrakis(n-butyrato)diruthenium(II,III) Chloride
RU2(but)^C1 (0.20 g, 0.34 mmol) was suspended 1n Ch^C^ (3 mL)
under nitrogen. To this was added pyridine (0.20 mL, 2.5 mmol). A dark
brown solution immediately resulted. After stirring 15 min, the solvent
was removed and washed several times with hexane. Anal. Caled, for
Ru2c26H38N2°8cl: c* 41«96! h> 5.15; n* 3.76; C1* 4>76* Found: C,
41.61; H, 5.14; N, 4.01; Cl, 4.36.
Magnetic Susceptibility Models
Method 1. This model used the full spin Hamiltonian for an
octahedral S=3/2 system as follows:
D and E are scalar zero-field splitting parameters. With only axial
distortion, E=0 and gx=gy=g_L. The matrix elements for this spin
Hamiltonian are given in Appendix B.
Method 2. This model used the exponential form for the zero-field
susceptibility of an octahedral S=3/2 complex with axial zero-field
splitting. The equations were taken from O'Connor173 and are as
follows:
2 2
Ng-A 3 4 + (3kT/D) (1 - exp(-2D/kT))
kT 4(1 + exp(-2D/kT))
kT 4(1 + 2 exp(-2D/kT))

195
An orientational average, x-jso=(xw + 2Xj_)(l/3) was used.
Method 3. This model used the Islng model which considers a one-
dimensional infinite chain of antiferromagnetically coupled spins. The
full exponential form for the zero-field susceptibility for S=3/2 (and
S=1) has been worked out by Suzuki, Tsujiyama, and Katsura.165 The
equations are quite lengthy and will not be reproduced here. No
provisions are made for effects other than an anti ferromagnetic
interaction along the linear chain. Based on the crystal structure of
¡^(but^Cl,147 this model is not unreasonable since there is an
infinite approximately linear chain of chloro-bridged Ru2(but)^+ units.
Method 4. This model attempted to include both intramolecular
zero-field splitting and intermolecular anti ferromagnetic exchange.
This was done using the molecular field approximation.17^ The parameter
zJ was included to account for weak magnetic interactions between S=3/2
units. The equation is as follows:
x; X1
1 1 - (2zJ/Ng.i!S;i)xi
Here x-j =xH or Xj_> 9i=9// or > and the equations for xí are those given
in Method 2.
Method 5. This model used a dimer of 5^=52=372 units that are
antiferromagnetically coupled with both and S2 undergoing the same
axial zero-field splitting. This model treats only interactions between
a pair of Ru2(but)4+ units and ignores any longer range interactions.
To develop a model including long range interactions by using a trimer
(either linear or joined) or higher polymers and including zero-field

196
splitting on all the units would be very complex. Laskowski and
Hendrickson1^5 have studied an Sj=S2=5/2 dimer with axial zero-field
splitting on both and S2 using the following spin Hamiltonian:
K = 9(|BHz.Sz + gj.B(Hx.Sx + H^.Sy) + D[S^-{1/3)S(S + 1)] - 2JSr$2
In this equation a coupled basis set, S=S1+S2, is used.18® This basis
set derived for an S=3/2 dimer is given in Appendix C. D is the axial
zero-field splitting parameter. J is the Isotropic exchange parameter
(Heisenberg-Dirac-Van Vleck form). Only an isotropic J is needed since
and S2 are symmetry related.1^8 The matrix elements for this spin
Hamiltonian are given in Appendix D.

CHAPTER VI
GENERAL CONCLUSIONS
There are several interesting conclusions that can be drawn from
the work described in this thesis. One is that the metal carboxyl ate
dimer is a relatively stable species even though metal-metal bonds, such
as the one existing in the molybenum dimer, are rarely found in
inorganic complexes and have no analogy in organic compounds. However,
in most cases, particularly those involving interpretation of
spectroscopic results, the metal dimer can be treated as a single unit
using a simple MO scheme. The metal-metal interaction is strong enough
that the complex is no longer a species containing two metals, but can
be best thought of as a complex containing a single metal, but with
twice the normal size and coordination number. The reactivity of the
metal carboxylate dimer can also be explained by this MO scheme, but it
1s not always sufficient. In many cases, the reaction products are the
same as would be obtained using monomeric complexes of the metal as
reactants, and not carboxylate dimers of a different metal, even though
the two dimers might have the same MO formulation. Furthermore, the
preference of certain dimers for specific oxidation states is not always
fully rationalized by the MO scheme. It also depends on which oxidation
states are commonly found for monomeric complexes of the metal. This is
particularly true for ruthenium. Another important point is that the
nature of the carboxylate ligand is crucial in determining the
reactivity of these dimers. There is often the tendency in inorganic
197

198
chemistry to emphasize comparisons between different complexes based
solely on the metals involved, but it is no less important to study the
effects of different ligands and hold the metal constant. This can be
seen in the reactivity of the rhodium carboxyl ate dimer. This kind of
systematic investigation can then be applied to more complex multi-metal
systéms such as those in biological systems or of industrial importance.

APPENDIX A. EXPERIMENTAL AND CALCULATED MAGNETIC SUSCEPTIBILITY DATA
Temp¬
erature
Expt
xlO J
a
x 10"
r Calc,
‘6 1
• *m2x 10'
Methods 1-5
3 4
Expt. u
5 ett 1
Calc
2
• 3eff
4
5
299.30
6.855
3.4
6.838
6.948
5.790
6.916
6.837
4.0535
4.0483
4.0809
3.7254
4.0716
4.0481
148.60
13.243
12.3
13.278
13.152
11.589
13.168
13.264
3.9672
3.9725
3.9535
3.7111
3.9560
3.9703
147.90
13.272
12.1
13.335
13.207
11.643
13.224
13.272
3.9622
3.9616
3.9524
3.7110
3.9549
3.9694
74.40
23.942
14.2
23.957
23.813
22.799
23.875
24.001
3.7744
3.7756
3.6842
3.6832
3.7691
3.7790
74.20
24.050
23.4
24.009
23.867
22.858
23.928
24.053
3.778
3.7746
3.7634
3.6830
3.7682
3.7780
60.08
28.606
25.5
28.422
28.412
28.030
28.447
28.479
3.7074
3.6955
3.6949
3.6699
3.6971
3.6992
59.98
28.645
12.5
28.459
28.451
28.975
28.485
28.517
3.7069
3.6948
3.6943
3.6898
3.6965
3.6986
50.00
33.084
11.9
32.893
33.002
33.429
32.998
32.942
3.673
3.6267
3.6328
3.6561
3.6325
3.6294
42.90
37.072
3.6
37.195
37.371
38.674
37.337
37.215
3.5664
3.5723
3.5808
3.6426
3.5791
3.5733
35.01
43.724
15.3
43.920
44.114
46.837
44.059
43.873
3.4989
3.5069
3.5144
3.6214
3.5123
3.5049
34.99
43.754
15.3
43.941
44.132
46.862
44.078
43.894
3.4991
3.5066
3.5142
3.6213
3.5121
3.5047
27.00
54.443
31.4
54.675
54.766
59.600
54.726
54.502
3.4287
3.4360
3.4389
3.5875
3.4376
3.4306
20.00
70.698
45.9
71.064
70.934
78.194
70.925
70.717
3.3628
3.3715
3.3684
3.5366
3.3682
3.3632
15.00
91.801
44.1
92.069
91.692
100.53
91.666
91.575
3.3168
3.3234
3.3166
3.4728
3.3161
3.3145
11.50
117.19
27.5
117.59
116.96
125.50
116.84
116.984
3.2830
3.2876
3.2798
3.3975
3.2781
3.2801
9.00
147.27
92.4
147.59
147.04
152.31
146.79
147.231
3.2558
3.2594
3.2533
3.3111
3.2505
3.2554
7.50
175.19
63.0
175.00
174.72
174.41
174.41
175.027
3.2416
3.2398
3.2373
3.2344
3.2344
3.2401
6.00
216.74
78.7
215.52
216.23
203.38
216.21
216.603
3.2250
3.2159
3.2212
3.1240
3.2210
3.2239
5.00
257.40
156.7
255.22
257.74
227.88
258.80
257.954
3.2083
3.1946
3.2104
3.0187
3.2170
3.2217

APPENDIX B. UPPER RIGHT HAND NON-ZERO MATRIX ELEMENTS FOR SPIN HAMILTONIAN
USED IN METHOD 1

<3/2, +3/2 |J|13/2, +3/2> = 3/2 g„ SH/( + 9D/4 (or +D)
<3/2, +3/2 |K 13/2, +l/2> = /m <3M BH^
<3/2, +1/2|k|3/2, +l/2> = 1/2 g, BH, + D/4 (or -D)
<3/2, +l/2|-jf |3/2, -l/2> = gx 6Hi
<3/2, -1/2 |K 13/2, -l/2> = -1/2 g# BH, + D/4 (or -D)
<3/2, -1/21M13/2, -3/2> = /3jZ 9^ 6HX
<3/2, -3/2 |K|3/2, -3/2> = -3/2 g, BH/(, + 9D/4 (or +D)
The constant term (-1/3)S(S + 1) was not included, inclusion leads to ±D
rather than 9D/4 or D/4.
200

APPENDIX C. COUPLED BASIS SET FOR S = Sj + S2 WHERE S2 = 3/2, USED IN
METHOD 5 (DERIVED USING REF. 180)
Is, MS>=|M , M >
|3, ±3>=[±3/2, ±3/2>
13, ±2>=(l/v/2) |±3/2, ±l/2> + (1//2) |±l/2, ±3/2>
|3, ±l>=(l//5) |±3/2, ±l/2> + (1//5) 1 + 1/3, ±3/2> + {/ifs) ±1/2, ±l/2>
13, 0>=(l//20) 1+3/2, -3/2> + (1//20) |-3/2, +3/2>
+(/5720)|+l/2, -l/2> + (/5720)1-2/1, +l/2>
12, ±2>=±(l//2) 1 ±3/2, ±l/2> (1//2) |±1/2, ±3/2>
|2, ±l>=±(l//2) |±3/2, l/2> (1//2)| 1/2, ±3/2>
12 , 0>= (1/2) [+3/2, -3/2> - (1/2) |-3/2, +3/2>
+(1/2) |H/2, -l/2> - (1/2) |-l/2, +l/2>
|1, ±1>= (/37T0) I±3/2, l/2> + (/37T0)| 1/2, ±3/2> - (/47IÓ) |±l/2, ±l/2>
11, 0>= (^720)|+3/2, -3/2> + (-/9/2Ó) | -3/2, +3/2>
-(1//20) | + l/2, -1/2> - (1//20) | -1/2, +l/2>
10, 0>= (1/2) |+3/2, -3/2> - (1/2) |-3/2, +3/2>
-(1/2) | + l/2, -l/2> + (1/2) |-l/2, +l/2>
201

APPENDIX D.
UPPER RIGHT HAND NON-ZERO MATRIX ELEMENTS FOR SPIN HAMILTONIAN
USED IN METHOD 5
.> = < 3, ±3
i
< 3, ±2
< 3, ±1
<3,0
< 2, ±2
< 2, ±1
3, ±3> = -12J + 9D/2 ± 3qf/ SH/(,
3, ±2> = -12J + 5D/2 ± 2g# SH;/
3, ±1> = -12J + 13D/10 ± g# m„
3, 0> = -12J + 9D/10
2, ±2> = -6J + 5D/2 ± 2g BH/y
2, ±1> = -6J + 5D/2 ± qu
< 2,
0|H|2,
0> =
-6J
+ 5D/2
< 1,
±1|H|1.
±1> =
-2J
+ 17D/10 ± g/y SH/;
< 1,
0|K|1,
0> =
-2J
+ 41D/10
< o,
o|K|o,
0> =
5D/2
< 3,
±i|<|i.
1+
1—*
V
II
/24D/5
< 3,
0|3i|l,
0> =
6D/5
< 2,
oiilo,
0> =
2D
< 3,
3|K|3.
2> =
.372 gx 3HX
< 3,
2|K|3,
1> =
â– m gx 3Hj_
< 3,
1|*[3,
0> =
/3 qx 6H_¿
< 3,
-1|K|3,
-2> =
m q¿ SHj.
< 3,
-2|*|3,
-3> =
.172 g_i 6H x
< 2,
2 ¡í(|2,
1> =
h SHi
< 2,
1|1*|2,
0> =
/572 gx SHX
< 2,
0|«|2,
-1> =
Jm 6HX
< 2,
-1|H|2,
II
A
CM
l
gx eH L
< 1,
1|*|1,
0> =
1//2 q^ 2H x
< 1,
0|H|1,
-1> =
1//2 9X 2Hx
202

APPENDIX E
COMPUTER PROGRAMS USED FOR EPR SPECTRAL SIMULATIONS
This appendix contains the computer programs used for EPR spectral
simulations of both powder pattern and single crystal S=l/2 systems.
The original versions of the programs titled XPOW, XTAL, XCAL, and
EPRLIBS can be found in Reference 144. XPOW calculates a powder pattern
spectrum; XTAL a single crystal spectrum, and XCAL calculates field
positions and intensities for a series of single crystal spectra.
EPRLIBS contains subroutines which set up the spin Hamiltonian matrices
which are diagonalized to give eigenvalues and eigenvectors from which
the transition fields and intensities are calculated. EISPACK
subroutines, developed at Argonne National Laboratory, are used for the
matrix operations. Further details can be obtained by Inspection of the
programs and from the literature.144 The program titled DXTLFIT
calculates EPR parameters (g and A values) for single crystal spectra by
fitting the experimental field positions to calculated transitions using
the DSTEPIT non-linear least-squares curve fitting program.

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bB
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C********X*******************X*XX**************XX*******X*******
C*********************** XPQW *******************************
C
C XPDW VERSION OF QPOW EPR SIMULATION PROGRAM AS MODIFIED
C FOR USE AT THE UNIVERSITY OF FLORIDA (J. TELSER 2/1/84).
C
C***»***********************************************************
C
C "QPOW" EPR SIMULATION PROGRAM.
C 0 COPYRIGHT 1980 BY R. L. BELFORD AND COUORKERS
C
C WHEN PUBLISHING MATERIAL USING THIS PROGRAM, PLEASE
C USE THE FOLLOWING REFERENCES:
C
C 1. BELFORD, R.L.; NILGES, M.J. "COMPUTER SIMULATION
C OF POWDER SPECTRA", EPR SYMP05IUM, 21ST ROCKY
C MOUNTAIN CONFERENCE, DENVER, CO; AUGUST, 1979.
C 2. NILGES, M.J. PH.D. THESIS, UNIVERSITY OF ILLINOIS,
C 1981. ALTMAN. T.E. IBID. 1981. MAURICE, A.M.
C IBID. 1902. DULIBA, E.P. IBID. 1983.
C
C
C
C THI5 PROGRAM SIMULATES ELECTRON PARAMAGNETIC RESONANCE
C 5PECTRA OF POWDERS FOR 5YSTEM5 WITH ELECTRON SPIN EQUAL TO
C 1/2 AND NUCLEAR SPIN OF THE MAJOR NUCLEUS (SPINA) LESS THAN
C OR EQUAL TO 7/2. NUCLEUS A MAY HAVE ONE OR TWO ISOTOPES.
C THE TWO MUST HAVE THE SAME SPIN.
C SPECTRA CAN BE COMPUTED AS EITHER FIRST OR SECOND OERI-
C VATIVE.
C THE ZEROTH ORDER HAMILTONIAN, INCLUDING ELECTRONIC
C ZEEMAN AND NUCLEAR ZEEMAN, HYPERFINE ANO QUAORUPOLAR
C TERMS, IS DIAGONALIZED BY MEANS OF EISPACK ROUTINES. THE
C TRANSITION FIELOS ARE OBTAINEO FROM THE EIGENENERGIES WITH
C A FIR5T ORDER FREQUENCY-SHIFT PERTURBATION FORMULA. THE
C EIGENVECTORS ARE USED TO OBTAIN THE TRANSITION INTENSITIES.
C THE COORDINATE FRAME IS ASSUMED TO BE THE ONE IN UHICH
C THE G TENSOR IS DIAGONAL. OTHER MATRICES MAY BE ROTATED
C TO THIS FRAME BY COORDINATE TRANSFORMATIONS ABOUT EULER
C ANGLES ALPHA, BETA, GAHMA, A5 DEFINED BY ROSE. SEE:
C ROSE, M.E. "ELEMENTARY THEORY OF ANGULAR MOMENTUM";
C WILEY NEW YORK, 1963.
C MAGNETIC PARAMETERS MAY BE PUT IN AS PRINCIPAL VALUES
C AND EULER ANGLES, OR AS MATRICES (FROM SINGLE CRYSTAL DATA).
C IN THE LATTER CASE, PRINCIPAL VALUES ANO EULER ANGLES ARE
C CALCULATED BY THE PROGRAM.
C SUPERHYPERFINE CONTRIBUTIONS FROM AS MANY AS 2 5ET5 OF
C EQUIVALENT NUCLEI (SPINB AND 5PINC) CAN BE COMPUTED FOR THE
C CONDITIONS WHERE THE NUCLEAR ZEEMAN TERM (GN*BN*B*I) IS
C EITHER VERY LARGE OR VERY SMALL COMPARED TO THE HYPERFINE
C TERM. THE NUCLEAR G VALUE IS ASSUMED TO BE ISOTROPIC.
C SPECTRA ARE INTEGRATED NUMERICALLY BY A 2-OIMENSIONAL,
C 4X4-PQIN T GAUSS-POINT FORMULA, COUPLED WITH A 4-POINT
C INTEGRATION OF FIELO POSITIONS, INTENSITIES AND WIDTHS.
C THERE IS A PROVISION THAT ALLOWS THE LINEWIDTH TO BE
C DEPENDENT ON THE MAGNETIC QUANTUM NUMBER, MI.
C THE LINE5HAPE IS WRITTEN OUT TO UNIT 12. A PLOTTING
C FILE 15 CREATED USING THE PLOT79 ROUTINES OF THE UF/QTP VAX.
C A PROVISION HA5 BEEN MADE TO ALLOW ADDITION OF A
C PREVIOUSLY COMPUTED SPECTRUM. THIS SPECTRUH IS REAO IN
C FROM UNIT 13.
C
C
C
C INPUT QUANTITIES
C IN THIS VERSION ALL DATA ARE REAO IN USING FREE FORMAT
C THE PARAhETEPS NEEO ONLY BE SEPARATEO BY BLANKS.
C ALL PARAMETERS MU5T BE SPECIFIED lCAN BE=0I AND MUST
C BE ON THE CORRECT LINE.
C

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07
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140
205
C LINE *1:
C
C KRY5TL,NUCLQ,NZB,NZC,I PHASE,I5PECP.MARKTR
C
C KRY5TL: =0 FOR INPUT AS PRINCIPAL VALUES AND EULER ANGLES
C (OBTAINED FROh POWDER PATTERN SPECTRUM).
C KRY5TL: =1 FOR INPUT A5 FULL MATRICES (TENSORS, OBTAINED
C FROM SINGLE CRYSTAL SPECTRUM).
C NUCLQ: =0 IF NO QUADRUPOLAR PARAMETERS ARE TO BE READ IN
C NUCLQ: -1 IF QUAORUPOLAR PARAMETERS ARE TO BE READ IN FROM
C THE DATA FILE (UNIT 8).
C NZB, NZC: =0 FOR "NORMAL" U5E OF HYPERFINE-5QUAREO MATRIX
C PROJECTIONS FOR SUPERHYPERFINE NUCLEI B ANO C RESPECTIVELY
C =1 FOR USE OF FIRST-POWER PROJECTIONS SUITABLE FOR THE
C CASE OF A NUCLEAR ZEEMAN TERM DOMINANT OVER THE HYPERFINE
C TERM.
C IPHASE: *0 SPECTRUM IS MULTIPLIED 8Y 1. IPHASE NONZERO
C CALCULATED SPECTRUM IS MULTIPLIED BY -1 SO THE RESULT
C 15 180 DEGREES OUT OF PHASE WITH THE ORIGINAL (IPHA5E- 0)
C ISPECP: A NONZERO VALUE FOR I5PECP WILL PRINT INTO A FILE
C (LOGICAL UNIT 12) A DIGITIZED RECORD OF THE SPECTRUM.
C MARKTR: A NONZERO VALUE FOR MARKTR WILL CAUSE THE PROGRAM
C TO COMPUTE THE FIELD POSITIONS OF THE TRANSITIONS ALONG
C THE PRINCIPAL AXES. THEY ARE PLOTTEO OUT ALONG THE BOTTOM
C OF THE SIMULATION IN THE ORDER X,Y,Z (TOP TO BOTTOM).
C THIS FEATURE IS AUTOMATICALLY TURNEO DFF WHEN
C THE THETA RANGE IS NOT THE OEFAULT, I.E., WHEN THETA1 IS
C NOT ZERO ANO/OR THETA2 IS NOT 90 OR 1BO DEGREES.
C
C LINE #2:
C
C FREQ,IDERIV,IFQRBD,8ZEMN
C
C FREQ: THE EXCITATION FREQUENCY IN GHZ.
C IDERIV: FOR A SECOND DERIVATIVE SPECTRUM. OTHER THAN
C 2 GIVES A FIRST DERIVATIVE SPECTRUM.
C IFORBO: «0 FOR NORMAL SPECTRUM. WHEN IFORBO IS NONZERO
C THE INTENSITIES OF THE ALLOWED TRANSITIONS WILL BE SET
C TO ZERO. THE SPECTRUM WILL THEN CONTAIN ONLY FORBIDOEN
C CONTRIBUTIONS.
C BZEMN: THE FIELO AT WHICH THE HAMILTONIAN WILL BE
C DIAGONALIZED. A ZERO WILL GIVE THE SAME CALCULATION
C AS WITH THE ORIGINAL QPOW PROGRAM. THIS FEATURE ALLOWS
C THE ACCURACY OF THE FREQUENCY-SHIFT PERTURBATION FORMULA
C TO BE TESTED. (USEFUL ESPECIALLY AT LOW FIELDS).
C
C LINE *3:
C
C SPINA,SPINB,5PINC,NEB,NEC
C
C SPINA: THE SPIN OF THE MAJOR NUCLEUS
C 5PINB SPINC: SPINS OF THE SUPERHYPERFINE NUCLEI B ANO C
C NEB, NEC: NUMBER OF EQUIVALENT NUCLEI FOR SPINB AND
C SPINC, RESPECTIVELY
C
C LINE *4:
C
C VERTSF,5CLPK
C
C VERT5F: SCALING FACTOR FOR INTENSITY. THE OEFAULT VALUE
C IS 100. VERTSF MAY BE GREATER THAN 100, IN WHICH CASE
C ANY PEAK OVER 100.0 WILL BE OFF-SCALE (TRi IWCATEDI .
C SCLPK: A NONZERO VALUE FOR 5CLPK INDICATES THAT THE VALUE
C IS TO BE USED AS AN ARTIFICIAL MAXIMUM INTENSITY.
C THIS ALLOWS THE USER TO COMPARE RELATIVE INTENSITIES OF
C VARIOUS PLOTS. A ZERO VALUE DIRECTS THE PROGRAH TO FINO
C THE MAXIMUH INTE5ITY OF THE SPECTRUM ANO USE THIS AS A
C SCALING PARAMETER.
C
C LINE *5:

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aoo
aoi
aoa
aoa
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205
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aoa
209
aio
206
c
C NTR,NTH,NPH, LPH,THETA 1,THET A2
C
C NTR. NUMBER OF HYPERFINE TRANSITIONS FOR SPINA, CALCULATES
C THE PRIMARY TRANSITIONS FIRST (DELTA MI-O), THEN
C /DELTA MI-1/, /DELTA MI-2/,...,/OELTA MI-2*HI/. BECAUSE
C OF SIZE LIMITS ON P AND TM ARRAYS, NTR MAX-64 (1-7/21.
C FOR A GIVEN SPINA, NTR MAX-(2ÍMI+1)**2 SO THE DEFAULT VALUE
C 15 SET TO THIS NUMBER IN THE DEFAULT ASSIGNMENT SECTION.
C NTH: -NUMBER OF THETA DIVISIONS (VERTICAL CRIO I
C NPH: -NUMBER OF PHI DIVISIONS (HORIZONTAL GRID I AT THE
C EQUATOR.
C THERE ARE SIZE LIMITS ON NTH AND NPH BECAUSE OF THE SIZE
C OF THE ARRAYS CT,ST,CP,5P. NTH MUST BE SHALLER THAN 1BO.
C THE LIMIT FOR NPH VARIES WITH NTH. IN PRACTICE, IT
C 5H0ULD NOT BE NECE5SARY TO EXCEED NTH-50 OR NPH-EO.
C LPH INDICATES THE PHI (HORIZONTAL) RANGE USED.
C LPH-1 FOR PHI RANGE OF 0 TO 90 DEGREES
C LPH-2 FOR PHI RANGE OF 0 TO 180 DEGREES
C THETA1 AND THETA3 INDICATE THE THETA (VERTICAL I RANGE USEO.
C THETA1-INITIAL THETA 10 TO CALCULATE THE ENTIRE SPECTRUM,
C ABOUT 40 DEGREES TO CALCULATE ONLY THE PERPENDICULAR PARTI
C THETA2-FINAL THETA
C**** RULE5 ON THETA AND PHI RANGES:
C A IS USED AS AN EXAMPLE. THE RULES ALSO APPLY TO B,C AND Q
C IF THE GX,Y,Z AXES ARE COINCIDENT WITH THE AX,Y,Z AXES,
C THEN ALPHA,BETA,GAMMA-0 AND THETA RANGE IS 0 TO 90,
C PHI RANGE IS 0 TO 90. (LPH-1)
C IF ONLY THE GZ ANO AZ AXES ARE COINCIDENT,
C THEN BETA-0 AND ALPHA AND/OR GAMMA ARE NONZERO AND
C THETA RANGE IS 0 TO 90, PHI RANGE IS 0 TO 180. (LPH-2)
C IF ONLY THE GY AND AY AXES ARE COINCIDENT
C THEN ALPHA,GAMMA-0 AND BETA IS NONZERO ANO THETA RANGE
C IS 0 TO ISO, PHI RANGE IS 0 TO 90. (LPH-1)
C IF NO AXES ARE COINCIDENT,
C THEN BETA IS NONZERO AND ALPHA AND/OR GAMMA ARE NONZERO
C AND THETA RANGE IS 0 TO 100, PHI RANGE 15 0 TO 180.
C VALUES FOR LPH AND THETA1 AND THETA2 WILL BE AUTOMATICALLY
C COMPUTED BY THE PROGRAM WHEN THEIR INPUT VALUE5 ARE SET-0.
C THE ECHO OF THE INPUT PARAMETERS INDICATES THE RANGE USED.
C
C LINE *6:
C
C U(I) 1-1,3; CUTOFF,L5
C
C Will: HALF-WIDTH AT HALF-HEIGHT, ASSUMED COAXIAL WITH
C G-MATRIX. UIDTHS IN MHZ. READ IN ORDER UX.WY.WZ.
C CUTOFF: CONTRIBUTIONS TO THE SPECTRAL LINESHAPE ARE
C CALCULATED ONLY UP TO A DISTANCE OF CUTOFF* W (THE PRODUCT
C OF THE LINESHAPE ANO CUTOFF) FROM EACH RESONANCE FIELD
C POSITION.
C LS: LINESHAPE FUNCTION. LS-0 FOR LORENTZIAN, NONZERO
C FOR GAUSSIAN.
C
C LINES 7-B:
C
C CONE(I) 1-1,3; CTUO(J) J-l,3
C EPSILN(I) 1-1,3
C
C LINEWIDTH VARIES AS THE MAGNETIC QUANTUM NUMBER. MI. AND
C THE FREQUENCY, AS DESCRIBED BY FRONCI5Z AND HYDE. SEE:
C FRONCI5Z, W.; HYQE, J.5. J. CHEM. PHYS. 1980, 73, 3123.
C THE LINEWIDTH FORMULA IS:
C
c u**a= wo**2 + ici*Mi)**a + ica*FREQi**a
C + 2*EPSILQN*C1*C2*MI*FREQ
C
C W IS THE OBSERVED LINEWIDTH (FUHH) , WO THE RESIDUAL LINE
C WIDTH ¡FWHH). Cl (CONE) MEASURES A-STRAIN, CH ICTWC)
C MEASURES G-STRAIN. EPSILON MEA5URE5 THE CORRELATION

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2B0
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn
207
BETWEEN THE TWO. WHEN USING THIS FORMULA, USE A GAUSSIAN
LINE5HAPE. CONE.CTUO IN MHZ, EPSILN UNITLESS. READ IN
ORDER CONEX,CONEY,CONEZ,CTQWX,CTUOY,CTUOZ,
EP5ILNX,EPSILNY,EPSILNZ
LINE *9:
GN,GR,QR,GUT(11,NIS
GN: NUCLEAR G-VALUE FOR THE FIRST ISOTOPE OF THE MAJOR
NUCLEUS SPINA (GN ASSUMED TO BE ISOTROPIC!.
GR: =RATIO OF GN (2N0 ISOTOPE / 1ST ISOTOPE).
QR: -RATIO OF OUADRUPOLE MOMENT (2ND ISOTOPE / 1ST ISOTOPE)
GUT(1 I : -(PERCENT ABUNDANCE OF 1ST ISOTOPEI/100.
NIS: -NUMBER OF ISOTOPES TO BE CALCULATED. ( 1 OR 2).
LINE #10:
BCNTR,BTOTAL,HINT,BANK
BCNTR: CENTER OF SPECTRUM (GAUSS).
BTOTAL: FIELD SWEEP (GAUSS).
HINT: SIZE OF INTERVAL FOR POINTS TO BE PLOTTED (GAUSS).
NOTE 1. BTOTAL/HINT—NTOT, WHICH IS THE NUMBER OF POINTS
TO BE PLOTTED. NTOT SHOULD BE LESS THAN 3000 BECAUSE
OF SIZE LIMITS ON THE ARRAYS USED.
NOTE 2. HINT SHOULD BE SMALL COMPARED TO BTOTAL SO
A SMOOTH SPECTRUM IS OBTAINED.
BANK: -0 FOR ANY INDEPENDENT SPECTRUM; BANK >0 IF A
PREVIOUS SPECTRUM IS TO BE MULTIPLIED BY /BANK/ AND ADDED
TO THIS ONE; BANK <0 IF A PREVIOUS SPECTRUM IS TO BE
MULTIPLIED BY /BANK/ AND SUBTRACTED FROM THIS ONE.
(FREO, BCNTR, BTOTAL, HINT HU5T BE IDENTICAL FOR THE TWO
SPECTRA). THE SECOND SPECTRUM IS READ IN FROM UNIT 13.
LINE *11:
GUI 1 = 1,3
GII). PRINCIPAL VALUES OF THE G MATRIX READ IN ORDER
GX.GY,GZ
LINES 12-14:
A(II 1-1,3; ANGSA(J) J-l,3
B(I) 1=1,3; ANGSB(J) J-l,3
C(II 1-1,3; ANGSC(J) J-l,3
A(I): PRINCIPAL VALUES OF THE HYPERFINE MATRIX FOR SPINA
IN OROER AX,AY,AZ (IN MHZ).
ANG5AIJ): EULER ANGLES UHICH ROTATE THE A-MATRIX FROM THE
COORDINATE SYSTEM WHERE THE G-MATRIX IS DIAGONAL TO THE
COORDINATE SYSTEM WHERE THE A-MATRIX IS DIAGONAL.
READ IN ORDER 1,2,3- ALPHA, BETA, GAMMA
BID, CID, ANGSBÍJI, ANGSC(J): PRINCIPAL VALUES AND EULER
ANGLES FOR THE 5UPERHYPERFINE NUCLEI B ANO C IN ORDER
X,Y,Z AND ALPHA,BETA.GAMMA.
LINE #15:
QD,GE,ANGSQ(11 1-1,3
C**#* IN THE COORDINATE SYSTEM WHERE THE OUADRUPOLE TENSOR IS
C DIAGONAL, QD-(3/2)*0Z AND QE-11/21 *(QX-QY) (IN MHZ);
C ANG5G: ARE THE EULER ANGLES UHICH ROTATE THE Q TENSOR
C FROM THE COORDINATE SYSTEM IN UHICH THE G-TENSOR IS DIAGONAL
C TO THE COORDINATE SYSTEM IN UHICH THE Q-TENSOR IS DIAGONAL.
C
C

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IMPLICIT REAL*4 {A - H, 0 - Z>
EXTERNAL PL2CA
C
DATA ZER, ONER, TWOR, THRER, FOUR, SIXTN /0,1,2,3,4,16/
DATA ZERO. ONE, TUO, THREE /0.O,1.0,2.0,3.0/
DATA W0NPT3, PNT5, NINETY, HUNO /1.5,0,5,90.0,100.0/
DATA HUNOBO, ATEY, ATEY5 /180.0,80,0,85.6/
DATA PT0H1, PNT51 /O,01,0.51/
DATA GELEC /2.0023193134/
OATA BETA, PI /1.399612386,1.745329252E-2/
C
C**# GELEC - FREE ELECTRON G VALUE.
C**» BETA = (BOHR MAGNETON/PLANCK'S CONSTANT) MHZ/GAUSS
C*** PI = PI/180 CONVERTS DEGREES TO RAOIANS.
C
COMPLEX V(16,16)
COMPLEX SUM13I,SII,SIJ,YINT
DIMENSION
DIMENSION
DIMENSION
X
DIMENSION
DIMENSION
DIMENSION
DIMENSION
DIMENSION
DIMENSION
DIMENSION
DIMENSION
DIMENSION
DIMENSION
X
DIMENSION
X
ANGSAO) , ANGS8 (3) , ANGSCO) .ANGSQO)
A(3),B(3),CI3),Gt3l,Qt3l,Rt3l,S(3l,UI3)
GXTAL(3,3),AXTAL(3,3),BXTAL(3,3),CXTAL(3,3),
QXTALO ,3)
8213),02(3),G2(S>,UG(3,32),GBETA(3)
AA(3,3),BB(3,3),00(3,3),98(3,31
EULER(3),ZRTN(3,3),ZR1(3,3)
CONE(3),CTUO(3),EPSILN(3>
AR(16,16),AI(16,16),ZR(16,16),ZI(16 16)
D(161,E(16) ,TAU(2,16) .GP14.4),GPI[4 I ,E2(16)
ITBI2Ó),ITC(20 I ,SPECTRI4000 Í.GUT(2),TA8LS<1000)
ST(181,41,CT(18i,4) ,SP(181,41,CP(181,4)
P(193,32),TH(193),AQ(16162).IUL12.64)
AQ1(16,16),AQ2(16,16),G81(3,16),GB2t3,16),
GBN(3,16,2)
POINTX ( 2000 ) . POINTY (2000 ) .XPLOTOOOO) ,
YPLOT(3000 > ,SCRCH1(3000) ,SCRCH2I3000)
EQUIVALENCE (AQ(1 ) ,AQ1(1) I,(AQ(1,1,2),A82(1)1
EQUIVALENCE (G8N(1) ,GB1(1) ) , (G8NI1 ,1,2) ,GB2(1) )
C
OATA MAXEIG /16/
C
C***« MAXEIG-2*(2*SPINA+1) IS ORDER OF SPIN-HAMILTONIAN MATRIX
C TO BE OIAGONALIZED AT PRESENT, DIMENSION MAXEIG IS SET
C FOR 5PINA-7/2. IF MAXEIG IS CHANGED, DIMENSIONS MUST
C CORRESPONDINGLY BE CHANGED: (Z-MAXEIG)
C GBN(3,Z,2),P(3+3*Z*Z/4.32),TM(3+3*Z*Z/4),AQIZ.Z,2),AQ1(Z,Z),
C AQ2(Z,Z) GB11 3,Z) ,GB2I 3 , Z ) ,AR(Z,Z),AI(Z.ZI.ZRlZ,Z),D(Z) ,
C IUL(2,Z*Z/4I,E(Z),E2(ZI,TAU(2,Zf,V(Z,Z),NTRD-(ZÍ2)**2.
C
DATA GPI /.91300474, .38499326, .41300474, .08499326/
C
C***» ARRAY GPI CONTAINS COEFFICIENTS WHICH OETERMINE
C POSITIONS OF OIAGONALIZATION POINTS AT WHICH
C SPIN HAMILTONIAN 15 DIAGONALIZED.
C
DATA GPF /0.33340094/
DATA GP / 0.3772313, 1.201637, -0.649133, 0.0702477,
X 0 1800498, 1.3476184, -0.5847209, 0.0370327,
X 0.0370327, -0.3847209, 1.3476184, 0.1300498,
X 0.0702447, -0.649133, 1.201637, 0.3772313 /
C
C*** ARRAY CP CONTAINS COEFFICIENTS FOR COMPUTING INTERPOLATED
C VALUES OF THE FUNCTION TO BE INTEGRATED NUMERICALLY. THESE
C INTERPOLATION POINTS ARE OF LESSER WEIGHTS COMPARED TO
C OIAGONALIZATION POINTS.
C*** GPF IS THE RELATIVE WEIGHT FOR THE POINTS. SEE:
C CONTE, 5.0.; OE BOOR, C. "ELEMENTARY NUMERICAL ANALYSIS";
C MCGRAW-HILL: NEW YORK, 1972; P 304.
C
DATA G,A,8,O,Q,ANGSA,ANG5B,ANGSC,ANGSQ,QD,QE /29*0.0/

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c
C**** REAO IN PARAMETERS AND WRITE OUT TO OUTPUT LISTING.
C
READ(8,*)KRYSTL,NUCLQ,NZB,NZC,I PHASE,ISPECP,MARKTR
READ(8,* I FREQ,IDERIV,IFOR0D,8ZEMN
READ(8,*)SPINA.5PINB,5PINC,NEB,NEC
REA0(8,*IVERT5F,SCLPK
READ 18,* INTR,NTH,NPH,LPH THETA1,THETA2
READ(8,*I ((Utl>,1-t,31.CUTOFF,LS>
READ(8,*I ((CONE(I), 1-1,3),(CTUO(JI, J-1,3)>
REA0<8,*> (EPSILNdl, I-Í.3Í
READ 18,*>GN,GR,QR.GUTI1) HIS
READ(8,* 1BCNTR,BTOTAL,HINT,BANK
IFIKRYSTL.NE.ZER> GO TO 30
READ (8 ,* I READÍ 8,* > (I Al I>,1-1,3>,(ANGSA(J) ,J-l,3> >
READ(8,*> ((Bill.1-1 .31 ,(ANGSBIJ> ,J*1,3)1
READ IB,* > ((C(I),1-1,3), (ANGSC1J> ,J-l,3> >
IF ( NUCLQ. NE.ZER) REA0I8,*) (QD ,QE , IANGSQ (I > , 1-1,3 > I
GO TO 100
ALTERNATIVE INPUT WHEN KRYSTL IS NONZERO.
G,A,B,C AND Q READ IN A5 TENSORS BY ROW SO THE FIRST
VALUE IS GXX THEN GXY THEN GXZ THEN GYX ETC.
50 CONTINUE
DO 80 1-1 ,3
READ<8,*1 IGXTALd , J) , J-l,3>
80 CONTINUE
CALL PREP(GXTAL.ZRTN.G,EULER)
G21-A8S(G(TW0R>-G(0NER> >
G32=ABS(GdHRER)-GdU0R> >
IF í GH1 . LT. G3S1 GO TO 82
SCRAM-G(ONER >
G(ONER)-G(THOR)
G(TUOR)«G(THRER)
G(THRERI-SCRAM
DO 82 J-l,3
SCRAM-ZRTNIJ.ONER)
ZRTN(J,ONER)-ZRTNIJ,TUOR)
ZRTNÍJ,TUOR)-ZRTN(J,THRER)
ZRTN(J,THRER)-SCRAM
82 CONTINUE
DO 84 1-1,3
READ18,*)(AXTALI I,J) , J-l,3)
84 CONTINUE
CALL TRNFMt AXTAL ZRTN,AXTALI
CALL PREP(AXTAL,ZR1,A,ANGSA)
DO 86 1-1,3
READ(8,*)(BXTAL(I,J), J-1,3)
86 CONTINUE
CALL TRNFM!BXTAL.ZRTN,BXTAL)
CALL PREP(8XTAL,ZR1,B,ANGSB)
DO 88 1-1,3
READ(8,*)(CXTAHI,J) , J-1,3)
88 CONTINUE
CALL TRNFM(CXTAL,ZRTN,CXTAL >
CALL PREPICXTAL.ZRl,C,ANGSCt
IF(NUCLQ.EQ.ZER) GO TO 100
DO 90 1-1,3
READ(8,*)(QXTAL(I,J), J-1,3)
90 CONTINUE
CALL TRNFM(QXTAL.ZRTN,QXTAL)
CALL PREPIQXTAL.ZRl,Q,ANGSQ)
IJO-1.5*Q t THRER)
QE-0.5*IQ(ONER)—Q(TUOR))
C
Ct*********** END OF PARAMETER READ-IN SECTION. **•*••****<
C
C *******START OF PARAMETER PRINT-OUT*********

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100 CONTINUE
WRITE!7,102IKRY5TL,NUCLQ,NZB,NZC,IPHA5E,I5PECP,MARKTR
102 FORMAT! Í1X ,'KRY5TL,NUCLQ,NZ8,NZC,I PHASE,I5PECP,MARKTR1 ,/
X 12X, II, IX, II, IX ,11, IX, II, IX, II, IX, II, IX, ID
WRITE(7,112)FREQ,IDERIV,IFORBD,BZEMN
112 FORMAT(12X,'FREQ IDERIV IFORBO BZEMN ',/,
X 10X,F8.5,2I8,F8.2)
WRITE(7,122)SPINA,5PINB.5PINC,NEB,NEC
122 FORMAT(13X,'SPINA SPINB SPINC NEB NEC',
X MOX ,3F8.1 ,2IB>
WRITE(7,132)VERT5F,5CLPK
132 FORMAT(12X,'VERTSF SCLPK‘ ,/10X,FB.4,E16.8)
WRITE(7,1421NTR,NTH,NPH,LPH,THETA1,THETA2
142 FORMAT!15XNTR NTH NPH LPH THETA1 THETA2'
X / 10 X , 418.2F8.2 )
WRITE(7,1521W,CUTOFF,LS
152 FORMAT(15X,' WX WY WZ CUTOFF LS'./iOX,
X 4F8.2,7X , 12)
WRITEl7,156) CONE,CTWO
156 FORMAT(12X,' CONEX CONEY CONEZ CTWOX CTWDY CTWDZ‘
X /10X,6F8.4)
WRITE!7,158) EPSILN
158 FORMAT!12X,'EPSILNX EP5ILNY EP51LNZ',/10X,3F8.2)
URITEIT.lóElGN.CR.QR,GWT(1),NI5
162 FORMAT 113X, 1 GN GR QR GWT11) NIS'./BX,
1 FB.4,3FB.2,118)
WRITE!7,172)BCNTR,8T0TAL,HINT,BANK
172 FORMAT<12X,‘8CNTR BTOTAL HINT BANK’,/10X,4F8.2)
WRITEl7,2621G
262 FORMATI14X,1 GX GY GZ' ,/10X,3F8.51
290 WRITE!7,330)
330 FORMAT!///15X.17H PRINCIPAL VALUES , 18X , 13H EULER ANGLES,
1 //13X,'X',11X,1Y1,11X,'Z'I
WRITEÍ 7,340 J G
WRITE!7,350)A,ANG5A
WRITE(7,360)B,ANG5B
WRITEl7,370)C.ANGSC
WRITE I 7,3B0)Q,ANGSQ
WRITE 17,3901W
WRITE174001QDQE
IF(LS.EQ.ZER)WRITE!7,410 I
IF ILS.NE.ZER)WRITE!7,420)
340 FORMAT(6H G .3F12.5)
350 FORMAT(6H A/MHZ,3F12.3,3X,3F10.2)
360 FORMAT t 6H 0/MHZ , 3F12.3 ,3X , 3F10.21
370 FORMAT!6H C/MHZ,3F12.3,3X,3F10.21
3B0 FORMAT ( 6H Q/MHZ , 3F12.3,3X , 3F10.2)
390 FORMATí 6H W/MHZ,3F12.3>
400 FORMAT!//10X.4H QD-,F12.3,4H QE«,F12.3)
410 FORMAT!/1H , 'LINE5HAPE - LORENTZIAN' I
420 FORMAT!/1H ,1LINESHAPE - GAUSSIAN')
C
CM*»«******* END OF PARAMETER PRINT-OUT **************
C
C
C******** SET UP DEFAULT VALUES FOR VARIABLES ******
C IDERIV,VERT5F,NTR,LPH,THETA1,THETA2
C
IF(IOERIV.NE.TWOR) IOERIV-ONER
DRVSYM-(-ONE)**IDERIV
IF(VERTSF.EQ.ZERO » VERTSF-HUNO
NTRD-ll5PINA*TUai+0NEI#*TW0
IFINTR.GT.NTRDI NTR-NTRD
IFILPH.EQ.TUORIGO TO 391
LPH-ONER
IF(ANGSQ11 I .NE.ZERO.OR.ANGSQ(3 I .NE.ZERO) LPH-TWQR
IF(ANGSA!1). NE . ZERO . QR.ANGSA(3).NE.ZERO) LPH-TWOR
IF(ANGSBll) . NE. ZERO. OR . ANG5BO ) . NE . ZERO 1 LPH-TWOR
IF(ANGSC(1).NE.ZERO.OR.ANGSC(3).NE.ZERO) LPH-TWOR

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nnnn n n n n
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391 CONTINUE
JPH- (NPH/TU0)+PNT51
LTH- ONER
IFITHETAl.LT.ZEBOI THETA1-ZER0
IF 1THETA2.GT.HUN080) THETA2-HUN080
IF(THETA 1.EQ.ZERO.AND.THETA2.EQ.ZERO) THETA2-NINETY
IF(THETA1.NE.ZERO 1 MARKTR-ZER
IF!THETA2.NE.NINETY.ANO.THETA2.NE.HUNDBOI MARKTR-ZER
IF(ANGSQ(2) .NE.ZERO.OR.ANG5A(2).NE.ZERO 1 THETA2-HUN080
IF ( ANG5B (2 ) . NE . ZERO . OR . AMG5C12 > .ME.ZERO) THETA2-HUNDBO
IF(THETA2.EQ.HUN080 > LTH-TWOR
392 CONTINUE
JTH- JTHL-(JTH/LTHI+PNT51
WRITEl7,3941 LPH,THETAl,THETA2
394 FORMAT í/5X,'LPH-‘ ,I3,5X, 'THETA1»1 ,F8.2,3X,'THETA2-',F8.2)
C
C ******** INITIALIZATION section ******
c
DLN2- -LOG (TWO)
KZERO- ZER
NTR3- NTR+THRER
NTR4- NTR3+0NER
NTR2P3-TU0R*NTR+THRER
NTR3P3-THRERÍNTR+THRER
NSPA- TUQ*SPINA +1.01
NSPA1- N5PA+0NER
NEIG5T-TU0R*N5PA
NEIGP1-NEIG5T+ONER
5PBNEB°5PINB*NEB+ONE
5PCNEC-SPINC*NEC+ONE
FREQTH-FREQ*100Q.0
C
C SET THE RANGE OF FIELD TO BE COVERED BY THE GRAPH
C THE PLOT HAS NTOT POINTS (NOTE SIZE LIMIT ON NTOT GIVEN
C IN LINE 10 INPUT). THE RANGE IS BLO TO BHI. POINTS
C OUTSIDE ARE CALCULATED SO THEY CAN CONTRIBUTE TO THE
C SPECTRUM. THEIR RANGE IS BMIN TO BMAX.
C
BHALF - BTOTAL/TUO
BLO - BCNTR - BHALF
BHI - BCNTR + BHALF
NTOT-IBTOTAL/HINTI+1.01
TYPE *,'NTOT-'.NTOT
IF (NTOT.GT.3000) STOP 'NTOT OUT OF RANGE'
BDELTA-TUO*(U(ONER)+U(TWOR)+U(THRER))/(GELEC*BETA)
BMAX - BHI + BDELTA
BMIN - BLO - BOELTA
KLOT-(BOELTA/HINT)+PTOH1
KLOT1-KLOT+ONER
KMOT»(BTOTAL+BDELTA)/HINT+PTOH1
KMOT1-KMOT+ONER
KTOT-KMOT+KLOT+ONER
TYPE *, ' KTOT-' , KTOT
A LINESHAPE TABLE (TABL5I IS CONSTRUCTED.
THIS ARRAY CONTAINS 1/2 OF A LORENTZIAN OR GAUSSIAN
1ST OR 2N0 DERIVATIVE LINESHAPE WITH AN ARBITRARY
WIDTH. IN THE LINESHAPE CALCULATION SECTION, THESE
VALUES WILL BE 5CALEO TO FIT THE UI0TH5 OF THE
PARTICULAR LINES.
CUTHIN-CUTOFF/HINT
KUTOT- CUTOFF+ONE
KP=KUTOF*1O0
00 42B KC-1,KP
XK-(KC-ONER)/100
IFIL5.NE.ZER) GO TO 424
IF(I DERI V.EQ.TUOR) GO TO 422
TABLS(KC)-XK/(XK*XK+ONE)**2

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nnnn n nnn nnnnnn onnn
212
GO TO 42B
422 TABLS(KCI- GO TO 4SB
424 IF(IDERIV.EQ.TUOR) GO TO 4S6
TABLS(KC)-XK*EXP(DLN2*XK*XK)
GO TO 428
426 TABLS 428 CONTINUE
INITIALIZE ARRAY "SPECTR" FOR LATER 0EPO5ITIQN OF
LINE5HAPE 0ATA.
00 430 NZ3-1.KT0T
5PECTR(NZ3)-ZERO
430 CONTINUE
OPTIONAL AOOITION OR SUBTRACTION OF A PREVIOUS SPECTRUM
PREVIOUS SPECTRUM IS READ OFF UNIT 13, AND IS AOOEO TO
(BANK ) 0) OR SUBTRACTED FROM lBANK < 0) THE PRESENT
SPECTRUM.
IF (8ANK) 440, 480, 440
440 CONTINUE
DO 470 N-l.NTOT
READ!13,45015PECTRÍKLOT1+N-1)
430 FORMAT(13X,E23.161
SPECTRÍ KLDT1+N-11»BANK*SPECTR(KLOT1+N-1I
470 CONTINUE
480 CONTINUE
** FIRST ISOTOPE OF THE MAJOR NUCLEUS, AND NUCLEI B,C
CALL BINO(SPINB,NEB,NSPB,ITB)
CALL BINO(SPINC,NEC,NSPC,I TCI
DO 490 1-1,3
G21 I I =G(I>*G(I I
GBETA(I>-GII)*BETA/TUO
B2(I)-BtI>*B C2I I1*C( IUC1II
490 CONTINUE
AMI-SPINA
IF(SPINA.Ed.ZERO) AMI-ONE
CALCULATE LINEUIDTH5 FOR ALL MI VALUES OF
EACH OF THE X,Y,Z COMPONENTS.
DO 492 J-l.NSPA
DO 491 1-1,3
UG(I,J)-(U(I)*«(!) + (CONE(I I*CONE11>/4.0)*AMI*AMI
X + ( CTWO ( I) *CTW011 ) /4. 0)*FREQ*FREQ
X +IEPSILNII)/TUO)*CONE(11*CTUO(I)*AMI*FRE0)
X *GII)*G(I)
HG(I,NEIGP1-JI-UG(I,J)
491 CONTINUE
AMI-AMI—ONE
492 CONTINUE
Q(ONER)- QE-OD/THREE
Q(TUOR)- -OE-QO/THREE
8(THRER)-TUO*QO/THREE
CALL TRANS(ANGSA,A,AA)
CALL TRAN5(ANG5Q,Q,8Q)
IFINZB .EQ. ZERIGO TO 500
CALL TRANS(ANG5B,B,BB)
GO TO 310
500 CALL TRAN5(ANG5B,B2,BBI
510 IFÍNZC .EQ. ZERIGO TO 320
CALL TRANSIANGSC.C.CC)
GO TO 330

631
633
633
63 A
635
636
637
638
639
640
641
642
643
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645
646
647
648
649
650
631
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633
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694
695
696
697
698
699
700
213
520 CALL TRANS1ANGSC,C2,CC)
530 CALL QUAD1(AA,QQ,GN,NEIGST,MAXEIG,AQ1,GB1]
00 540 J-1,3
DO 340 1-1 ,J
GG-GII)*G(J>
BB(I,J)-BB(I,J)*GG
CC(I,J)»CC(I,J)*GG
540 CONTINUE
C
C4444444444 SET UP TRANSITION LABELS REQUIRED 4444444444
C
CALL QUA02(IUL,NTR,NEIGST)
IFINIS.EQ.ONER) GO TO 370
C
C4444444444 SECOND ISOTOPE OF THE MAJOR NUCLEUS 4444444444
C
WRITE(7,350)
550 FORMAT I///13HOSECONO ISOTOPE)
DO 560 1-1,3
AIII-AII)*GR
Q I I) -Q I I >*QR
360 CONTINUE
QD-QD4QR
QE-QE4QR
GN=GN*GR
GWT1TUOR)-ONE-GUT 1 ONER)
URITE(7,330)A,ANGSA
URITE(7,400)QO,QE
CALL TRANS(ANGSA,A,AA)
CALL TRANSIANGSQ.Q,QQ)
CALL QUA01IAA,QQ,GN,NEIGST,MAXEIG,AQ2,G82)
570 CONTINUE
C
C44444 DETERMINE (THETA, PHI) CRIO FOR INTEGRATION 44444
C THE SPHERICAL SURFACE IS DIVIDED INTO SU8-REGIDNS OF
C (ZIG)*1ZEP>.
C
KPH- ZER
THETA1- PI * THETA1
THETA2- PI * THETA2
ZIG- ITHETA2-THETA1)/JTH
DO 580 J»1,A
DO 580 1-1,JTH
TH=THETA1+ II-GPI I J ) >*ZIG
CTII.Jl-COSITH)
STII,J)-SIN(TH)
580 CONTINUE
C
C444444444 8EGIN THETA-INTEGRATION LOOP. 4444444444444444444444
C LATITUDINAL I THETA) RANGE 15 COVERED BY MT-1,2,3, JTH.
C LONGITUDINAL (PHI ) RANGE IS COVERED BY MP-1,2,3 ...... MPH .
C THERE ARE 16 OIAGONALIZATION AND 16 INTERPOLATION POINTS
C WITHIN EACH SUB-REGION. INDICES (MT, MP) IDENTIFY A 5UB-
C REGION, INDICES (LT, LP) IDENTIFY A 01AGONALIZATION POINT
C IN THE SUB-REGION.
C
DO 900 MT-l.JTH
C
MPH=JPH*ST(MT ONER)+ONER
IF1MPH.EQ.KPH) GO TO 600
MPHL-MPH/LPH+PNT31
C
C RANDOM DISTRIBUTION OF POINTS ON THE SURFACE OF UNIT SPHERE
C WILL RESULT IN THE NUMBER OF POINTS AT A GIVEN LATITUDE
C PROPORTIONAL TO SINITHETA). THE VALUE OF MPH IS WEIGHTED
C ACCORDINGLY.
C
ZEP=PI*NINETY4LPH/MPH
00 390 J-l, A
DO 390 I-l.MPH

701
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766
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768
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770
nnnnnnnnn
214
PH=(I-GPI(J))*ZEP
CPU , J ) -C05 ( PH 1
5P( I ,JI-SINIPH)
590 CONTINUE
KPH=MPH
600 CONTINUE
C
C*t*M****« BEGIN PHI-INTEGRATION LOOP ***********
C
DO 890 MP-l.MPH
C
DO BBO NT-1,NIS
C
DO 730 JN-1,16
C
LI- tJN-ONER)/FOUR + PT0H1
LT- JN - FOURXLI
LP- LI + ONER
: JN 1834 3678 9 10 11 18 13 14 13 16
: : : : : LT 1834 1834 1 8 3 4 1 8 3 4
: : : : : LP 1111 8888 3 3 3 3 4 4 4 4
UNIT VECTOR 0C-(DCX, OCY.DCZ) REPRESENTS MAGNETIC FIELD
DIRECTION ALONG WHICH THE 5 PIN-HAMILTON IAN WILL 8E
DIAGONALIZED. (I.E. A OIAGONALIZATION POINTI
DC STANDS FOR DIRECTION COSINE
DCX- 5T(MT,LT)*CP(MP,LP1
DCY- ST(MT,LT)*5P(MP,LP)
DCZ- CT(MT,LT)
DCXX-DCX*DCX
DCYY-DCYXDCY
OCZZ=DCZ*OCZ
DCXY=DCX*DCY
DCYZ=DCY*DCZ
DCZX-DCZ*DCX
C
C***5ET UP MAGNETIC FIELDS H AT WHICH HYPERFINE MULTIPLETS
C OCCUR FOR FIXED FREQUENCY "FREQ". H IS THE MAGNETIC FIELO
C MAGNITUDE FOR CALCULATION OF THE ENERGY LEVELS AT EACH
C ORIENTATION. IGEFF- G EFFECTIVE)
C
GEFF-SQRT(G8(ONER)«DCXX+G8(TWOR)«0CYY+G8(THRER)*DCZZ)
GB-GEFFXBETA
GCB-GEFF*GB
H-FREQTH/GB
HZEMN-BZEMN
IF(HZEMN.EQ.ZERO) HZEMN-H
TWOH-H+HZEMN
HDCX=HZEMN*DCX
HDCY»HZEMN*DCY
HOCZ-HZEMN*DCZ
STGMPH-GWT(NT)*5T1MT,LT)/ â–¡CXXM1-ONE-OCXX
DCYYM1-ONE-OCYY
DCZZM1-ONE-OCZZ
C
C***SET UP MAJOR STORAGE ARRAY P
C IN COLUMNS 1-16: THE TOP 2 ROUS STORE MATRIX PROJECTIONS OF
C BB AND CC (SUPERHYPERFINE), THE THIRD ROW STORES PROJECTIONS
C OF WIDTH ALONG THE 16 DIAGONALIZATION POINTS OF A 4 X 4
C BLOCK. THE NEXT NTR ROU5 STORE THE TRANSITION ENERGIES.
C THE NEXT NTR ROWS STORE INTENSITIES WEIGHTED TO THEIR
C RELATIVE IMPORTANCE DUE TO THEIR LOCATION ON THE UNIT SPHERE
C THE FINAL NTR ROWS STORE THE TRANSITION WIDTHS.
C
IF(NZ9 EQ. ZER)GO TO 610
PI ONER.JNI-A8SIBB(ONER, ONER I «DCXX+B8 X BBITHRER,THRERI*OCZZ
X + TUO*(BB(ONER,TWOR)«DCXY+BB(TWOR,THRER)«DCYZ+

771
772
773
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777
778
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781
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783
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797
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793
794
795
796
797
798
799
800
801
808
803
804
805
806
807
aoa
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810
au
818
813
814
815
816
B17
818
819
880
081
888
883
884
885
886
887
888
889
830
831
838
833
834
835
836
937
838
839
840
oonn nnn n nno
215
X 8B(0NER,THRERI*0CZX t 1 /CGB
GO TO 680
610 PI ONER,JN)-SORT(BB(ONER,ONER)«0CXX+BB t TU0R,TWOR)«0CYY+
X BBITHRER,THRER)*OCZZ
X + TU0*(BB(ONER,TUOR)«DCXY+BB(TUDR,THRER)«DCYZ+
X BB Í ONER,THRERI*DCZX))/CGB
680 IFINZC .Ed. ZER1G0 TO 630
P(TUOR,JNI-ABS(CCI ONER , ONER ) «0CXX+CC ( THOR , TUOR I Í0CYY+
X CPI THRER THRFPHDPZ7
X + TUO*(CC(ONER,TUOR)«0CXY+CC(TUOR,THRER)ÍDCYZ+
X CC(ONER THRERI*0CZXI I/GGB
GO TO 640
630 P(TUOR,JN)-SQRT(CC(ONER,ONER)«0CXX+CC(TUOR,TUOR)ÍDCYY+
X CC(THRER,THRER)*DCZZ
X +TU0*(CC(ONER,TUOR)«DCXY+CC(TUOR,THRER)«DCYZ+
X CC(ONER,THRERl*DCZXI I/GGB
640 CONTINUE
C
C***5ET UP 5PIN-HAMILT0NIAN MATRIX: REAL PART-AR, IMAGINARY PART
=AI. SET UP UNIT MATRIX ZR (INPUT FOR TQL2)
AQ KNOUN OIA EQUIVALENCE WITH Afll, OBTAINED IN QUA01.
DO 660 I“8,NEIGST
JJ* I - ONER
00 650 J-l.JJ
ZR(I,J)«ZER0
ZR(J,11"ZERO
AR(I,J)-AQ(I,J,NT)
AI(I,J>=*AQ(J,I,NT)
650 CONTINUE
660 CONTINUE
00 6B0 1*1,NEIGST
N* ONER
IF (I.GT.NSPA) N- -ONER
API I,It-AQ(I,I,NT!+HOCZ*(G8N(THRER,I,NT)+GBETAITHRER)*NI
ZR(I,I)-ONE
All I, I)-ZERO
IF (I . EQ .ONER .OR. I.EQ.N5PA1) GO TO 670
J=* I - ONER
ARI I,JI-ARII, J)+HOCX*GBN(ONER,I,NT)
AKI,J)-A III,J! +H0CY*G8N I TUOR , I , NT]
670 IF(I.LT.N5PA1] GO TO 680
J-NEIGP1-I
AR11,J)-AR AKI . JI-AI (I, J ) +HOCYÍGBETAI TWOR)
680 CONTINUE
♦•♦♦*♦♦♦♦ OIAGONALIZATI ON OF 5PIN-HAMILTONI AN MATRIX **********
CALL HTRIOHMAXEIG,NEIGST,AR.AI.0,E,E8,TAUI
CALL TQL8(MAXEIG,NEIGST,0,E,ZR,IERRI
IFIIERR.NE.ZER) GO TO 930
0 15 THE SET OF M PRINCIPAL ENERGY VALUES, IN ASCENDING
ORDER.
CALL HTRIBK(MAXEIG,NEIGST,AR,AI,TAU.NEIGST,ZR,ZIt
C
C THE COMPLEX NUMBER ARRAY V IS PARTITIONED INTO 8 BL0CK5 OF
C NSPA COLUMNS EACH, INTO UHICH ARE DEPOSITED EIGENVECTORS
C (ZR,ZI) OF SPIN HAMILTONIAN AND COMPLEX CONJUGATES OF THOSE.
C
DO 700 K-l.NSPA
K4-K+NSPA
DO 690 J*1,NEIG5T
SIPR3-ZR(J,K4]
5IPR4-ZIIJ,K4)
SIPR1-ZRIJ,Kl
5IPR8-ZIIJ,K)

841
842
843
844
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851
852
853
854
855
856
857
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872
873
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875
876
877
878
879
880
881
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886
887
883
889
890
891
B92
893
894
895
896
897
898
899
900
901
902
903
9C4
905
906
907
908
909
910
216
U( J,K4I-CHPLXISIPR3,SIPR4)
VIJ,K)=CMPLXI5IPR1.-5IPR2)
690 CONTINUE
700 CONTINUE
C
C TRANSITION FIELDS DETERMINED FROM SPECTROMETER FREQUENCY
C AND EICENENERCIES USING 1ST ORDER FREQUENCY-SHIFT
C PERTURBATION FORMULA. STORE TRANSITION FIELDS IN ARRAY P.
C
DO 740 JA-l.NTR
IU-IULIONER,JA]
IL-IULITUOR,JA)
JO- THRER + JA
P(J0,JN1-TU0H+1D(ILI-D(IU))/G8
C
«♦«CALCULATE TRANSITION INTENSITIES FROM THE EIGENUECTOR5««
C STORE RELATIOE TRANSITION INTENSITIES ( TI I IN ARRAY P
C
SUM (ONER)- ZERO
SUM(TUOR)- ZERO
SUM(THRER(“ZERO
C
DO 720 I-l.NEIGST
J-NEIGP1-I
SII-VII,IU1«01I,ILI
SIJ-UU ,IU)»VIJ,IL)
SUHIONERI- SUM 1 ONER t +51J
IFII.GT.NSPAI GO TO 710
SUMITUORI- SUM(TUOR í +5IJ
SUM(THRERl-SUM < THRER1+SII
GO TO 720
710 CONTINUE
SUMITUORI- 5UMITWOR ) -51J
SUM ITHRERI-SUM(THRER)-SII
720 CONTINUE
SUMITUORI- SUMITUOR)«IO.0,1.0)
DO 730 J-l,3
YINT-GIJIXSUHIJ)
RIJ)-REAL IYINTI
SIJl-AIMAGIYINT)
730 CONTINUE
C
R1PS1-RI ONER)*«2 + S(0NER)««2
R2PS2-R I TUOR I «*2 -I- SI TUOR) ««2
R3PS3-RI THRER) ««2 + SI THRER) «2
CROTRM-TUOtlIRI ONER)«RITUOR)+ 5 I ONER)«SITUOR) l«OCXY+
X (R(TU0R)«RITHRER)+5(TUOR)«51THRER)I
X «OCYZ+IRITHRER)«RI ONER 1+5ITHRER)*SI ONER I l«OCZX!
C
TI- R1P51«0CXXM1 + R2PS2MCYYM1 + R3PS3*DCZZM1 - CROTRM
JV-JV+NTR
P(JV,JN)-TI«STGMPH
C
«♦♦STORE THE WIDTH FOR EACH TRANSITION IN THE P ARRAY
C
JV-JV+NTR
PIjy,JN)-PNT5«( SORT IUGI ONER,IU)«DCXX+UGITUOR,IU)«DCYY+
X UC(THRER,IU)«0CZZ1+ SORT(UGI ONER,IL)«OCXX+UGITUOR,IL)*
X DCYY+UGITHRER,IL)«OCZZ)I7GG8
C
740 CONTINUE
750 CONTINUE
C
C INTERPOLATION POINTS ARE DETERMINED USING LAGRANGIAN FORMULA
C INTERPOLATED VALUES OF ENERGIES. INTENSITIES ANO UIDTHS ARE
C STORED IN COLUMNS 17 - 32 OF THE P ARRAY.
C
DO 770 1-1,4
J- I + FOUR
K= J + FOUR

911
912
913
914
915
914
917
918
919
920
921
922
923
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925
926
927
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966
967
968
969
970
971
972
973
974
975
976
977
978
979
900
UUUUUUU
217
L= K + FOUR
00 770 N-1,4
JM=L + F0UR*N
DO 760 JU-1.NTR3P3
P(JO,JM)»GPIONER,N)*P X +GP ( THRER , N)*P(JU,K)+CP( FOUR , N) *P < ,L)
760 CONTINUE
C
C INTENSITIES AT INTERPOLATED POINTS ARE SCALED BY CPF.
DO 770 JV-NTR4.NTR2P3
PtJU,JM)-P(JO,JH1 *GPF
770 CONTINUE
IF ONLY FORBIOOEN TRANSITIONS ARE UANTEO
THIS SECTION ARBITRARILY SETS THE INTENSITIES OF THE
ALLOWED TRANSITIONS EQUAL TO ZERO.
IF(IFORBO.EQ.ZERI GO TO 780
NTR3AL-NTR3+NSPA
C
OO 784 JN-1 ,32
DO 784 JO- NTR4,NTR3AL
PiJU,JNJ-ZERO
784 CONTINUE
780 CONTINUE
C
BEGIN LINESHAPE CALCULATION ****»**4**»i
C
DO 810 N-1,32
BNG-P(ONER,NI
CNG-P < TWOR,N1
C
00 810 JA-1.NTR
HA=P(3+JA,N)
WIDTH-PiNTR2P3+JA,N)
W2=UI0TH*WIDTH
IFiIDERIU.EQ.TWOR) U2-W24WIDTH
NS5-CUTHIN*WIDTH+PTOH1
SS=P/U2
DO 810 JB-1,NSP8
HB-HA-BNG*!SPBNEB-JB)
DO BIO JC-1,N5PC
HC-HB-CNG*i5PCNEC-JC)
IFiHC.LT.8MIN.OR.HC.GT.BMAX) GO TO 810
C
C IF TRANSITION MARKS ARE WANTED (MARKTR NONZERO),
C PUT X,Y ANO Z MARKS AT TRANSITIONS IHCI.
C
IF(MARKTR.EQ.ZER1 GO TO 788
IF(MT.NE.ONER.OR.HP.NE.ONER.OR.N.NE.ONER > GOTO 786
IFiJA.GT.NSPA)GO TO 788
KZERO-KZERO+ONER
POINTXlKZERO)-HC
POINTY iKZERQ1--80.0
GO TO 788
786 IFiMT.NE.JTHL.OR.MP.NE.ONER.OR.N.NE.FOUR)GOTO 787
IFiJA.GT.N5PA1GOTO 788
KZERO-KZERO+ONER
POINTX Í KZERO)-HC
POINTY l KZERO I —60.0
GO TO 788
787 IFiMT.NE. JTHL. OR. MP.NE.MPHL. OH. N . NE . SIXTN) GOTO 788
IFiJA.GT.N5PA1G0T0 7BB
KZERO-KZERO+ONER
POINTX1KZEROI-HC
POINTYi KZERO)— 70.0
788 CONTINUE

981
982
983
989
985
986
987
988
989
990
991
992
993
999
995
996
997
998
999
100 0
1001
1.002
1003
1009
1005
1006
1007
1008
1009
1010
1011
1012
1013
1019
1015
1016
1017
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1021
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1029
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1026
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1038
1039
1090
1091
1092
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1099
1095
1096
1097
1098
1099
1050
218
L
C
c
c
c
U5=5S*IT81JB)*ITC(JC)
USOV5M= -U5*ORVSYM
KH=(HC-BMIN1/HINT
C0Nl=W0NPT5+(HC-BMIN l*HUND/UIOTH
C0N3=U0NPT5-(HC-BMIN>*HUND/WIDTH
C0N9=HINT*HUND/WIDTH
CDN2=-C0N9
NI= KH-NS5
N J = KH+NSS
NK1=KH + ONER
IFINI.LT.oner)ni=qner
IF1NJ.GT.KTDT}NJ“K TOT
00 790 KL=NI,KH
L.SPTn=C0Nl+C0N2*KL
rJPECTn(KL)=SPECTR(KLI+W50VSM*TABL5(L5PTRI
790 CONTINUE
DO 800 KL=NK1,NJ
L5PTR=C0N3+C0N9*KL
5PECTR1KL)=SPECTR(KL1-WS*TABLS(LS PTR)
800 CONTINUE
810 CONTINUE
DO 870 1=1,32,9
J= I + ONER
K= J + ONER
L= K + ONER
DO 870 N-1,9
DO 820 JV-1.NTR3P3
TM(JV)=GP(ONER,N)*P1JV,I)+GP(TUOR,N>*P X +GP tTHRER,N)*P(JV,K)+GP(FOUR,N)*PIJV,L)
820 CONTINUE
BNG-TM(ONER)
CNG-TM1TWORI
DO 860 JA-l.NTR
HA=TM(3+JA)
WIDTH=TM(NTR2P3+JA)
U2=UIDTH*UIDTH
IF(IDERIV,EQ.TUOR) U2=U2*UI0TH
NSS=CUTHIN*UIDTH+PT0H1
55= DO 860 JB-1.NSP8
HB=HA-BNG* DO 860 JC=1,N5PC
HC-H8-CNG*(JC-5PCNEC)
IF1HC.LT.BMIN.OR.HC.GT.BHAX) GO TO 860
US=SS*ITB W5DV5H* -W5*DRVSYM
KH=1HC-BMIN)/HINT
CON 1=U0NPT5+(HC-BMINI*HUND/WIDTH
CDN3=UONPT5-(HC-BMINI«HUND/UIDTH
C0N9=HINT*HUND/WIDTH
CON2=-CON9
NI=KH-NS5
NJ=KH+NSS
NK1=KH+QNER
IFINI.LT.ONERINI-ONER
if DO 825 KL=NI,KH
LSPTR-C0N1+C0N2*KL
SPECTR1 KLI=-5PECTR(KL)+W5DVSM*TABLS (L5PTR)
825 CONTINUE
DO 830 KL=NK1,NJ
LSPTR=C0N3+C0N9*KL
SPECTR1KL)“SPECTRt KLI-WS*TABLSILS PTR)
B30 CONTINUE
860 CONTINUE

1051
105H
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870 CONTINUE
880 CONTINUE
890 CONTINUE
900 CONTINUE
C
C************ END OF INTEGRATION £ INTERPOLATION. **************
C
c
c *******5CALE, PLOT AND STORE SPECTRA*******
C
C DETERMINE MAXIMUM SPECTRUM INTENSITY
C
904 PEAK-ZERO
DO 910 N-l.NTOT
TESTPK=ABS(SPECTR(KL0T1+N-1I)
IF(PEAK.LT.TE5TPK) PEAK-TESTPK
910 CONTINUE
WRITE Í 7,912) PEAK
912 FORMAT!/10X,'PEAK «',aX,E16.B>
IF í 5CLPK.NE.ZERO) PEAK-SCLPK
IF!PEAK.NE.ZERO) WGF-UERT5F/PEAK
IF(PEAK.EQ.ZERO) WGF-ONE
PHASE-ONE
IF ( I PHASE . NE . ZER ) PHASE—PHASE
C
DO 920 N-1.NT0T
XPLOT(N)=BLO+!N-1)*HINT
YPLOTINl-SPECTR!KLDT1+N-1)*WGF*PHASE
C
C THESE IF STATEMENTS TRUNCATE PEAKS WHEN UERT5F > 100.0
C THIS PERMITS BASELINE TO BE BLOWN UP U/OUT GOING OFF SCALE
C
IF(YPLOTINI.GT.HUNO) YPLOT(N)«HUNO
IF(YPLOTIN) .LT. -HUNDI YPLOT (N )—HUNO
IF DESIRED (I5PECP NONZERO), THEN C0NTENT5 OF STOR ARRAY
ARE WRITTEN TO UNIT 12 FOR FUTURE USE.
IF(I5PECP.EQ.ZERI GO TO 920
WRITE(12,919) XPLOT(N),SPECTR(KLOT1+N-11,YPLOT(N)
919 FORMAT IIX,FIO.3,HX,E23.16,2X,F10.31
920 CONTINUE
C
C
C
c
c
c
c
c
************** BEGIN PLOTTING SECTION *********************
FILL UP THE SCRATCH ARRAYS
DO 925 I-l.NTOT
5CRCH1!Il-XPLOTII)
5CRCH2(I)-YPLOT11)
925 CONTINUE
*** USE PLOT79 ROUTINES ON UF/8TP UAX ***
INITIALIZE THE PLOT SYSTEM
920 CALL PLTOO
SET PLOT SIZE TO 25.0 CM LONG, 20 CM WIDE.
CALL SETSZ!25.I
CALL SET052I1.,.81
PLOT THE AXES USING THE ROUTINE PLTAX
CALL PLTAX(X,Y.TITLE,NCHAR,SIZE,THETA,UMIN,OU,VMAX,TICK,MODE)
X X COORDINATE OF ORIGIN
Y Y COORDINATE OF ORIGIN. IX,Yl IN WORLD UNITS

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TITLE HOLLERITH CHARACTER STRING AS AXIS LABEL
NCHAP LENGTH OF STRING
SIZE LENGTH OF AXIS IN WORLD UNITS
THETA ROTATION ANGLE OF AXIS: 0 FOR HORIZONTAL,
90 FOR VERTICAL
VMIN MINIHUM VARIABLE ON AXIS
DV DIVISIONS TO BE MARKED ON AXIS
VMAX MAXIMUM VARIABLE ON AXIS
TICK LENGTH OF TICK MARKS, 0.005 TO 0 015 IS GOOD
< 0 CLOCKWISE FROM AXIS, > 0 COUNTERCLOCKWISE
MODE ORIENTATION OF TITLE WITH RESPECT TO AXIS
-1 FOR BOTTOM HORIZONTAL AXIS, +2 FOR LEFT
VERTICAL AXIS
PLOT AND LABEL THE X-AXIS
CALL PLTAXI3./25. ,3./25. ,18HFIELD STRENGTH 10,18,
1 20./25.,0.,BLO,20.,BHI,.015,-1)
PLOT ANO LABEL THE Y-AXIS
CALL PLTAXI3./23. ,3 /25. , 9HINTENSITY , 9 ,
1 15 . /25. ,90. ,-100. ,20. ,100. ,-.015,2)
CALL 5ETVP2(3./25.,23./25.,3./25.,1B./25.)
DRAW THE LINE FOR THE SPECTRUM
CALL GRFGI XI
X LOWER LIMIT
X(N)
ARRAY OF X VALUES IN ASCENOING OROER WITH NO
TWO VALUES EQUAL
X2
X UPPER LIMIT
Y1
Y LOWER LIMIT
YIN)
ARRAY OF Y VALUES N ELEMENTS LONG
Y2
Y UPPER LIMIT
N
NUMBER OF POINTS
WORK 1(N)
SCRATCH ARRAY OF N ELEMENTS
U0RK2INI
SCRATCH ARRAY OF N ELEMENTS
NINT
NUMBER OF POINTS TO INTERPOLATE BETWEEN X(ll
AND X(N)
SIGMA
TENSIONED SPLINE PARAMETER
PL2
2-0 PEN MOVEMENT SUBROUTINE, USUALLY PL2CA
MUST BE DECLARED EXTERNAL
CALL GRFGI (BLQ,XPLQT,BHI,-100.,YPLOT,100.,NTOT,
1 SCRCH1,SCRCH2,NT0T,1.,PL2CA)
MARK THE TRANSITIONS WITH PLUS SIGNS
CALL GRFGP (XI,X,X2,Y1,Y,Y2,N,MARK,PL2I
XI X LOWER LIMIT
X (N) ARRAY OF N X VALUES
X2 X UPPER LIMIT
Y1 Y LOWER LIMIT
Y(N) ARRAY OF N Y VALUES
Y2 Y UPPER LIMIT
N NUMBER OF POINTS
MARK SYMBOL NUMBER (1,2,...) ACCORDING TO MARKS CODE
PL2 2-D PEN MOVEMENT ROUTINE NAME E.G. PL2CA
MUST BE DECLARED EXTERNAL TYPE.
IF(MARKTR.EQ.ZERI GO TO 929
CALL GRFGP (8LO,POINTX,BHI,-100.,POINTY,100.,KZERO,
1 2,PL2CA)
EJECT THE FRAME
929 CALL PLTEJ

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930 WRITE<7,940)IERR
940 F0PMAT STOP
END
* FOR RSDaOISK:CJT1XPOU
* FOR RSDaOISK:IJT.ILL0EPRLIB5
f LINK XPOU,EPRLI8S,UTIL*OI5K:CEISPACK3EI5PACK.OLB/LIB,-
0PLT:PTIGERLIB
t IF PI .EQ5. "" THEN INQUIRE PI ”Naae of filo with XPOW data I NO .ext!)
t ON CONTROL Y THEN t GOTO DONE
a ASSIGN ' 'PI'.DAT FOROOB
* ASSIGN 'Pl'.LST FOR007
a ASSIGN 'Pl'.PTI F0R021
* RUN RSDaOISK:CJT1XPOW.EXE
* DONE.
* 0EA5SIGN FOROOB
* OEA5SIGN F0R007
* OEAS5IGN F0R021
t WRITE SYSiQUTPUT "Your output Hating ia in 'â– Pl'.LST."
a WRITE SYStOUTPUT "Your plot file ia in "Pl'.PTI."
a INQUIRE PLOTIT "Do you want it plotted at the printer on your terainal
a IF PLOTIT THEN 0PLT:PLDTTIGER.COM 'Pl'.PTI TT :

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CS**********y«**«**»»X*S**S***S»»*S******X**X**S*XSX*»*t»»****t*
C*****»*****S»X»*S**«S*» XTAL *******************************
C
C XTAL VERSION OF QXTAL EPR SIMULATION PROGRAM AS MODIFIED
C FOR USE AT THE UNIVERSITY OF FLORIDA (J. TELSER 3/15/B4).
C
C***************************************************************
c
C "QXTAL" EPR SIMULATION PROGRAM.
C 8 COPYRIGHT 1980 BY R. L. BELFORD AND COWORKERS
C
C WHEN PUBLISHING MATERIAL USING THIS PROGRAM, PLEASE
C USE THE FOLLOWING REFERENCES:
C
C 1. BELFORD, R.L.; NILGE5, M.J. "COMPUTER SIMULATION
C OF POWDER SPECTRA", EPR SYHP05IUM, 21ST ROCKY
C MOUNTAIN CONFERENCE, DENVER, CO; AUGUST, 1979.
C 2. NILGES, M.J. PH.D. THESIS, UNIVERSITY OF ILLINOIS,
C 1991. ALTMAN, T.E. IBID. 1981. MAURICE, A.M.
C IBID. 1982. uULIBA, E.P. IBID. 1983.
C
C
C
C
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THI5 PROGRAM SIMULATES ELECTRON PARAMAGNETIC RESONANCE
SINGLE CRYSTAL SPECTRA FOR SYSTEMS WITH ELECTRON SPIN EQUAL
1/2 AND NUCLEAR SPIN OF THE MAJOR NUCLEUS (SPINA) LESS THAN
OR EQUAL TO 7/2. NUCLEUS A MAY HAVE ONE OR TWO ISOTOPES.
THE TWO MUST HAVE THE SAME SPIN.
THE ZEROTH ORDER HAMILTONIAN. INCLUDING ELECTRONIC
ZEEMAN AND NUCLEAR ZEEMAN, HYPERFINE AND QUADRUPOLAR
TERMS, IS DIAGONALIZED BY MEANS OF EISPACK ROUTINES. THE
TRANSITION FIELDS ARE OBTAINED FROM THE EIGENENERGIES WITH
A FIRST ORDER FREQUENCY-SHIFT PERTURBATION FORMULA. THE
EIGENVECTORS ARE USED TO OBTAIN THE TRANSITION INTENSITIES.
THE HYPERFINE AND QUADRUPOLE MATRICE5 MAY BE ROTATED
TO THE G TENSOR BY COORDINATE TRANSFORMATIONS ABOUT EULER
ANGLES ALPHA, BETA, GAMMA, AS DEFINED BY ROSE. SEE:
ROSE, M.E. "ELEMENTARY THEORY OF ANGULAR MOMENTUM";
WILEY: NEW YORK, 1963.
SUPERHYPERFINE CONTRIBUTIONS FROM AS MANY AS 2 SETS OF
EQUIVALENT NUCLEI (SPINS AND SPINC) CAN BE COMPUTED FOR THE
CONDITIONS WHERE THE NUCLEAR ZEEMAN TERM (GN*BN*B*I) IS
EITHER VERY LARGE OR VERY SMALL COMPARED TO THE HYPERFINE
TERM. THE NUCLEAR G VALUE IS ASSUMED TO BE ISOTROPIC.
THE PROGRAM ALSO TAKES INTO ACCOUNT ANISOTROPIC LINE
BROADENING DUE TO CRYSTAL IMPERFECTIONS.
INPUT QUANTITIES
IN THIS VERSION ALL OATA ARE REAO IN USING FREE FORMAT
THE PARAMETERS NEED ONLY BE SEPARATED BY BLANKS.
ALL PARAMETERS MUST BE SPECIFIED (CAN BE-O) AND MUST
BE ON THE CORRECT LINE.
LINE *1:
FREQ
FREQ: THE EXCITATION FREQUENCY IN GHZ.
LINE *2:
5PINA, 5PINB, 5PTNC, NEB, NEC
SPINA: THE SPIN OF THE MAJOR NUCLEUS
SPINB SPINC: SPINS OF THE SUPERHYPERFINE NUCLEI B ANO C
NEB, NEC: NUMBER OF EQUIVALENT NUCLEI FOR SPINB AND SPINC
LINE *3:

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C
C VERTSF,5CLPK
C
C VERTSF: SCALING FACTOR FOR INTENSITY. THE DEFAULT VALUE
C IS 100. VERTSF MAY BE GREATER THAN 100, IN UHICH CASE
C ANY PEAK OVER 100.0 UILL 8E OFF-SCALE (TRUNCATED ).
C 5CLPK: A NONZERO VALUE FOR SCLPK INDICATES THAT THE VALUE
C IS TO BE USED AS AN ARTIFICIAL MAXIMUM INTENSITY.
C TH15 ALLOWS THE USER TO COMPARE RELATIVE INTENSITIES OF
C VARIOUS PLOTS. A ZERO VALUE DIRECTS THE PROGRAM TO FINO
C THE MAXIMUM INTE5ITY OF THE SPECTRUM AND USE THIS AS A
C SCALING PARAMETER.
E LINE *4:
C
C NTR NOR
C
C NTR: NUMBER OF HYPERFINE TRANSITIONS FOR SPINA; CALCULATES
C THE PRIMARY TRANSITIONS FIRST (DELTA MI-01, THEN
C /DELTA MI-1/, /DELTA MI-2/,,..,/DELTA MI-2ÍMI/. BECAUSE
C OF SIZE LIMITS ON THE ARRAYS, NTR MAX-64 (1-7/21.
C FOR A GIVEN SPINA, NTR MAX-(2*MI+11**2 SO THE DEFAULT VALUE
C IS SET TO THIS NUMBER IN THE DEFAULT ASSIGNMENT SECTION.
C NOR: NUMBER OF ORIENTATIONS FOR UHICH SPECTRA ARE TO
C BE CALCULATED.
C
C LINE *3:
C
C CUTOFF, OMEGA, LS
C
C CUTOFF: CONTRIBUTIONS TO THE SPECTRAL LINESHAPE ARE
C CALCULATED ONLY UP TO A DISTANCE OF CUTOFF* U (THE PRODUCT
C OF THE LINESHAPE AND CUTOFF) FROM EACH RESONANCE FIELD
C POSITION.
C OMEGA: HALF-WIDTH AT HALF-HEIGHT OF THE ANGULAR
C MISALIGNMENT DISTRIBUTION FUNCTION. OMEGA IN DEGREES.
C LS: LINESHAPE FUNCTION. LS-0 FOR LORENTZIAN, NONZERO
C FOR GAUSSIAN.
C
C LINE *6:
C
C Will 1-1,3; ANGSU(J) J-1,3
C
C Will: PRINCIPAL VALUES OF THE LINEUIDTH MATRIX,
C HALF-WIDTH AT HALF-HEIGHT. WIDTHS IN MHZ.
C ANG5U1J): EULER ANGLES WHICH ROTATE THE U HATRIX FROM
C THE COORDINATE SYSTEM WHERE G*G IS DIAGONAL TO THE ONE
C WHERE U IS DIAGONAL.
C
C LINE *7:
C
C GN.GR.BR.GWTIl),NI5
6 G«ücLHJ5LiMNS-WhuSsiBREÍHfoF¡65ls5fBSiíüi?,r THE MAJ0R
C GR: -RATIO OF CN (2ND ISOTOPE / 1ST ISOTOPE).
C DR: -RATIO OF GUADRUPOLE MOMENT (2ND ISOTOPE / 1ST ISOTOPE)
C GUT II): -(PERCENT ABUNDANCE OF 15T ISOTOPE)/100.
C NIS: -NUMBER OF I5DTOPES TO BE CALCULATED. ( 1 OR 2).
C
C LINE *B:
C
C BCNTR,BTOTAL,BZEMN,HINT
C
C BCNTR: CENTER OF SPECTRUM (GAUSS). IF BCNTR- 0.0,
C THEN THE PROGRAM WILL CALCULATE A CENTER DF THE PLOT.
C BTOTAL: FIELD SWEEP (GAUSS). MUST BE SPECIFIED.
C BZEMN: THE FIELD AT UHICH THE HAHILTONIAN UILL BE
C DIAGONALIZED. A ZERO UILL GIVE THE SAME CALCULATION
C AS UITH THE ORIGINAL qPQW PROGRAH. THIS FEATURE ALLOWS

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nnnnnnnnnnnnnnnnnnnnnnnnnnnnnn nonoononnnonnnnnnnnnnonnnnnnnnooonnonnno
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THE ACCURACY OF THE FREQUENCY-SHIFT PERTURBATION FORMULA
TO BE TESTED. (USEFUL ESPECIALLY AT LOW FIELDS).
HINT: SIZE OF INTERVAL FOR POINTS TO BE PLOTTED (GAUSS).
NOTE 1. BTOTAL/HINT-NTOT, WHICH IS THE NUMBER OF POINTS
TO BE PLOTTED. NTOT SHOULD BE LESS THAN 3000 BECAUSE
OF SIZE LIMITS ON THE ARRAYS USED.
NOTE 2. HINT SHOULD BE SMALL COMPARED TO BTOTAL SO
A SMOOTH SPECTRUM IS OBTAINED.
LINE *9:
G(I ) 1 = 1,3
GII): PRINCIPAL VALUES OF THE G MATRIX READ IN ORDER
GX,GY,GZ
LINES 10-12:
All) 1-1,3; ANGSA(J) J-1,3
8(1) 1=1,3; ANGSB(J) J=l,3
C(I) 1 = 1,3; ANGSCUI J-1,3
AíIÍ : PRINCIPAL VALUES OF THE HYPERFINE MATRIX FOR SPINA
IN ORDER AX,AY,AZ (IN MHZ).
ANGSA(J): EULER ANGLES WHICH ROTATE THE A-MATRIX FROM THE
COORDINATE SYSTEM WHERE THE G-MATRIX 15 DIAGONAL TO THE
COORDINATE SYSTEM WHERE THE A-MATRIX IS DIAGONAL.
READ IN ORDER 1,2,3- ALPHA, BETA, GAMMA
B(I) , C(I), ANGSB(J), ANGSCIJ): PRINCIPAL VALUES AND EULER
ANGLES FOR THE SUPEPHYPERFINE NUCLEI B AND C IN ORDER
X,Y,Z AND ALPHA,BETA.GAMMA.
LINE *13:
QD,QE,ANGSQ(I) 1=1,3
* IN THE COORDINATE SYSTEM WHERE THE QUAORUPOLE TENSOR IS
DIAGONAL, Q0=(3/2I*QZ ANO QE-(1/2I *(QX-QY) (IN MHZ I ;
ANGSQ: ARE THE EULER ANGLES WHICH ROTATE THE Q TENSOR
FROM THE COORDINATE SYSTEM IN WHICH THE G-TENSOR IS DIAGONAL
TO THE COOROINATE SYSTEM IN WHICH THE Q-TENSOR IS OIAGONAL.
LINES 14-15:
TH1 , PHI , DL1
TH2, PH2, DL2
TH1 PHI, DU: FIRST REFERENCE VECTOR. THETA AND PHI
ARE WITH RESPECT TO THE PRINCIPAL AXES OF THE G MATRIX,
WHILE DL1 15 THE CORRESPONDING ANGLE IN THE CRYSTAL PLANE,
(THE GONIOMETER ANGLE I .
TH2, PH2, DL2: SECOND REFERENCE VECTOR.
FOR THE XY PLANE: TH1- 90, PHI- 0 (X-AXIS);
TH2- 90, PH2- 90 I Y-AXIS).
FOR THE XZ PLANE; TH1= 90, PHI- 0 (X-AXI5);
TH1- 0, PHI- 0 (Z-AXIS).
FOR THE YZ PLANE: TH1- 90, PHI- 90 (Y-AXIS);
TH1- 0, PHI- 0 (Z-AXIS).
DL1 ANO DL2 EQUAL O ANO 90 UNLESS THE CRYSTAL ANO
G*G TENSOR AXES ARE NONCOINCIDENT.
LINE SET 16:
DL, UGT
NUM8ER OF LINES IN SET- NOR.
DL: ANGLE IN THE CRYSTAL PLANE FOR WHICH A SPECTRUM
IS TD BE GENERATED.
UGT: SCALING FACTOR FOR THIS ORIENTATION I USUALLY 1.0).

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c
C
IMPLICIT REAL*4 IA-H, 0-ZI
EXTERNAL PL2CA
DATA BETA, PI /1.399612386, 1.743329252E-2/
C
C*** BETA» I BOHR MAGNETON/PLANCK'5 CONSTANT) MHZ/GAUSS
C*** PI= PI/180 CONVERTS DEGREES TO RAOIANS.
C
COMPLEX 0(16,161,SUM(3),511,SIJ,YINT
C
DIMENSION ANGSAI3),ANG5B(3>,ANG5C<3],ANG5Q(3),ANGSU(3)
DIMENSION 5PECTR(4000).UGUI64I,TABLS(1000)
DIMENSION XPLOTI 3000) ,YPL0T(3000I ,SCR1(3000) ,SCR2(3000)
DIMENSION A(3) ,8(3) ,C(3 I ,G(3) ,QI3i ,R(3I ,S(3 I ,W(3),
X A2(3),82(3),02(3)
DIMENSION G2I3I,W2(3),AAI3,31,88(3,3),CC(3,3),QQ(3,3I
DIMENSION AAA(3,3),GUT(2),ITB(20t.ITC(20).UU(3,3)
DIMENSION AQI16,16,2) ,IULÍ2,641 ,G8N(3,16,2) ,GBETA(3 I
DIMENSION AQK 16,16) ,AQ2(16,16) , GB1 ( 3,16 > ,G82(3,16)
DIMENSION ARI16.16),All16,161,ZR(16,16),ZIC16,161
DIMENSION 0(16),E<1¿),E2(Í6),TAUI2,16)
C
EQUIVALENCE (AQI 1 ) ,AQ1(1)) ,(AQI1,1,2) ,AQ2(1))
EQUIVALENCE (CBN(1),GB1(1)>,(GBNI1,1,2),GB2(1)I
C
DATA MAXEIG /16/
C
C**#* MAXEIG-2*(2*SPINA+1) IS ORDER OF 5PIN-HAMILTONI AN MATRIX
C TO BE DIAGONALIZED. AT PRESENT, DIMENSION MAXEIG 15 SET
C FOR SPINA-7/2. IF MAXEIG IS CHANGED, DIMENSIONS MUST
C CORRESPONDINGLY BE CHANGED: (Z-MAXEIG1
C GBN(3,Z,2),P(3+3*Z*Z/4,32>,TM(3+3*Z*Z/4) AQ(Z,Z,2),AQI C AQ2(Z,Z),GB1(3,Z),GB2(3,Z),AR(Z,Z),AI(Z,Z),ZR(Z,ZI,D(Z),
C IUL(2,Z*Z/4I ,E(Z) ,E2(Z) ,TAU(2,ZI ,V(Z,Z),NTRD-(Z/21**2.
C
C#*** READ IN PARAMETERS AND URITE TO OUTPUT LISTING.
C
READ(5,*)FREQ
REA0(5,*1SPINA,SPINB,SPINC,NEB,NEC
READ(5,*)VERT5F,5CLPK
READ(5,*)NTR NOR
READ(5,*)CUTOFF,OMEGA,LS
REA0I5,*I (1U(I), 1-1 ,31 , (ANGSUCJI , J-1,31)
READ(5,*)GN,GR,QR,GUT(1).NIS
REAO(5,* IBCNTR,BTOTAL,0ZEMN,HINT
READ(5,*) (G(I), 1-1,3)
REAO(5,* I ((All), I-i ,3),(ANG5AIJ) , J-1,3))
READ(5,*) ( (B(I), 1-1,3) ,< ANG5BlJ) , J-l,3()
REAO(3,*) ( (C(11 , 1-1 ,3),(ANGSC(J) , J-1,311
READ(3,*) (QD.QE,(ANGSQ(I), 1-1,31)
READ(5,#)TH1,PHI,DL1
READ < 5,* ITH2,PH2,DL2
C
C»*** WRITE OUT PARAMETERS
C
WRITE!6,11IFREQ
11 FORMAT I13X, * FREQ‘ ,/10X,F8.3)
WRITE!6,12)SPINA 5PINB,SPINC,NEB,NEC
12 F0RMATI13X,'SPINA SPINB SPINC NE3 NEC',
1 /10X.3FB.1,218)
WRITE(6,13)VERTSF,SCLPK
13 FORMAT(12X,'VERT5F SCLPK',/10X,F8.2,E16.8)
WRITE(6,14)NTR,N0R
14 FORMAT(13X,‘NTR NOR',/13X,13,3X,13)
WRITE!6,13)CUTDFF.OMEGA,LS
15 F0RMATI12X,'CUTOFF OMEGA LS',/10X,2F8.2,7X,12)
URITE(6,16)GN,GR,QR,GUT(1),NIS
16 FORMAT(12X,' GN GR QR GUT(1) NIS’,/8X,
1 FB.4,3FB.2,1IB>

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WRITE(6.17 IBCNTR,8T0TAL,BZEMN,HINT
17 FORMAT(12X,'BCNTR 9TOTAL BZEMN HINT ',
1 / 1 OX , 4F8.2 >
URITEC6,1B)G
10 FORMAT ( 14X , ' GX GY GZ' , / 10X , 3F8.5)
URITE{6,20)
20 F0RMAT(///15X17H PRINCIPAL 0ALUE5,1BX,13H EULER ANGLES,
1 //13X,’X* ,11X, * Y' , 11X , lZ' )
WRITE!6,21>G
WRITE(6,22 IA, ANG5A
WRITE(6,23)B,ANG5B
WRITE(6,24)C,ANG5C
URITE(6,23)Q, ANG5Q
WRITE(6,26) W , ANG5W
WRITE (6,27 > QD,QE
IF(L5.EQ.0) WRITE{6,20)
IF(LS.NE. 0)WRITE! 6,29)
21 FORMAT(6H G ,3F12.3)
22 FORMAT(6H A/MHZ,3F12.3,3X,3F10.2)
23 FORMAT(6H B/MHZ,3F12.3,3X,3F10.2)
24 FORMAT 16H C/MHZ,3F12.3,3X,3F10.2>
25 FORMAT(6H Q/MHZ,3F12.3,3X,3F10.2)
26 FORMAT 16H U/MHZ ,3F12.3.3X,3F10.2>
27 FORMAT(//10X,4H QD-,F12.3,4H QE-.F12.3)
28 FORMAT!/1H , LINE5HAPE - LORENTZIAN')
29 FORMAT(/1H , *LINESHAPE - GAU55IAN')
URITE(6,30 >
URITE{6,31)TH1,PHI,DL1
WRITE!6,31) TH2,PH2,DL2
30 FQRMATt/lOX,'THETA PHI DELTA')
31 FORMAT!8X,3F8.2)
S****** INITIALIZATION SECTION ******
C
NTRD-II 2.0*SPINA) + 1.0)*((2.0*SPINA1+1.01
IFINTR.GT.NTRDI NTR-NTRD
IFIWERTSF.EG.O.OI UERTSF-100.0
0LN2=* -LOGI2.0)
NSPA-2.0*5PINA+1.1
N5PA1=NSPA+1
NEIG5T=2*N5PA
NEIGP1=NEIG5T+1
SPBNEB=5PINB*NEB+1.0
5PCNEC=*SPINC*NEC+1 .0
C
C DETERMINE NUMBER OF POINTS FOR PLOT 1NT0T) AND FOR
C CALCULATION (KTOT).
C
NTOT”(BTOTAL/HINT1+1.01
TYPE *, 1NTOT” 1 NTOT
IF(NTOT.GT.3000) STOP ’NTOT OUT OF RANGE'
BHALF-BT0TAL/2.0
BOELTA” 2.0*1U(1l+U(2)+U<3)1+0.01
KLOT«(BDELTA/HINT 1+0.01
KMOT”(BDELTA+BTOTALI/HINT+O.01
KTOT*KLOT + KM0T + 1
TYPE *, ’KTOT” ',KTOT
C
C SET UP LINE5HAPE TABLE (TABL51
C
CUTHIN”CUTOFF/HINT
KUTDF-CUTOFF+1.0
KP-KUTOF*100
00 50 KC»1 ,KP
XK”(KC-11/100.0
IFIL5.NE.01 GO TO A3
TABL5(KC>«XK/ GO TO 30
45 TABLS(KC)»XK*EXP 50 CONTINUE

351
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227
OME“OMEGA*PI
C
C INITIALIZE LINESHAPE ARRAY "5PECTR".
C
DO 55 NZ3-1,KTOT
5PECTRINZ3I-0.0
55 CONTINUE
C
C FIRST ISOTOPE OF THE MAJOR NUCLEUS, ANO NUCLEI 0 AND C
C
CALL BINOÍ5PIN8,NE8,N5PB,ITBÍ
CALL BINO(SPINC,NEC,N5PC,ITC)
DO 100 1-1,3
G2(I) =G< I >*C( I)
GBETA(I)“G(II*BETA/2.0
A2(II»AÍI)*A(I)
82 ( I)=B(I)*B(I)
C2(II-C U2(I>-U(I)tU 100 CONTINUE
Q< 1>— QE-QD/3.0
q(2)- QE-QO/3.0
8(31-2.0*00/3.0
CALL TRAN5(ANG5A,A,AAAI
CALL TRANS Í ANGSA,A2,AA t
CALL TRANS(ANG5B,82,BB)
CALL TRANS(ANGSC,C2,CC)
CALL TRANS(ANG5Q,Q,QQ)
CALL TRANSÍANG5W,W2,WU)
CALL QUAD11 AAA,QQ,GN,NEIGST,MAXEIG,AQ1,GB11
DO 105 J-1,3
00 105 1=1,J
GG-GÍI)*G(J)
AA(I,J)-AA(I,J)*GG
BBÍI , J1-BBÍI, J)«GG
CC íI,J)-CC1 I,J)«GG
UUÍI , J1-WUÍI ,J)*GG
105 CONTINUE
CALL 0UAD2ÍIUL.NTR,NEIGST)
IFÍNIS.EG.1) GO TO 130
C
C SECOND ISOTOPE OF THE MAJOR NUCLEUS
C
DO 110 1-1,3
A(i)-A(ii*en
an i-a 11 )*qr
110 CONTINUE
qo-qo*GR
QE-QEÍQR
GN-GN4GR
GWTI2I-1-GWTÍ1I
WRITE(6,112)
112 FORMAT(/10X,1 SECOND ISOTOPE ')
WRITE(6,22)A.ANG5A
WRITE(6,27)QD,QE
CALL TRANS(ANGSA,A,AAA)
CALL TRANSÍANG5Q,Q,00)
CALL qUADl(AAA,QQ,GN,NEIGST,MAXEIG,A92,GB2)
130 CONTINUE
C
C DETERMINE ORIENTATION (DIRECTION COSINES).
C
THI=TH1»PI
PHI=PH1*PI
THF=TH2*PI
PHF=PH2*PI
DCX1-5INÍ THI)«COSÍ PHI)
DCY1=5IN(THI)»SIN(PHI)
DCZ1-C05(THI1
0CX2-SIN(THF)«C05(PHF)

228
421
DCY2=5IN(THF)*5 IN(PHF)
422
DCZ2-C05(THF )
423
0CNX=0CY1*DCZ2-DCZ1*DCY2
424
DCNY=DCZ1*DCX2-DCX1*DCZ2
425
0CNZ=0CX1*DCY2-0CY1*DCXH
426
CANG-OCX1*OCX2+OCY1*DCY2+DCZ1*OCZ2
427
SAG2-DCNX*DCNX+DCNY*QCNY+OCNZ*OCNZ
422
5ANG-SQRTÍ5AG2)
429
5CK=SIN((DL2-DL1)*PI)
430
IF I5CK.LT. 0.0) SANG —5ANG
431
DNXX-DCNX*DCNX/SAG2
432
DNYY=DCNY*OCNY/5AG2
433
0NZZ»DCNZ*DCNZ/5AG2
434
DNXY=OCNX*DCNY/SAG2
435
DNYZ=DCNY*DCNZ/5AG2
436
DNZX=DCNZ*DCNX/ SAG2
437
c
438
C******* BEGIN CALCULATION LOOP OVER THE ORIENTATIONS
439
c
440
00 500 NA-l.NOR
441
REA0(5,*)0L,WGT
442
WRITE(6,130)OL,WGT
443
130 FORMATI /10X, 'DL- '.Fa.i,' UGT- \FA.2>
444
AGI - (DL-DL1t #PI
445
AGC-COS(AGI)-CANG*SIN(AGI1/SANG
446
AGS-SIN(AGI)/SANG
447
0CX-DCX1*AGC+DCX2*AG5
448
DCY=0CY1*AGC+0CY2*AGS
449
0CZ-0CZ1*AGC+DCZ2*AG5
450
THH-ACOSIOCZ)
451
TH-THR/PI
452
IFlTHR.Eg.O.OlGO TQ 130
453
FC=DCX/5INITHR)+1.0
454
FC-AB5(M0D(FC,2.0))-l.0
455
PH-ACOS(FC)/PI
456
IFIDCY.LT.0.0) PH-360.O-PH
457
150 CONTINUE
458
DCXX-DCX*OCX
459
DCYY«OCY*DCY
460
OCZZ=OCZ»DCZ
461
DCXY»DCX*DCY
462
DCYZ-OCY*OCZ
463
DCZX-DCZ*OCX
464
c
465
c
SET UP FIELDS AT WHICH TRANSITIONS OCCUR
466
c
AND DETERMINE RANGE TO BE PLOTTED (IF NOT GIVEN BY
467
c
468
GE2-G2I1)*DCXX+G2(2)*DCYY+G2(3I»0CZZ
469
GEFF-SQRT(GE21
470
GB=GEFF*BETA
471
GGB=GEFF*GEFF*BETA
472
H-FREQ*1000.O/GB
473
HZEMN-H
474
IF(BZEMN.NE.O.O) HZEMN-BZEMN
475
IF(8CNTR.E3- 0.0) BCNTR-ANINT(H)
476
8L0-BCNTR-BHALF
477
BHI-BCNTR+BHALF
478
8HAX-BHI+BDELTA
479
BMIN-BLO-BOELTA
480
WRITE(6,139)BCNTR
481
158 FORMAT(/10X,1BCNTR- ',FB.2>
482
TWOH- H + HZEMN
483
HOCX- DCXÍHZEMN
464
HDCY- DCYHHZEMN
485
HDCZ* DCZ»HZENN
486
AN2* AAA(1,1I*DCXX+ AAA 12,21«DCYY+ AAA(3, ■
487
X +2.0*AAI1,2)*DCXY+2.0*AA(2,3)*DCYZ+2.0*AA(1,
488
BNG-SQRTIBBI1,1)*DCXX+ BB(2,2)*DCYY+ BB C 3 ,
489
X +2.0*BB(1,2)*DCXY+2.0*BB(2,3)*0CYZ+2.0*BBI1,
490
X ÍGGB

491
492
493
494
495
496
497
49B
499
500
501
502
503
504
505
506
507
508
50?
510
511
512
513
514
515
516
517
518
519
520
521
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523
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527
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529
530
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541
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545
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547
548
549
550
551
552
553
554
555
556
557
558
559
560
non
229
CNG-SQRTICCI1 ,1)*DCXX+ CCI 2,2>*DCYY+ CC(3,3)*QCZZ
X +2.0*CC(1,2)*QCXY+2.0*CC<2,3l*DCYZ+2,0*CC<1,3I»0CZX>
X / GG8
UN2- (WU!1 , 1)*DCXX4 UU(2,2)*DCYY+ UUI3,3)*DCZZ
X +2.0*WW<1,2>*DCXY+2.0*UUI2,3)*DCYZ+2.0*UU<1,3)*0CZX>
X /IGG8*GG8)
DGX-(G2(2I-G2I3> l*DCYZ/GE2
DGY=(G2(3)-G2(1I)*DCZX/GE2
0GZ=(G2<1I-G2I2)>*0CXY/GE2
IF I SPINA.EQ.0.0)GO TO 130
OAX-I*DCYZ + AAA(2,3)*(0CZZ-0CYYI
X + AAA(1,2I *0CZX - AAAI 1,31 *DCXYI/AN2
OAY=( IAAA(3,3)-AAA(1,1 I )*OCZX + AAA 11 ,31 *(DCXX-DCZZI
X + AAA(2,31 *OCXY - AAAI 1,2) «DCYZ1/AN2
OAZ-I I AAA(1,1)—AAA(2,2) )#OCXY + AAA 11,2 I * IDCYY-DCXXI
X + AAA (1,3) *DCYZ - AAAI2.3) «OCZXWAN2
180 CONTINUE
C
C SET UP SPIN HAMILTONIAN MATRIX. AR- REAL; AI- IMAGINARY.
C
190
200
214
220
DO 450 NT-1,NIS
00 200 I-2.NEIGST
JJ=I-1
00 190 J-l.JJ
ZRII,JI-0.0
ZR(J,II-0.0
ARI I,J)-AQ11,J,NT)
AI(I,J)-AQ(J,I,NT)
CONTINUE
CONTINUE
DO 220 1-1,NEIG5T
N—l
IF II.GT.N5PA) N—l
AR11,1)-AQI I,I,NT I + HDCZ*!GBN(3,I,NT) + GBETA(3)*NI
AI 11,1)—0.0
ZRII , I > = 1 .0
IF(I.EU.1.OR.I.EQ.NSPA1) GO TO 214
U-I-l
ARI I,J)- AR11 ,J) +
A111,J)- AIII.J) +
IF(I.LT.N5PA1I GO TO
J-NEIGP1-I
ARI I , J)-AQI I,J,NT) +
All I,J)-AQ(J,I,NT) +
CONTINUE
H0CX*G8N(1,I,NT)
H0CY*GBN(2,I,NTI
220
HDCX*GBET All)
HOCY*GBETAI 2)
DIAGONALIZATION OF SPIN HAMILTONIAN MATRIX
CALL HTRIDI IMAXEIG,NEIG5T,AR,AI,0,E,E2,TAU)
CALL TQL2(MAXEIG,NEIG5T,0,E,ZR,IERR)
IFIIERR.NE.O) CO TO 990
CALL HTRIBKIMAXEIG,NEIGST,AR,AI,TAU,NEIGST,ZR,ZI)
C
C STORE EIGENVECTORS (Z).
C
00 230 K-l.NSPA
K4-K+N5PA
DO 225 J-l.NEIGST
5IPR3-ZRlJ,X4)
SIPR4-ZIIJ , K4t
SIPR1-ZRlJ,K)
5IPR2-ZIIJ , K)
VÍJ,X4)—CMPLXI5IPR3, 5IPR4)
U(J,X) -CMPLXISIPR1,-5IPR2)
225 CONTINUE
230 CONTINUE
C
C DETERMINE TRANSITION FIELDS
C
DO 300 JA-1,NTR

561
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5 64
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572
573
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57 6
577
578
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583
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5BQ
589
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618
619
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nn n
230
IU-IULÜ,JA)
IL-IULÍ2,JA)
HA*TUOH + (0 IIL >-0(IU)>/GB
H0=H-2*HA
H1*HA-H
CALCULATE TRANSITION INTENSITIES
SUM(1)"0.0
5UMI21-0.0
SUMOl-O.O
00 240 1*1,NEIG5T
J*NEIGP1-I
SII=U(I,IUI*U SIJ-VII,IU)*V(J,IL)
SUM(1)=SUM(1l+SIJ
IF(I.GT.NSPA) GO TO 233
SUM(2)-5UM(2)+SIJ
5UM(3)-5UM(3>+SII
GO TO 240
233 CONTINUE
5UM(2I-5UM(2)-SIJ
5UM(3)*SUM(3>-SII
240 CONTINUE
SUM(2)=SUM(2>*(0.0,1.0)
DO 243 J-l,3
YINT-GÍJ)*SUM(J)
RtJ)-REALlYINT1
5(J)“AIMAG(YINT)
243 CONTINUE
R1PS1*R(1>*R(1>
R2PS2-R(2)*R(2)
R3PS3-R(3)*R(3>
R512* R(11*R(2>
RS23- R < 2)*R(3)
R513- R(1)*R<3)
TI*
X +2
5(11*5(1)
S(2)*SI 2)
5(31*5(3)
5(11*5(2)
5(21*5(3)
5(11*5(3)
R1P51*DNXX + R2PS2*DNYY
0*R512*DNXY + 2.0*RS23*DNYZ
+
+ 2
R3PS3*DNZZ
0*R513*DNZX
CALCULATE LINEWIDTHS
| IH0*DGX
+
H1*DAX
)*<
[ HOtDGX
+
H1*DAX)
+ (HO*OGY
+
H1*DAY
)*l
(HOtDGY
+
H1*DAY)
+ 1HO*OGZ
H1*DAZ
it 1
IHOtOGZ
+
H1*DAZ)
WG= UN2 + WUU*DME*OME
UIDTH*SQRT < WGI
N55*CUTHIN*WI0TH+0.01
UGU(JAI*UIDTH
55*TI*GUT(NT)/(UG*GBI
DO 290 JB-1.N5PB
HB=HA-BNG*(5PBNEB-JB)
DO 290 JC-1.N5PC
HC-HB-CNG*(5PCNEC-JC)
IF < HC.LT.BMIN.OR.HC.GT.BMAX) GO TO 290
U5=S5*ITB(JB)*ITC(JC)
KH=(HC-BMIN>/HINT
C0N1»1.5+(HC-BMIN)*100.07UI0TH
C0N3-1,3-(HC-BMIN)*100.0/WIDTH
C0N4-HINT*100 . O/UIOTH
CON2—CON4
NI=KH-NSS
NJ=KH+NSS
NK1-KH+1
IFINI.LT.1)NI*1
IF(NJ.GT.KTOTINJ*KTQT
DO 270 KL-NI.KH
LSPTR-C0NX+C0N2*KL
SPECTR(KL)»5PECTR(KL)+U5*TABL5(L5PTR)
270 CONTINUE
DO 200 KL-NK1.NJ

631
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633
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635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
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651
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654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
m
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
nno non o nnn non n cino nnonn noocnn nnn
231
L5PTR=C0N3+C0N4*KL
5PECTR!KLI“5PECTR(KLI-W5*TA8LS(L5PTR)
280 CONTINUE
290 CONTINUE
300 CONTINUE
WRITE(6,410)(UGUIIN),IM-1,NTR)
410 FORMAT(1HF6.1(
450 CONTINUE
SCALE AND STORE SPECTRUM
PEAK-0.0
DO 460 N=1,NT0T
TESTPK-ABS15PECTR(KL0T+NI I
IF (PEAK.LT.TESTPK) PEAK-TE5TPK
460 CONTINUE
WRITE!6,462) PEAK
462 FORMAT!/10X,'PEAK- ',E16.8)
IFISCLPK.NE.0.0) PEAK-SCLPK
IFtPEAK.E0.0.0) PEAK-1.0
UGF-WGT#VERTSF/PEAK
00 480 N-l,NT0T
XPLOT(N)«BLO+ YPLOTIN)-SPECTR(KLOT+NI*UGF
IF1YPL0TIN).GT.100.0) YPLOTIN>-100.0
IF! YPLOT (N) . LT.-100.0 ) YPLOT 480 CONTINUE
500 CONTINUE
*********** PLOTTING SECTION **********
FILL UP THE SCRATCH ARRAYS
DO 520 I=1,NT0T
5CR1!I)—XPLOT(IÍ
SCR2!I I-YPLOT(11
520 CONTINUE
*** U5E PL0T79 ROUTINES ON UF/QTP VAX ***
INITIALIZE THE PLOT SYSTEM
CALL PLTOO
SET UP PLOT SIZE 15. CM HIGH, 25. CM LONG
CALL SETSZI2S.)
CALL SET052I1.,.8)
PLOT ANO LABEL THE X-AXIS
CALL PLTAXO . /25 . ,3.725. , 18HFIELD STRENGTH l G) ,18,
1 20, 725.,0. ,BLQ,20. ,BHI, .015,-1)
PLOT AND LABEL THE Y-AXIS
CALL PLTAXO, /25. ,3./25. , 9HINTEN5ITY ,9 ,
1 15. /25. ,90. ,-100. ,20. ,100. ,-.015,2)
CALL SETVP2!3./25.,23./25.,3-/25.,18./25.)
DRAW THE LINE FOR THE SPECTRUM
CALL GRFGI SCR1 ,5CR2 ,NTOT,1. ,PL2CA)
EJECT THE FRAME
CALL PLTEJ

232
701
990
WRITEI6,999)IERR
702
999
FORMAT í/2X,SHI ERR
703
STOP
704
END
t FOB R5DSDI5K:CJTIXTAL
t FOR RSDIDISKiCJT.ILLOEPRLIBS
* LINK XTAL,EPRLIB5,UTIL*0I5K:CEI5PACK0EI5PACK.OLB/LI8,-
QPLT:PTIGERLIB
l IF PI EQ5. THEN INQUIRE PI "Naa* oF File with XTAL data I NO .«it! I"
i ON CONTROL Y THEN * GOTO DONE
* ASSIGN * 'PI‘.OAT FOR003
Í ASSIGN 'PI ' .LST FOROOA
$ ASSIGN 'PI'.PTI F0R021
* RUN PSOtOISK:CJTOXTAL.EXE
$ DONE:
f DEASSIGN FOROOS
$ DEA55IGN F0R004
i OEAS SIGN FOR021
» WRITE 5YS10UTPUT "Your output lilting ii in ''PI'.LST."
» WRITE 5YS10UTPUT "Your plot Fila is in ''PI'.PTI."
% INQUIRE PLOTIT "Do you want it plottad at th« ppintar an your taminal?
» IF PLOTIT THEN GPLT:PLOTTIGER.COM 'PI'.PTI TT:

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cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
CXXXXXXXXXXXXXXXXXXXXXXX XCAL XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
c
c
c
XCAL VERSION OF QCAL EPR SIMULATION PROGRAM AS MODIFIED
FOR U5E AT THE UNIVER5ITY OF FLORIDA (J. TELSER 5/15/B4)
"«CAL" EPR SIMULATION PROGRAM.
(? COPYRIGHT 19B0 BY R. L. BELFORO AND COWQRKERS
UHEN PUBLISHING MATERIAL USING THIS PROGRAH,
USE THE FOLLOWING REFERENCES:
PLEASE
cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
c
c
c
c
c
c
c
c
c
c
c
c
c
c
BELFORD, R.L.; NILGE5, M.J. "COMPUTER SIMULATION
OF POWDER SPECTRA", EPR SYMPOSIUM, 21ST ROCKY
MOUNTAIN CONFERENCE, DENVER, CO; AUGUST, 1979.
NILGES, M.J. PH.D. THESIS, UNIVERSITY OF ILLINOIS,
1981. ALTMAN, TE. 1810. 1981. MAURICE, A.M.
IBID. 1982. OULIBA, E.P. IBID. 19B3.
C
C DETERMINATION OF G, A ANO « (P) VALUES FOR EPR SPECTRA
C OF SINGLE CRY5TALS IS DONE BY RECORDING SPECTRA AT VARIOUS
C ANGLES IN THREE ORTHOGONAL PLANE5 OF THE CRY5TAL. FOR EACH
C OF THE THREE SETS OF SPECTRA ONE PLOTS THE FIELD POSITION
C ANO INTENSITY OF EACH PEAK AS A FUNCTION OF ANGLE IN THE
C PLANE. THE G, A AND « VALUES CAN BE OBTAINED BY 50LVING
C SIMULTANEOUS EQUATIONS RELATING THESE VALUES TO THE ANGLES.
C UHEN THE SPECTRUM IS CONGESTED, THIS CAN BE DIFFICULT SO
C COMPUTER SIMULATIONS ARE NECE5SARY USING TRIAL PARAMETERS
C WHICH CAN BE VARIED UNTIL THE EXPERIMENTAL AND SIMULATED
C rpR SPECTRA AGREE
C THIS PROGRAM WILL PRODUCE PLOTS OF FIELD P05ITI0N AND
C INTENSITY FOR EACH TRANSITION VERSUS ANGLE. THE USER MUST
C SUPPLY THE PLANE OF ROTATION, THE ANGULAR RANGE AND
C INCREMENT OF ROTATION AND THE FIELD RANGE. FIELD POSITIONS
C AND INTENSITIES ARE CALCULATED BY DIAGONALIZING A SPIN
C HAhILTONIAN WHICH INCLUDES ELECTRONIC AND NUCLEAR ZEEMAN,
C HYPERFINE AND QUAORUPQLAR TERMS. THE HAMILTONIAN 15 CON-
C 5TRUCTED IN THE AXI5 SYSTEM IN WHICH THE G TENSOR IS
C DIAGONAL. THE HYPERFINE ANO QUADRUPOLAR TENSORS CAN BE
C ROTATEO TO THIS COORDINATE SYSTEM BY TRANSFORMATIONS ABOUT
C EULER ANGLES, ALPHA, BETA AND GAMMA, AS DEFINED BY ROSE.
C SEE: ROSE, M.E. "ELEMENTARY THEORY OF ANGULAR MOMENTUM";
C UI LET: NEW YORK, 1963.
C THE HAMILTONIAN IS RESTRICTED TO SYSTEMS WHERE 5- 1/2 AND
C r<= 7/2.
c
c.
c
C INPUT QUANTITIES
C IN THI5 VERSION ALL DATA ARE READ IN USING FREE FORMAT
C THE PARAMETERS NEEO ONLY BE SEPARATED BY BLANKS.
C ALL PARAMETERS MUST BE SPECIFIED (CAN BE-0) AND MUST
C BE ON THE CORRECT LINE.
C
C LINE *1:
C
C FREQ
C
C FREQ: THE EXCITATION FREQUENCY IN GHZ.
C LINE *2:
C
C SPINA, GN, TICOFF
C
C SPINA: THE SPIN OF THE MAJOR NUCLEUS
C GN: NUCLEAR G VALUE FOR THE MAJOR NUCLEUS SPINA.

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nnnnnnnnnonnnnnnnnnnoonnninnnnonnnnnncjnnnnnnnnrinnnnnnnnnnnnnnnnnnnnn
234
(GN ASSUMED TO BE ISOTROPIC ) .
TICOFF: PERCENTAGE OF MAXIMUM INTENSITY BELOW WHICH
TRANSITIONS ARE IGNORED. FOR TICOFF- 0.50: POINTS
FOR WHICH THE INTENSITY IS LESS THAN 50t OF THE
MAXIMUM WILL NOT BE PLOTTED.
LINE *3:
NTR, NOR
NTR: NUMBER OF HYPERFINE TRANSITIONS FOR SPINA; CALCULATES
THE PRIMARY TRANSITIONS FIRST (DELTA MI-O), THEN
/DELTA MI-1/, /DELTA MI-2/ /DELTA MI=2*MI/. BECAUSE
OF 5IZE LIMITS ON THE ARRAYS, NTR MAX-64 (1=7/2).
FOR A GIVEN 5PINA, NTR MAX-(2*MI+1)**2 50 THE DEFAULT VALUE
IS 5ET TO THIS NUMBER IN THE DEFAULT ASSIGNMENT SECTION.
NOR: NUMBER OF ORIENTATIONS FOR WHICH SPECTRA ARE TO
BE CALCULATED. MAXIMUM IS 90.
LINE *4:
NPP,N5ETRN.NBOSC
NPP: -0 FOR PLOT OF FIELD POSITIONS VERSUS ANGLE.
NONZERO FOR PLOT OF INTENSITY VERSUS ANGLE.
N5ETRN: =0,1 FOR PLOT OF THE PRIMARY TRANSITIONS'
POSITION OR INTENSITY. -2 FOR SECONDARY AND
=3 FOR TERTIARY.
NBOSC: =0 WHEN THE OSCILLATING MAGNETIC FIELO (Bl)
IS PERPENDICULAR TO THE 5TATIC FIELD (BO). NONZERO
WHEN Bl IS PARALLEL TO BO.
LINE *5:
BCNTR,BTOTAL.BZEMN
BCNTR: CENTER OF SPECTRUM (GAUSS). IF BCNTR- 0.0,
THEN THE PROGRAM WILL CALCULATE A CENTER OF THE PLOT.
BTOTAL: FIELD SWEEP IGAU55). MUST BE SPECIFIED.
BZEHN. THE FIELD AT WHICH THE HAMILTONIAN WILL BE
DIAGONALIZEO A ZERO (JILL GIVE THE SAME CALCULATION
A5 WITH THE ORIGINAL QPDW PROGRAM. THIS FEATURE ALLOWS
THE ACCURACY OF THE FREQUENCY-SHIFT PERTURBATION FORMULA
TO BE TESTEO. (USEFUL ESPECIALLY AT LOW FIELD5).
LINE *6:
GlI) 1 = 1,3
Gill. PRINCIPAL VALUES OF THE G MATRIX READ IN ORDER
GX,GY,GZ
LINE »7:
All) 1=1,3; ANGSA(J) J=l,3
All): PRINCIPAL VALUES OF THE HYPERFINE MATRIX FOR 5PINA
IN ORDER AX,AY,AZ (IN MHZ).
ANGSA(J): EULER ANGLES UHICH ROTATE THE A-MATRIX FROM THE
COORDINATE SYSTEM WHERE THE G-MATRIX IS DIAGONAL TD THE
COORDINATE SYSTEM WHERE THE A-MATRIX IS DIAGONAL.
READ IN ORDER 1,2,3= ALPHA, BETA, GAMMA
LINE *8:
QD,QE,ANGSQ(I) 1=1,3
C«*** IN THE COORDINATE SYSTEM WHERE THE QUADRUPOLE TENSOR IS
C DIAGONAL, QD=(3/2)*QZ AND QE=(1/2)* IqX-QYI (IN MHZ);
C ANGSQ: ARE THE EULER ANGLES WHICH ROTATE THE Q TENSOR

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C FROM THE COORDINATE 5YSTEM IN WHICH THE G-TEN50R IS DIAGONAL
C TO THE COORDINATE 5Y5TEM IN WHICH THE Q-TEN50R IS DIAGONAL.
C
C LINE5 9-10;
C
C TH1, PHI, DL1
C TH2 , PH2 , DL2
C
C TH1, PHI, DL1: FIRST REFERENCE VECTOR. THETA AND PHI
C ARE WITH RE5PECT TG THE PRINCIPAL AXES DF THE G MATRIX,
C WHILE OL1 15 THE CORRESPONDING ANGLE IN THE CRYSTAL PLANE,
C (THE GONIOMETER ANGLE).
C TH2, PH2, DL2: SECOND REFERENCE VECTOR.
c
FDR
THE
XY
PLANE:
TH1-
90 ,
PHI*
0
(X-AXIS &;
c
TH2=
90 ,
PH2-
90
(Y-AXIS).
c
FOR
THE
XZ
PLANE:
TH1 =
90,
PH1*
0
(X-AXI5I;
c
TH1»
0 ,
PHI*
0
(Z-AXIS).
c
FOR
THE
YZ
PLANE:
TH1-
90,
PHI*
90
(Y-AXIS);
c
TH1 =
0,
PHI*
0
Í Z-AXIS).
c
DL 1
ANO
DL2
EQUAL
0 AND
90
UNLESS
THE CRYSTAL
C G*G TENSOR AXES ARE NQNCOINC I DENT.
C
C LINE *11:
C
C DL(11,DLINT
C
C DL(1); INITIAL ANGLE OF ROTATION.
C DLINT: INTERVAL DF ROTATION. FOR 0L(1J* 0.0 AND
C DLINT= 1.0 AND NOR* 61; A RANCE OF 0.0, 1.0,
C 59.0, 60.0 DEGREES WILL BE CALCULATED OVER.
C
C
c
IMPLICIT REALM (A-H, O-Z >
FXTFRNAL PLPCA
DATA BETA, PI /1.399612386, 1.745329252E-2/
C
C*** BETA= (BOHR MAGNETON/PLANCK'S CONSTANT) MHZ/GAUSS
C*** PI* PI/1B0 CONVERTS DEGREES TO RADIANS.
C
COMPLEX V 116,16) ,SUM I 3),511,51J,YINT
C
DIMENSION ANG5AO) ANG5GM3)
DIMENSION XPLOT(100),YPLOT(100),SCR1(100),SCR2(100)
[DIMENSION A(3) , G (3 > . Q (3 ) ,R(3) ,5(3)
DIMENSION G2 (3 ) , A2 ( 3 ) ,AA(3.3) ,AAA(3,3) , QQ ( 3,3 >
DIMENSION AQ(16,16 I ,IUL(2,64) ,G8N(3,16) ,GBETA O)
DIMENSION AR(16,16),AI(16,16),ZR(16,16),ZI<16,16)
DIMENSION D(16),E(16),E2(16),TAU(2,16)
DIMENSION DL(IOO) , 8FIELDl64,1001 ,TRANINT(64,100)
C
DATA MAXEIG /10/
C
C**** MAXEIG=2*(2*SPINA+1) IS ORDER OF SPIN-HAMILTONIAN MATRIX
C TO BE DIAGONALIZED. AT PRESENT, DIMENSION MAXEIG IS 5ET
C FDR SPINA*7/2. IF MAXEIG IS CHANGED 0IHEN5I0NS MUST
C CORRESPONDINGLY BE CHANGED: (Z-MAXEIG)
C GBN(3.Z,2),P(3+3*Z*Z/4,32),TM(3+3*Z*Z/4),AQ(Z,Z,E), AQKZ.Z),
C AQ2(Z,Z Í ,GB1(3,2) ,G82(3,Z) ,AR(Z,Z) ,AIlZ,Z) ,ZR(Z,Z) ,D(Zi ,
C IUL(2,Z*Z/4),E(Z),E2(Z),TAU(2,Z),V(Z,Z),NTRD-(Z/2)**2.
C
C**** REAO IN PARAMETERS ANO WRITE TO OUTPUT LISTING.
C
REAO(3,*)FREQ
READ(3,*)SPINA,GN,TICOFF
READ(3,*)NTR,NOR
READ(3,*)NPP.N5ETRN,NB05C
READ(3 , *)BCNTR,BTQTAL.BZEMN
REAO(3,* 1 (G(11 , 1 = 1,3)
READ(3,*) ((A(I) , 1*1,3) ,(ANGSAÍJ) , J-1,3))

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nnnnn
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READO,*) READ 13,* ITH1,PHI,DL1
READO ,*>TH2, PH2 , DL2
READO, *>DU1> ,0LINT
C
C**»* WRITE OUT PARAMETERS
C
URITEM , 111 FREQ
11 FORMAT(13X , 'FREQ * ,/10X,F8.5)
WRITE!A,12)SPINA,GN.TIC0FF
12 FORMAT 110X, ‘5PINA GN TIC0FF',
X /5X,F8.1,5X,FB.A,5X,FB.2>
WRITE(A,13)NTR,NOR
13 FORMAT(13X,'NTR NOR',/13X,13,3X,13)
WRITE!A,1AINPP,NSETRN,N805C
1A FORMAT!13X, ' NPP NSETRN NBQ5C' ,/10X,318 I
WRITE(A,13)BCNTR,8T0TAL,8ZEMN
15 FORMAT 112X, 'BCNTR BTOTAL BZEMN • ,/10X,3F8.2)
WRITE!A,16)G
16 FORMAT!1AX, 1 GX GY GZ' ,/1 OX,3FB.5)
WRITE I A,17)
17 FORMAT!///15X,17H PRINCIPAL VALUES,18X,13H EULER ANGLES,
X / / 13X , 'X' ,UX, ' V • ,11X, 'Z' )
WRITE(A,IS >G
WRITE(A,19IA,ANG5A
WRITE! A,20)Q,ANGSB
WRITE!A,211QD,QE
18 FORMAT!6H G .3F12.5I
19 FORMAT(6H A/MHZ,3F12.3,3X,3F10.2)
20 FORMAT(6H Q/MHZ,3F12.3 3X,3F10.2)
21 FORMAT!//10X,AH t}D-, F12.3 , AH QE-.F12.3)
WRITE(A,22)
WRITE(A,23)TH1,PHI,0L1
WRITE(A,23 ITH2,PH2,0L2
22 FORMAT!/10X 'THETA PHI OELTA')
23 FORMAT!BX,3FB.2)
WRITE(A,2A)0L(1),0LINT
2A FORMAT ( 6X, 'OH 1) OLINT ' ,/10X ,2FB . 21
C
C*##**# INITIALIZATION SECTION ******
C
NTRD*!(2,0*SPINA)+1,0)*!(2.0*SPINA)+1.0)
IF(NTR,GT.NTRDI NTR-NTRD
N5PA=2.0*5PINA+1.1
NSPA1»NSPA+1
NEIG5T=2*N5PA
NEIGP1=NEIGST+1
BHALF=BT0TAL/2.0
SET UP HAMILTONIAN HATRIX WITH QUAD2 AND REARRANGE
IUL IF NECESSARY TO CHOOSE THE SET OF TRANSITIONS
SELECTED BT NSETRN.
CALL aUA02(IUL,NTR,N£IG5T)
IULDIM=36
C PRIMARY TRANSITIONS: THERE ARE NSPA OF THEM
C
IF!N5ETRN.GT.1) GO TO 72
NTR=N5PA
GO TO 80
C
C SECONDARY TRANSITIONS: A*SPINA OF THEH.
C
72 CONTINUE
IF Í NSETRN.GT.2 I GO TO 75
CALL NEWIUL(IUL,NSPA,IULDIM)
NTR=A.0*5PINA
GO TO BO

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nnn no
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TERTIARY TRANSITIONS: 4*SPINA-2 OF THEN.
75 CONTINUE
IF(NSETRN. GT.3 1 CO TO 80
NROT=4*5PINA+NSPA
CAUL NEUIUL(IUL,NRDT,IULDIMt
NTR-4.OtSPINA -2.0
80 CONTINUE
OO 100 1*1,3
G2II)-G(I)*Cm
CBETAII > -GI I K8ETA/2.0
A2 100 CONTINUE
ail > — QE-QD/3,0
CII2J* QE-QD/3.0
Q<3)=2.0*QD/3.0
CAUL TRANS IANC5A,A,AAA)
CALL TRAN5 CAUL TRANS(ANG5Q,Q,QQ)
CALL QUA01I AAA,QQ,GN,NEIGST,MAXEIG,AQ,G8N)
DO 105 J-1,3
DO 105 I-l.J
GG-GII)*G(J>
AA(I,J)-AA(I,J)*GG
105 CONTINUE
DETERMINE ORIENTATION (DIRECTION COSINES I .
THI=TH1*PI
PHI-PHUPI
THF=TH2*PI
PHF-PH2*PI
OCX 1-SIN DCY1-5IN(THI)*SIN(PHI>
OCZl-COSITHI)
DCX2-5IN(THF1*COS(PHFI
0CY2»5IN(THF)*5IN(PHF>
DCZ2-C05 (THF I
DCNX=OCY1*DCZ2-OCZ1*DCY2
DCNY=DCZ1*0CX2-DCX1*0CZ2
DCNZ-DCX1*0CY2-0CY1*0CX2
CANG=0CX1*0CX2+0CY1»DCY2+0CZ1*DCZ2
5AG2=DCNX*DCNX+OCNY*OCNY+OCNZ*OCNZ
SANG=SaRT(5AG21
SCK=5IN((DL2-0L1)*PI1
IF(5CK.LT.0.0 I 5ANG—5ANG
0NXX-DCNX*DCNX/SAG2
0NYY-0CNY*DCNY/5AG2
ONZZ-DCNZ*DCNZ/ 5AG2
0NXY=DCNX*DCNY/SAG2
DNYZ=0CNY*DCNZ/SAG2
DNZX=DCNZ*0CNX/SAG2
C
CM44*t* BEGIN CALCULATION LOOP OVER THE ORIENTATIONS CHOSEN
C
00 300 NA-1,NOR
OL ( NA Í =0L(1 í + OLINTKMNA-1)
AGI=IOUNA)-OL11*PI
AGC=C05 AGS-SINIAGI 1/SANG
DCX-DCX1*AGC+DCX2*AGS
0CY-0CY1*AGC+DCY2*AG5
DCZ-OCZ1#AGC+DCZ2#AC5
THR-ACOS(DCZ)
TH-THR/PI
IF(THR.EQ.0.0)GQ TO 150
FC=0CX/5IN(THR)+1.0
FC-AB5IM00IFC.2.011-1.0
PH=AC05iFC1/PI
IF(OCY.LT.O.O) PH-360.0-PH

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nnn nnn nnn non
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150 CONTINUE
DLL-OL(NA)
IF(DLL.GT.3¿0.0I 0LL-DLL-360.0
IF(OLL.LT.0.0 I 0LL-0LL+360.0
WRITEI4, 152ITH.PH.DLL
152 FORMATl/2X. 1 THETA-1 ,F8.2,' PHI-',FS.2,' DELTA-â– ,FB.21
DCXX-DCXÍDCX
DCYY-DCY4DCY
DCZZ=DCZ*DCZ
DCXY-DCX40CY
DCYZ=DCY*OCZ
DCZX-0CZ4DCX
SET UP FIELDS AT WHICH TRANSITIONS OCCUR
GE2-G2I1)*DCXX+G2(2)*0CYY+G2(3)*0CZZ
GEFF-5QRT(GE21
GB»GEFF#BET A
GGB-GEFF*GEFF*BETA
H-FREQ*1000.0/C8
HZEHN-H
IF(BZEMN.NE.O.O) HZEHN-BZEMN
IF BLO-BCNTR-BHALF
BHI-BCNTR+BHALF
TWOH-H+HZEMN
HDCX-HZEMN4DCX
H0CY-HZEMN4DCY
HDCZ-HZEMN*DCZ
SET UP SPIN HAMILTONIAN MATRIX. AR- REAL; AI- IMAGINARY.
DO 200 1-2 . NEIGST
JJ-I-1
DO 190 J-l.JJ
ZR 11,J J-0.0
ZR(J,11-0.0
ARI I,J)«AQ(I,Jl
AI (I J ) -AQ Í J , IJ
190 CONTINUE
200 CONTINUE
00 220 1-1.NEIGST
N=1
IF tl.GT.NSPA) N —1
AR(I.I)- Afl(I.I) + HDCZ*(GBN(3,I> + G8ETA(3)*N)
AKI ,11- 0.0
ZRU.Il— 1.0
IF J-I-l
ARd.J)- ARd.J) + HOCXtGBN(1,1)
AKI.J)- AI(I.J) + HDCY4GBN (2,1)
214 IF(I.LT.N5PA1I GO TO 220
J-NEIGP1-I
AR íI , J)- AQ(I,J1 + HOCXtGBETA{11
AI(I.J)» AQ(J,I) + HDCY*G8ETA(2)
220 CONTINUE
DIAGONAL!ZATION OF SPIN HAMILTONIAN MATRIX
CALL HTRIDI(MAXEIG,NEIGST,AR,AI,D,E.E2.TAU)
CALL TQL2lMAXEIG,NEIGST,D,E,ZR,IERR I
IF(IERR.NE.O) GO TO 990
CALL HTRIBK(MAXEIG,NEICST,AR,AI,TAU.NEIGST,ZR,ZI)
STORE EIGENVECTORS (Z).
00 230 K-1.N5PA
K4-K+N5PA
DO 225 J-l.NEIGST
5IPR3-ZRÍJ,K4)

239
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5IPR4-ZI(J,K4>
5IPR1=ZR(J,Kl
5IPR2=ZI(J,K1
U(J,K4)-CMPLX(5IPR3, 5XPR4)
O(J,K) -CMPLXISIPR1.-SIPR2I
225 CONTINUE
230 CONTINUE
C
C DETERMINE TRANSITION FIELDS
C
DO 300 JA-l.NTR
IU-IULÍ1 , JA)
IL-IULI2,JA)
HA-TUOH + (O(IL)-D(IU) WGB
SFIELO(JA,NA)“HA
C
C CALCULATE TRANSITION INTENSITIES
C
SUM(1>-0.0
SUM(21-0.0
SUM[3 >“0.0
DO 240 1-1,NEIG5T
J-NEIGP1-I
sii-uii,iu>*vri,XL>
su-uu ,iu>*u(J,il>
SUM(1>-SUM(1)+SIJ
IF(I.GT.N5PA) GO TO 233
SUM(2I-SUM(2I+SIJ
SUM(3)-SUM(3>+SII
GO TO 240
233 CONTINUE
5UM(2)-SUH(2I-5IJ
5UM(3)-SUM(3I-SII
240 CONTINUE
SUM(2>-5UM(2 > X (0.0,1.0)
DO 245 J-l,3
YINT-GIJ)*SUM R(J1-REAL(TINT 1
S(J)-AIMAGIYINT)
245 CONTINUE
R1PS1=R(1)*R(11 + 5(1)*5(11
R2P52-R(21*R(2> + 5(2>*S<2)
R3PS3-R(31*R(3> + S<3>*5(3>
RS12- R(1l*R(2) + 5(1>*S(2>
RS23- R(2)*R(3) + 5<2)*5(3>
RS13- R(1)*R<3) + S111XSI3!
IF(NB05C.NE.01 GO TO 250
TI- R1PS1ÍDNXX + R2PS2H0NYY + R3PS3XDNZZ
X + 2.0*R5I2*DNXY + 2.OXRS23XONYZ + 2.0XRS13XDNZX
GO TO 255
250 CONTINUE
TI= R1PS1XDCXX + R2PS2XDCYY + R3PS3XDNZZ
X + 2.0XRS12XDCXY + 2.0*RS23*DNYZ + 2.0XRS13XDNZX
255 CONTINUE
TRANINT1JA.NAl-TI
C
C WRITE OUT THE RESULT5 AT THIS ORIENTATION.
C
URITE(4,262>8FIEL0(JA,NA>,TRANINT(JA,NA1
262 FORMATI2X,'FIELD- ’ , F8.2,2X , 'INTENSITY- ',E16.8I
300 CONTINUE
C
C FIND MAXIMUM INTENSITY FOR CUTOFF (TICOFF).
C
TIMAX-0.0
DO 350 JA-l.NTR
DO 350 NA-1,NOR
TITEST-TRANINTIJA,NA>
IFITITEST.GT.TIMAX>TIMAX-TITEST
350 CONTINUE

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on n o non
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URITEM .332ITIMAX
35£ FDRMAT(/HX,'TIMAX=',£23,16)
IFITIMAX.LE.0.01 TIMAX-1.0
TILIH=TIMAX*TICQFF
C
C FIND OUT THE NUMBERS OF TRANSITIONS TO BE PLOTTED.
C
IF(N5ETRN.EQ.3 I GO TO 370
IF(N5ETRN.EQ.21 GO TO 360
C
C PRIMARY TRANSITIONS
C
LINE1=1
NLINE5=NSPA
CO TO 400
C
C SECONDARY TRANSITIONS
C
360 CONTINUE
LINE1=N5PA+1
NLINE5-NSPA + 4*SPINA
GO TO 400
C
C TERTIARY TRANSITIONS
C
370 CONTINUE
LINE1-NSPA1 + 4*5PINA
NLINES-NSPA + 4*5PINA + 4*SPINA - 2
400 CONTINUE
IF(NPP.NE.O) GO TO 600
C
C PLOT OF FIELO VERSUS ANGLE.
C
C *** USE PL0T79 ROUTINES ON UF/QTP VAX *»*
C
C INITIALIZE THE PLOT 5Y5TEH
C
CALL PLTOO
SET UP PLOT SIZE 13. CM HIGH, 23. CM LONC
CALL 5ET5ZI23.)
CALL SETDS2I1.,.01
PLOT AND LABEL THE X-AXIS
CALL
1
C
C PLOT
c
CALL
1
C
CALL
PLTAXO. /2S . ,3. /23. , 7HDEGREES , 7 ,
20. /23 . ,0 . , OLI 1 1 ,20 . , OLI NOR 1 , .013,-1)
ANO LABEL THE Y-AXIS
PLTAXO. /23. ,3./23. , 18HFIELD STRENGTH IG>,18,
15 . /25 . ,90 . , BLO ,20 . , BHI , - . 013,2 )
5ETVP2 0. /23. ,23. /23. , 3. / 23 . ,1B. /2S. t
C
C ONLY TRANSITIONS BETWEEN BLO AND BHI THAT HAVE SUFFICIENT
C INTENSITY WILL BE PLOTTED.
C
DO 500 JA-LINE1,NLINE5
NPT5-0
OQ 430 NA«1,N0R
IF IBFIELD{JA,NA >.GT.BHII GO TO 4S0
IF(0FIELO(JA,NA).LT.BLOl CO TO 4B0
IF 1TRANINTíJA,NA 1 .LT.TILIM1GO TO 490
NPT5-NPTS+1
XPLOT(NPT5)»OL(NA)
YPLOT(NPTSI»BFI£LOI JA,NA I
SCR1INPT5)»XPLOT(NPTSI

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nnnnnnnn nnn n n n non non o n nnn non
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SCR2INPTS)-YPLOT(NPTS)
480 CONTINUE
DRAW THE LINE FOR EACH TRANSITION
CALL GRFGI (0Ll1),XPLOT,DL 1 SCR1,SCR2,NPT5,1. ,PL2CA)
500 CONTINUE
GO TO 980
600 CONTINUE
PLOT OF INTENSITY VERSUS ANGLE.
CALL PLT00
CALL 5ETSZ(25.)
CALL 5ETD52(1...8)
PLOT AND LABEL THE X-AXIS
CALL PLTAXO./25. ,3./25. , 7HOEGREES , 7 ,
1 20./25. ,0. ,0L(1I ,20. ,DL PLOT ANO LABEL THE Y-AXIS
CALL PLTAXI3./25.,3./25.,9HINTEN5ITY,9,
1 13./23. ,90. ,0.,0.2,1. ,-.015,2)
CALL 5ETUP20. /23 . ,23 . /23. ,3./23. ,18./23. )
00 700 JA-LINE1.NLINES
NPTS-0
00 680 NA-l.NOR
NPT5-NPT5+1
XPLOT(NPTS)-OLINA)
YPLOT(NPTS)-TRANINTtJA.NAI/TIMAX
IF(YPLOT(NPTS).GT.1.0) YPLOTINPTS)-1.0
IFlYPLOT < NPT5 Í .LT.0.0 I YPLOT(NPTSI-0.0
SCR1(NPTSl-XPLOTINPTS)
SCR21NPTSI-YPLOT (NPTS I
680 CONTINUE
CALL GRFGI (OL(1>,XPLOT,DL,0.,YPLOT,1.,NPTS,
1 5CR1,5CR2,NPTS,1.,PL2CAI
700 CONTINUE
EJECT THE FRAHE
980 CALL PLTEJ
990 URITE(4,999IIERR
999 FORMAT(/2X,5HIERH-,13)
STOP
END
SUBROUTINE TO ROTATE THE ARRAY IUL, WHICH CONTAINS
THE INTEGER LA8EL5 OF THE INITIAL ANO FINAL STATES FOR EACH
TRANSITION. THIS ARRAY IS CREATED IN THE SUBROUTINE OF DLIB.
SUBROUTINE NEWIUL(IUL,NROT,IULDIM)
DIMENSION IULI2.36) ,NUIUL(2,36)
C
DO 500 K-l.NROT
C
C ONE ROTATION DONE IN THIS LOOP
C
00 200 1=1,2

242
631
IUL0M1=IULDIM-1
632
DO 100 J-l,IULDhl
633
NWIULII , Jl-IULI I ,W+1)
634
100
CONTINUE
635
NWIULI I , IULDIMI-IULI I , 11
636
200
CONTINUE
637
C
638
DO 400 1*1,2
639
DO 400 J*1,IULOIH
640
IULII,Jl-NUIULII,Jl
641
400
CONTINUE
642
500
CONTINUE
643
RETURN
644
END
* FOR RSDSDI5K:CJTDXCAL
* FOR RSDSOISK;CJT.ILLDEPHLI8S
* LINK XCAL,EPRLIB5.UTILSDI5K:CEI5PACK3EI5PACK.OLB/LIB, -
0PLT:PTIGERLIB
» IF PI .EQ5. "" THEN INQUIRE PI "Naaa of file with XCAL data IND ,e*t!>"
t ON CONTROL Y THEN * GOTO DONE
t ASSIGN * 'PI'.DAT FOR003
* AS5IGN 'PI 1 .L5T FOR004
* A55IGN 'PI'.PTI FOR021
$ RUN R5DÍDI5K:CJTIXCAL.EXE
* DONE:
* DEA5SIGN FOR003
Í DEASSIGN F0R004
* DEASSIGN FOR021
Í WRITE 5Y5SOUTPUT "Your output listing is in ‘“Pl'.LST."
s WRITE 5YSS0UTPUT "Youp plat fila is in ' ' PI ' . PTI."
* INQUIRE PLDTIT "Da tjau want it platted at the printer an gour terainalT"
» IF PLOTIT THEN 0PLT:PLOTTIGER.COM 'PI'.PTI TT:

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nnnnonnnnnrjrjonnonnnnnnninnnonnnnnrjrinnnnnnnnnnnnonnnn nonnnnnnnnnn
243
ciitHtmmttitttiiimiitMMUMMOiMtMtxiimmtMHt*
EPRLIB5 «* *«* 11*1 % ****!« S «» « ** »$* t ***
EPR-ELECTRON PARAMAGNETIC RESONANCE; LIB5=5UBROUTINE LIBRARY
THIS FILE CONTAINS SUBROUTINES USED IN THE EPR POWDER
PATTERN SIMULATION PROGRAMS QPOU AND XP0W WRITTEN BY THE
R. L. 9ELF0R0 GROUP AT THE UNIVERSITY OF ILLINOIS. FOR
THE PROPER REFERENCES, SEE THE MAIN PROGRAM XPOW.
THESE 5UBROUTINE5 HAVE BEEN MOOIFIEO FOR USE BY THE
R. S. ORAGO GROUP AT THE UNIVERSITY OF FLORIDA.
*************** (J. TEL5ER 2/18/BA) **********************
SUBROUTINE QUAD1(AA,Qq,GN,M,NH,AQ,GBNI
*$*ts*l**$»**l***l****$*$*****»****lt**tts*tt»**t««*t*»*tt*»llt
THIS SUBROUTINE CALCULATES THE HYPERFINE ANO QUADRUPOLE
PART5 OF THE HAMILTONIAN. IT SETS UP A AI+2 BY 41+2 MATRIX,
NAMED A5 AS FOLLOW5:
!MS,HI>!M5PMI-1>...IMS,-MI> !-MS,-MI>!-M5,-MI+l>...¡-ms,mi>
< MS, Ml!
< MS,-MI!
<-M5,-MI!
<-M5; MI!
THIS HAMILTONIAN MATRIX WILL BE USED TO CALCULATE ENERGY
SPLITTINGS AND EVENTUALLY TRANSITION FIELDS. A WORD OF
CAUTION IS IN DROER, SINCE THE IMAGINARY ELEMENTS, WHICH
ARE STORED IN THE UPPER TRIANGLE, ACTUALLY ORIGINATE FROM
THE LOWER TRIANGLE. THIS SUBROUTINE ALSO DETERMINES THE
NUCLEAR ZEEMAN ENERGIES. THE INPUT VARIABLES ARE A5 FOLLOWS:
AA - THIS ARRAY CONTAINS THE HYPERFINE MATRIX.
IF THE HYPERFINE AXIS SYSTEM IS COINCIDENT WITH THAT
OF THE G TENSOR, AA WILL BE DIAGONAL. IF NOT, THE
EULER ANGLES WILL ROTATE THE HYPERFINE AXIS GENRATING
OFF-OIAGONAL ELEMENTS.
(ONLY THE UPPER TRIANGLE OF AA IS NEEOEO).
QQ - ARRAY CONTAINING THE QUADRAPOLE TENSOR.
¡ONLY THE UPPER TRIANGLE IS REQUIRED).
GN - THE NUCLEAR G FACTOR FOR THE PRINCIPAL NUCLEUS
M - AI+2; THIS VARIABLE, WHICH IS THE TOTAL NUMBER OF
STATES, SETS THE SIZE OF THE MATRIX.
NM - MAXIMUM SIZE OF THE ARRAY AQ , (lá X 161. THIS WOULD
CORRESPOND TO 1=7/2 SINCE WHEN 1=7/2, THERE ARE 16
STATES IS WITH MS-1/2 AND B WITH MS—X/HI
THE OUTPUT VARIABLES ARE:
AQ - HAMILTONIAN MATRIX CONTAINING QUADRUPOLE ANO HYPERFINE
TERMS ONLY. IT IS SET UP SUCH THAT THE UPPER TRIANGLE
CONTAINS THE IMAGINARY TERMS AND THE LOWER TRIANGLE,
THE REAL TERMS. OF COURSE, THE DIAGONAL TERMS ARE
REAL SINCE H 15 HERMITIAN.
GBN- THIS IS A THREE ROW ARRAY CONTAINING THE NUCLEAR ZEEMAN
TERMS. THE FIRST ROW CONTAINS THE OFF-DIAGONAL REAL
ELEMENTS (OELTA MI- +1,-11; THE SECOND ROW CONTAINS
THE OFF-DIAGONAL IMAGINARY ELEMENTS (OELTA MI- +1,-11;
THE THIRD ROW CONTAINS THE DIAGONAL ELEMENTS.
Int NUCLEAR ZEEMAN INTERACTION COUPLES LEVELS FOR
OELTA MI EQUAL TO +1,-1 (DELTA MS =0)
DIMENSION AA(3,3>,QQ(3,3),AQINM.M),GBN O,H)
REAL MS,MI
C
C
C THI5 PART SETS UP THE INITIAL VARIABLES:

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nonnnn nnnnnn nnnon oonno
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C BN - NUCLEAR MAGNETON
C N5PA - 21+1 WHICH 15 THE DEGENERACY OF EACH MS LEVEL
C N5PA1 - 21 + 2 THIS SIGNALS THE START OF M5—1/2
C N5PA2 - 21+3
C SPINA - I (THE NUCLEAR SPIN)
C 5PNA - 1(1 + 1 I, ENERGY OF 1**2 ¡Mil
C
DATA BN /7.6223322E-4/
NSPA«REAL(M)*0.5 + 0.01
NSPA1-NSPA+1
NSPA2-N5PA1+1
SPINA=(REAL(N5PA)-1.01*0.5
SPNA=5PINA*(SPINA+1.0)
C
C
C THIS LOOP SETS UP THE AQ MATRIX WITH ALL ZEROES
C
00 119 I-1,M
00 119 J«1,M
AQ(I,J>«0.0
119 CONTINUE
00 111 I-l.M
THIS CHECKS FOR UPPER OR LOWER LEVEL (MS-+1.-1);
MI UILL VARY FROM MI TO -MI AND -MI TO MI, RESPECTIVELY.
IF(I.GT.NSPA) GO TO 112
MI-5PINA + 1.0 - REAL(II
MS-0.5
N-l
GO TO 113
112 CONTINUE
MI-REAL(I) - 2.0 - 3.0*SPINA
MS —0.5
N— 1
113 CONTINUE
THIS SETS UP THE DIAGONAL ELEMENTS OF AS AND OF THE
NUCLEAR ZEEMAN MATRIX.
AQ( I ,I)-AAO,3l*MS*MI + QQ (3,3 ) * ( 3.0*MI*MI - 5PNA1/2.0
G0NÍ3,11—GN*BN*MI
IF(I.EQ.l.OR.I.EQ.NSPAl) GO TO 114
THIS PART LOOKS AT THE OFF DIAGONAL ELEMENTS; LEVELS FOR
WHICH DELTA MI-+1.-1 ARE COUPLED TOGETHER. SLO 15 THE
ENERGY OF A RAISING OR LOWERING OPERATOR.
J-I-l
SLO-SQRT(SPNA - MI*MI - MI*REAL(NI I/2.0
GBN< 1 ,1 >— GN*BN*SLO
GBN(2,I I=G8N(1,1)*REAL(N)
ACM I , JI-IAAI1,3)*MS + QQ(1,31*(2.0*MI + REAL(N)))*5LO
Aq(J,I)=(AA(2,3I*M5 + QQ(2,3)*(2.0*MI + REAL(NIII*SLO*
REAL(N)
IF(I Eq.2.OR.I .EQ NSPA2) GO TO 114
THIS PART LOOKS AT THE OFF DIAGONAL ELEMENTS FOR
DELTA MI= +2,-2. SRSL IS THE ENERGY OF TWO RAISING OR
LOWERING OPERATORS.
J = I-2
SRSL=SL0*SQRTI5PNA - MI*MI - 3.0*MI*REAL(N) - 2.01/2.0
AQ ( I , J) -1 QQ ( 1 ,11—QQ(2,2M*SR5L
AQ(J,11-2.0*QQ(1,21*5R5L*REAL(NI
114 CONTINUE

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nnnnnnnnnnnnnnnn n nnn nnnnnn
245
THE BEST OF THI5 SUBROUTINE COMPUTES SOME ADDITIONAL OFF-
DIAGONAL ELEMENT5 OF AQ. THESE ARISE FROM OFF DIAGONAL
HYPERFINE VALUES.
IFlI.LT.NSPAlt GO TO 111
J=M+1-I
AQ(I , JI-AAIl,3)*HI/a.O
AQ(J,Il-AA(a,3l*MI/a.O
IFII.EQ.NSPA1) GO TO 115
J-H+2-I
AQ(i,j)»(AA(i,i)+AAia,an*SLO/a.o
115 CONTINUE
IFII.ED.Ml GO TO 111
J-M-1
5RA“5QRT(SPNA - MI*MI + MI»REALIN)I/a.0
AQ( I,JI»(AA(1,1l-AAia,21)*SRA/a.0
AQ[J,I>=AA(l,a>*SRA
111 CONTINUE
RETURN
END
SUBROUTINE QUA02IIUL,NTR,M)
• ««*M»«**M*t$**tMt»t««M**«*»«M»*«t«t«***»«**t«*«tM**tt**«
THIS SUBROUTINE GENERATES ALL POSSIBLE HYPERFINE TRANSITIONS
FOR A NUCLEUS WITH SPIN I (M-AI+2). IT SETS UP A TWO ROW
MATRIX: IUL. THE FIRST ROW CONTAINS THE FINAL STATE OF A
TRANSITION AND THE SECOND ROW CONTAINS THE INITIAL STATE.
THE INPUT VARIABLES ARE A5 F0LL0U5:
NTR - THE NUMBER OF TRANSITIONS TO BE GENERATEO; NTR CAN
HAVE A MAXIMUM OF H*M
M - THE TOTAL NUMBER OF STATES.
THE OUTPUT VARIABLES ARE:
IUL - ARRAY CONTAINING THE INITIAL ANO FINAL STATES,
IULia.MI AND IUL11,M1 , RESPECTIVELY. THE PRIMARY
TRANSITIONS ARE FOLLOWED BY THE SECONOARY WHICH ARE
FOLLOWED BY THE TERTIARY... UP TO A MAXIMUH OF M*N
TRANSITIONS.
DIMENSION IULia.NTR)
N=REAL(M)IS.0 + 0.01
Ml-M+1
C
C
C THIS LOOP SETS UP THE PRIMARY TRANSITIONS (DELTA MI»OI.
C
DO 101 1=1,N
IUL11,1)=M1-I
iUL 101 CONTINUE
I=N
NJ=1
103 CONTINUE
KJ=N-NJ
C
C THIS LOOP WILL SET UP AS MANY TRAN5 AS REQUIRED BY NTR.
C
00 loa K=1,KJ
I-I+l
J=I+1
IUL11,1)=M1-K-NJ
IUL ( 3 , I > *K
IUL11,J) = IUL(1,1)+NJ
iul i a, j ) “Iul (a, i) +nj
i=j

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nnnnnnnnnnnnnnnn
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102 CONTINUE
NJ=NJ+1
IFll.LT.NTRI GO TO 103
RETURN
END
C
C*************************************************************
C
SUBROUTINE TRANS IANG5,A,AA)
*****S***(t»**(*(**I**t**tt«*(***********t«t**»StM**»***«««t«*
THIS SUBROUTINE PERFORMS A SIMILARITY TRANSFORMATION ON THE
DIAGONAL HYPERFINE MATRIX, A. THIS TRANSFORMATION U5ES THE
EULER ANGLES TO ROTATE THE HYPERFINE AXIS SYSTEM TO THAT OF
THE G TENSOR. THE INPUT VARIABLES ARE AS FOLLOWS:
ANG5 - THESE ARE THE EULER ANGLES DESCRIBED BY ROSE
(ALPHA, BETA AND GAMMA).
A - THIS THE DIAGONAL HYPERFINE MATRIX
THE OUTPUT VARIABLES ARE:
AA - THIS 15 THE TRANSFORMED HYPERFINE MATRIX;
AA = (T-l) (A) (T+l), WHERE (T-l) AND (T+ll ARE
UNITARY TRANSFORMATION MATRICES <(T-1) 15 THE INVERSE
OF (T+l) >. ONLY THE UPPER TRIANGLE IS COMPUTED
SINCE AA IS SYMMETRIC.
DIMENSION A(3),ANG5(3),AA(3,3),SN(3),CS(3>,T(3,3)
C
C
C PI CONVERTS DEGREES TO RADIANS
C
DATA PI 71.74532952E-2/
C
C
C THIS LOOP COMPUTES THE SINE AND C05INE OF THE EULER ANGLES
C
00 101 1*1,3
ANG=ANG5(I)*PI
SN=5IN CS(II=COSIANG>
101 CONTINUE
FOLLOWING
SEQUENCE SETS
UP THE TRANSFORMATION MATRICES
1(1,1)* CS(1
T(2,ll—CS(1
Til,21* 5N<1
T(2,2)*-SN(1
T(3,1 I* CS!1
T ( 3 ,2 ) * SN (1
T(1,31=
T(2,31=
T (3,3 I *
)*CSI2)*CS(31-SN<
l*CS(3)*5N(3l-5N(
l*CS(2)*CS(3)+C5(
)*CS(2)*SNI3)+CS(
> XSN(2)
)*5N(2)
-SN(2)*CS(3)
SN(2}*SN(3)
CS (2)
1
1
1
1
)*5NI3I
iXC5(3 )
1*5N(3)
)*C 5(3)
C
c
c
c
THIS LOOP
PERFORMS
THE TRANSFORMATION ON A
DO 102 J=1,3
DO 102 1=1,J
AA(I,J1=AI1>*T(1,I)*T(1,J)+A(2)*T(2,I)*T(2,J)+AI3)*T(3,I)
X *T(3 , J)
102 CONTINUE
RETURN
END
C
C************************************************************
c
SUBROUTINE BIND(SPINA,NEA,NSPA,ITA)
C*»í»*n***»»***»»*í******»******»»*******r'*********************
C THIS SUBROUTINE GENERATES THE INTENSITY DISTRIBUTION FOR A

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nnnnnnn
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C SET OF EQUIVALENT NUCLEAR SPINS. FOR EXAMPLE, IF NEA=2 AND
C SPINA=l/2, BINO WILL COMPUTE THE INTENSITY DISTRIBUTION OF
C THE PEAKS TO BE 1:2:1. THE INPUT VARIABLES ARE AS FOLLOWS:
C NEA - THE NUMBER OF EQUIVALENT ATOHS (E.G. IF NEA= 3,
C THERE ARE THREE ATOMS WITH SPINA I
C SPINA-THE NUCLEAR SPIN, I
C THE OUTPUT VARIABLES ARE:
C N5PA- NUMBER OF NONDEGENERATE TRANSITIONS WHICH ARE ALLOWED
C ITA - A ONE DIMENSIONAL ARRAY CONTAINING THE INTENSITY
C DISTRIBUTION. THE CORRECT RATIO WILL BE IN THE TOP
C OF THE ARRAY WITH THE REMAINDER ZEROS.
C
ctxtsttmKKtttmmmmtsisHiiKtiiimmHitsttitttttt
DIMENSION ITA(20I ,ITS C SO 1
NSA=2.0*5PINA + 1.01
ITA(11=1
NSPA=1
COMPUTES INTENSITY FDR EACH NUCLEUS. IT USES A CUMULATIVE
METHOD WHICH BUILDS UP AN INTENSITY IN ITB AND THEN EMPTIES
THESE VALUES INTO ITA. THE PROCESS 15 THEN REPEATED FOR
THE SPECIFIED NUMBER OF NUCLEI.
DO 2 J*1 , NEA
C
C
C THIS LOOP INITIALIZES THE ARRAY, ITB, WITH ALL ZEROES.
C
DO 72 NZ2=1,20
ITBÍNZ2)-0.0
72 CONTINUE
C
C
C HERE, ITB IS COMPUTED
C
DO 3 K = 1,NSPA
DO A L=1 , N5A
ITB(L+K-1)=ITA A CONTINUE
3 CONTINUE
C
C
C THIS LOOP TRANSFERS VALUES FROM ITB TO ITA BEFORE CLEARING
C ITB.
C
DO 5 M=1,20
ITA(M)=IT8(M)
5 CONTINUE
NSPA=2.0*5PINA*REAL + 1.01
2 CONTINUE
RETURN
END
C
c**************************************************************
C
SUBROUTINE PREP(XTAL,ZR,D,EULER)
C
C DETERMINES PRINCIPAL VALUES AND EULER ANGLES FOR A GIVEN
C MATRIX. 0 CONTAINS PRINCIPAL VALUES; EULER CONTAINS EULER
C ANGLES.
C
IMPLICIT REAL*A (A-H.O-Z)
DIMENSION XTAL<3,3),CZER0I3,3) ,ZR(3,3> ,ZI13,3),0(3),E t 3 I,
X EH(3 >, T AU ( 2,3),EULER(3)
DATA PI /I.7A5329252E-2/
DATA IQNE , ITWO,ITHR /1,2,3/
DD 1 J=1,3
DO 1 1 = 1 ,3
ZR
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IF (J EC) I)ZR(I,I>-1.0
1 CONTINUE
DATA CZEfiO /9*0.0 /
CALL HTRIDI(3,3,XTAL,CZERO,0,E,E2,TAUI
CALL TQL2(3,3,D,E,ZR,IERR)
IF(IERR .E3. 0)GO TO 20
URITE(7,101 IERR
10 FORMAT(28H0ERR0R EXIT FROM TQL2: IEHR-,121
GO TO 90
20 CALL HTRIBK(ITHR,3,XTAL,CZER0,TAU,3,ZR,ZI)
XTAL(ITUO , IONE)-XTAL(IONE , ITUO)
XTALIITHR,IONE)-XTAL(IONE,ITHR)
XTAL(ITHR,ITUO)=XTAL(ITUO,ITHR)
IF í ZR(IONE,ITHRI 130,40,30
30 EULER(IONE)-ATAN2 GO TO 50
40 EULER(IONE)-SIGN I 90.0, ZR(ITUO,ITHR1 1
ZRIITHR,ITHRI=5IPR1
50 EULERÍITU01-AC05 f 5IPR11/PI
IF(ZR(ITHR,IONE)160,70,60
60 EULER(ITHR)=ATAN2(-ZH(ITHR,ITUO),ZR(ITHR,IONE))/PI
GO TO 80
70 EULERÍITHR)-5IGN(90.0, -ZRIITHR,ITUO)I
BO CONTINUE
RETURN
90 STOP
ENO
C
c**************************************************************
c
SUBROUTINE TRNFM(ORIG,ROTN,UGET)
PERFORMS TRANSFORMATION INU IMPLICIT REAL*4 (A-H.O-Z)
DIMENSION ORIG(3,3),R0TN(3,3),UGET<3,3>,AMIDL(3,3I
DO 10 JT-1,3
DO 10 IT-1,3
AM IDL(IT,JT1=0.0
00 10 KT-1,3
10 AMIOLlIT,JT)-AMIDHIT,JT) + ROTN(KT,IT) * ORIG(KT.JT)
00 20 JT-1,3
DO 20 IT-1,3
UGETI IT,JT)-0.0
DO 20 KT-1,3
20 UGETIIT,JTI-UGETÍIT,JT) + AMI QUIT , KT ) * RDTN ( KT , JT)
RETURN
END

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c***************************************************************
C***t*«*****«********** DXTLFIT ******************************
Q-DOU8LE PRECISION; XTLFIT-SINGLE CRYSTAL EPR G TEN50R FIT
THIS PROGRAM WAS WRITTEN BY JOSHUA A. TEL5ER AT THE
UNIVERSITY OF FLORIDA (6/1/84).
THIS IS THE HAIN PROGRAM THAT REA05 IN THE PARAMETERS FOR
OSTEPT AS WELL AS THE THE PARAMETERS TO BE MINIMIZED,
THE EXPERIMENTAL OATA, ANO INFORMATION FOR PLOTTING.
DEFINITIONS OF THE PARAMETERS FOR 05TEPT CAN BE FOUND IN
THE LISTINGS OF THE SUBROUTINES FOR DSTEPT, D5TERR AND
OSTBEG. THIS PROGRAM CALCULATES THE G OR A VALUES
FOR A SINGLE CRYSTAL SYSTEM. THE PROGRAM 15 DESCRIBED
IN TERMS OF G, BUT EVERYTHING 15 THE SAME FOR A,
IMPUT QUANTITIES
LINE *1
LINE *2
LINE SET *3
LINE *4
LINE *5
TITLE (10A4)
ANY ALPHANUMERIC CHARACTERS IN THE
FIRST 40 COLUMNS
NV,KU,IAG (FREE FORMAT)
NV- NUMBER OF VARIABLES TO BE MINIMIZED
SHOULD BE 6 IN THIS PROGRAM.
KU- OUTPUT UNIT OF THE COMPUTER
(USE 16 FOR OUTPUT IN F0R016I
IAG- -=0 FOR G TENSOR, NONZERO FOR A.
X,XMAX,XMIN,OELTX,OELHN ,MASK
(FREE FORMAT)
NUMBER OF LINES IN THE SET IS NV
ONE LINE FOR EACH PARAMETER
X- PARAMETER TO BE MINIMIZED
THESE CORRESPOND TO INITIAL
GUE55E5 FOR ELEMENT5 OF THE
G-EFFECTIVE SQUARED TENSOR IN THE
ORDER: XX, XY, XZ, YY , YZ, ZZ.
SAME FDR A, VALUES IN MHZM2
XMAX- UPPER LIMIT OF PARAMETER X
XMIN- LOWER LIMIT OF PARAMETER X
DELTX- INITIAL STEP SIZE FOR X
DELMN- LOWER LIMIT (CONVERGENCE) ON
THE STEP SIZE FOR X
MASK- -0 IF X IS TO BE VARIED
MA5K- > OP < 0 IF X IS TO BE HELD FIXED
DEFAULT VALUES SET BY DSTBEG:
XMAX59 1 . D37
XMIN" -1.037
DELTX= 1.0-2
DELMN- 5.D-8
NTRAC,MATRX,NFMAX,NFLAT
(FREE FORMAT!
NTRAC- —1 FOR NO OUTPUT
=0 FOR FINAL VALUES PRINTED ONLY
«+1 FOR TRACE OF MINIMIZATION
PROCESS.
(0 IS GENERALLY BEST VALUE)
MATRX- -0 FOR NO ERROR CALCULATION
-100 TO 110 FOR ERROR CALCULATION
(105 IS GENERALLY BEST VALUE)
NFMAX- MAXIMUM NUMBER OF FUNCTION
COMPUTATIONS
(1000 IS A GOOO VALUE)
NFLAT- -0 FOR SEARCH TO TERMINATE WHEN
CHANGE5 IN X ARE EQUAL TO OELMN
> OR < 0 FOR 5EARCH TO TERMINATE
WHEN ALL TRIAL STEPS GIVE
IDENTICAL FUNCTION VALUES
IFPL IEXPT,ICALC,IPP (FREE FORMAT I

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LINE *6
LINE *7
LINE *8
LINE SET 9
IFPL- =0 IF NO PLOTTING IS DESIRED
> OR < 0 FOR ANY PLOTTING
IEXPT- =0 IF NO PLOT OF EXPERIMENTAL
POINTS IS DESIRED
NONZERO IF PLOT IS DESIRED
ICALC- *0 IF NO PLOT OF CALCULATED
CURVE 15 OESIRED
NONZERO IF PLOT 15 DESIRED
IPP- =1 FOR PLOT OF XY PLANE DATA
=2 FOR XZ, =3 FOR YZ.
THMIN,THMAX,GMIN,GMAX I FREE FORMAT)
THMIN- MINIMUM VALUE OF THETA TO APPEAR
ON THE X-AXI5.
THMAX- MAXIMUM VALUE OF THETA.
GMAX- MAXIMUM G VALUE TO APPEAR ON THE
Y-AXIS. SAME FOR A, IN MHZ.
GMAX- MAXIMUM G VALUE
ALL POINTS MUST FALL WITHIN THESE VALUES
FREQ(I) , 1*1,3 (FREE FORMAT I
FREQ(II- THE FREQUENCY IN GHZ AT WHICH
THE SPECTRA WERE RECORDED IN
THE ORDER: XY, XZ, YZ.
NP(I), 1-1,3 (FREE FORMAT)
NP(I)- THE NUMBER OF DATA POINTS IN
IN EACH PLANE: XY, XZ, YZ.
MAXIMUM OF 100 IN EACH PLANE.
THETA Cl,JI,H 11,JI ,WTII,J) (FREE FORMAT)
NUMBER OF LINES IN THE SET IS NPll) +
NP ( 2 I + HP (3) .
THETA(I,J)- ANGLE IN CRYSTAL PLANE I
OF SIGNAL J (DEGREES).
H(I,J> — VALUE IN GAU55 FOR FIELD OF
SIGNAL J (FOR G> OR HYPERFINE
SPLITTING (FOR Al.
UT(I,J)- RELATIVE WEIGHT OF THAT POINT
NORMALLY-1.0 UNLESS POINT IS
VERY ROUGHLY ESTIMATED.
EACH SET OF OATA MUST HAVE THETAS IN
ASCENDING ORDER WITH NO TWO VALUES EQUAL
IMPLICIT REAL#8 (A-H, O-ZI
EXTERNAL 5CALC PL2CA
COMMON /CSTEP/ ’XMAX(20),XMIN(20) ,DELTXI20) ,DELMNÍ20),
1 ERR(20,HI),NV,NTRAC,MATRX,MASK(20),NFMAX,JVARY,
2 NXTRA,KFLAG,NOREP,KERFL,KU,NFLAT
COMMON / CXF 7 XI20I ,FOBJ,NFFIT
COMMON /C5CAL/ THETA(3,100 I ,H(3,100 I ,WT(3,100) ,NP(3 I ,IAG,
1 G2EXP(3,100) ,G2CALC(3,100) ,G2(3,3) ,FREQ(3I
DIMENSION GHI(3,3),0(3),E(3>,E2(3> ,TAU(2,3),G(3>,
1 ZR(3,3) ,ZIC 3,3)
REAL*4 TITLE(20),5CRCH1(100),SCRCH2(100I.XPOINTIIOO),
1 YPOINTI100),YPLOTI100),THMIN,THMAX,GMIN,GMAX
DATA NMAX 13/
C
0 READ IN PARAMETERS
C
READ(15,14) (TITLE(I), 1=1,10)
16 FORMAT 110A4)
READI15,*) NV,KU TAG
READ(IS,#! (XI11 ,XMAXI I) ,XMIN(I) ,OELTX(I),OELHN(I),
1 MASK(II, 1=1,NV)
READ(15,* I NTRAC,MATRX , NFMAX,NFLAT
READ(IS,*) IFPL.IEXPT, ICALC, IPP
READU5,*) THMIN, THMAX, GMIN, GMAX
READ(15,*) (FREQ(I), 1=1,3)
READ!15,*) (NP(I) , 1 = 1 ,31
DO 20 1=1,3
N=NP(I I
READ(15,* I (THETAII,J),H(I,J) ,WT(I,J) , J-l.N)
20 CONTINUE

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C BYPASS DSTEPT IF ALL PARAMETERS ARE FIXED
C
MASKS=0
â–¡0 25 1=1,NU
IF(MASK(It) 22,25,22
22 MASK5=MA5KS+1
25 CONTINUE
IF(MASKS.NE.NV1 GO TO 30
CALL 5CALC
GO TO 35
30 CONTINUE
CALL DSTEPT (SCALCI
35 CONTINUE
TABULATE THE RESULTS OF THE FITTING PROCEDURE.
WRITE(KW,AO > lTITLE CI>, 1-1,101
AO FDRMATÃœH1 ,30<2H* > ,/23X,10AA,/30(2H *))
DO 40 IP = 1,3
N=NP WRITEIKW.AI) FREQ IIPI
A1 FORMAT!/2X,'FREQUENCY- ',F10.3,‘ GHZ‘1
IF!IAG.NE.0) GO TO A5
WRITE(KW,A2)
A2 FORMAT!/3X, ‘THETA' ,3X,‘EXPT G2EFF' ,3X,‘CALC G2EFF' ,/)
GO TO AS
A5 WRITE(KW,A6)
46 FORMAT!/5X,‘THETA 1 ,7X, ‘EXPT A2EFF■ ,3X, 'CALC A2EFF1 ,/I
AS CONTINUE
DO 60 J-l,N
WRITE 1KU,53) THETAIIP.J) ,G2EXP(IP,J) ,G2CALC(IP,J)
53 FORMAT 12X,FI 2.A,IX,F12.A,5X,F12.A I
60 CONTINUE
IF!IAG.NE.O) GO TO 6A
WRITE(KW,61)
61 FORMAT!/2X,'G SQUARED TENSOR ' I
GO TO 69
6A WRITE ! KW , 63)
65 FORMAT!/2X,'A SQUARED TENSOR ',/)
69 CONTINUE
DO 70 1=1,3
WRITE(KW,73 Í (G2(I,JI, J=l,3>
73 F0RMAT!2X,3F12.A)
70 CONTINUE
DIAGONALIZE THIS G2 TENSOR USING EISPACK ROUTINES
75
C
C
c
c
BO
81
BA
35
DO 75 1=1,3
ZR!I,11=1.00
CONTINUE
IERR=0
CALL DHTRI0I(NMAX,3,G2,G2I,D,E,E2,TAU)
CALL DTQL2(NMAX,3,D,E,ZR,I ERR)
IFIIERR.NE.OI GO TO 199
CALL OHTRIBK(NMAX,3,G2,G2I,TAU,3,ZR,ZI)
SQUARE ROOT OF EIGENVALUES EQUALS G VALUES OF
MOLECULAR SYSTEM.
DO 00 1=1,3
IF!D D!I)=0.DO
G(I)=DSQRT(D!I))
CONTINUE
IF(IAG.NE.O) GO TO 8A
WRITE t KW,811 (I, Gil) , 1-1,3)
FORMAT(/2X, 'G VALUE! • ,11 , ' 1= ' ,F10.5)
GO TO 86
WRITEIKW,85 I (I, Gil), 1 = 1 .31
FORMAT(/2X, 1 A VALUE!',II,')â– 
' ,F12.A,‘ MHZ' I

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86 CONTINUE
EIGENVECTORS GIVE DIRECTION COSINE MATRIX RELATING
THE CRYSTAL TO THE MOLECULAR COORDINATE SYSTEM.
EACH ROU PRINTED OUT 15 A ROU OF THE MATRIX CORRESPONDING
TO THE EIGENVALUES (A OR G VALUES I IN ASCENDING ORDER.
SEE: WERTZ, J.E.; BOLTON, U.R. “ELECTRON 5PIN RESONANCE"
MCGRAW-HILL: NEW YORK, 1972; P 148.
DO 90 1=1,3
WRITE(KW,881 (I,IZR!I,J), U=l,3)1
38 FORMAT(/2X, 1 EIGENVECTOR Í ' ,11, 1 )= ',3F12.5>
90 CONTINUE
CHECK IF ANY PLOTTING IS DESIRED.
IF(IFPL.EQ.O) GO TO 199
CHECK IF PLOT OF EXPERIMENTAL POINT5 IS DESIRED.
IF(IEXPT.EQ.0) GO TO 150
CHANGE DOUBLE PRECISION ARRAYS TO SINGLE PRECISION
SINCE PL0T79 ONLY U5ES SINGLE PRECISION.
NPTS=NP(IPPI
00 100 J=1,NPT5
XPOINT(J)=THETAIIPP,J)
IF í G2EXP(IPP,J).LT.0,DO I G2EXPIIPP,J1=0.DO
YPOINT(U)=D5QRTlG2EXP(IPP,JII
100 CONTINUE
INITIALIZE PLOT SYSTEM
CALL PLTOO
SET PLOT SIZE TD 25.0 CM LONG, 20.0 CM WIDE.
CALL SET5Z Í 25. I
CALL 5ETD52Ü. , .B)
PLOT THE AXES USING THE ROUTINE PLTAX.
CALL PLTAXO./25, ,3./25. , 7HDEGREE5,7,20.125. ,
1 0..THMIN,20.,THMAX,-.005,-1)
CALL PLTAXI3./25.,3./2S.,11HG EFFECTIVE.il,
1 15. /25. ,90. ,GMIN,0.2,GMAX, .005,21
5ET UP A 2-DIMENSIONAL FIELD ON WHICH THE PLOTS APPEAR.
CALL SETVP20 . / 25. ,23 . /25. ,3./25. ,IS. /25. >
PLOT THE DATA POINTS A5 PLUS SIGNS USING THE ROUTINE GRFGP.
CALL GRFGP(THMIN,XPOINT,THMAX,GMIN,YPOINT,GMAX,
1 NPTS,2,PL2CA)
CHECK IF PLOT OF CALCULATED LINE 15 DESIRED.
150 IF(ICALC.EQ.0) GO TO 190
NPTS=NP(IPP)
DO ieo J-l.NPTS
XPOINT(J)“THETA(IPP,J)
IFÍG2CALC1IPP,J).LT.0.00) G2CALC(IPP,J)=0.DO
YPLOT(J)“D5QRT(G2CALC(IPP,J)I
5CRCH1(JI«XPOINT(J)
SCRCH2(J)“YPLOT1J)
ISO CONTINUE

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C
C REPEAT THE PLOTTING ROUTINES.
C
CALL PLTOO
C
CALL 5ET5Z(25 . )
C
CALL 5ET0S2Í1.,.8)
C
CALL PLTAX(3./25.,3./23.,7HDEGREE5,7,20./25. ,
1 0.,THHIN,20..THMAX,-.005,-1»
C
CALL PLTAXO./23. ,3./23. ,11HG EFFECTIVE ,11,
1 15 . /25. ,90. , CHIN,0.2,GHAX, .005,2»
C
CALL 5ETVP2(3./25.,23./25.,3./25.,18./25.J
C
C ORAW THE THEORETICAL CURVE USING THE ROUTINE GRFGI.
C
CALL GRFGI(THMIN,XPOINT,THMAX,GMIN,YPLOT,GMAXf
1 NPTS,SCRCH1,5CRCH2,100,1.,PL2CA)
C
C EJECT THE FRAME.
C
190 CALL PLTEJ
199 CALL EXIT
WRITE(KU 200 I I ERR
200 FORMATÍ1ÓX,‘IERR -',110)
END
C
c *********:M**:M************************** ********************
C
C THIS SUBROUTINE CALCULATES THE G2 TENSOR U5EO FOR THE
C LEAST SQUARES FIT OF THE EXPERIMENTAL SIGNALS.
C
SU8R0UTINE SCALC
IHPLICIT REAL*8 < A-H , O-Z)
COMMON /CSTEP/ XMAX(20) ,XMINÍ20) ,OELTX(20) ,OELMN(20),
1 ERR(20,211 ,NV,NTRAC,MATRX,MASK(20 1 , NFMAX , JVARY,
2 NXTRA,KFLAG(NOREP,KERFL,KW,NFLAT
COMMON /CXF/ X(20>,F0eJ, NFFIT
COMMON /CSCAL/ THETA(3,100) , H(3,100) ,UT13,100),NP(3) ,IAG,
1 G2EXPI 3 100) ,G2CALC(31001 ,G2(3,3) .FREQ(3)
DATA BETA. PI, GELEC /1.399612386D0.1.7453292520-2,
1 2.0023193134DO/
C
C*** BETA = (BOHR MAGNETON/PLANCK’5 CDN5TANT) MHZ/GAU55
C*** PI = PI/180 CONVERTS DEGREES TO RADIANS.
C*** GELEC * FREE ELECTRON G VALUE.
C
C CONVERT INPUT VARIABLE PARAMETERS (X) TO G2 VALUES
C TO GIVE INITIAL G2 TENSOR. FILL UP WHOLE TENSOR
C USING LOOP SINCE IT IS SYMMETRIC.
C
FOBJ=0.00
N=0
00 10 1=1,3
00 10 J=I,3
N=N+1
G2(I,Jl-XINl
10 CONTINUE
DO 15 J=1,3
N = J-f 1
00 15 I=N,3
G2(I , J)=G2(J,I)
15 CONTINUE
C
C CALCULATE EXPERIMENTAL G2 EFFECTIVE VALUES.
C CONVERT A IN GAUSS TO MHZ USING GELEC. THIS IS
C INACCURATE IF GEFF DIFFERS GREATLY FROM GELEC.

254
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saa
C
C
C
C
C
00 30 IP-1 ,3
N=NP(IP)
00 30 J-l ,N
IF(IAG.NE.O) GO TO 18
GEFF-IFREQt IP 1*1.031/ G2EXP< IP , J)=GEFF*GEFF
GO TO 30
18 AEFF-GELEC*8ETA*H(I,Jl
G2EXP(IP,JI-AEFF*AEFF
20 CONTINUE
USE EXPERIMENTAL THETAS AND THEORETICAL G2'S TO
CALCULATE EFFECTIVE G3 VALUES.
DO 50 IP-1 ,3
N-NPIIP)
OO 50 J-l ,N
GO TO (30,33,40), IP
30 THRAD- THETA(IP,J)*PI
G3CALCIIP,J)- C2(2,2)*DSIN(THRAD)*0SIN(THRA0>
+ 2.D0*G2(1,2)*D5INITHRADI*DC05(THRAD)
+ G2!1,1)fDCO5(THRAD)*0C05(THRAD)
GO TO 45
35 THRAD- THETA!IP,J)*PI
G2CALC(IP,J)- GH(1 ,1)*D5IN ITHRAD)SDSIN(THRAD)
+ 2.00*G2<1,3)3DSIN(THRAD)*OCOS(THRADI
+ G213,3)*OCOS(THRAO)*OCOS(THRAD)
GO TO 45
40 THRAD- THETA!IP,J)*PI
G3CALCIIP,Jl- G2(2,2)*DSIN(THRAD)*0SIN(THRAD)
+ 2.DO*G2(2,3)*05IN(THRAD)*OC05(THRADI
+ G2(3,3)*DC05(THRAD)*DC05ITHRAD>
45 FOBJ- FOBJ + (G2EXP(IP,J)-G2CALC(IP,J))
*(G2EXP(IP,J )-G2CALC(IP,J))*UT(IP,J)»UT(IP,J)
50 CONTINUE
RETURN
END
i FUR R50SDI5K:CJT3DXTLFIT
* FDR RSDSDISK:CJT ILL1DSTEPIT
* FOR R5DÍ0I5K:CJT.ILL30EI5
% LINK OXTLFIT.DSTEPIT,0EI5,0PLT:PTIGERLIB
s
(
(
s
(
i
»
5
$
1
t
•i
IF PI . EQ5 . "" THEN
ON CONTROL Y THEN *
ASSIGN 'PI‘.DAT
A5SIGN 'PI'.LST
ASSIGN 'PI'.PTI
INQUIRE PI
CO TO DONE
F0R015
FOR016
FOR021
"Naae of Tile with DXTLFIT data (NO
txt! >"
RUN RSDÍDISK:CJT30XTLFIT.EXE
DONE :
DEASSIGN F0R015
DEASSIGN F0R016
DEASSIGN FDR021
WRITE 5YSÍ0UTPUT "Your output listing is in ''PI'.LST."
WRITE SY560UTPUT "Your plot file ia in ''PI'.PTI."
INQUIRE PLOTIT "Da gou want it plotted at the printer on gour terminal?"
IF PLOTIT THEN 8PLT.PLOTTIGER.COM 'PI'.PTI TT:

APPENDIX F
COMPUTER PROGRAMS USED FOR MAGNETIC SUSCEPTIBILITY DATA SIMULATIONS
This appendix contains computer programs used in the magnetic
susceptibility data analysis. The original version of the program
titled DSUSFIT can be found in References 173-177. DSUSFIT is the
master program for data input and output. The subroutines which
calculate susceptibilities are titled DSDHAM, DSDX, D3ISNG, DSJX, and
D3DJHAM. DSDHAM was used for Method 1 as described in Chapter V; DSDX
for Methods 2 and 4; D3ISNG and DSJX for Method 3; and D3DJHAM for
Method 5. Further details can be obtained by inspection of the programs
and from the literature.162,173-177 jpese programs also use EISPACK
subroutines for matrix operations and the DSTEPIT curve fitting
program.^®
255

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c***************************************************************
cxxxxxxxxxxxxxxxxxxxxxx dsusfit xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
D-DOUBLE PRECISION; 5USFIT-MAGNETIC SUSCEPTIBILITY FIT
THIS PROGRAM WAS WRITTEN BY THE HENDRICKSON GROUP AT
THE UNIVERSITY OF ILLINOIS. THIS VERSION WAS WRITTEN
BY WAYNE FEOERER AND MARK Ü. TIMKEN (B/10/B1).
IT CONTAINS PLOTTING ROUTINES FOR USE BY THE DRACO
GROUP AT THE UNIVERSITY OF FLORIDA (J. TELSER 1/31/84).
THIS IS THE MAIN PROGRAM THAT READS IN THE PARAMETERS FOR
OSTEPT AS WELL AS THE THE PARAMETERS TO BE MINIMIZED,
THE EXPERIMENTAL OATA, ANO INFORMATION FOR PLOTTING.
DEFINITIONS OF THE PARAMETERS FOR OSTEPT CAN BE FOUND IN
THE LI5TINGS OF THE SUBROUTINES FOR D5TEPT, D5TERR AND
DST8EG.
INPUT QUANTITIES
LINE ♦!
LINE *2
LINE SET #3
LINE *4
LINE *5
TITLE (10A4)
ANY ALPHANUMERIC CHARACTERS IN THE
FIRST 40 COLUMNS
NV , KU,PARA (FREE FORMAT I
NV- NUMBER OF VARIABLES TO BE MINIMIZED
(MAXIMUM NUMBER IS 201
KU- OUTPUT UNIT OF THE COMPUTER
(USE 16 FOR OUTPUT IN F0R016I
PARA- THE NUMBER OF PARAMAGNETIC METAL
CENTERS IN THE MOLECULE
X,XMAX,XMIN,DELTX,DELMN,MASK
(FREE FORMAT)
NUMBER OF LINE5 IN THE SET IS NV
ONE LINE FOR EACH PARAMETER
X- PARAMETER TO BE MINIMIZED
XMAX- UPPER LIMIT OF PARAMETER X
XMIN- LOWER LIMIT OF PARAMETER X
OELTX- INITIAL STEP SIZE FOR X
DELMN- LOWER LIMIT (CONVERGENCE! ON
THE STEP SIZE FOR X
MASK- -0 IF X 15 TO BE VARIED
MASK- > OR < 0 IF X 15 TO BE HELD FIXED
DEFAULT VALUES SET BY D5TBEG:
XMAX- 1.D37
XMIN- -1.D37
DELTX- 1.0-2
DELMN- 5.D-8
NTRAC, MATRX NFMAX,NFLAT
(FREE FORMAT)
NTRAC- —1 FOP NO OUTPUT
-0 FOP FINAL VALUES PRINTED ONLY
-+1 FOR TRACE OF MINIMIZATION
PROCESS.
(0 15 GENERALLY BEST VALUE)
MATRX- -0 FOR NO ERROR CALCULATION
-100 TO 110 FOR ERROR CALCULATION
(105 IS GENERALLY BEST VALUE)
NFMAX- MAXIMUM NUMBER OF FUNCTION
COMPUTATIONS
(3000 IS A GOOO VALUE)
NFLAT- -0 FOR SEARCH TO TERMINATE WHEN
CHANGES IN X ARE EÃœUAL TO DELMN
> OR < 0 FOR 5EARCH TO TERMINATE
WHEN ALL TRIAL 5TEP5 GIVE
IDENTICAL FUNCTION VALUES
NP,IFPL,ISU5,IMU (FREE FORMAT)
NP- NUMBER OF EXPERIMENTAL DATA P0INT5
MAX I Huh NUMBER OF POINTS 15 lóS

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IFPL- =0 IF NO PLOTTING 15 DESIRED
> OR < 0 FOR ANY PLOTTING
ISUS- *0 NO PLOT OF MAGNETIC SUSCEPT¬
IBILITY VERSUS TEMPERATURE
> OR < 0 FOR PLOT OF SUSCEPT¬
IBILITY VERSUS TEMPERATURE
IMU- -0 NO PLOT OF MAGNETIC MOMENT
VERSUS TEMPERATURE
> OP < 0 FOR PLOT OF MAGNETIC
MOMENT VERSUS TEMPERATURE
XT 1,XT2,Y5US1,YSU52,YMU1,YMU2
(FREE FORMAT]
XT1- MINIMUM VALUE DF TEMPERATURE IK]
TO APPEAR ON THE X-AXIS
(GENERALLY SHOULD BE ZERO)
XT2- MAXIMUM VALUE OF TEMPERATURE
TO APPEAR ON THE X-AXIS
YSU51- MINIMUM VALUE OF THE MAGNETIC
SUSCEPTIBILITY TO APPEAR ON THE
Y-AXIS, GENERALLY SHOULD BE ZERO
Y5US2- MAXIMUM VALUE OF THE MAGNETIC
SUSCEPTIBILITY TO APPEAR ON THE
Y-AXIS
YMU1- MINIMUM VALUE OF THE MAGNETIC
MOMENT TO APPEAR ON THE Y-AXIS
(GENERALLY 5HOULD BE ZEROI
YMU2- MAXIMUH VALUE OF THE MAGNETIC
MOMENT TO APPEAR ON THE Y-AXIS
T 5U5 (FREE FORMAT!
NUMBER OF LINES IN THE SET IS NP
ONE LINE FOR EACH DATA POINT
T- TEMPERATURE
SUS- SUSCEPTIBILITY
TEMPERATURES AND SUSCEPTIBILITIES
MUST BE ASCENDING IN TEMPERATURE
WITH ALL TEMPERATURES DIFFERENT.
IMPLICIT REALX8 IA-H , O-Z)
EXTERNAL 5CALC PL2CA
COMMON /C5TEP/'XMAX(20),XMIN(20),0ELTX(20I,DELMN(20),
1 ERR(20,21),NV,NTRAC.MATRX,MASK(20),NFMAX,JVARY,
2 NXTRA,KFLAG,NOREP,KERFL,KW,NFLAT
COMMON 1CXF/ X(20),FOBJ, NFFIT
COMMON /C5CAL/ SUS<163),C5U5(165),T(165),TCAL(163>,
1 UEFF(165 í ,UCAL(165) , NP
REALXA TITLE(20),5CRCH1(165I,SCRCH2(163),5T(163),
1 5TCALÍ165) ,55U5(163 1 ,SCSUS(165) ,SUEFF(165) ,
2 5UCAL(1651,XT1,XT2,YSU51,YSU52,YMU1,YMU2
READ IN PARAMETERS
REAO(13.16) (TITLE(I>, 1=1,10)
16 FORMAT(10AA)
READ(15,X) NV KW,PARA
READ(15,*) ,XMAX(I) ,XMIN(I) ,0ELTXtI> , DELMN(I),
1 MASK(I). I-l.NV)
REAO(15,* I NTRAC,MATRX,NFMAX,NFLAT
REAO(15,*) NP,IFPL,ISUS,IMU
READ!15,*) XTÍ XT2,Y5U5Í,YSUS2 YMU1,YMU2
REAO(15,*) (T(I),5U5(I), I-l.NP)
00 180 I-l.NP
TCAL(I I=T(I)
180 CONTINUE
C
C BYPA55 DSTEPT IF ALL PARAMETERS ARE FIXED
C
MA5K5-0
00 105 1-1,NV
IF I MASK(II) 182,1B3,1B2
182 MASK5-MA5K5+1
LINE *6
LINE SET *7

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185 CONTINUE
IF t MASKS NE.NV ) GO TO 190
CALL SCALC
GO TO 195
190 CONTINUE
CALL 05TEPT (SCALC)
195 CONTINUE
C
C IF ANY SUSCEPTIBILITIES ARE < 0 THEN QUIT
C
DO 210 T-1,NP
IF(C5U5i I) 1205,210,210
205 URITEIKM,207) (TCAL(JI,SUS(JI,C5US(J), J-l.NPI
207 FORMAT!1H1,10X,‘A DIAMAGNETIC SUSCEPTIBILITY HAS BEEN',
1 ' CALCULATED'//5X, 'TEMP' ,10X, 1 SUS' ,10X, 1CSU5'/
2 (3X,F6.1,3X,F10.6,5X,E10.3)I
GO TO 600
210 CONTINUE
C
C CALCULATE HU-EFFECTIVE. DHU- SUM OF SQUARED DEVIATIONS
C
DMU-0.DO
DO 220 >1 , NP
UCAL(I)=2.82800*D5QRT(CSUS(I)*TCAL(I I/PARA)
UEFF(I)“2.82800*058RT(SUSI I)*T(I)/PARAI
DHU-IUCAL 220 CONTINUE
0
0 CALCULATE GOODNESS OF FIT USING EQUATION IN
C GINSBERG, A.P.; ET AL. INORG. CHEM. 1972, 11, 2884.
C NAC= NUMBER OF ACTIVE PARAMETERS
C
NAC=0
DO 250 1-1,NV
IF(MASK(I)) 250,240,250
240 NAC-NAC+1
250 CONTINUE
5E=D5QRT!DMU/(FLOAT(NPI-FLOATlNAC)I)
C
C URITE OUT RESULTS
C
URITEIKW,350) SE
350 FORMAT( / / ' GINSBERG 5TANDARO ERROR OF ESTIMATE-',E16.8)
URITEfKU,4001 I TITLE(I), 1*1,10)
400 FORMAT!1H1,3012H* ),/25X,10A4,/30(2H *>,
1 /19X, 'EXPT' ,8X, ' CALC 1 , 8X , 'EXPT ' ,8X , 'CALC' ,
2 /IX,'TEMPERATURE',9X,'SUSCEPTIBILITY',BX,
3 'MAGNETIC MOMENT',//)
URITEIKU.42) (T(J> ,SUS(J) ,CSUS(J),UEFFlJ) ,UCAL(J) ,J-1,NP)
42 FORMAT(HX,F10,2,2X,F10 6,2X,F10.6,2X,F10.4,2X,F10.41
C
C CHECK IF ANY PLOTTING IS OESIREO.
C
600 IF(IFPL.EQ.O) GO TD 999
PL0T79 SECTION FOR USE ON UF/QTP VAX.
CHECK IF PLOT OF SU5CEPTI8ILITY IS DESIRED.
IF(ISUS.EQ.O) GO TO 700
C
C CHANGE DOUBLE PRECISION ARRAYS TO SINGLE PRECISION
C SINCE PLOT79 ONLY USES SINGLE PRECISION 5-SINGLE PREC.
C
DO 610 1-1 , NP
ST(I)-T(I)
S SUS (11 -SU5 Í II
5C5U5(I)-C5U5II)
5CRCH1(11*T11)
5CRCH2II)-C5U5!II

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nnnonnnnnnnnnnnn nnn nnn nnnonnnnnnnnnnnnonnonnn nno n no non
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610 CONTINUE
INITIALIZE PLOT SYSTEM
CALL PLTOO
SET PLOT SIZE TO HS.0 CM.
CALL 5ET5ZI23.)
INDICATE HORIZONTAL, RECTANGULAR PLOT: 23 CM LONG, 20 CM WIDE
CALL SETD52I1.,.8)
PLOT THE AXES USING THE ROUTINE PLTAX.
CALL PLTAX(X,Y.TITLE,NCHAR,SIZE,THETA,VMIN,0V,VHAX,TICK,MODE)
X X COORDINATE OF ORIGIN
Y Y COORDINATE OF ORIGIN. TITLE HOLLERITH CHARACTER STRING AS AXIS LABEL
NCHAR LENGTH OF STRING
SIZE LENGTH OF AXIS IN WORLO UNIT5
THETA ROTATION ANGLE OF AXIS: O FOR HORIZONTAL,
90 FOR VERTICAL
VMIN MINIMUM VARIABLE ON AXIS
OV DIVISIONS TO BE MARKED ON AXIS
VMAX MAXIMUM VARIABLE ON AXI5
TICK LENGTH OF TICK MARKS, 0.003 TO 0.013 IS GOOD
< 0 CL0CKUI5E FROM AXIS, > 0 COUNTERCLOCKWISE
MOOE ORIENTATION OF TITLE WITH RESPECT TO AXIS
-1 FOR BOTTOM HORIZONTAL AXIS, +2 FOR LEFT
VERTICAL AXIS
PLOT ANO LABEL THE X-AXIS.
CALL PLTAX(3 . / 23.,3./23.,15HTEMPERATURE IK),13,20./23.,
1 0. , XT1 ,50. ,XT2,-.005,-1 I
PLOT AND LABEL THE Y-AXIS.
CALL PLTAX!3./25.,3./23.,1AHSUSCEPTIBILITY,14,
1 13 . /23. ,90. ,YSU51, .01,Y5U52, .005,21
SET UP A 2-01MENSIGNAL FIELO ON WHICH THE PLOTS APPEAR.
CALL 5ETVP2[3./23. ,23. /23. ,3./23. ,IB./25. >
PLOT THE DATA POINTS AS PLUS SIGNS USING THE ROUTINE GRFGP.
CALL GRFGP (XI,X,X2,Y1,Y,Y2,N,MARK,PL2)
XI
X MINIMUM VALUE
X(N>
ARRAY OF N X VALUES
X2
X MAXIMUM VALUE
Y1
Y MINIMUM VALUE
Y (N)
ARRAY OF N Y VALUES
Y2
Y MAXIMUM VALUE
N
NUMBER OF POINTS
MARK
SYMBOL NUMBER (1,2,...) ACCORDING
TO MARKS CODE
PL2
2-0 PEN MOVEMENT ROUTINE NAME E.G.
MUST BE DECLARED EXTERNAL TYPE.
PL2CA
CALL GRFGPÍ XT1,ST,XT2,YSU51,SSUS,YSUS2,NP,
1 2,PL2CA)
C
C DRAW THE THEORETICAL CURVE USING THE ROUTINE GRFGI.
C
C CALL GRFGI (X1,X,X2,Y1,Y,Y2,N,WORK1,U0RK2,NINT,SIGMA,PL2)
C

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xi
X(N>
X2
Y1
Y (N 1
Y2
N
UORK1IN)
W0RK2IN)
NINT
SIGMA
PL2
CALL GRFGIIXT1 ST,XT2,Y5U51.SCSUS,
1 YSU52,NP,5CRCH1, SCRCH2,143,1.,PL2CAI
C
C CHECK IF PLOT OF MAGNETIC MOMENT IS DESIRED.
C
700 IF(IMU.EQ.O) GO TO 990
DO 800 1-1,NP
STII1-TII)
5UEFF (I)-UEFF(IJ
5UCALIII-UCALII1
5CRCH1III-Till
SCRCH2(IJ *UCAL(I)
800 CONTINUE
C
C REPEAT THE PLOTTING ROUTINES. THE SAME A5 ABOVE EXCEPT
C THE Y—AXIS GOES FRDM YMU1 TO YMU2.
C
CALL PLTOO
C
CALL SETSZ123.)
C
CALL 5ETDS2 11. , .8)
C
CALL PLTAXO./25. ,3./23. . 13HTEMPERATURE ( K ) , 13,20 ./23 . ,
1 0.,XT1,50.,XT2,-.005,-1)
C
C PUT Y-AXI5 ON OPPOSITE SIDE IF SUSCEPTIBILITY 15
C TO BE PLOTTED, OTHERWISE ON LEFT SIDE.
C
IFlI5U5.EQ.0) GO TO 810
CALL PLTAX(23./25.,3./23.,13HMAGNETIC MOMENT,13,
1 15 . /23 . ,90 . , YHU1 , . 5 , YMU2 , - 005 , -2)
GO TO 820
810 CONTINUE
CALL PLTAX(3./25.,3./23.,13HMAGNETIC MOMENT,15,
1 13. /25 . ,90 . , YMU1,.5,YMU2 , .003,2!
820 CONTINUE
C
CALL 5ETVP2I3./23.,23./23.,3./23.,IB./23.)
C
CALL GPFGPIXTl,5T,XT2,YMU1,SUEFF,YMU2,NP,
1 2.PL2CAI
C
CALL GRFGI(XT1.ST.XT2.YMU1.SUCAL,
1 YMU2,NP,SCRCH1,5CRCH2,163,1.,PL2CA)
C
C EJECT THE FRAME.
C
990 CALL PLTEJ
999 CALL EXIT
END
X MINIMUM VALUE
ARRAY OF X VALUES IN ASCENDING ORDER WITH NO
TWO VALUES EQUAL
X MAXIHUM VALUE
Y MINIMUM VALUE
ARRAY OF Y VALUES N ELEMENTS LONG
Y MAXIMUM VALUE
NUMBER OF POINTS
SCRATCH ARRAY OF N ELEMENTS
SCRATCH ARRAY OF N ELEMENTS
NUMBER OF POINTS TO INTERPOLATE BETWEEN X C1»
ANO X (N )
TENSIONED SPLINE PARAMETER
2-D PEN MOVEMENT SUBROUTINE, USUALLY PL2CA
MUST BE DECLARED EXTERNAL

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non nnnn nnn nr>onn nnnn n n n n n on no n
261
««miimmiimftmintuttmutimisummituttimi
mtimmttmttt dsdham ««Mmtitmmmmumdi
D=D0U8LE PRECISION; 5=ANY SPIN; D=AXIAL ZF5; HAH=SPIN
HAMILTONIAN
THIS PROGRAM CALCULATES MAGNETIC SUSCEPTIBILITIES
FOR A MONOMER OF SPIN = 1/2 TO 5/2 WITH AXIAL ZERO-FIELD
SPLITTING USING THE FULL SPIN HAMILTONIAN.
SUBROUTINE 5CALC
IMPLICIT REAL*8 (A-H,0-Z)
R£AL*8 5CALT(165,2), SCALB(165,2),5CAL(165,2I
REAL*8 AR(6,6>,AI(6,6>,D<6),E(6>,£2(6),TAU(2,6I,Z(6,6)
REAL*8 XMMNT(6,21,ENG(6,3,21
COMMON /CXF/ X(201,F08J,NFFIT
COMMON /CSCAL/ SUS(165) ,C5US1165 I,T(165) ,TCAL(165),
UEFFI165),UCAL(165),NP
COMMON /C5TEP/ XMAX(201 ,XMIN(201 ,OELTX(201 ,DELMN(20 I,
ERR(20,21),NU,NTRAC,MATRX.MASK(20),NFMAX,
JOARY.NXTRA.KFLAG,NOREP,KERFL,KU,NFLAT
DATA NMAX 16/
OATA BK, AN /6.950300-1, 6.022045023/
DATA BCM, BERG, ERGCM /4.663600-5, 9.274080-21,
1 1.98647B0-Í6/
8K= 80LTZMANN CONSTANT IN CM-1; AN= AOOGAORO'S NUMBER
BCM, BERG= BOHR MAGNETON IN CM-1, ERG
INPUT PARAMETERS AS FOLLOWS:
5= 5PIN, 0= ZFS (CM-1), G PARALLEL (Z), G PERPENDICULAR
(X=Y), HF = EXPERIMENTAL MAGNETIC FIELD (GAUSS), XUT=
WEIGHTING PARAMETER.
5= X(1)
XD=X(2)
GZ=X(3>
GX=X(4)
HF-X(5)
XWT=X<6)
NSPN= SPIN MULTIPLICITY (SIZE OF HAMILTONIAN MATRIX)
N5PN- 2.00*5 + 1.0100
FOBJ- 0.DO
IERR- 0
L=l: FIELD IN Z DIRECTION I PARALLEL 1; L = 2: IN X IPERP)
M=l: H-DELTA(HI; M-2: H; M=3 : H+OELT A(H)
DO 25 L=1,2
DO 22 M=l,3
ZERO OUT ALL EI5PACK ARRAYS. Afi 15 HAMILTONIAN MATRIX.
DO 4 1=1,NSPN
0 I I)= 0.DO
E I I)= 0.DO
£2(11= 0.00
TAU(1,I)= O.DO
TAU(2,11 - 0.00
DO 4 J=1,N5PN
AR( I,J)=0.DO
AI(I,J)=0.00
Z(I,J)= 0.00
4 CONTINUE
GO TO (5,6,7),M
5 HA=HF-(1.0-2*HF)
GO TO 8
6 HA=HF

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non non n
262
Gü Tü 8
7 HA=HF+(1.0-2*HFI
3 IFIL.EQ.1) GO TO 9
HX=HA
HZ=0.00
GO TO 10
9 HX=0.00
HZ=HA
FILL UP HAMILTONIAN MATRIX, ALL VALUES ARE REAL SO
AI IS IGNORED. FIRST 00 DIAGONAL ELEMENTS. ( XM5= MSI
10 CONTINUE
DO 12 1=1,NSPN
XM5= 5 + 1.DO - D8LE AR(I,I)= XM5*GZ#BCM*HZ + XM5*XMS*XD
IE CONTINUE
00 OFF DIAGONAL ELEMENTS USING LOWERING OPERATORS.
NSPM1=N5PN-1
OD 1A I=1,N5PM1
11=1+1
XMS= S + 1.00 - DBLEIII
AR(I,111= 0.500*05QRT(S*(S + 1.00) - XMS*(XM5 - 1.00)1
*GX#BCM*HX
14 CONTINUE
C FILL UP ENTIRE MATRIX USING LOOP SINCE IT IS SYMMETRIC.
C
DO 16 I-1.N5PN
11=1+1
DO 16 J=I1,NSPN
ARIJ,I)= ARII.JI
16 CONTINUE
C
C USE EI5PACK ROUTINES TO OIAGONALIZE MATRIX ANO FIND
C EIGENVALUES.
C
CALL DHTRIDI(NMAX.NSPN,AR,AI,D,E,Ea,TAU)
CALL D TQL2INMAX,NSPN,0.E,Z,IERRI
IF(IERR.NE.O) GO TO 199
DO IB IE=1 , NSPN
ENG(IE,M,L)=D(IEI
18 CONTINUE
IF(h.NE.3) GO TO 22
C
C MOMENT=DELTA(E>/DELTA(H) TAKE AVERAGE OF E SLOPES
C
DO ao IE-1,NSPN
SLP1=(ENGIlE.a.LI-ENGlIE,1,LI I/I 1.D-E*HFI
SLPa=lENG(IE,aiL)-ENG(IE,a,L)1/ll.0-a*HF)
XMMNTIIE,L)=-1.D0*ERGCM*(5LP1+5LPE)/2.00
ao CONTINUE
aa CONTINUE
25 CONTINUE
OQ 30 10 = 1 , 165
00 30 J0=1,2
5CALT[10,JO I = 0.00
5CALB(IO,JO)=O.DO
SCAL110,J0Í-0.DO
30 CONTINUE
00 110 1=1,NP
00 50 10=1,a
DO 40 IE=1,NSPN
C
C SET LOWEST ENERGY LEVEL=0. THIS ACCOUNTS FOR 5(5+11/3
C TERM.
C
R=( ENGlIE,E,ID I-ENG(1,2,10 I)/
141
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144
145
146
147
14B
149
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156
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158
159
160
161
162
163
164
165
166
167
168
169
170
263
Y=DAB5(R)
IF!Y.GT.30.DO) GO TO 40
C
C USE STANDARD FORMULAE FOR SUSCEPTIBILTY.
C
SCALTlI,IQ)= SCALT11,101 + XMMNT SCALBlI ,ID)= SCALBII , ID) + UEXP<-1.00*R)
40 CONTINUE
5CALII,ID)=*SCALT 50 CONTINUE
C
C TAKE AWERAGE QF ORIENTATIONS
C
C5US(I)= (5CALIII) + 2.00*5CAL(1,21)/3.DO
IF(SUS(11 .LE.0.001 GO TO 100
IFIXWT) 52,53,54
52 UT=5U511)
GO TO 101
53 UT=1.00
GO TQ 101
54 UT-1.DO/SUSlI)
GO TO 101
100 UT=0.D0
101 FOBJ= FOBJ + (CSUStl)-SUSlI))*(CSUSlI)-SUS(I))*UT*UT
110 CONTINUE
GO TO 205
199 URITEI16,200) IERR
200 FORMAT!10X,'IERR =‘,110)
205 RETURN
END

2
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dsdx
C Q=DOUBLE PRECISION; S-ANY SPIN; D-AXIAL ZFS;
C X=EXPONENTIAL EQUATION.
C
C
C THIS PROGRAM CALCULATES THE MAGNETIC SUSCEPTIBILITY FOR
C A MONOMERIC TRANSITION METAL COMPLEX USING
C THE EXPONENTIAL FORM FOR THE ZERO-FIELD SUSCEPTIBILITY.
C THE COMPLEX CAN HAVE SPIN 5= 1/2, .... 3/2.
C AN AXIAL ZERO-FIELD SPLITTING PARAMETER IS INCLUDED.
C AXIAL G VALUES C INTERACTIONS IN BOTH THE Z AND X,Y DIRECTIONS ARE INCLUDED
C AS ZJ USING THE MOLECULAR FIELD METHOD. PAR IS THE
C CONTRIBUTION OF PARAMAGNETIC IMPURITES. THE DATA CAN BE
C WEIGHTED EQUALLY IXWT=0), BY 5U5 OR BY 1/SUS
C {XWT > 0} .
C IF S=1/2, THERE IS NO ZERO-FIELD SPLITTING AND GX-GY-GZ.
C
SUBROUTINE SCALC
IMPLICIT REAL*8 IA-H.O-Z)
COMMON /CXF/ X (20 ) ,FOBJ,NFIT
COMMON /C5CAL/ 5US(165»rCSU5(1651,T(165) ,TCALi165\,
UEFF(165),UCAL <165), NP
COMMON /C5TEP/ XMAX(20 I ,XMIN(20> , DELTX(20> rDELMN(20),
ERR(20,21) NO,NTRAC MATRX,MA5K(20),NFMAX,JVARY,
NXTRA,KFLAG,NQREP,KERFL,KW,NFLAT
C
C BK= BOLTZMANN CONSTANT IN CM-1; AN» AVOGADRO’S NUMBER
C BCM, 0ERG= BOHR MAGNETON IN CM-1, ERG
C
OATA BK, AN /6.95030D-1, 6.022045D23/
DATA BCM, BERG, ERGCH /4.Ó6860D-5, 9.2740BD-21,
1 1.9B647BD-16/
C
C INPUT PARAMETERS: XD=0, ZJZ & ZJX ARE THE INTERMQLECULAR
C INTERACTIONS IN THE Z AND X.Y DIRECTIONS.
C
S- X(ll
XD=X(2)
Z JZ=X{3)
ZJX»X(4)
GZ=X(5 >
GX=X{6)
PAR»X(7)
XWT = X < 8 )
FDBJ=0.DO
00 110 1*1,NP
IF C 5.GT.O.5D0) GO TQ 20
CHIZT= 1.00
CHIZ8= 4.DO
CHIXT» CHIZT
CHIXB= CHIZB
GX= GZ
ZJX= ZJZ
GO TO 60
20 CONTINUE
A= -XO/( BK*TCAU I ) )
B=-2.DQ#XD/(BK*TCAL(I) )
C=-4. D0*XD/(BK*TCALm )
D=-6.D0*X0MBK*TCAL(I> )
AA=DABS(A I
DB=DAB5(B)
CC=DABS í C)
0D=DAB5(D)
IFIS.EQ.2.5DQ) GO TO 22
IF(S.EQ.2.000) GO TO 24
IF(S.EQ.1 .5D0) GO TO 26
IF I 5.EQ.1.ODO) GO TO 2B
C

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C MAKE SURE MAXIMUM SIZE IS NOT EXCEEDED.
C
22
IF (
DA.
LE.
170.
00)
GO
TO
3B
GO
TO
30
2 A
IF 1
CA .
LE.
170
DO)
GO
TO
36
GO
TO
30
26
IF 1
:sa
LE.
170.
. DO 1
GO
TQ
34
GO
TO
30
28
IF 1
: aa .
LE.
170
. DO 1
GO
TO
32
30 CONTINUE
CHIZ=0.00
CHIX-0.DO
GO TO 90
32 CHIZT- 2.D0#DEXP(A)
CHIZB= 1.DO + 2.DO*DEXP Í A)
CHIXT = 12.00*BK*TCAL*U.DO + DEXPIAI)
CHIXB* 1.00 + 2.D0*DEXPIA>
GO TO 60
34 CHIZT* 1.00 + 9.00*DEXP(8)
CHIZB* 4.DO*(1.00 + 0EXP1B))
CHIXT* 4.00 + (3.D0*BK*TCALII)/XD)*11.D0 - QEXP18))
CHIXB* 4.00*11.DO + 2.DO*DEXP(B))
GO TO 60
36 CHIZT* 2.DOÍOEXP1 A I + 8.D0*DEXP(C)
CHIZB* 1.00 + 2.DOÍDEXP1A) + 2.D0*DEXP(C)
CHIXT=Í6.D0*BK*TCAL1I)7X01*11.00 - DEXPIAI) +
1 14.D0*8K*TCAL1 I)/13.OQ*XOI I * 1DEXP1 A) -OEXP(C))
CHIXB* 1.00 + 2.DO*DEXP1A I + 2.00*DEXP(C)
GO TO 60
38 CHIZT* 1.DO + V.Oa*OEXP(B) + 25.DO*OEXPl0)
CHIZB* 4.DO*(1.00 + DEXP(B) + DEXP1D1)
CHIXT* 9.DO + 18.D0*BK*TCAL11)/XO)*11.DO - DEXP18)) +
1 (9.D0*BK*TCAL1I)/(2.D0*XD)l*(OEXP(B) -DEXP1D1)
CHIZB* 4.00*11.DO + OEXP1BI + DEXP1D)I
C
C INCLUDE ZJ PARAMETERS TO MODIFY CHI'S INOIUIOUALLY.
C
60 CONTINUE
THETAZ=2.D0*ZJZ*1CHIZT/CHIZ8)
CHIZ*1 AN*GZ*GZ*BCM*BERG)*(CHIZT/CHIZB) / (BK*TCAL( II-THETAZ)
THET AX=2.D0*ZJX*1CHIXT/CHIXB)
CHIX=(AN*GX*GX*8CM*8ERG)*(CHIXT/CHIXB)/ C
C TAKE AVERAGE OF ORIENTATIONS.
C
70 CSU51I)=(CHIZ + 2.D0*CHIX)/3.DO +
PAR*4.2D0/TCAL(I)
IF15U51I).LE.0.D0I GO TO 100
IF(XUT) 77,96,99
97 WT=SU511)
GO TO 101
98 UT=1.DO
GO TO 101
99 WT*1 . D0/SU5 11 )
GO TD 101
100 1*JT = 0 . DO
101 FOBJ=FOBJ+ICSU5(I)-5US(I))* 1CSUS11)-SUS 11) l*WT*UT
110 CONTINUE
RETURN
END

1
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1
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9
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2B
£9
30
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39
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49
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nnnnno non non nnnn noonnnnnnnrjo
266
D3I5NG »»«**t***»»«»****»»$»***tt»J»»»*»»
D-DOUBLE PRECISION; 3-SPIN 3/2; I5NG-I5ING MODEL FOR CHI
THIS PROGRAM CALCULATES THE MAGNETIC SUSCEPTIBILITY
OF AN INFINITE ONE DIMENSIONAL CHAIN OF 5PIN-3/2
UNITS USING THE I5ING MODEL. AN ISOTROPIC G VALUE
IS USED ALONG UITH J, THE ANTIFERROMAGNETIC EXCHANGE
PARAMETER. THE DATA CAN BE WEIGHTED EQUALLY (XWT-01,
BY SUS (XWT(0) OR BY 1/5US 1XWT>0).
SUBROUTINE SCALC
IMPLICIT REAL*8 IA-H, O-ZI
COMMON /CXF/ X(20),FOBJ,NFFIT
COMMON /CSCAL/ SUS(165] ,CSU5(165),T <165) ,TCAL(163),
UEFF(165).UCAL1165),NP
COMMON /C5TEP/ XhAX120) ,XMIN(201 ,DELTX(20) ,OELMN(20),
ERR 120,21í ,NV,NTRAC.MATRX,MASK(20 >,NFMAX,
JVARY , NXTRA , KFLAG , NOREP , KERFL , KU , NFLAT
BK= 80LTZMANN CONSTANT IN CM-1; AN- AVOGADRO'S NUM8ER
BCM, BERG- BOHR MAGNETON IN CM-1, ERG
OATA BK, AN /6.950300-1, 6.022043D23/
OATA BCM, BERG, ERGCM /A.668600-5, 9.2740B0-21,
1 1.9864780-16/
INPUT PARAMETERS AS OESCRIBED ABOVE.
XJ-Xl1)
G-X12I
XUT-X13)
FOBJ-O 0D0
DO 101 I-l.NP
A-XJ/14.D0*BK*TCAL1I) )
AA=DAB5(AI
MAKE SURE MAXIMUM SIZE NOT EXCEEDED.
IF1AA.GT.9 001 GO TO 95
USE THE EQUATIONS GIVEN BY SUZUKI, T5UJIYAMA AND KATSURA
I5UZUKI, M,; T5UJIYAMA, B.; KATSURA, 5. J. MATH. PHYS.
1967, B, 124.I
SLIGHT MODIFICATION IN NAMES: AX-K, XL-L, XM-M, U-T
AX-DEXP(A Í
£TA=(AX**1B.001+11.D0/AX**18. DO)- IAX*AX)-11.00/1 AX*AX)I
V— I AX** 10.00 ) + ( 1.00/AXM1B. DO 1 + 1 AX*AXI-( 1 .00/IAX*AX) I
XL=1ETA*ETA1+4.00*11AX**6.DO)+11.DO/AX**6.DO)>
*1 IAX**6.DO) + (1.DO/AX**6.001)
IFIXL.LE.O.DO) GO TO 93
Xh=(V*V)+4.00*1(AX**6.00)-(1.D0/AX**6.00)1
*1(AX**6.DO>-I1.DO/AX**6.DO))
R-11.DO/AX**18.DO) + (1.DO/1AX*AX) I
+ I 1 . DO/2 . DOUDSQRTIXL)
P-12.DO*lAX**6.DO)-(1.00/AX**6.0011*1D5QRTlDSQRT1 XL I+ETAI I
+ 1 AX*AX)* 1D5QRT1DSQRT1 XL)-ETA) )
Q-3.DO*1AX**18.DO 1*1DSQRT1DSQRT(XL)+ETA)I
+ 12.DO* 1 AX**6.DO 1 + 11.D0/AX**6.DO))*DSQRT1DSQRT1 XL)-ETA>
U-V*1P*P-Q*QI+4.DO*P*Q*(1AX**6.DO)-(1.DO/AX**6.DOJI
XLAMOO-11.00/2.DO)*(1AX**1B.DO)+1AX*AX)+(1.DO/AX**18.DO)
+ 11.DO/(AX*AX)) ) + (11.00/2.DO)*0SQRT1 XL I I
XLAMOl-l 1 . DQ/4.00)*(9.DG*!AX**18.D0)+(AX*AX) )
+11.00/4.DOl*(ETA*(9.00*(AX**18.00)-1AX*AXI)
+ 4 00*1 1AX**6.00) + 11.DO/AX**6.DO) I * 1 A.DO*1AX**4.DO)
+ 11.DO/AX**6.00))1/DSQRT1 XL I
XLAM34-1(2.DO*R*1P*P+Q*QI l+U)/I 14.DO*R*R-XM)*OSQRT1 XL))
CSUS(11 = 11AN*G*G*8CM*BERG)/1BK*TCAL Í11))

71
72
73
74
75
76
77
78
79
80
81
B2
83
84
85
267
*{(XLAM01+XLAM34)/(2.DO*XLAMOO)>
IF < SUS(11 .LE.0.DO) GO TO 99
IF(XUT) 12,13,14
12 UT=SU5(II
GG TO 100
13 U1T-1 .DO
GG TQ 100
14 UT«l.DO/SUS(II
GG TO 100
95 CSUS(I)=0.DO
99UT-O.DO
100 F0BJ=F0BJ+tCSU5lIJ-5U5(Il)**UT*UT
101 CONTINUE
RETURN
END

1
2
3
4
5
ó
7
B
9
10
11
12
13
14
15
16
17
IB
19
20
21
22
23
24
25
26
27
2B
29
30
31
32
33
34
35
36
37
3B
39
40
41
42
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45
46
47
40
49
50
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57
50
59
60
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65
6 6
67
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nnnnn nnnn nnnnnnnnnnnnnn
268
*»*»$$S»*t*S*St»*******»**t*»*»*M*t*»****M»**»*****»****»*M*
ntiinittiKU >ii osjx »*»ttst«$***t»»**«»t**$***t*»»***
O-OOUBLE PRECISION; 5-ANY SPIN; J-ANTIFERR. EXCHANGE;
X=EXPONENTIAL EQUATION.
THIS SUBROUTINE CALCULATES THE MAGNETIC 5U5CEPTI8ILITY
FOR ANY S1=S2=S OIMER (MAX-S/2). INTERDIMER INTERACTIONS
ARE INCLUDED AS ZJ . PARAMAGNETIC IMPURITIES AS PAR.
BOTH THE ANTIFERROMAGNETIC EXCHANGE INTERACTION (J) ANO
THE G UALUE ARE ISOTROPIC.
OATA CAN BE WEIGHTED EQUALLY (XWT=0), BY SUS BY 1/SUS (XWT>0 I .
SUBROUTINE SCALC
IMPLICIT REAL*B (A-H. O-Z)
COMMON /CXF/ X(£0 í FOBJ.NFFIT
COMMON /C5CAL/ 5U5(145),C5US(145 I ,T(165 I,TCAL(163) ,
UEFF(145) ,UCALI165 I .NP
COMMON /CSTEP/ XMAX(£0),XMIN(HO),OELTX(20>,OELMNI£0Í,
ERR(20 ,21 I , NU ,NTRAC,MATRX,MASK(201 ,NFMAX,
JUARY,NXTRA,KFLAG,NOREP,KERFL,XU,NFLAT
8K = BOLTZMANN CONSTANT IN CM-1; AN- AVOGAORO'S NUMBER
BCM, BERG- BOHR MAGNETON IN CM-1, ERG
DATA BK, AN 16.950300-1, 4.022045023/
OATA BCM, BERG, ERGCM M.468400-3, 9.274080-21,
1 1.9844780-14/
XJ=J, ZJ- INTEROIMEP PARAMETER USING THE MOLECULAR FIELO
MOOEL. PAR TAKES INTO ACCOUNT THE PRESENCE OF MONOMERIC
IMPURITIES WITH NORMAL CURIE LAW BEHAUIQR.
S= XIII
XJ-XI2)
ZJ=X(3)
G= XI At
PAR-XI51
XWT-X14I
FOBJ=0.QDO
DO 101 1=1,NP
A- 2.00*XJ/(BK*TCAL(III
B= 6.00*XJ/IBKSTCAL(11 I
C = 12.00*XJ/ D=£0 DO*XJ/(BK#TCAL(I)I
E = 30.DOSXJ/(BK*TCAL(I) >
AA = DABS(A I
BA=OABSIBl
CA=0ABS(C)
OA-DABS(0 t
EA=DAB5(El
IFIS.EQ.2.5D0) GO TO 7£
IF ( 5 . EQ . 2.000 ) GO TO 74
IFI5.EQ.1.5DO) GO TO 74
IF(S.EQ.1.000) GO TO 78
IF(S.EQ.0.500 I GO TO 80
MAKE SURE MAXIMUM SIZE NOT EXCEEDED.
72 IF1EA.LE.170.00t GO TO 90
74 IF 74 IFICA.LE.170.DO) GO TO 86
78 IF(BA.LE.1/0.00) GO TO 84
80 IFIAA.LE.170.D0) GO TO 82
TDP-0.DO
BTM=1 DO
GO TO 95
82 TOP=2.DO*OEXP(A)
BTM-1.D0+3.00*OEXP(AI

269
71
GO TO 95
7E
8 A
TDP=2.DOaDEXP( AH 10 . DOtOEXPI B)
73
BTM=1.D0+3.00*DEXPIA)+5.00*DEXP(B)
7 A
GO TO 95
75
86
T0P=2.DOaDEXP(A>+10.DOaDEXP
76
BTH»1.DO+3.DOaDEXP(A1+5,DO*DEXP(BI+7.DOtDEXP(C)
77
GO TO 95
73
88
T0P=2.DOaDEXP(At+10.D0*DEXP(8)+28.DOaDEXP(C>+60.DOaDEXP!D>
79
8TM=1.00+3,D0*DEXPIA)+5.DO*OEXP(BI+7.D0*DEXP(C)
SO
+9.DO*OEXP(OI
01
GO TO 95
as
90
T0P=2.DOaDEXP(A I + 10.DOaDEXP(B)+28 DOaOEXPlC)+60,DOaDEXPl0 I
B3
+110.DOaDEXP(E)
34
BTh-1.DO+3.DOaDEXP(A1+5.DOaDEXP(B>+7.DOaDEXPIC)
85
+9.DOaDEXP(01+11.DOaDEXP(E)
66
95
THETA=2.DOaZJ*TOP/BTH
87
CSUS 88
+4.2D0aPAR/TCALlI)
89
IF(SUS(II .LE.0.DO I GO TO 99
90
IF(XUT) 12,13,14
91
12
UT = 5U5(11
92
GO TO 100
93
13
WT=1 . DO
9 4
GO TO 100
95
14
UT=1.D0/SUS(I)
96
GO TO 100
97
99
UT=0.DO
99
100
FDBJ=FDBJ+(CSUS(II-5U51I))*(CSUS(II-5US1I1)aWTaUT
99
101
CONTINUE
100
RETURN
101
END
* IF PI .EOS. "" THEN INQUIRE PI "Naee af file with SCALC routine to be used (NO
.EXT!1"
* FOR RSD4DISK : CJTIDSUSFIT
4 FOR RSD4DISK:CJT.ILL1DEI5
4 FOR RSD4DISK:CJT.ILL IOSTEPIT
$ FOR R5D4DISK:CJT.ILL]'PI'
t LINK DGU5FIT.D5TEPIT.DEI5,'PI',0PLT:PTIGERLIB
4 ON CONTROL Y THEN I GO TO DONE
4 IF PE EQ5 ~ "" THEN INQUIRE P2 "Naee of file with D5U5FIT date to be ueed (NO
EXT!
4 ASSIGN 'P2 * .OAT F0R015
4 ASSIGN 'P2'.L5T F0R016
4 ASSIGN 'P2'.PTI FDR021
4 RUN D5USFIT.EXE
4 DONE
$ OEASSIGN FORO 15
4 OEASSIGN FOR016
4 OEASSIGN FOROH1
4 URITE SYS40UTPUT "Your output is in 1'P2'.LST."
4 URITE 5Y540UTPUT "Your plot file is in ' 'Pa'.PTI."
4 INQUIRE PLOTIT "Do you want it plotted at the printer jn your tereinal?"
$ IF PLOTIT THEN 3PLT : PLOTTIGER. COM ‘P2’.PTI TT:

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27
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nnnnnooonon nnnnnnnnnn
270
D30JHAM »$*$*S$**»*t$$***$*t*$***t«*
D=D0UBLE PRECISION; 3=SPIN 3/3; 0- AXIAL ZF5; J=DIMER
WITH ANTIFERROMAGNETIC EXCHANGE; HAM=SPIN HAMILTONIAN.
THIS PROGRAM CALCULATES MAGNETIC SUSCEPTIBILITIES
FOR A DIMER OF 51=52=3/2 WITH AXIAL ZERO-FIELD
SPLITTING OF BOTH SPINS EQUALLY USING THE FULL SPIN
HAMILTONIAN.
SUBROUTINE 5CALC
IMPLICIT REALfcB REAL*B SCALTI165,2),SCALE(165,2 I ,SCAL(165,2)
REAL*8 AR<16,16I,AI116,16),D116),EU6I,E2(16I,TAU12,16)
REAL*8 Z(16,16),XMMNT(16,2i,ENG(16,3,21
COMMON /CXF/ XÍ20I,FOBJ,NFFIT
COMMON /C5CAL/ SUS(165 I ,CSUS1165) ,T(165 I,TCAL(165) ,
UEFFÜ65I , UCAL (165) , NP
COMMON /CSTEP/ XMAX(20 I ,XMIN(20 i ,DELTX(20) ,OELMNI 20) ,
ERR Í 20 ,211 , NO ,NT RAC,MATRX, MASK(£01 ,NFMAX,
JUARY,NXTRA,KFLAG,NOREP,KERFL,XU,NFLAT
DATA NMAX, NSPN /16,16/
DATA BX, AN /6.950300-1, 6.022045023/
OATA BCM, BERG, ERGCM /4.668600-5, 9.274080-21,
1 1.9B6478D-16/
N5PN= SPIN MULTIPLICITY (SIZE OF HAMILTONIAN MATRIX!
= 2*151+521+1 + 2*151+52-11+1 + ... + 2*101+1
BX= BOLTZMANN CONSTANT IN CM-1; AN= AVOGADRO'S NUMBER
BCM, BERG= BOHR MAGNETON IN CM-1, ERG
INPUT PARAMETERS: J= EXCHANGE, 0= ZFS, G PARALLEL ANO
PERPENDICULAR (X=YI, HF= MAGNETIC FIELO (GAUSS!, XUT=
WEIGHTING PARAMETER. XUT EQUALLY; XUT10: WT BY 1/SU5.
XJ=X(11
X0=X(2)
GZ=X(3)
GX=X(4)
HF = X15 Í
XWT = X(61
FOBJ=0.DO
IERR=0
C L=1: FIELD IN Z DIRECTION (PARALLEL!; L=2: IN X (PERP1
C M=1: H-DELTA(HI; M=2: H; M=3: H + DELT A(H)
C
DO 17 L=1,2
DO 15 M=1,3
C
C ZERO OUT EI5PACX ARRAYS. AR IS HAMILTONIAN MATRIX.
C
00 4 1=1,NSPN
D(11= 0.00
El 11= O.DO
E2(I!= 0.00
T AU(1,11= 0.00
TAU (2,1 I = 0.00
00 4 J=1 , NSPN
AR(I,Jl=0.DO
AI(I,J)=0.00
Z1I,JI= 0.DO
4 CONTINUE
GO TO (5,6,7! ,M
5 HA=HF-(1.0-2*HF1
GO TO 8
6 HA=HF
GO TO 8

FILL UP HAMILTONIAN MATRIX, ALL VALUES ARE REAL SO
AI IS IGNORED.
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272
15 CONTINUE
17 CONTINUE
DO IB 10=1,165
DO 18 J0=1,2
SCALT(I0,J0)=0.00
SCALB1IO,J0) = 0.DO
5CAL(I0,J0>=0.00
18 CONTINUE
00 110 1=1,NP
00 21 ID=1 ,2
DO 20 IE=1, N5PN
C
C SET LOWEST ENERGY LEVEL=0. THI5 ACCOUNTS FOR CONSTANT
C QUANTITIES IN J AND D TERMS IN HAMILTONIAN.
C
R=IENG Y=DAB5(R)
IF(Y.GT.SO.OO) GO TO 20
C
C USE 5TANDAR0 FORMULAE FOR SUSCEPTIBILTY.
C
SCALT 11,ID)=5CALT(I,ID)+XMMNT(IE,ID)*OEXP(-1.DO*R)
5CALBII,ID)=5CALB(I,ID)+ DEXPÍ-1.DO*R)
20 CONTINUE
5CALÍI,IDI=(AN/HF)*5CALT(1,10)/SCALB(I,ID)
21 CONTINUE
C
C TAKE AVERAGE OF ORIENTATIONS
C
C5U5II)=<5CAL IFISUS(I).LE.O.DO) GO TO 100
IF(XUT) 22,23,24
22 UT = 5US(I 1
GO TO 101
23 UT=1.DO
GO TO 101
24 UT = 1.DO/SUS(I)
GO TO 101
100 UT=0.00
101 FQBJ= FOBJ + (CSUS(Il-5U5(I)1*(CSUS-SUS(I)1*UT*UT
110 CONTINUE
GO TO 205
199 WRITE(16,200) IERR
200 FORMAT)10X,'IERR =',1101
205 RETURN
END

APPENDIX G
COMPUTER PROGRAMS USED FOR MOSSBAUER AND NMR SPECTRAL SIMULATIONS
This appendix contains computer programs for Mossbauer and NMR
spectral simulations. These programs were not used for the work
described in this thesis, but were developed in conjunction with the
programs listed in Appendices E and F. The program titled DMOSFIT fits
experimental to calculated Mossbauer spectra using the DSTEPIT
program.^ The program titled DMOSFIT calculates Mossbauer spectra and
can be used for Ml nuclear transitions of the following six types: 1/2
<—> 3/2, 3/2 <—> 5/2, and 5/2 <—> 7/2. Nuclear energy levels are
calculated using a spin Hamiltonian which is diagonalized by EISPACK
subroutines. The program titled DNMRFIT calculates NMR spectra for AX
systems with first order splittings. Further details can be obtained by
inspection of the programs and from the literature.®® Both programs use
the DSTEPIT routine^® to fit experimental to calculated spectra.
273

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cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
CXXXXXXXXXXXXXXXXXXXXXXX DhOSFIT xxxxxxxxxxxxxxxxxxxxxxxxxxxx
D= DOUBLE PRECISION; MOSFIT> M05SBAUER EFFECT SPECTROSCOPY
SIMULATION PROGRAM
THIS VERSION UAS WRITTEN BY JOSHUA A. TEL5ER AT THE
UNIVER5ITY OF FLORIDA [MARCH, 1984). IT IS BA5ED ON
EARLIER VERSIONS WRITTEN BY WAYNE 0. FEDERER AND
MICHAEL K. KROEGER AT THE UNIVERSITY OF ILLINOI5
(I960). THE ORIGINAL VERSION UAS WRITTEN BY H. HOLLIS
WICKMAN. SEE FOR EXAMPLE: UICKMAN, H. H.; KLEIN, M. P.;
SHIRLEY, D. A, PHYS REV. I960, 152, 345.
THIS PROGRAM CALCULATES hOSSBAUER EFFECT SPECTRA FOR
POWDER SYSTEMS. IT IS AS5UMED THAT THE NUCLEAR 5PIN
QUANTUM NUMBER (MI) DOES NOT CHANGE DURING RELAXATION
ANO THAT ONLY MAGNETIC DIPOLE ALLOWED TRANSITIONS OCCUR
IDELTA M1= 0, +1, -1). THREE TYPES OF NUCLEAR TRANSITIONS
ARE POSSIBLE: 1= 1/3 <--> 3/3, 3/3 < —> 5/2, 5/2 < — > 7/2
FOR OTHER TRANSITIONS, THE SUBROUTINES MTRANS AND MINTEN
MUST BE MODIFIED.
TWO STATE5, A AND B, ARE POS 51 BLE FOR THE SYSTEM AND
EXCHANGE 0CCUR5 BETWEEN THEM AT A RATE U. THE EFFECT OF
THIS EXCHANGE IS CALCULATED BY THE RATE EQUATION METHOD
AS IN NMR THE ENERGIES OF THE GROUND AND EXCITED STATE
NUCLEI ARE CALCULATED EXPLICITLY USING A SPIN HAMILTONIAN
WHICH INCLUDES ISOTROPIC NUCLEAR ZEEMAN EFFECTS AND
RHOMBIC qUAORUPOLE SPLITTING EFFECTS. THESE ARE DEFINED
AS q= VZZ AND ETA= IVXX-VYY)/VZZ. THESE CAN ALSO BE
DEFINED AS QO = 3QZZ= 3eQ/I 41(21-1)1XVZZ AND
QE= iQXX-QYYI“ eQ/(41(21-1 I )*(VXX-VYY)
INPUT QUANTITIES
LINE *1
LINE *2
LINE SET X3
LINE *4
TITLE (10A41
ANY ALPHANUMERIC CHARACTERS IN THE
FIRST 40 COLUMNS
NV,KW,IFIT (FREE FORMAT I
NV- NUMBER OF VARIABLES TO BE MINIMIZED
KW- OUTPUT UNIT OF THE COMPUTER CKW= 18
FOR OUTPUT IN F0R01BI
IFIT- -0 IF LEAST SQUARES FITTING USING
D5TEPT 15 TO BE DONE. THUS DATA
POINTS MUST BE READ IN. (LINE *B)
> OR < 0 IF NO LEAST SQUARES FIT
IS TO BE DONE. IN THIS CA5E NO
DATA ARE READ IN.
X ,XMAX,XMIN,DELTX,DELMN,HA5K
(FREE FORMAT)
THE NUMBER OF LINES IN THE SET IS NV
ONE LINE FDR EACH PARAMETER (MAX= 20)
X- PARAMETER TO BE MINIMIZED
XMAX- UPPER LIMIT OF PARAMETER X
XMIN- LOWER LIMIT OF PARAMETER X
DELTX- INITIAL STEP SIZE FDR X
DELMN- LOWER LIMIT (CONVERGENCE) ON THE
STEP SIZE FOR X
MASK- =0 IF THE PARAMETER 15 TO VARIED
> DR < 0 IF X IS TO BE HELD FIXED
DEFAULT VALUES SET BY D5TBEG:
XMAX= 1.D37
XMIN=-1.037
OFLTX=l.D-2
OELMN=5.0-8
NTRAC,MATRX,NFMAX,NFLAT
(FREE FORMAT)
NTRAC- =-l FDR .-10 OUTPUT
=0 FOR ONLY FINAL VALUES PRINTED
»+l FOR TRACE OF MINIMIZATION

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LINE #5
LINE *6
LINE *7
LINE *8
LINE SET *9
PROCESS
(0 IS GENERALLY BEST VALUE)
MATRX- =0 FOR NO ERROR CALCULATION
=100 TO 110 FOR ERROR CACULATI0N
(105 IS GENERALLY BEST VALUE)
NFMAX- MAXIMUM NUMBER OF FUNCTION
COMPUTATIONS
NFLAT- =0 FOR SEARCH TO TERMINATE WHEN
CHANGES IN X ARE EQUAL TO DELMN
> OR < 0 FOR SEARCH TO TERMINATE
UHEN ALL TRIAL STEPS GIVE
IDENTICAL FUNCTION VALUES
NCH,NP,BKG,CAL (FREE FORMAT)
NCH- NUMBER OF CHANNELS (DEFAULT- 512,
hAXIMUM= 1024)
NP- NUMBER QF DATA POINTS I MAX- 512)
BKG- NUMBER OF COUNTS OF BACKGROUND
CAL- VELOCITY SCALE CALIBRATION FACTOR
(MM/SEC)/CHANNEL
T,FRACA,FRACB (FREE FORMAT)
T- TEMPERATURE AT UHICH DATA UERE
COLLECTED IN DEGREES KELVIN
FRACA- MOLE FRACTION OF STATE A
FRACB- MOLE FRACTION OF STATE B
ENTER 0.0 FOR BOTH IF MOLE
FRACTIONS ARE TO BE CALCULATED
USING A BOLTZMANN DISTRIBUTION
FRACA + FRACB MUST » 1.0
STD,ENRGY,XI(1),XI(2),G(1),G(2I,QR
(FREE FORMAT)
STO- CORRECTION FOR ISOMER SHIFT OF
50URCE RELATIUE TO THE VELOCITY
STANDARD (STD- 0.112 FOR DATA
OBTAINED USING A CO-57 SOURCE IN A
RHODIUM MATRIX WITH VELOCITIES
REFERENCED TO IRON METAL)
ENRGY- CONVERSION FROM MM/SEC TO MHZ:
11.625 FOR FE-57; FOR OTHER
NUCLEI U5E DOPPLER SHIFT EQN.
XI(1)- NUCLEAR SPIN DF GROUND STATE:
0.5 FOR FE-57, 3.5 FOR 1-129.
XI (2)- NUCLEAR SPIN OF EXCITED STATE:
1.5 FOR FE-57, 2.5 FOR 1-129.
Gill- NUCLEAR G-VALUE FOR GROUND STATE:
+0.1804 FOR FE-57
G(2)- NUCLEAR G-UALUE FOR EXCITED STATE:
-0.1031 FOR FE-57.
QR- RATIO OF EXCITED STATE TO GROUND
STATE QUADPUPOLE SPLITTING.
QR= Q*/Q, SET TO 1.0 IF Q- 0.
IFPL , IEXPT,ICALC,IHALF (FREE FORMAT)
IFPL- =0 IF NO PLOTTING 15 DESIRED
NONZERO IF ANY PLOTTING DESIRED
IEXPT- =0 IF NO PLOT DF EXPERIMENTAL
POINTS IS DE5IRE0
NONZERO IF PLOT IS DESIRED
ICALC- =0 IF NO PLOT OF CALCULATED
CURVE IS DESIRED
NONZERO IF PLOT IS DES I RED
IHALF- =1 FDR FIRST HALF, ELSE SECONO
HALF. FIRST HALF OF DATA- CH*
1 TO NCH/2 DECREASING IN ENERGY.
SECOND HALF OF DATA= CH* NCH/2 +
1 TO NCH INCREASING IN ENERGY.
XDAT A,YDATA (FREE FORMAT)
NUMBER OF LINES IN THE SET IS NP
ONE LINE FDR EACH POINT
XDATA- CHANNEL NUMBER OF DATA POINT
VALUES MUST BE A5CENDING IN CHANNEL
NUMBER WITH NO TUO NUMBERS EQUAL

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C YDATA- INTENSITY (NUMBER OF COUNTS I
C
C
C*** EXPLANATION OF INPUT PARAMETERS: XII) #**
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
*1 RFBA- RATIO OF RECOILLESS FRACTION FOR
STATE B TO STATE A. MULTIPLIED BY
A FUDGE FACTOR TO GIVE CORRECT
STATE POPULATIONS. THIS HELPS
ACCOUNT FOR NON-EQUILIBRIUM
BEHAVIOR WITHOUT USING A WRONG
VALUE FOR DEL. DEFAULTS. DO
IGNORED IF POPULATIONS OF A ANO B
ARE FIXED BY FRACA ANO FRACB.
*2 DEL- ENERGY OF STATE A MINUS ENERGY OF
STATE B IN CM-1. IGNORED IF POP¬
ULATIONS OF A AND B ARE FIXED.
*3 W- PHENOMENOLOGICAL RELAXATION RATE
IN HZ. WARNING: FLOATING POINT
OVERFLOW MAY OCCUR IN RATE EQN IF U
15 NOT ALLOWED TO VARY BY MORE THAN
1.0-7 HZ. UNDERFLOW MAY OCCUR FOR
VALUES > 1.0+20 HZ.
*4 GAMMA- NATURAL LINEWIDTH IN MM/5EC:
HALF-WIDTH AT HALF-HEIGHT.
LORENTZIAN LINESHAPE.
*5 DA- ISOMER SHIFT OF STATE A
#6 OB- ISOMER SHIFT OF STATE B
DA,08 IN MM/SEC
*7 QA- QUADRUPOLE SPLITTING OF GROUND
STATE AT SITE A - eQ(VZZ)
*B QB- QUADRUPOLE SPLITTING OF GROUND
STATE AT SITE B = eQ(VZZ)
QA, QB IN MM/SEC.
*9 ETA 111- NON-AXIAL QUADRUPOLE SPLITTING
FOR SITE A. ETA- (VXX-VYY>/VZZ
AND MUST BE BETWEEN 0.0 AND 1.0
*10 ETAI2I- ETA FOR SITE B.
*11 HA- INTERNAL FIELD AT SITE A IN KGAU55
*12 HB- INTERNAL FIELD AT SITE B IN KGAU5S
IN THIS PROGRAM, THE INTERNAL MAGNETIC
FIELD5 CORRESPOND TO THE PRESENCE OF
SLOW ELECTRONIC RELAXATION. THUS THEY
SHOULD BE ZERO FOR THE CASE OF FAST
ELECTRONIC RELAXATION, REGARDLESS OF
THEIR TRUE VALUES. THE CASE OF RATES
WHICH DIFFER FOR A AND B AND APPROACH
THE FAST LIMIT CAN BE CRUDELY APPROX¬
IMATED BY CAUSING BROADENING OF THE
PATTERN FOR THE MORE SLOWLY RELAXING
STATE BY USING AN HA GR HB VALUE
SLIGHTLY GREATER THAN GAMMA. (1.0
MM/SEC = 49.2 KG FOR FE-57 1-3/2)
IMPLICIT REAL#8 IA-H, O-Z)
EXTERNAL 5PECTR PL2CA
COMMON /CSTEP/ XHAX(20) tXMIN(20> ,DELTX(20) ,DELMNI 201 ,
1 ERR(20,21),NV,NTRAC,MATRX,MA5K(20),NFMAX,JVARY,
2 NXTRA,KFLAG,NOREP.KERFL KW,NFLAT
COMMON / C X F/ X(20 > .FOBJ.NFFIT
COMMON /SPEC/ XDATA1512I,YDATA(512).XP0INTI312),
1 YPOINT1512) , YPLOT(312) ,5PEX(512) ,
2 PEFF(512),WT(512),XL,XR,NP,NCH,
3 T,TEFF,FRACA,FRACB
COMMON /NUC/ 5TD,ENRGY,XI(2) ,G12) ,QR
REAL#4 TITLE(20) ,SCRCH1(512 >,5CRCH2(512I ,
i 5YPL0TO12: , 5XPOINT ( 312 I , 5YPOINT ( 512 I , 5XL , SXR
C
C REAO IN PARAMETERS
C

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READ (17,5) < TITLE(It, 1*1,10)
5 FORHAT (10A4I
READ (17,*) NV,KW,IFIT
READ (17,*) (XII) ,XMAX< 11 ,XMIN< I) , DELTXI II ,DELMN< I) ,
MASK(I), 1=1,NO)
REAO (17,*) NTRAC,HATRXNFMAX.NFLAT
READ (17,*) NCH.NP.BKG.CAL
REAO (17,*) T,FRAGA,FRACB
READ (17,*) STD,ENRGY ,XI(1) ,XI(2) ,G(1) ,G(2) ,QR
READ (17,*) IFPL,IEXPT,ICALC,IHAUF
IF(IFIT . EQ.0) READ (17,*) IXDATA11) ,YDATA(I) , 1 = 1,NP)
ASSIGN DEFAULT VALUES FOR KW, NCH, QR, ENRGY (FE-57 VALUE)
IF(KU.EQ.O) KU=18
IF(NCH.EQ.O) NCH-512
IFIQR.EQ.0.DO) QR-1.00
IF(ENRGY.EQ.0.DO I ENRGY= 11.625D0
NCHAF= NCH/2
NCHAF1=NCHAF + 1
CONVERT CHANNEL NUMBERS TO VELOCITIES
AND FIND ENDPOINTS OF PLOT. XL* LEFT, XR= RIGHT ENDPOINT
XTOT = DBLE(NCHAF)*CAL
XL= -(XT0T/2.D01+STD
XR= (XTOT/2.DO)+STD
IF NO CURVE FITTING 15 TO BE DONE, BYPASS CONVERTING,
WEIGHTING AND SCALING THE DATA POINTS
IF(IFIT.NE.O) GO TO 30
IF FIR5T HALF DATA ARE USED, REORDER TD INCREASING ENERGY
THEN SWITCH CHANNEL NUMBERS SO LOW * MEANS LOU ENERGY.
IF(IHALF.NE.1) GO TO 17
NPHAF=NP/2
DO 14 1 = 1 , NPHAF
J= NP + 1 - I
XSWAP= XDAT A(I)
Y5WAP= YDAT All)
XOATA(II=XDATA(J)
YDATAtIÍ = Y0ATA(J)
XDAT A(J)=XSWAP
YDATAIJI=YSWAP
14 CONTINUE
DO 16 1=1,NP
XDATAÍI1=0BLE(NCHAF1) - XDATAIII
16 CONTINUE
GO TO 18
IF SECOND HALF DATA ARE USED, CHANGE CH* SO THEY
RUN FROM 1 TO NCH/2.
17 CONTINUE
DO 18 1=1,NP
XDAT A(I)=XDAT A(I) - DBLElNCHAF)
18 CONTINUE
C
C CONVERT CH* TO VELOCITY.
C
DO 20 1=1,NP
XPOINT(I)= XL+(CAL*XDATA ( 11)
20 CONTINUE
C
C CALCULATE LEAST-SQUARES WEIGHTING FACTORS FOR EXPERIMENTAL
C DATA POINTS. WEIGHT THEM ACCORDING TO THE INVERSE DF
C THEIR STANDARD DEVIATIONS, 5QRT(* COUNTS)
C

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nnnnn onnn non noon noon
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00 22 1=1,NP
UT(11=1.D0/DSQRTIYDATAII)1
22 CONTINUE
CONVERT NUMBER OF COUNTS TO SCALED INTENSITIES
AND CALCULATE PERCENT EFFECT.
Y MAX=0.DO
YHIN=0.DO
RANGE=0.00
DO 24 1=1,NP
PEFF(11= lBKG-Y0ATA(I) )/BKG*100 .00
YPOINT11)=PEFF(I>
IF IYPOINT(I I .LT.0.DO) YPOINT(11=0.00
IF l YPOINT(I).GT.YMAX > YMAX=YPOINT(I>
34 CONTINUE
DO 26 1=1,NP
YDIFF=YMAX-YP0INT(11
IF (YDIFF.LT.RANGE) GO TO 26
RANGE=YDIFF
YMIN=YPOINT(I)
26 CONTINUE
DO 28 1=1,NP
YPOINT(I)= 1.DO - (YPOINT(I1-YMIN)/(YMAX-YMIN)
IF (YPOINT(I).GT.l.DO) YPOINT!I>-1.DO
28 CONTINUE
GO TO 32
IF NO FITTING IS TO 8E DONE, CALCULATE POINTS AT EACH
CHANNEL NUMBER OVER A HALF RANGE.
30 CONTINUE
NP= NCHAF
DO 32 1=1,NP
XPOINT(I)= XL + CALÍDBLE(I)
32 CONTINUE
WRITE TITLE AT TOP OF PAGE PRIOR TO OUTPUT FROM OSTEPT
WRITE (KW.33) (TITLE II), 1 = 1,10)
33 FORMAT11X,601'*'),//IX,'M0SS8AUER SIMULATION PROGRAM',
1 /IX,10A4,//IX,601'*'))
BYPASS OSTEPT IF NO FITTING IS TO 8E DONE OR
IF ALL THE PARAMETERS IX) ARE FIXED
IFIIFIT.NE.O) GO TO 3B
MASK5= 0
00 35 1=1,NV
IF I MASK 11)>34,35,34
34 MASK5= MASKS+1
35 CONTINUE
IF I MASKS.EQ.NV) GO TO 38
CALL D5TEPT (SPECTR)
GO TO 40
38 CONTINUE
CALL SPECTR
40 CONTINUE
i*** WRITE OUT RESULTS ****
TABULATE THE PARAMETERS FOR THE LEAST-SOUARES FIT
WRITE (KW,41)
41 FORMAT(IX,1 I XII) XMAXII) XMIN(I)
1 ' DELTX(I) DELMN(I) MASK I I) ' ,//)
DO 44 1=1,NV
WRITE (KW,42) I ,X MASK 11)
42 FORMAT IIX,12,2X,El 0.4,1X,E10.4,IX,E10.4,IX,El 0.4,IX,

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1 £10.4,2X,12,/)
44 CONTINUE
C
C OUTPUT CONSTANTS USED IN CALCULATIONS
C
WRITE (KU.46I BKG, CAL
46 FORMAT{/2X, 1 BACKGROUND *COUNT5= ' ,E20.12,/2X,
1 '5CALE CALIBRATION» ' ,F10.4)
WRITE IKW,47) STD, ENRGY, XI. G, QR
47 FORMAT(/2X,1 STD ENRGY 10 I*',
1 'GO G* QR',
2 /2X,2F10.4,2F6.1,3F9.5)
WRITE (KW.48) T, TEFF, FRACA, FfiACB
48 FORMAT I/IX,'INPUT TEMP ',F5.1,' CHANGED TO ' ,F5.1,
1 ' TO ACCOMODATE THE DIFFERENCE I IF ANY! IN',
2 /IX,'RECOILLESS FRACTIONS BETWEEN STATES A AND 8',
3 //2X,'MOLE FRACTION OF A= '.FB.4,
4 //2X,'MOLE FRACTION OF B= ',FB.4,/I
C
C TABULATE THE OATA POINTS IF DATA WERE READ IN
C
IF(IFIT.NE.0 I GO TO 56
URITE(KW,52)
52 FORMAT(13X , 'EXPERIMENTAL' ,20X, 'CALCULATED' ,
1 /5X,'CHANNEL#',3X,'«COUNTS',9X,'SCALED*',5X,
2 'OELOCITY' ,6X, '* EFFECT ', 5X,'SCALED*',//)
DO 56 1=1,NP
WRITE ( KW , 54 Í XDATA(I) , YOATA (I) , YPOINTU) ,XPO INTUI ,
1 PEFF(I),YPLOT(I)
54 FORMAT(1X,F10.2,3X,E12.6,1X,F1Q.4,3X,F10.4,6X,
1 F10.4,1X,F10.41
56 CONTINUE
C
C CHECK IF ANY PLOTTING IS DESIRED.
C
IFIIFPL.EQ.0) GO TO 999
C
C***« PL0T79 SECTION FOR USE ON UF/QTP OAX. ****
C
C CHANGE DOUBLE PRECISION NUMBERS TO SINGLE PRECISION
C SINCE PL0T79 ONLY USE5 SINGLE PRECISION S=SINGLE PREC.
C ROUND UP RIGHT ENDPOINT, ROUND DOWN LEFT ENDPOINT.
C
SXL= REAL f INT f XL-1.DO I I
SXR= REAL Í INT tXR+1 . DOM
00 500 1=1,NP
5XP0INT(11= XPOINTII)
500 CONTINUE
C
C INITIALIZE PLOT SYSTEM
C
CALL PLTOQ
C
C SET PLOT SIZE TO 25.0 CM LONG AND 20 CM WIDE.
C
CALL 5ET5Z125.I
C
CALL SETDS2Í1.,.81
C
C PLOT THE AXES U5ING THE ROUTINE PLTAX.
C
CALL PLTAX(3. /25. , 3./25. ,17HUELOCITY íMH/SEC) ,17,20. /25. ,
1 0. ,SXL,1.0,SXR,-.005,-lI
C
CALL PLTAX(3./25.,3./2S.,12HTRAN5MI5SION,12,
1 15./25. ,90. ,0. , .2,1. , .005,2)
C
CALL SETVP20. /25 . , 23 . / 25 . , 3. /25 . , 18 . /25 . )
C
C CHECK IF PLOT OF EXPERIMENTAL POINTS IS DESIRED.

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IF(IFIT.NE.O) GO TO 700
IF DO 610 I®1,NP
5YPOINT(I)*YPOINT 610 CONTINUE
C
C PLOT THE OATA POINTS AS PLUS SIGNS USING THE ROUTINE GRFGP,
C
CALL GRFGP < SXL,5XPOINT,SXR,0.,SYPOINT,l. ,NP,
1 2,PL2CA)
C
C CHECK IF PLOT OF CALCULATED LINE IS DESIRED
C
700 IF (I CALC,EQ.0) GO TO 990
OQ 710 1=1,NP
5YPLÃœT(I \ =YPLOT(I)
SCRCH1(I I =XPGINT(I)
5CRCH2 710 CONTINUE
C
C DRAUI THE THEORETICAL CURVE USING THE ROUTINE GRFGI .
C
CALL GRFGIiSXL.SXPOINT,SXR,0.(SYPLOT,1.,NP(
1 5CRCH1,SCRCH2, NP, 1.,PL2CA)
C
C EJECT THE FRAME.
C
990 CALL PLTEJ
999 CALL EXIT
ENO

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OMOSLIB «Mí*******»»»**** **********
C 0= DOUBLE PRECISION; HOSLIB= MOSSBAUER SUBROUTINE LIBRARY
C
C***************************************************************
C THIS SUBROUTINE CALCULATES THE POSITIONS ANO INTEN5IIE5
C OF THE SPECTRAL LINES.
C
SUBROUTINE SPECTR
IMPLICIT REALTB (A-H, O-Z)
EXTERNAL RE3
COMMON /C5TEP/ XMAX<201 ,XMIN(201 ,DELTX120 I,OELMN(201,
1 ERR(20,21).NVNTRACtMATRX,MA5K(20> ,NFMAX,JVARY,
2 NXTRA,«FLAG,NOREP,KERFL,KW,NFLAT
COMMON /CXF/ X(20l,FOBJ,NFFIT
COMMON /SPEC/ X0ATAI512).Y0ATAÍ512I,XP0INT(512),
1 YPOINT(5121.YPL0TI512),5PEX(512>,
2 PEFF1512I,UT(512),XL,XR,NP,NCH,
3 TTEFF.FRACA, FRACB
COMMON /NUC/ STD , ENRGY , XI <2) ,GI21 ,QR
COMMON /TRAN5/ ENG(2,8) ,FREQ(2,10 I ,XIWIia,512 I ,OEI 2 I ,
1 QE(2,2),ETA(2),H(2I,NTR
DIMENSION AR(8.81,AI{8,8),0(8),£<0),E2(81,TAU(2,B),Z(8,BI
DIMENSION NEIG5T(2 I
DATA NMAX IB/
DATA BET A,BK /0.76225087DO, 0.69503000/
C
C NMAX= MAXIMUM HAMILTONIAN MATRIX SIZE, SET FOR I- 7/2
C BETA» NUCLEAR HAGNETON IN MHZ/KGAU55
C BK = BOLTZMANN CONSTANT IN CM-1 K-l
C
C ASSIGN VARIABLES INCLUDING DEFAULT VALUES
C
RFBA= X<1)
DEL= X(2)
U= XI3)
GAMMA» X < AI
OE(1 I = X151
DEI 21» XI 6)
QE(1 ,11» X(7)
QEI2,1I= X(S)
ETA I 1 1» X {9 1
ETA(2I= XÍ10)
HUI» Xllll
H12) = X ( 12)
IF(U.LE.O.DO) U- l.DO
IF(RFBA.LE.O.DOI RFBA- 1.00
C
C CALCULATE RELATIVE POPULATIONS OF STATES A ANO B USING
C THE SUBROUTINE MPDP.
C
CALL MPOP(FRACA,FRACS,T,RFBA,DEL,TEFF,POPA,POPBI
C
C SET UP HAMILTONIAN MATRIX TO FIND THE NUCLEAR ENERGY LEVELS
C NEIG5T» SIZE OF HAMILTONIAN MATRIX {SPIN MULITPLICITY1
C
NEIG5T(11 = 2.00*XI(11 + 1.01D0
NEIG5T(H)— 2.D0*XI(2) + 1.01DO
C
C CORRECT QUADRUPOLE SPLITTINGS FOR THE NUCLEAR 5PIN5
C AND CONVERT EVERYTHING FROM MM/SEC TO MHZ.
C
QE C 1 ,21= QE (1,1)
QE(2,2)= QE(2,1t
DO 9 1=1,2
OE(I)= 0E(I)*ENRGY
DO B J = 1,2
IF{XI(J).LT.1.001 GO TO 7
GO TO iA,51, J
A QEI I,JI= QE
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GO TG 6
5 QE(I , J1= QE(I,J)*QR*ENRGY
6 QCOR= 4.D0*XI(J)#(2.D0#XI(J) - l.DO)
QE(I , J ) = QE(I,J)/QCOR
GO TO 8
7 QEf I , J) = 0 . DO
8 CONTINUE
9 CONTINUE
C
C ALL VALUES ARE REAL SO AI IS IGNOREO. OUTER LOOP IS
C FOR STATES A AND B, INNER IS FOR GROUND ANO EXCITED STATES.
C
DO 50 1=1,2
DO 40 J=1,2
C
C ALL THE EI5PACK ARRAYS MUST BE ZEROED OUT BEFORE USE.
C
DO 12 K = 1 ,NHAX
D ( K)= 0.DO
E ( K ) = 0.00
E2(K)= 0.DO
TAW(1 , K)= 0.DO
TAU(2 , K )* 0 . DO
DO 11 L~1,NMAX
AR(K,LI» 0 . DO
AI(K , L)= 0.DO
Z < K , L ) = 0 . DO
11 CONTINUE
12 CONTINUE
C
C DEFINE CÃœN5TANT5 FOR NUCLEAR STATE GIVEN BY J
C
NST= NEIGST(J)
X11= XIt J > + 1.DO
XII1= XI(J)*(XI(J) + l.DO)
C
C FIRST DO DIAGONAL ELEMENT5
C
DO 14 K=1,N5T
XMI= XII - DBLE(K)
AR(K , K) = -G(J)*8ETA*H + QÉ(I(J)*(3.Ü0*XMI*XMI - XIII)
14CONTINUE
C NEXT DO OFF OIAGONAL ELEMENTS USING LOWERING OPERATORS.
C
NM2= N5T-2
00 15 K*1,NM2
K2= K+2
XMI= XII - 0BLEÍKI
AR(K,K2)= QE(I , J)*0.5D0*ETA *DSQRT(XIII - XMI*{XHI - l.DO))
CDSQRTíXIIl - 1XNI - 1.00XÍXHI - 2.DO))
15 CONTINUE
C
C FILL UP ENTIRE MATRIX SINCE IT IS 5YHHETRIC.
C
DO 16 K = 1,N5T
K1= K+l
DO 16 L=K1,N5T
AR(L , K)= AR(K,L)
16 CONTINUE
C
C FIND EIGENVALUES USING EI5PACK ROUTINES.
C
IERR=0
CALL DHTRIDI(NMAX.NST,AR,AI,D,E,E2,TAW)
CALL DTQLc: ( NHAX , NST , D , E , Z , IERR )
IF(IERR.NE.O) GO TO 199
C

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C HATCH EIGENVALUES WITH ENERGIES. THIS DEPENDS ON WHETHER
C THE QUADRUPOLE SPLITTING OR THE ZEEHAN SPLITTING IS
C DOHINANT AND ON THE SIGNS OF Q ANO G.
C
QTEST= DABS (QE( I , Jl*( 3. DO*XI I JI*XI I J) - XIID1
GTE5T- DABSIGIJ)*8ETA*H(I)*XIIJ)I
IFIGTEST.GT.QTEST) GO TO 30
IQV5G= 0
IFIQEII,J).GT.0.DO) GO TO 25
00 18 K=1,NST
ENG(J,K)= 0(K>
18 CONTINUE
IF(G(J) . GT.O.DO) GO TO 40
DO 23 K=1,NST,2
Kl= K+1
5WAP= ENG ( J , K)
ENG(J,K)= ENG IJ , K1)
ENGIJ,K1)= SWAP
23 CONTINUE
GO TO 40
25 CONTINUE
DO 27 K=1,NST
ENG(J,K>= D(NST-K+1 )
27 CONTINUE
IFIGIJ).LT.0.00) GO TO 40
00 28 K=1,N5T,2
Kl* K+l
SWAP83 ENG(J,K1
ENG(J,K>= ENGIJ,K1>
ENGIJ.KII- SWAP
28 CONTINUE
GO TO 40
30 CONTINUE
IQVSG=» 1
IFIGIJ) LT.O.DO) GO TO 34
DO 32 K=1,NST
ENGIJ,K)= OIK)
32 CONTINUE
GO TO 40
34 CONTINUE
DO 36 K=1,NST
ENGIJ,K)= DINST-K+ll
36 CONTINUE
40 CONTINUE
SINCE ENERGIES HAVE BEEN ORDERED IN THE SAME WAY,
USE MTRANS SUBROUTINE TO FIND THE CORRECT H05S8AUER
TRANSITIONS FOR A GIVEN NUCLEAR SYSTEM.
CALL MTRAN5IIQVSG,I)
50 CONTINUE
C
C CALCULATE A NORMALIZATION FACTOR SF FDR EACH OF THE
C TRANSITIONS USING SIMPSON'S METHOO FOR NUMERICAL
C INTEGRATION
C
DO 60 N= l.NTR
CALL 5IMPSN I FRED(1 , N) ,FREQ I 2,N) ,REQ, 5F , U , XL , XR .GAMMA,
POPA,POP8,NCH >
C
C CALCULATE THE SPECTRUM FOR EACH TRANSITION USING THE RATE
C EQUATION METHOO
C
DO 55 IPT= 1 ,NP
XIWCN,IPT>= REQIXPOINTIIPT) ,U,FREQ I 1 ,N> ,FREQ I 2,N) ,
POPA,POPS,GAMMA)75F
55 CONTINUE
60 CONTINUE
C
C SUM THE TRANSITIONS WITH THE CORRECT INTENSITY UEIGHTINGS

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C USING THE SUROUTINE MINTEN.
C
CALL MINTEN
C
C FIND THE LARGEST AND SMALLEST PEAKS AS BEFORE AND SCALE
C CALCULATED SPECTRUM
C
YMAX=0 . DO
YMIN=0.DO
RANGE=0.DO
DO 70 1=1,NP
IF (SPEXin .LT.O.DO) 5PEX(II = O.DO
IF (SPEXIII.GT.YMAXI YMAX=5PEX(I>
70 CONTINUE
DO 80 1=1,NP
YDIFF = YHAX-5PEX (11
IF (YDIFF.LT.RANGE) GO TO 80
RANGE=YDIFF
YMIN=SPEX(I)
80 CONTINUE
DO 90 1=1,NP
YPLOT(I)= 1.DO - (5PEXÍIÍ-YMIN)f (YMAX-YMIN)
IF 1YPLOTII).LT.O.DO) YPLOT(I)=O.DO
IF (YPLOTII) .GT.1.DO) YPLOT1 11 = 1 .00
90 CONTINUE
IF(IFIT.NE.O I GO TO 100
C
C CALCULATE FOBJ THE MEASURE OF GOODNESS OF FIT
C
FOBJ= 0.DO
DO 100 1=1,NP
FOBJ= FOBJ + (YPLOT!I)-YPOINT(I))*(YPLOTI Il-YPOINTII))
*WT ( I í *WT (I)
100 CONTINUE
GO TO 205
199 WRITE(KW,200 í IERR
200 F0RMAT110X,‘IERR =',1101
205 RETURN
END
C
C** XU#** ****************************************** **************
C
C THIS SUBROUTINE CALCULATES THE POPULATIONS OF STATES A AND B
C
SUBROUTINE MPOP(FRACA,FRACB,T,RFBA,DEL,TEFF,POPA,POPB1
IMPLICIT REALX8 (A-H, O-Z)
DATA BETA,8K /0.7622508700, 0.693030DO/
TEFF= T
IFIFRACA.EQ.O.DO.AND.FRACB.EQ.0.001 GD TO 5
POPA= FRACA
PQPB= FRACB
GO TO 20
C
C CALCULATE AN EFFECTIVE TEMPERATURE TO ACCOUNT FOR
C DIFFERENCES IN RECOILLESS FRACTIONS BETWEEN THE TWO
C 5TATE5 A ANO B, AND TO CORRECT POPULATIONS FOR
C NON-EQUILIBRIUM BEHAVIOR. THIS WILL NOT BE DONE
C WHEN DEL IS NEAR ZERO OR TEFF TURNS OUT TO OIFFER
C GREATLY FROM T: TEFF/T < 0.5 OR > 2.0
C
5 CONTINUE
IF(OABS(RFBA-1.00).LT.1.D-2I GO TO 10
IF(DABSIOEL).LT.l.D-1) GOTO 10
TFUJ= RFBAXDEXPI-DEL/(EKXT ) )
IFITFUJ.GT.O DO) TEFF= -DEL/(BKXDLOG1TFUJ)1
IF(TEFF,LE.0.00) TEFF= T
IF I (TEFF/T) .LT.0.5D0 .OR. (TEFF/T) .GT.2 , DO 1 TEFF=T
10 CONTINUE
C
C CALCULATE POPULATION RATIOS ASSUMING A BOLTZMANN

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C DISTRIBUTION.
C
ABRAT* DEXP!-DEL/(BKYT))
BARAT» DEXP( DEL/CBKYT)I
POPA» 1.00/(1.DO + BARAT)
POPB» 1 00/(1.00 + ABRAT)
20 CONTINUE
RETURN
END
C
CYYYYXY*********************************************************
C
C TH15 SUBROUTINE FINDS THE CORRECT MOS5BAUER TRANSITIONS
C FOR A GIUEN NUCLEAR SYSTEM BY PAIRING UP THE CORRESPONDING
C GROUNO AND EXCITED STATE ENERGIES. THESE TRANSITIONS AND
C THEIR INTENSITIES ARE TAKEN FROM GREENWOOD, N. N.; GIBB,
C T. C. "MOSSBAUER SPECTROSCOPY'1; CHAPMAN & HALL: LONDON,
C 1971; APPPENOIX 2.
C
SUBROUTINE MTRAN5(IQU5G , I )
IMPLICIT REALY8 (A-H.O-Z)
COMMON /NUC/ STD,ENRGY,X I(2) ,G(2) ,QR
COMMON /TRANS/ ENG(2,8) ,FREQl2.18) .XIU(1B,512) ,DE(2) ,
1 QE(2,2) .ETA!2 J ,H(2 I ,NTR
IFtXI (1) .GT.XII2M GO TO 3
JL=2
JR = 1
PL= 1.DO
PR—1 . DO
GO TO 5
3 JL=1
JR*2
PL»-1.DO
PR» 1.DO
5 CONTINUE
IF(XI(1) .EQ.0.5D0.AND.XI(2 I .EQ.l.500)
IF(XI(1).EQ.1.500.AND.XI(2).EQ.0.500)
IF(XI(1) .Eq.l.500.AND.XI(2 I .EQ.2.500)
IF(XI(1).EQ.2.5D0.AND.XI(2).EQ.1.500)
IF(XIil).EQ.2.500.ANO.XI(2).EQ.3.5D0)
IF (XI (1) . EQ.3.5D0.AND.XK2) .EQ.2.500)
NT R=0
GO TO 10
GO TO 10
GO TO 15
GO TO 15
GO TO 20
GO TO 20
GO TO 25
10 NTR* 6
IF(IQ05G.NE
FREQ(I,1)«
FREQ 11,2)»
FREQ(I,3)*
FREQ FREQ(1,5)*
FREQ(1,6)*
GO TO 25
13 CONTINUE
FREQ(I,1 1 =
FREQ <1,2)»
FREQÍI,31=
FREQ(I,4 ) =
FREQ(1,51=
FREQ(I , 6) =
GO TO 25
15 NTR= 12
IF(IQUSG.NE
FREQ(I , 1 ) =
FREQ!I,21*
FREQ FREQ(I,4)=
FREQ(I ,5) =
FREQ(I,61=
FREQ(I,7)=
FREQ(I , 8) =
0) GO TO 13
PLYENG(JL,1)
PL*ENGIJL,2)
PLYENG(JL,3)
PLYENG(JL,4>
PL*ENG(JL,4)
PLYENG(JL,3)
PLYENG(JL,11
PLYENG!JL,4)
PLYENG!JL,2)
PLYENG!JL,3)
PLYENG!JL,3)
PLYENG!JL,2)
0) GO TO 17
PLYENG!JL,1)
PLYENG!JL ,2)
PLYENG!JL,3)
PLYENG!JL,4)
PLYENG!JL,5)
PLYENG!JL,6)
PLYENG!JL,5 I
PLYENG!JL,6)
+ PR*ENG(JR,1) + DE C I )
+ PRYENG!JR,2) + DE!I)
+ PR*ENG(JR,1) + DE!I)
+ PRYENG(JR,2) + 0E(I)
+ PRYENG!JR,1) + DE(I)
+ PRYENG!JR,25 + DE(I)
+ PRYENG(JR,1) + DE!I)
+ PRYENG!JR,2 > + DE!I)
+ PRYENG!JR,1) + OE(I)
+ PRYENG!JR,2) + DE!I )
+ PRYENG!JR,1) + DE!I)
+ PRYENG(JR,2) + DE!I)
+ PRYENG(JR,1) + DE!I)
+ PRYENG(JR,?) + DE(Ii
+ PRYENG!JR,3) + DE(I)
+ PRYENG(JR,4 I + DE(I)
+ PRYENGI JR,4) + DE(I)
+ PRYENG(JR , 3) + DE(I)
+ PRYENG!JR,1) + DE(I)
+ PRYENG(JR,2) + DE(I)

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IMPLICIT REAL*8
COMMON /SPEC/ XDATAI512),YDATA(512> ,XP0INT(512),
1 YPOINT(512) .YPLOTI 512) .5PEXI512) ,
2 PEFF(512) ,UTI512) ,XL,XR,NP,NCH,
3 T TEFF,FRACA , FRACB
COMMON /NUC/ STD,ENRGY,X112 > ,G(2 I ,QR
COMMON /TRAN5/ ENG(2,8) .FREQ 12,10) ,XIUI18,512) ,DE I 2) ,
1 QE(2,2) , ETA I 2) rH(2) .NTR
IF{XI(1).EQ.O.500.ANO.XI(2 >.EQ.l.500) GO TO 5
IF(XI{1).EQ.l.500.AND.XI(2).EQ.0.5D0) GO TO 5
IF(XI( 1 ) .EQ.1.500.ANO.XI(2> .EQ.2.500) GO TO 10
IF(XIIl) .EQ.2.5D0 .AND.XK2) .EQ.l .5D0I GD TO 10
IF(XI(1) . EQ . 2.500 . AND .XI(2) . EQ . 3.5D0 ) GO TO 15
IF(XI(1).EQ.3.500.ANO.XI(2).EG.2.5DG) GO TO 15
GO TO 20
5 CONTINUE
DO 7 IPT= 1(NP
5PEX IIPT)= 3.DO*(XIU<1,IPT)
+2.D0*IXIUI3,IPT>
I XIUI 5 ,IPT)
7 CONTINUE
GO TO 20
10 CONTINUE
DO 12 IPT=1 , NP
SPEXIIPT)- 10.DO*(XIWI1,IPT)
+ 6 . DO* I XIWO , IPT I
+ 3.DO*(XIU(S,IPT)
+ 1.DO*IXIUI7,IPT)
+ 4.DO*(XIW(9.IPT)
+ XIUI 2,IPT) )
+ XIUI4,IPT) )
+ XIWI 6,1PT ) )
XIU(2,IPT))
XIUI 4,IPT)>
XIU(6 , IPT) )
XIU(8,IPT)I
XIUI10,IPT))
XIU(12.IPT))
6.DO*(XIU(li,IPTI +
12 CONTINUE
GO TO 20
15 CONTINUE
DO 17 IPT=1 , NP
SPEXIIPT)= 21.D0*(XIU(1 , IPT) +
+15.D0*tXIU(3,IPT) +
+ 10.DO*(XIW<5 , IPT) +
+ 3.DO*IXIUI 7,IPT) +
+ 1.DO*IXIU(9 , IPT) +
+ 6.D0*IXIU(11,IPT)+ XIUl12,IPT))
+ 10.DO*(XIU C13,IPT)+ XIU(14,IPT) )
+12.DO*(XIU(15,IPTI+ XIU(16,IPT1)
+ 6.00*(XIU(17,IPT)+ XIU(18,IPT))
17 CONTINUE
20 CONTINUE
RETURN
END
XIU(2,IPT))
XIUI4,IPT))
XIU(6,IPT))
XIWI8,IPT))
XIU <10.IPT))
c
c##*************************************************************
c
C THIS SUBROUTINE N0RHALIZE5 COMPONENT SOLUTIONS.
C PARAMETER DEFINITIONS ARE GIUEN IN ,,REQ,, .
C
SUBROUTINE 5IMP5N IXA, XB, F, 5F, U, XL, XR, GAMMA,
POPA, P0P8, NCH)
IMPLICIT REAL*8 t A-H , 0-Z)
H= IXR-XL)/D8LE(NCH*2I
X= XL
SUM= 0.DO
10 SUM= SUM + FIX, U, XA, XB, POPA, POPS, GAMMA)
+ 4.D0*FIX+H, U, XA, XB, POPA, POPS, GAMMA)
+ FIX+2. D0*H , U, XA, XB, POPA, POPS, GAMMA)
XH= X+2.D0*H
IF IXH-XR) 20,30,30
20 X- X+2.QO*H
GO TO 10
3.) SUM* I H/3 . DO )
RETURN
END
C

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CJULJLJUf-lCJUrjf-lLJULJLJLJLJ
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ex**************************************************************
THIS FUNCTION CALCULATES THE LINESHAPE USING THE RATE
EQUATION METHOD. PARAMETERS ARE AS FOLLOWS:
UA= RESONANCE FREQUENCY OF STATE A IN RADIAL MEGAHERTZ
UB* RESONANCE FREQUENCY OF STATE B IN RADIAL MEGAHERTZ
UX* FREQUENCY AT POINT X IN RADIAL MEGAHERTZ
WA0D= UA + UB
WSUB- UA - UB
GE= HALF-WIDTH AT HALF-HEIGHT IN RADIAL MEGAHERTZ
W= EXCHANGE RATE BETWEEN STATES A ANO 8
TAU= LIFETIME OF STATES A ANO B (STEADY STATE)
POPA— POPULATION OF STATE A (NA)
POPB* POPULATION OF STATE B (NB)
A8DIF- DIFFERENCE BETWEEN A AND B POPULATIONS (NA-NB)
P,Q,R= RATE EXCHANGE EQUATION FACTORS
FUNCTION REQ (X, U, XA. X8, POPA. POPB, GAMMA)
IMPLICIT REALXS (A-H, O-Z I
COMMON /NUC/ 5TD,ENRGY,XI(2),G(2),QR
DATA BETA,BK /O.762250B700, 0.69503000/
DATA TUOPI /6.283185300/
C
C CONUERT ANGULAR MEGAHERTZ TO RAOIAL MEGAHERTZ (OMEGA)
C
UA* XAXTWOPI
UB* XBXTUOPI
UX= X*ENRGY*TUOPI
UAOD* UA+UB
WSUB- UA-UB
GE= GAMMA*ENRGY*TWOPI
UU= U*TUOPI*l.0-6
TAU= 1.00/UU
ABDIF= POPA-POPB
C
C CALCULATE LINESHAPE AT POINT UX USING CLOSED FORM
C SOLUTION OF STEADY STATE BLOCH EQUATIONS. 5EE:
C GUTOUSKY, H.S.; HOLM, C.H. J. CHEM. PHYS. 1956, 25, 1228.
C
P= TAU*(GE*GE-(IWADD/2.D0)-WX)*((UADD/2.DO)-UXI
+(USUB*USUB/4.D0)) + GE
Q* TAU*(((UADD/2.00)-UX)-(ABDIF*USUB/2.DO I)
R = ((UADD/2.DO I-UXI *(1.DO+2.D0*TAU*GE) + (AB0IF*USUB/2.00)
TOP* P*(1.DO+T AUXGE) + Q*R
BTM= P*P + R*R
REQ= TOP/BTM
RETURN
END

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nnnnnnnnnnnnoonnnnnonnnonnnnnnnonnnnnnnnnnnnnnnnonnnnnonnnnnnnnnnrjon
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c***************************************************************
C*********************** 0NMRFIT ****************************
0» DOUBLE PRECISION; NHRFIT- NUCLEAR MAGNETIC RESONANCE
SPECTROSCOPY SIMULATION PROGRAM
THIS PROGRAM WAS WRITTEN BY JOSHUA A. TELSER FOR USE AT
THE UNIVERSITY OF FLORIDA (MARCH, 1984). THE PROGRAM
USES THE HATE EXCHANGE METHOO TO CALCULATE NMR SPECTRA
FOR TWO STATES, A ANO B, WHICH ARE EXCHANGING AT SOME
RATE U. FURTHER INFORMATION CAN BE FOUND IN:
POPLE, J.A.; SCHNEIDER, W.G.; BERNSTEIN, H.J. "HIGH-
RESOLUTION NUCLEAR MAGNETIC RESONANCE"; MCGRAW-HILL:
NEW YORK, 1959; PP 218-225.
INPUT QUANTITIES
LINE *1
LINE *2
LINE SET *3
LINE *4
LINE *5
TITLE (10A4)
ANY ALPHANUMERIC CHARACTERS IN THE
FIRST 40 COLUMNS
NV.KU.IFIT (FREE FORMAT I
NV- NUMBER OF VARIABLES TO BE MINIMIZED
SHOULD BE 8 IN THIS PROGRAM
XW- OUTPUT UNIT OF THE COMPUTER (KW= 20
FOR OUTPUT IN FOR020I
IFIT- =0 IF LEAST SQUARES FITTING USING
05TEPT IS TO BE OONE. THUS OATA
POINTS MUST BE READ IN. (LINE *9)
> OR < 0 IF NO LEAST SQUARES FIT
IS TO BE DONE. IN THIS CASE NO
DATA ARE REAO IN.
X,XMAX,XMIN,DELTX,OELMN,MASK
(FREE FORMAT)
THE NUMBER OF LINES IN THE SET IS NV
ONE LINE FOR EACH PARAMETER
X- PARAMETER TO BE MINIMIZED
XMAX- UPPER LIMIT OF PARAMETER X
XMIN- LOWER LIMIT OF PARAMETER X
OELTX- INITIAL STEP SIZE FDR X
OELMN- LOWER LIMIT (CONVERGENCE) ON THE
STEP SIZE FOR X
MASK- -0 IF THE PARAMETER IS TO VARIED
> OR < 0 IF X IS TO BE HELO FIXED
DEFAULT VALUES SET BY DSTBEG:
XMAX* 1.D37
XMIN—1.037
0ELTX*1.o-a
0ELMN-3.D-B
NTRAC,MATRX,NFMAX,NFLAT
(FREE FORMAT)
NTRAC- —1 FOR NO OUTPUT
=0 FOR ONLY FINAL VALUES PRINTED
â– +1 FOR TRACE DF MINIMIZATION
PROCESS
(0 IS GENERALLY BEST VALUEI
MATRX- *0 FOR NO ERROR CALCULATION
=100 TO 110 FOR ERROR CACULATION
(105 IS GENERALLY BEST VALUE)
NFMAX- MAXIMUM NUMBER OF FUNCTION
COMPUTATIONS
NFLAT- *0 FOR SEARCH TO TERMINATE WHEN
CHANGES IN X ARE EQUAL TO DELMN
> OR < 0 FOR SEARCH TO TERMINATE
WHEN ALL TRIAL STEPS GIVE
IDENTICAL FUNCTION VALUES
T,CONCA,CONCB (FREE FORMAT)
T- TEMPERATURE AT WHICH DATA WERE
COLLECTED IN DEGREES KELVIN
CONCA- CONCENTRATION OF A (MOLAR)
CONCB- CONCENTRATION OF B (MOLAR)

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LINE *ó
LINE *7
LINE *8
LINE *?
LINE *10
LINE 5ET *11
EXPLANATION OF
PARAMETER *1
PARAMETER *2
PARAMETER *3
PARAMETER *4
ENTER 0.0 FOR BOTH IF POP¬
ULATIONS ARE TO BE CALULATED
USING A BOLTZMANN DISTRIBUTION
NP.NTR (FREE FORMAT I
NP- THE NUMBER OF EXPERIMENTAL DATA
POINTS, NP-0 IF IFIT IS NONZERO
NTR- THE NUMBER OF TRANSITIONS FOR THE
TWO PEAKS A ANO B. NTR«1 IF THEY
ARE EACH SINGLETS. 2 IF THEY ARE
EACH DOUBLETS, ETC. UP TO NTR=9
PKINT (FREE FORMAT!
PKINT- ARRAY OF SIZE NTR CONTAINING
THE INTENSITIES OF THE TRANSITIONS FOR
THE TWO PEAKS A ANO 8. AN EXAMPLE IS:
1.0 2.0 1.0 FOR A 1:2:1 TRIPLET.
FPROB,FSTO (FREE FORMAT!
FPROB- PROBE FREQUENCY IN MHZ
F5TD- RESONANCE FREQUENCY OF NMR
STANDARD IN MHZ (TMS, ETC.)
C5CNTR,CSTOT,CSINT,VERTSF (FREE FORMAT)
CSCNTR- CENTER OF RANGE (PPM)
C5T0T- TOTAL CHEMICAL SHIFT RANGE (PPM)
CSINT- INTERVAL AT UHICH POINTS WILL BE
CALCULATED (PPM). IF DATA POINTS ARE
TO BE FITTED, CSINT IS IGNORED SINCE
CALCULATIONS ARE MAOE AT EACH DATA
POINT. IF NO FITTING IS TO BE DONE,
CSINT SHOULD BE SMALL ENOUGH TO GET A
SMOOTH SPECTRUM BUT LARGE ENOUGH SO
THAT < 1000 POINTS ARE CALCULATED.
VERTSF- VERTICAL SCALING FACTOR FOR
INTENSITY. (MAXIMUM INTENSITY» 100.0)
VERTSF MAY BE > 100, IN WHICH CASE ANY
PEAK OVER 100 WILL BE TRUNCATED.
IFPL,IEXPT,ICALC (FREE FORMAT)
IFPL- -0 IF NO PLOTTING IS DESIRED
NONZERO IF ANY PLOTTING DESIRED
IEXPT- =0 IF NO PLOT OF EXPERIMENTAL
POINTS IS DESIRED
NONZERD IF PLOT IS DESIRED
ICALC- »0 IF NO PLOT OF CALCULATED
CURVE IS DESIRED
NONZERO IF PLOT IS DESIRED
XDATA,YDATA (FREE FORMAT)
NUMBER OF LINES IN THE SET IS NP
ONE LINE FOR EACH POINT (MAX- 1000)
XDATA- CHEMICAL SHIFT OF DATA POINT
VALUES MUST BE ASCENOING IN CHEMICAL
SHIFT WITH NO TWO NUMBERS EQUAL
YDATA- INTENSITY (ARBITRARY UNITS)
INPUT PARAMETERS: X(I) ***
T2A- RELAXATION TIME OF STATE A
IN SECONOS IN THE ABSENCE OF
EXCHANGE BROADENING
T2B- RELAXATION TIME OF STATE B
IN SECONDS IN THE ABSENCE OF
EXCHANGE BROADENING
DEL- ENERGY OF STATE A MINUS ENERGY OF
STATE B IN CM-1. ENTER 0.0 IF
CONCA ANO CQNCB DETERMINE THE
POPULATIONS OF SihiES A AND B.
U- PHENOMENOLOGICAL RELAXATION RATE
IN HZ. WARNING: FLOATING POINT
OVERFLOW MAY DCCUR IN RATE EQN IF W
IS NOT ALLOWED TO VARY BY MORE THAN
l.D-7 HZ. UNDERFLOW MAY OCCUR FOR
VALUES > l.D+20 HZ.

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PARAMETER
*5
XNA-
PARAMETER
*6
XN0-
PARAMETER
*7
XJA-
PARAMETER
#8
XJB-
c
c
RESONANCE POSITION OF STATE A IN
PPM. THIS IS THE VALUE FOR THE
CENTER OF THE STATE A TRANSITIONS
RESONANCE POSITION OF STATE B
SPIN-SPIN COUPLING CONSTANT FOR
STATE A IN PPM
SPIN-SPIN COUPLING CONSTANT FOR
STATE B IN PPM
IMPLICIT REAL*8 (A-H, O-Z)
EXTERNAL 5PECTR,PLHCA
COMMON /C5TEP/ XMAX(20) ,XMIN(20 I ,DELTX(SO) ,DELMN120),
1 EPP <20,21) ,NU,NTRAC,MATRX,MASK < 20) ,NFMAX,JVARY,
2 NXTRA.«FLAG,NOREP.KERFL.KU,NFLAT
COMMDN /CXF/ X(20),FOBJ,NFFIT
COMMON /SPEC / XOATAdOOOl ,YDATA(1000> , XPOINT 1 100 0 > ,
1 YPOINT Í1000 I ,YPLOT(1000) ,SPEX(1000) ,
2 UTÍ1000), XL . XR ,NP,NTR,PKINT(81,VERTSF,
3 T,CONCA,CONCB
COMMON /NUC/ FPROB,F5TD
REAL*4 TITLE(20) ,SCRCH1(1000) ,5CRCH2I1000) ,
1 SYPLOT(IOOO) ,SXPOINT(1000 ) ,SYPOINTI 1000) ,SXL,5XR
C
C READ IN PARAMETERS
C
READ (19,5) (TITLE(I), 1-1,10)
FORMAT (10A4)
READ (19,*) NU,KW,IFIT
READ (19,*) (X(I) ,XMAX(I) ,XMIN MASK(I), I-1,NV)
READ (19,*) NTRAC,MATRX,NFMAX,NFLAT
READ (19,*) T,CONCA,CONCB
READ (19,*1 NP,NTR
READ (19,*) (PKINT(I), 1=1,NTR)
READ (19,*) FPRDB,F STD
READ (19,*) C5CNTR,C5TOT,C5INT,VERTSF
REAO (19,*) IFPL,IEXPT,IOALC
IF(IFIT.EQ.O) READ (19,*) (XOATA(I),YDATA(I), 1=1,NP)
IF(KU.EQ.O) KW-20
IF(VERTSF.EG.0.DO I VERTSF- 100.DO
FIND ENDPOINTS OF PLOT: XL- LEFT, XR- RIGHT ENDPOINT.
NOTE THAT CHEMICAL SHIFT INCREASES FROM LEFT TO RIGHT.
XL- CSCNTR-(CSTOT/2.DO)
XR- CSCNTR+(CSTOT/2.DO)
C
C IF NO CURVE FITTING IS TO BE DONE, BYPASS FILLING THE
C PLOTTING ARRAY AND WEGHTING AND SCALING THE DATA POINTS
C
IF(IFIT.NE.O) GO TO 17
DO 10 1=1,NP
XPOINT(II- XOATA(11
10 CONTINUE
C
C CALCULATE LEAST-SQUARES WEIGHTING FACTORS FOR EXPERIMENTAL
C DATA POINTS. WEIGHT THEM ACCORDING TO
C THEIR STANDARD DEVIATIONS, SQRT(INTENSITY)
C
DO 12 1=1,NP
WT1I1- DSQRT(YOATAll))
12 CONTINUE
C
C SCALE INTENSITIES BY FINDING MAXIMUM PEAK
C
YMAX-O.DO
YMIN-0 . DO
RANGE-0.DO
DO 14 1=1,NP
IF (YDATA(I) .GT.YMAX) YMAX-YOAT All)

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1A CONTINUE
DO 15 1=1,NP
YOIFF-YMAX-YDATAII)
IF (YDIFF.LT.RANGE) GO TO 15
RANGE=YDIFF
YMIN=YDATAlI)
15 CONTINUE
DO 16 1=1,NP
YP0INTII)=((YDATAIIl-YMIN)/(YMAX-YMIN))«0ERTSF
IF (YPOINT(I).LT.0.D0) YPOINT(I)=0.DO
IF (YPOINT(I).GT.100.00) YPOINT(I)=100.DO
16 CONTINUE
IF(IFIT.EQ.O) GO TO 20
IF NO FITTING 15 TO BE DONE, FIND POINTS AT WHICH CALC¬
ULATIONS WILL BE MADE. POINTS ARE AT INTERVALS OF CSINT.
17 CONTINUE
NP= (CSTOT/CSINT1+1.0100
DO IB 1=1,NP
XP0INT(11= XL + DBLE(I-1I*CSINT
IB CONTINUE
TYPE *, ' NP= ', NP
IFINP.GT.10001 STOP 'NTOT OUT OF RANGE'
20 CONTINUE
WRITE TITLE AT TOP OF PAGE PRIOR TO OUTPUT FROM DSTEPT
WRITE (KU,21) (TITLE(I>, 1=1,10)
21 FORMAT(1X,60(),//IX,'NMR SIMULATION PROGRAM',
/IX , 10AA ,//IX,6Q( '*'>>
BYPASS DSTEPT IF NO FITTING IS TO BE DONE OR
IF ALL THE PARAMETERS (X) ARE FIXED
IF(IFIT.NE.O) GO TO 35
MA5K5= 0
DO 25 1=1,NO
IF(MASK(I)123,25,23
23 MASKS” MASKS+1
25 CONTINUE
IF(MASKS. EQ . NO ) GO TO 35
CALL DSTEPT (5PECTR)
GO TO AO
35 CONTINUE
CALL 5PECTR
AO CONTINUE
*** WRITE OUT RESULTS ***#
TABULATE THE PARAMETERS FOR THE LEA5T-5QUARE5 FIT
WRITE (KU,A1)
A1 FORMAT(IX,' I X(I) XMAX(I) XMIN(I)
1 ' DELTXIII DELMN(I) MASK!I)',//)
DO AA 1 = 1 , NO
WRITE (KU,A2) I , X(I) , XMAX(I I ,XMIN(I) ,DELTX(I I ,DELMN(I) ,
MASK!II
A2 FORMAT(1X,I2,2X,E10.A,1X,E10.A,1X,E10.A,1X,E10.A,IX,
1 E10.A,2X,I2,/I
AA CONTINUE
OUTPUT CONSTANTS USED IN CALCULATIONS
WRITE (KW,A6) FPROB, F5TD
A6 FORMAT!/IX, ' FPROB F5TD ' ,/IX,F10.A , IX,F10.A,/)
WRITE (KU,A7> C5CNTR, CSTOT, 0ERT5F
A7 FORMAT!/IX,' CSCNTR CSTOT OERTSF ',/lX,
1 FIO.A,IX,FIO.A,IX,F10.A,/)
WRITE (KU,A8) T , CONCA , C0NC8

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AB FORMAT( / IX , ' TEMPERATURE= ' ,F6.2,' K',/,' CONCA= ‘ ,
1 F8.4,' MOLAR CONCB- ‘,FB.A,' MOLAR',/)
C
C TABULATE THE DATA POINTS IF ANY FITTING WAS DONE
C
IF(IFIT.NE.O) GO TO 56
WRITE(KU,52)
52 FORMAT OX,' EXPERIMENTAL CALCULATED',
1 /IX,' C5 (PPM) INTENSITY SCALED* CS (PPMI ',
2 'INTENSITY SCALED*1,//I
DO 56 1=1,NP
WRITE < KW,54) XDATAÃœI , YDAT A (I) ,YPOINT(I) ,XPOINT(I) ,
5PEX(I) ,YPLOT(11
54 F0RMAT(1X,6F10.4>
56 CONTINUE
C
C CHECK IF ANY PLOTTING IS DESIRED.
C
IF(IFPL.EU.O) GO TO 999
C
C***# PL0T79 SECTION FOR USE ON UF/QTP VAX. ****
CHANGE DOUBLE PRECISION NUMBERS TO SINGLE PRECISION
SINCE PL0T79 USES ONLY SINGLE PRECISION (S= 5INGLE PREC.)
5XL=XL
5XR=XR
DO 500 1=1,NP
5XPQINT 11)= XPOINT(I)
500 CONTINUE
C
C INITIALIZE PLOT SYSTEM
C
CALL PLTOO
C
C 5ET PLOT SIZE TO 25.0 CM LONG, 20 CM WIDE.
C
CALL 5ET5Z(25.I
C
CALL 5ET052(1.,.8)
C
C PLOT THE AXES USING THE ROUTINE PLTAX.
C
C PLOT ANO LABEL THE X-AXIS.
C
CALL PLTAX(3./2S.,3./25.,20HCHEMICAL SHIFT (PPM),20,
1 20./25.,0. ,SXL,1. ,SXR,-.005,-1)
C
C PLOT AND LABEL THE Y-AXIS.
C
CALL PLTAX(3./25.,3/25.,9HINTEN5ITY,9,
1 15./25. ,90.,0. ,20. ,100. , .005,2)
C
C SET UP A 2-0IMEN5I0NAL FIELD ON WHICH THE PLOTS APPEAR.
C
CALL 5ETVP2I3./25.,23./25.,3./25.,IB./25.)
C
C CHECK IF PLOT OF EXPERIMENTAL POINTS IS DESIREO.
C
IF(IFIT.NE.O) GO TO 700
IF(IEXPT.EQ.0) GO TO 700
DO 610 1=1,NP
SYPOINT(I>=YP0INT(11
610 CONTINUE
C
C PLOT THE DATA POINTS AS PLUS SIGNS USING THE ROUTINE GRFGP.
C
CALL GRFGP(SXL,SXPOINT,SXR,0.,SYPOINT,100.,NP,
1 2,PL2CA)
C

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CHECK IF PLOT OF CALCULATE0 LINE 15 DESIRE0
700 IF OO 710 1=1,NP
5YPL0TIII =YPL0T(I)
5CRCH1(I I
SCRCHHI I)
710 CONTINUE
“XPOINT(I)
=YPLOT(I)
0RAU THE THEORETICAL CURVE USING THE ROUTINE GRFGI.
CALL GRFGI(5XL,5XPOINT,SXR,0.,5YPLOT,100.,NP,
1 SCRCH1,5CRCH2,NP,1.,PL2CA)
EJECT THE FRAME.
990 CALL PLTEJ
999 CALL EXIT
ENO
C*******************************************«*******************
THIS SUBROUTINE CALCULATES THE POSITIONS ANO INTEN5IIE5
OF THE SPECTRAL LINES
SUBROUTINE SPECTR
IMPLICIT REAL*8 IA-H, O-Z)
EXTERNAL REQ
COMMON /CSTEP/ XMAX(20 I , XMIN(20 I ,DELTX(20! ,OELMNI 20),
1 ERR(20,21),NU,NTRAC,MATRX,MASK(HO),NFMAX,JVARY,
3 NXTRA.KFLAG,NOREP,KERFL.KU,NFLAT
COMMON /CXF/ X(2G),FOBJ,NFFIT
COMMON /SPEC/ XDATAl1000),Y0ATA(1000).XPOINT(IOOO),
1 YPOINT 11000 > ,YPLOT í1000 J ,5PEX(100Q> ,
E WT (1000),XL,XR,NP,NTR,PKINT(SI,VERTSF,
3 T,CONCA CONCB
COMMON /NUC/ FPROB.FSTO
DIMENSION FREQ(B,2 I , XIUIB.1000)
DATA BK.TUOPI /0.693030D0, 6.283185300/
BK = BOLTZMANN CONSTANT IN CM-1 K-l
T2A= Xtl)
T£B= xiai
0EL= X(31
U * XM>
XNA= XI 5)
XNB= X<61
XJA= X I 7)
XJB- X(B)
SET UP THE FREQUENCIES AT WHICH THE TRANSITIONS
OCCUR FOR STATES A ANO B
1= 0
K= 2*NTR
DO 10 J=1,K,E
1= 1+1
FREQII.ll- XNA + IJ-NTRMUXJA/2.O0)
FREQ(I,a í = XNB + (J-NTRl*(XJB/2.00>
10 CONTINUE
CONVERT THESE FROM PPM TO FREQUENCIES IN HERTZ
DO la 1=1,NTR
FREQ(1,11= (FREQ(1,1)*FPROB) + FSTD*1.06
FREQ(I,2)= (FREQ(1,21*FPROB> + F5TD*1.D6
12 CONTINUE
CALCULATE THE RELATIVE POPULATIONS OF STATE5 A AMO B.

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CALL NMRPOP C
C CALCULATE A NORMALIZATION FACTOR 5F FOR THE
C TRANSITIONS USING SIHPSON'S METHOD FOR NUMERICAL
C INTEGRATION
C
OO 20 1=1,NTR
CALL 5IMP5N (FREQ11,1 I ,FREQ 11,2) ,REQ,5F,U,XL,XR,
T2A,T2B,POPA,POPÓ,NP)
CALCULATE THE SPECTRUM FOR EACH TRANSITION USING THE RATE
EQUATION METHOD
00 20 ü= 1,NP
XIW(I,J)= REQ(XPOINT t J í ,U,FREQ(I , 1> ,FREQ(1,2),
P0PA,P0PB,T2A,T2BW5F
20 CONTINUE
INCLUDE THE INTENSITY SCALING FACTORS ADOINC THE PEAKS
PAIRWI5E.
DO 30 J=1,NP
5UM= O.DO
DO 25 1=1,NTR
SUM= SUM + PKINT(I I*XIU11,J)
25 CONTINUE
SPEX(J)= SUM
30 CONTINUE
C
C SCALE THE CALCULATED PEAKS AS WAS DONE WITH THE DATA
C
YMAX=0.00
YMIN=0.DO
YDIFF=0.00
RANGE=0.00
DO AO 1=1,NP
IF (SPEX(I).GT.YMAXI YMAX=SPEX(II
AO CONTINUE
DO A5 1=1,NP
Y0IFF=YMAX-5PEX(I)
IF (YDIFF.LT.RANGE) GO TO A5
RANGE=YDIFF
YMIN=5PEX(I)
AS CONTINUE
DO 50 1=1,NP
YPLOT(I)=((SPEX(Il-YMIN)/(YMAX-YMIN)UVERT5F
IF (YPLDT(I) .LT.O.DO) YPLOT(11=0 DO
IF (YPLOT(I).GT.100.D0) YPLOT(I)=100.DO
50 CONTINUE
IF(IFIT.NE.0) GO TO 100
C
C CALCULATE F08J THE MEASURE OF GOODNESS OF FIT
C
FOBJ= 0.00
DO 100 1=1,NP
FOBJ» FOBJ+(YPLOT(I)-YPOINT11))*(YPLOT(I)-YPOINT(I) )
*WT(I)*UT(I)
100 CONTINUE
RETURN
ENO
C
C***************************************************************
C
C THIS SUBROUTINE CALCULATES THE POPULATIONS OF STATES A AND B
C
SUBROUTINE NMRPOP (CONCA, C0NC8, T, DEL, POPA, POPBI
IMPLICIT REAL*8 (A-H, 0-Z)
OATA BK.TUOPI /0.695Ó3000, 6.203185300/
IFICONCA EQ.0.00.AND.CONCB Eg.0 DO) GO TO 10
PGPA= CONCA/(CONCA+CONCB)

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POPB- C0NC8/(C0NCA+C0NC8)
GO TO 20
C
C IF POPULATIONS ARE NOT FIXED BY CONCENTRATIONS, THEN
C CALCULATE POPULATION RATI05 A55UMING A BOLTZMANN
C DISTRIBUTION. QEL= EA-EB, ABRAT- NA/NB, BARAT- NB/NA
C
10 CONTINUE
ABRAT= DEXP(-0EL/(BK*TM
BARAT- DEXP( DEL/I BK*T))
POPA® 1 . 00/(1.DO+BARAT)
POPB* 1.DO/I 1.DO+ABRAT)
20 CONTINUE
RETURN
END
C
C***************************************************************
C
C THIS SUBROUTINE NORMALIZES COMPONENT SOLUTIONS.
C PARAMETER DEFINITIONS ARE GIVEN IN "REQ".
C
SUBROUTINE SIMPSN {XA. XB, Fr 5F. U, XL, XR, T2A T29,
POPA, POPB, NP)
IMPLICIT REAL*8 < A-H , O-ZJ
COMMON /NUC/ FPROB,F5TD
Hc IXR-XL)/D8LE(NP*4)
X= XI
SUM- 0.00
10 SUM- SUM + Ft X,U,XA.XB,POPA,POPB,T2A,T2B)
+ 4.00*F(X+H,W,XA,XB.POPA,POPB,T2A,T2B)
+ F(X+2.DO*H , U,XA,XB,POPA,POPB,T2A,T2B)
XH- X+2.DO*H
IF (XH-XR) 20,30,30
20 X® X+2.DO*H
GO TO 10
30 5F- SUM*(H/3.DO)
RETURN
END
C
C***************************************************************
C
C THIS FUNCTION CALCULATES THE LINE5HAPE USING THE RATE
C EQUATION METHOD. PARAMETERS ARE A5 FOLLOWS:
C UA* RESONANCE FREQUENCY OF STATE A IN RADIAL HERTZ
C UB= RESONANCE FREQUENCY OF 5TATE B IN RADIAL HERTZ
C WX- FREQUENCY AT POINT X IN RADIAL HERTZ
C WADD- UA + WB
C WSUB- UA - UB
C GAMA- HALF-WIDTH AT HALF-HEIGHT OF STATE A (1/T2A)
C GAHB* HALF-UIDTH AT HALF-HEIGHT OF 5TATE B U/T2B)
C U= EXCHANGE RATE BETWEEN STATES A AND B
C TAU- LIFETIME OF STATES A AND B (STEADY STATE 1
C POPA- POPULATION OF STATE A (NA)
C POPB* POPULATION OF STATE B C ABDIF= DIFFERENCE BETWEEN A AND B POPULATIONS (NA-NB)
C P,Q,R* RATE EXCHANGE EQUATION FACTORS
C
FUNCTION REQ (X, W, XA, XB, POPA, POPB, T2A, T2B)
IMPLICIT REAL*B (A-H, Q-Z)
CDMMON /NUC/ FPROB,F5TD
DATA BK.TUOPI /O.69503000, Ó.2B31853D0/
C
C CONVERT PPM AND ANGULAR HERTZ TO RADIAL HERTZ (OMEGA)
C
UA = XA*TUQPI
U8= XB*TUQPI
UX= <(X*FPROB) + F5TD*1.D6>*TUQPI
UADD- WA+UB
U5UB- WA-WB
GAMA- (1.00/T2A)*TWQPI

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GAMB = (l.DO/T2B)*TWOPI
UU= U*TUOPI
TAU = 1.D0/UW
ABDIF» PQPA-POPB
CALCULATE LINESHAPE AT POINT UX U5ING CL05E0 FORM
SOLUTION OF 5TEA0Y STATE BLOCH EQUATIONS. SEE:
ROGERS, M.T.; UOQDBREY, J.C. J. PHYS. CHEM. 1962, 66, 540
P= TAU*IGAMA*GAMB-((UAOD/2.DO)-UX)*((UADD/2.DO)-UXI
+ (U5UB*U5UBM . 00)1 + POPA*GAMA -I- POPB*GAMB
Q= TAU*(((UADO/2.00)-UX>-ABDIF*(USUB/2.00I)
R= ((UADO/2.00 >-UX)* C1.00+TAU*GAMA+TAU*GAMBI
+ A8DIF*(U5UB/H.D0)
+ TAU*(GAMB-GAMA)* TOP= P*(1.DO+TAU*(POPB*GAMA+POPA*GAMBI) + Q*R
BTM= P*P + R*R
REQ= TOP/BTM
RETURN
END

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1. Cotton, F.A. and Walton, R.A., "Multiple Bonds Between Metal
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2. Cotton, F.A., Acc. Chem. Res., 1978, JL1_, 225.
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Lindner, K., Z.
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Cotton,
F.A., Inorg. Chem., 1965, 4,
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and Webb, T.R., J. Am.
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Cotton,
F.A. DeBoer, B.G., LaPrade,
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18. Sheldon, R.A. and Kochi, J.K., "Metal-Catalyzed Oxidation of
Organic Compounds," Academic Press, New York, 1981, pp. 320.
19. Eichhorn, G.L., Ed., "Inorganic Biochemistry,” American Elsevier,
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20. Eickman, N.C., Himmelwright, R.S., and Solomon, E.I., Proc. Natl.
Acad. Sci. (USA), 1979, 76, 2094.
21. Muetterties, E.L., Rhodin, T.N., Band, E., Brucker, C.F., and
Pretzer, W.R., Chem. Rev., 1979, T9, 91.
22. Richman, R.M., Kuechler, T.C., Tanner, S.P. and Drago, R.S., J.
Am. Chem. Soc., 1977, 99, 1055.
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Chem. Soc., 1979, _101_, 2897.
24. Drago, R.S., Long, J.R., and Cosmano, R., Inorg. Chem., 1981, 20,
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25. Drago, R.S., Long, J.R., and Cosmano, R., Inorg. Chem., 1982, 21,
2196. —
26. Drago, R.S., Inorg. Chem., 1982, _21_, 1697.
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Inorg. Chem., 1972, _U» 2884.

BIOGRAPHICAL SKETCH
Joshua A. Telser was born in Chicago, Illinois, on November 27,
1958. He remained there more or less continually until 1976 when he
entered Cornell University, Ithaca, New York. He graduated from there
in 1980 at which time he entered graduate school in chemistry at the
University of Illinois, Urbana, Illinois. He completed graduate studies
at the University of Florida, Gainesville, Florida, in 1984.
308

I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy,
Russell S.
Professor of Chemistry
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
George Ryschkewitsch
Professor of Chemistry
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
Associate Professor of Chemistry
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarlly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
fi. 5. Maddala
Graduate Research Professor of
Economics

This dissertation was submitted to the Graduate Faculty of the
Department of Chemistry in the College of Liberal Arts and Sciences and
to the Graduate School, and was accepted as partial fulfillment of the
requirements for the degree of Doctor of Philosophy.
December, 1984
Dean for Graduate Studies and
Research

SiRSIT. OF FLORIDA
3 1262 08553 1100




PAGE 1

SYNTHETIC AND SPECTROSCOPIC STUDIES OF METAL CAR30XYLATE DIMERS 3Y JOSHUA A. TELSER A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR CF PHILOSOPHY UNIVERSITY OF FLORIDA 1984

PAGE 2

ACKNOWLEDGEMENTS There are many people and things responsible for a successful graduate career and I would like to take this opportunity to mention them. First of all, I would like to thank my research director, Professor Russell S. Drago, for his continuous help from near and from afar. It was a privilege to be part of a research group that has accomplished so much in so many areas over so long. Since a group is not one man, I would also like to thank the many members of the Drago group who have helped me out: Charlotte Owens, Rich Cosmano, Barry Corden, Pete Doan, Dave Pribich, Carl Bilgrien, Andy Griffis, and Ernie Stine. Since a group is not alone, I would also like to thank the faculty and students of other groups at both Illinois and Florida. In particular, thanks are due to Professor R. Linn Belford and Jeff Cornelius and to Professor William Weltner, Jr., and Richard Van Zee. Since faculty and students cannot do everything themselves, I would also like to thank the many support personnel who made my work a lot easier. In particular, I greatly appreciate the help of the glass shop and NMR and Elemental Analysis Labs at both Illinois and Florida. n

PAGE 3

TABLE OF CONTENTS PAGE ACKNOWLOGEMENTS i i ABSTRACT v CHAPTER I. GENERAL INFORMATION 1 CHAPTER II. THE ACTION OF STRONG ACIDS ON M 2 (0 2 CR) 4 SPECIES 15 Introduction 15 Results and Discussion 19 Concl usi on 57 Experimental Section 58 CHAPTER III. THE REACTIONS OF RHODIUM TRIFLUORACETATE WITH VARIOUS LEWIS BASES 65 Introduction 65 Results and Discussion 68 Concl usi on 113 Experimental Section 114 CHAPTER IV. SPECTROSCOPIC AND BONDING STUDIES OF RHODIUM CARBOXYLATE DIMER CATION RADICALS 123 Introduction 123 Results and Discussion 128 Concl usi on 144 Experimental Section 145 CHAPTER V. SPECTROSCOPIC AND REACTIVITY STUDIES OF RUTHENIUM BUTYRATE CHLORIDE 147 I n troductl on 147 Results and Discussion 153 Concl uslon 190 Experimental Section 191 CHAPTER VI. GENERAL CONCLUSIONS 197 APPENDIX A. EXPERIMENTAL AND CALCULATED MAGNETIC SUSCEPTIBILITY DATA 199 APPENDIX B. UPPER RIGHT HAND NON-ZERO MATRIX ELEMENTS FOR SPIN HAMILTONIAN USED IN METHOD 1 200 m

PAGE 4

PAGE APPENDIX C. COUPLED BASIS SET FOR S = Si + So WHERE S l = S 2 = 3/2, USED IN METHOD 5 201 APPENDIX D. UPPER RIGHT HAND NON-ZERO MATRIX ELEMENTS FOR SPIN HAMILTONIAN USED IN METHOD 5 202 APPENDIX E. COMPUTER PROGRAMS USED FOR EPR SPECTRAL SIMULATIONS 203 APPENDIX F. COMPUTER PROGRAMS USED FOR MAGNETIC SUSCEPTIBILITY DATA SIMULATIONS 255 APPENDIX G. COMPUTER PROGRAMS USED FOR MOSSBAUER AND MMR SPECTRAL SIMULATIONS 273 REFERENCES 298 BIOGRAPHICAL SKETCH 308 TV

PAGE 5

Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy SYNTHETIC AND SPECTROSCOPIC STUDIES OF METAL CARBOXYLATE DIMERS By Joshua A. Telser December 1984 Chairman: Professor Russell S. Drago Major Department: Chemistry Synthetic and spectroscopic studies on several complexes in the metal carboxylate series are described. These complexes are of general formula M 2 (0 2 CR) 4 where M is a transition metal and "0 2 CR is a bridging carboxylate ligand. The metals used in this study are molybdenum, rhodium, and ruthenium. The studies were undertaken to help understand the nature of the metal -metal interaction in these complexes and to see what effect this interaction has on the reactivity of these complexes. To effect removal of the bridging carboxylate ligands, acetonitrile solutions of Rh2(0 2 CCH 2 CH 2 CH3) 4 and Mo 2 (0 2 CCH 3 ) 4 were reacted with stoichiometric amounts of the strong non-complexing acids CF3SO3H and (CH 3 CH 2 ) 2 0.HBF 4 . This generated Rh 2 (0 2 CH 2 CH 2 CH 3 ) 2 2+ and Mo 2 (0 2 CCH 3 )? 2+ species in solution. The former was not isolated, but characterized in solution by NMR and UV-visible spectroscopy. Two derivatives of Mo 2 (0 2 CCH 3 ) 2 2+ were isolated: CMo 2 (0 2 CCH3) 2 (CH 3 CN) 4 ](CF 3 S03) 2 and [Mo 2 (0 2 CCH3) 2 (CH3CN) 5 ](BF 3 0H) 2 . The reactivity of the former complex towards oxidative addition was investigated. The complex was found to v

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be quite stable towards oxidation in contrast to other Mo(II) complexes. Rhodium trifluoroacetate was reacted with various Lewis bases to give adducts of general formula Rh 2 ( 02^3)482 as had been previously reported for Rh 2 (0 2 CR)4. However, with pyridine and £-butyl Isonitrile, complexes of general formula Rh2(0 2 CCF3)4B4 were isolated constituting a new class of adduct. With phosphorus donors, Rh-Rh bond cleavage occurred to give monomeric Rh(I) and Rh(III) complexes. This demonstrates enhanced reactivity for Rh2(0 2 CCF3)4 compared to rhodium alkyl carboxylate dimers. The chemical and electrochemical generation of Rh2(02CCH 2 CH 2 CH3)4B2 + is described. These results and EPR spectra of these species are explained using a molecular orbital model. The strength of the rhodium Lewis base interaction determines the chemical and spectroscopic properties of these species. The formally mixedoxidation state complex Ru2(02CCH 2 CH2CH3)4Cl was studied by powder magnetic susceptibility measurements over the temperature range 5-300 K, by EPR spectroscopy In various glasses at 4 K and by Far IR spectroscopy at room temperature. In agreement with previous reports, the complex has a quartet ground state with unpaired electron spin density delocallzed over both Ru atoms. Reactivity studies of this compound with Lewis bases are described. A bispyridine adduct of ruthenium butyrate chloride is reported. VI

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CHAPTER I GENERAL INFORMATION The discovery of transition metal complexes containing metal-metal bonds is a relatively recent one. This discovery and much of the subsequent progress towards understanding metal-metal bonded complexes have been discussed in detail by Cotton and Walton in their book "Multiple Bonds Between Metal Atoms"* as well as in various review articles by others. 2 " 6 Nevertheless, a brief summary of the historical background of this class of complexes is in order. For the first half of the 20th century, transition metal chemistry was dominated by the concepts developed by Alfred Werner. That is, most complexes were thought of as what are now referred to as classical coordination compounds, a central transition metal ion surrounded by electron donating ligands usually in an octahedral orientation. Square planar, tetrahedral and other geometries were known, but the concept that a compound could exist in which there were several metals interacting in various ways had not been suggested. Metal -metal interactions were something thought to occur in bulk metals and not in complexes with oxidized metals. This idea was so firmly held that compounds that were synthesized during that time that contained metal metal bonds were not investigated further. Notable examples are chromium acetate, first prepared in 1844, and various tantalum^ and molybdenum^ halides synthesized during the early part of the 20th century.

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With the advent of Improved methods of crystal structure determination by x-ray diffraction, the discovery of metal-metal bonds in dimeric and cluster compounds became inevitable. It was in the metal carbonyl complexes that metal -metal bonding was first demonstrated. The reason for this may be a practical one in that these compounds were relatively easy to study, but it may also be a philosophical one. Metal carbonyl s and other organometallic compounds are newer and quite different from classical coordination compounds and thus understanding them was not hampered by older ideas that would be invariably applied to complexes such as metal halides and carboxylates. In Fe 2 (C0)g in 1938 and with greater certainty in Mn 2 (C0)iQ ln 1957 metal-metal single bonds were first proposed. The existence of metal-metal single bonds in carbonyl complexes containing two to twelve or more metal atoms is widely accepted. The existence of multiple bonds between metal atoms was not originally found in carbonyl complexes, but in some rhenium halides. The stoichiometry and the structure, when it was eventually determined, 12 of [Re 2 C1 8 ] 2 ~ could not be explained by classical theories. It was necessary to invoke a multiple metal -metal bonding scheme. A qualitative diagram of this molecular orbital (MO) scheme is shown in Figure 1-1. In a compound such as Mn 2 (C0)iQ it is not surprising that the odd d electron on each manganese pairs up to give a single a bond. However, it is surprising that in a Re(III) compound all four d electrons pair up to give a quadruple bond. The evidence for this quadruple bond comes primarily from the crystal structure. The Ree Re distance is exremely short, 2.222 A in (_n_-Bu) 4 NRe 2 Cl3, and there is no twist angle between the ReCl^ subunits so that the chlorides are

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Figure 1-1. Formation of metal -metal bond molecular orbital s from individual metal d atomic orbital s.

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(J antibonding combinations u + dxy dxy + ,22 ,22 dx y dx-y -r dxz dxz IT dyz dyz dz dz' a — z

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fully eclipsed. 14 This sterically unfavorable structure is the result of the fourth bond, the 6 bond between the Re atoms which arises primarily from the in-phase addition of the d xy orbital s. The in-phase addition of the two d x 2_ y 2 orbitals could give another 5 bond; however these orbitals are usually primarily involved in forming metal-ligand bonds and are thus rarely considered in MO schemes for metal -metal bonded complexes. The other three Re-Re bonds are derived in a more conventional manner, analogous to the triple bond well known for alkynes. The in-phase addition of the two d z 2 orbitals gives the a bond and the in-phase addition of the four d xz and d yz orbitals gives a degenerate pair of tt orbitals. The out-of-phase addition of these Re d orbitals gives a corresponding set of higher energy anti-bonding 5*, a*, and it* orbitals. In the Re(III) dimer the eight d electrons just fill all the bonding orbitals giving a diamagnetlc compound with a total bond order of four. Subsequent to this work on the rhenium dimer, other dimerlc metal -metal bonded complexes were studied and their properties explained using this MO scheme. The previously known complex Cr2(0 2 CCH3) 4 (H 2 0)2 was reinvestigated and proposed 15 to have a quadruple bond resulting from the pairing up of the four d electrons on each Cr(II) in the same manner as described above for Re(III). Chromium 1s the only first row transition metal proposed to form a multiply bonded dimer. The small size of first as opposed to second and third row transition metals makes it less convincing that enough orbital overlap occurs to give a quadruply bonded complex. It has even been Suggested i fi that no Cr-Cr bond exists at all in the chromium dimers. ° Copper forms the well known complex Ci^^CCI^^fh^O^ which is isostructural with chromium acetate. This general structure is shown in Figure 1-2. This

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Figure 1-2. General structure for metal carboxylate dimer with idealized D.. symmetry. Axial ligands, L, need not be present.

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R R L M M L R .0 R

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8 copper complex was studied by Bleaney and Bowers 17 a number of years ago, before the multiple metal -metal bond theory was proposed. They found that the two copper atoms were strongly antiferromagnetically coupled, but there was no true Cu-Cu bond. Thus it is possible, by analogy between the two first row transition metal dimers, that chromium acetate has a bond order of less than four with the remaining d electrons antiferromagnetically coupled. A large number of second and third row transition metal dimers have been reported and in these there 1s little doubt that the metal -metal bond MO scheme 1s valid. In addition to crystal structure determinations of many metal-metal bonded complexes, other spectroscopic and theoretical studies have been performed to confirm the generality of this MO scheme. Metal -metal bonded complexes are known for molybdenum, tungsten, technetium, rhenium, ruthenium, osmium, rhodium, and platinum. The compounds are far too numerous to list; however some examples of each will be given. The first studied was the rehnium chloride and a variety of multiple metal-metal bonded rhenium, technetium, and molybdenum halides are known. 1 " 4 However, carboxylate complexes were also among the first known as with the chromium and copper acetates mentioned above. This thesis is concerned with the metal carboxylate dimers and thus to show the generality of this type of ligand in forming metal-metal bonded complexes, one should note the following compounds: Re 2 (0 2 C(CH 3 ) 3 ) 4 Cl 2 , Tc 2 (0 2 C(CH 3 ) 3 ) 4 Cl 2 , Mo 2 (0 2 CCH 3 ) 4 , W 2 (0 2 CCF 3 ) 4 , Ru ? (0 2 CCH 3 ) 4 Cl and Rh 2 (0 2 CCH 3 ) 4 . In these complexes the bond orders range from four in Re, Tc, Mo and W to 2.5 in Ru to one in Rh. These bond orders can be easily determined using the MO scheme in Figure 1-1 and adding the appropriate number of d electrons for both metals.

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Given that a great variety of metal -metal bonded complexes exist and that a qualitative MO scheme exists which can explain their overall properties, the question then arises as to why would one wish to study them further. There are several reasons to do so. First, as was indicated specifically with the chromium carboxylate, the exact nature of the metal -metal bonding in these complexes is not yet completely resolved. Second, the wide range in bond orders in metal-metal bonded complexes such as the carboxylate dimers means that there is a wide range in strength of metal-metal interaction. Thus, what exists here is an Isostructural series for which comparison of the reactivity and spectroscopic properties of members of the series affords a direct means of understanding the effect different metal -metal interactions have on the chemistry of transition metal complexes. One can also compare the reactivity and spectroscopic properties of a metal -metal bonded complex to that of a monomeric complex of the same metal. The presence of two or more metals in close proximity leads to the possibility of metal synergism. 1 ** This means that one metal can influence the chemistry and the other metal site leading to different reactivity than would be expected for noninteracting multi-metal or monomeric metal systems. Synergism from metal clusters is proposed in a number of biological systems such as the ferredoxins, nitrogenase, cytochrome oxidase, and copper type 3 proteins. ^»20 Synergism in metal carboxylate clusters has also been used to model surface reactions. 21 The variety of metals and their oxidation states that form metal carboxylate dimers makes this class of complexes a good model system to study synergistic effects. The nature of the synergistic effect in metal carboxylate dimers has been previously examined by Richman and co-workers. The enthalpies

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10 of Lewis base binding to the vacant coordination sites along the M-M axis in several complexes of general type M 2 (0 2 CR)4 were measured. These sites will hereafter be referred to as axial sites since they are along the metal-metal bond axis. Enthalpies of formation of both 1:1 and 2:1 Lewis base axial adducts were obtained for metal carboxylate dimers such as Rh 2 (0 2 CCH 2 CH 2 CH 3 ) 4 , Rh 2 (0 2 CCF 2 CF 2 CF 3 ) 4 and Mo 2 (0 2 CCF 2 CF 2 CF 3 ) 4 . These will be abbreviated as Rh 2 (but) 4 , Rh 2 (hfb) 4 and Mo 2 (hfb) 4 , respectively. Comparison of the enthalpies for 1:1 and 2:1 axial adduct formation clearly showed significant changes in the acidic properties of the second metal as a result of base coordination to the first. Significant differences between rhodium and molybdenum systems were also found. Use of the E and C equation 2 '"" and modifications thereof allowed quantitative understanding of these effects. It was found that inductive transfer of electrostatic properties of the base was more effective through the shorter Mo-Mo quadruple bond than through the longer Rh-Rh single bond. Inductive transfer of the covalent properties of the base was more effective through the more polarizable Rh-Rh bond than the Mo-Mo bond. Differences in the type of Lewis acid-base interactions were also found for the two metals. Using the MO scheme in Figure 1-1, disregarding the second 5 bond, it can be seen that the molydenum carboxylate dimer with the total of eight d electrons from the two Mo(II) subunits has no t* electron density. In contrast, the rhodium carboxylate dimers with a total of 14 d electrons from the two Rh(II) subunits have filled ir* orbital s. This it* electron density can interact with empty it* orbital s on bases with these orbital s of the right energy. Thus, a higher than expected enthalpy of adduct formation was found for the rhodium

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11 carboxylate dimers with Lewis bases such as pyridine and acetonitrile. These bases can function as ir-acceptors as well as a-donors. No such irbackbonding stabilization was found for the molybdenum carboxylate dimer since it has vacant u* orbital s. A final reason for studying metal-metal bonded complexes, in addition to understanding synergistic effects where one metal influences the reactivity of the other, is to understand reactions where both metals are directly involved. An example would be the reaction of M-M with some X-Y species to give M-X and M-Y. This can be considered an oxidative addition and would be analogous to many reactions of organic compounds, particularly those with carbon-carbon multiple bonds. The reactivity of metal -metal bonded complexes has been recently reviewed 30 and there are many examples of this type of reaction. However, most involve organometallic complexes such as metal carbonyl clusters. It is not clear that this reactivity would occur to as great an extent in carboxylate or halide complexes wherein the metals are generally in a higher oxidation state. One means of enhancing the reactivity of and understanding the metal-metal Interaction in metal carboxylate dimers is to achieve varied ligand coordination to other than just the axial sites. As can be seen in Figure 1-2, the sites perpendicular to the metal -metal axis are fully occupied by the bridging carboxylate ligands. These sites will be referred to hereafter as equatorial sites. If these ligands could be wholly or partly removed, then the reactivity of the metal-metal bond could be better investigated. It was reported a number of years ago by Legdzins and co-workers 3 * » 3 ^ that strong, non-complexing aqueous acids could protonate the bridging carboxylates generating in solution species

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12 with available equatorial coordination sites. The effect of strong, non-complexing acids on metal carboxylate dimers of rhodium and molybdenum in organic solvents, chiefly acetonitrile, is the subject of the second chapter of this thesis. Another approach to achieving ligand coordination to the equatorial sites is to use a more poorly coordinating bridging carboxylate to begin with. Recently, Girolami and co-workers obtained unusual products from the reaction of Mo 2 (0 2 CCF3) 4 with various Lewis bases, primarily phosphorus donors. In some of the products, equatorial rather than axial Lewis base coordination was observed. This was found for phosphines that were sterically small and good a-donors. Thus, use of a fluorocarboxylate rather than an alkyi carboxylate can lead to equatorial coordination without the need for protonation of the carboxylate by strong acid. The reactivity of Rf^t 02^3)4, towards Lewis bases was systematically investigated and is the subject of the third chapter of this thesis. Another interesting aspect of multi -metal systems, besides their variety of ligand coordination sites, is the variety of oxidation states available to them. A monomeric complex might have two accessible oxidation states, an oxidized and a reduced state. In contrast, a dimeric complex of this metal could well have more since the two metals could be both oxidized or both reduced or one of each to give a wider range of electrochemical behavior. This ability is one reason why metal clusters are proposed to play an important role in biological redox processes such as the photochemical oxidation of water in photosynthesis. Thus one would expect metal -metal bonded complexes to exhibit a wide range of oxidation states. For metal-metal bonded dimers

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13 this is only partly true. Some variety of oxidation state does exist. For Mo, W, Tc and Re stable complexes with bond orders of 3, 3.5, and 4 are known 1 and they can be electrochemical ly interconverted. In these the metals are in the (III, III), (II, III) and (11,11) oxidation states respectively for Mo and W with the order reversed for Re and Tc. Only the (11,11) oxidation state for Rh and the (11,111) state for Ru give stable metal-metal bonded complexes that have been well characterized. Thus, the range of oxidation states in some metal -metal bonded dimeric systems is no greater than in monomeric complexes. Nevertheless, the redox behavior of metal carboxylate dimers is of interest and the use of electrochemical methods and EPR spectroscopy is helpful in understanding this behavior. A number of studies of this nature have been made on metal carboxylate dimers and related complexes by Cotton and Pedersen 35 " 39 and by other workers 40 » 41 and show that the redox and EPR properties of these complexes can be explained by the qualitative MO scheme described above. In a study by Drago and co-workers 23 the effect of both axial Lewis base coordination and different caboxylate ligands was quantitatively examined. Oxidation of the dimer is easier when the base is strongly donating and the carboxylate is not electron with-drawing. This oxidation converts the diamagnetic dimers to paramagnetic complexes which can subsequently studied by EPR spectroscopy. This technique gives information on the electronic properties of the complex that can be directly compared to theoretical studies. In addition to the qualitative MO scheme described earlier, a number of quantitative studies using a variety of calculational methods have been performed. 42 " However, these results are not always in full agreement with experimental data. The generation of paramagnetic rhodium carboxylate

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14 dimer species and comparison between these experimental and various theoretical results is the subject of the fourth chapter of this thesis. In contrast to the normally diamagnetic metal carboxylate dimers of rhenium, molybdenum, rhodium, and others mentioned above, there exists a normally paramagnetic dimer. Ruthenium does not form a doubly bonded d 12 (11,11) or a triply bonded d 10 (III, III) dimer. Rather, a d 11 (11,111) dimer of formal bond order 2.5 is formed upon reaction of ruthenium salts with carboxylic acids. 48 This complex, of general formula Ru 2 (02CR)4X, is quite stable compared to the rhodium (II, III) species described above. Thus, it can be easily studied using EPR and magnetic susceptibility. These techniques were applied to Ru 2 (but) 4 Cl a number of years ago by Cotton and Pedersen. 36 However, due to experimental difficulties their results on the electronic and magnetic nature of the complex were not conclusive. Thanks to improved technology in EPR and magnetic susceptibility instrumentation, it was now possible to perform detailed studies on this ruthenium carboxylate dimer. These studies are the subject of the fifth chapter of this thesis. In addition, since in contrast to the rhodium and molybdenum systems the reactivity of the ruthenium dimer towards Lewis bases has not been widely Investigated, some reactivity studies were performed and are also described in this chapter.

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CHAPTER II THE ACTION OF STRONG ACIDS ON M 2 (0 2 CR) 4 Introduction When dissolved in a coordinating solvent, the counter anions bound to a transition metal cation often dissociate. For example, most first row transition metal salts dissolve in water to give M(H 2 0) 6 n+ species. * In contrast, metal carboxylate dimers do not readily give M2 n+ and RC0 2 ~. The bridging carboxylate ligands remain coordinated to give neutral species in solution of general structure as shown in Figure 1-2 where L could be solvent. To further understand the coordination chemistry of metal -metal bonded systems, it would be desirable to achieve ligand coordination to a variety of sites such as those equatorial as well as axial to the metal-metal bond. Furthermore, it is well known that generation of coordinative unsaturation about a metal center is crucial for the generation of a catalytic cycle. 50 This often occurs by reversible ligand binding. Thus, it would be desirable to prepare metal -metal bonded dimers with labile ligands so that they could be used in catalytic studies and be more effective than analogous complexes with more strongly bound ligands. These catalytic processes could involve thermally or photochemical ly activated ligand dissociation. In this way any synergistic advantages to using such a system as opposed to one with monomeric complexes cou'id be determined. A metal-metal bonded complex analogous to the M(H 2 0)g n+ species has been reported. Maspero and Taube51 prepared Rh24+(aq) by the reduction 15

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16 of RhCl 2+ (aq ) by Cr 2+ (aq). This species was identified by conversion to Rh ? (0 ? CCH 3 ) .(H„0) ? by addition of sodium acetate. This conversion from the solvated cationic species does not appear to be completely reversible. Legdzins and co-workers 31,32 treated various metal carboxylate dimers with strong, non-complexing aqueous acids such as HBF 4 (aq). They claim to have generated Rh 2 4+ in this manner. This claim was subsequently refuted by Wilson and Taube 52 who proposed that the treatment of Rh 2 (0 2 CCH3) 4 with, for example, hot 1 M_ aqueous CF3SO3 generated Rh 2 (0 2 CCH 3 ) 3 3+ (aq ) and Rh 2 (0 2 CCH 3 ) 2 2+ (aq) but no Rh 2 4+ (aq). The formulation of these species was based on UV-visible spectroscopy and column chromatography. Neither group reported the Isolation of any stable rhodium dimer containing zero, two or three bridging acetates. The action of strong acids does lead to carboxylate protonation which allows generation of equatorial coordination sites on the rhodium dimer. The use of this general method in wholly organic solvent systems was investigated here. It was hoped that in such solvents more complete ligand protonation of Rh 2 (0 2 CR)4 would occur since there would be no leveling effect from water. Furthermore, the species generated this way might prove easier to isolate. Very recently, Ford and co-workers 53,54 were able to prepare a series of complexes of formula Rh 2 (02CCH 3 )3l_ + , Rh 2 (0 2 CCH 3 ) 2 2+ , and Rh 2 L 4 4+ where L = l,8=naphthyridine or derivatives thereof such as 2,7-bis(2-pyridyl )-l,8-naphthyridine. These were prepared by addition of stoichiometric amounts of the ligand and aqueous 1 M HC1 to methanol solutions of rhodium acetate. Similar results using pyridine are discussed below and were carried out at roughly the same time. Thus, use of a strongly donating, preferably chelating ligand does allow isolation of cationic rhodium dimer species. However, these

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17 are not complexes with the type of labile ligand one would desire so that catalytic activity would result. Isolation of this type of rhodium dimer has not yet been achieved. The analogous ^((^CR^ system has proven somewhat more amenable to study. A very large number of complexes containing the Mo-Mo quadruple bond are known. Most have bridging carboxylate ligands, halides or a variety of other anionic groups. Complexes with neutral ligands are far fewer. Species such as M02X4L4 are known where X = halide or alkyl and L = phosphine such as P(CH 3 )3. 54 " 57 Fewer still are complexes which contain the Mo-Mo quadruple bond coordinated by neutral, weakly donating ligands. A number of years ago, Bowen and Taube 5 reported the Mo 2 4+ (aq) species. This was not isolated as solid, but prepared in solution in the following manner. First, K 4 M02Clg was reacted with K 2 $0 4 in 0.2 M CF 3 S0 3 H(aq) to give K 4 Mo 2 (S0 4 ) 4 , a stable salt. This sulfate was reacted with Ba(CF 3 S03)2 to precipitate BaS0 4 and give the red aquo molybdenum dimer in solution. This species was Identified by UV-visible spectroscopy and could be converted back to the acetate. This work and the corresponding study with rhodium described above showed that these metal -metal bonded dimers could exist in solution without the presence of bridging or even anionic ligands. As was found much later with rhodium, 53 ' 54 Bowen and Taube 58 were able to isolate salts of the molybdenum dimer by using strongly donating chelating neutral ligands. Addition of ethylendiamine (en) and 2,2'dipyridyl (dipy) to solutions of Mo2Cl 8 4 " led to isolation of Mo 2 (en) 4 Cl 4 and MOp(dipy) 2 Cl 4 . Although these complexes have not been structurally characterized, the former species presumably has no CI coordinated to the molybdenum atoms. The Mo? (aq) species and related

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18 complexes such as Mo 2 Cl 8 4 ~ have been used in a photochemical study by Trogler and co-workers. 59 Ultraviolet irradiation of aqueous solutions of these complexes produced dihydrogen. This reaction was proposed to proceed via Mo 2 (y-0H) 2 4+ (aq) which was generated directly from Mo 2 4+ (aq) and via Mo 2 (u-Cl ) 2 Cl 4 (u-H) 3 " with the halides. This indicates a potential application for molydenum dimer species. Analogous complexes that would be soluble in organic solvents might also show interesting photochemical behavior. Another approach towards generating molybdenum dimers with weakly coordinating ligands was taken by Abbott and co-workers. 60 Molybdenum acetate was reacted with neat CF3SO3H at 100 C. Removal of solvent and drying at 100 C under vacuum yielded a tan solid formulated as Mo 2 (CF3S03)4. This product was frequently contaminated by Mo 2 (0 2 CCH3)|_3 impurities which were very difficult to remove. Furthermore, the complex was extremely prone to decomposition making it difficult to use for subsequent reactions. Very recently, Mayer and Abbott 61 achieved greater success using Mo 2 (0 2 CH) 4 rather than the acetate as starting material. Molybdenum formate was reacted with CF3SO3H and (CF3S0 2 ) 2 for six days to yield CO and a tan product formulated as [Mo 2 (H 2 0) 4 (CF3S03) 2 ](CF 3 S03) 2 . This complex reacts with acetronile to yield blue [Mo 2 (CH 3 CN) 8 ](CF3S03)4. These very air and water sensitive complexes were characterized by IR and UV-visible spectroscopy and elemental analysis. This represents the first reported example of a quadruply bonded molybdenum dimer coordinated only by monodentate, weakly donating, netural ligands. The reaction of Mo 2 (0 2 CCH3) 4 with CF3SO3H and other strong nonaqueous acids in acetonitrile and other organic solvents is described here. These studies were carried out at roughly

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19 the same time as those of Mayer and Abbott 6 * and gave similar results. The reactivity of the resulting complexes was also investigated. Results and Discussion Rhodium Treatment of the purple solution of Rh 2 (but) 4 in acetonitrile with CF3SO3H leads to an immediate, although slight, color change to dark red. The jv-butyrate ligand was chosen for increased solubility; similar results were obtained with acetate. Trifluoromethanesulfonic acid was chosen since it is a very strong, poorly coordinating acid that is somewhat soluble in organic solvents. The effect of different amounts of CF3SO3H on the UV-visible absorption spectrum of Rh 2 (but) 4 is shown in Figure 2-1. Rhodium butyrate with no acid showed absorption bands at 552 (e=202) and 438 nm (e=101). These are virtually identical to the results reported for rhodium acetate in acetronitrile, bands at 552 (e=235) and 437 nm (e=125). 62 Single crystal polarized electronic absorption spectra of rhodium acetate led to a proposal that these bands correpond to (Rh-Rh)u* + (Rh-Rh)a* and (Rh-Rhju* * (Rh-O)a* transitions, respectively. 63 Some controversy has recently arisen as to this assignment and will be discussed in Chapter IV. Addition of two equivalents of CF3SO3H leads to a very little change in the UV-visible spectrum. However, addition to four equivalents of acid leads to a dramatic change. The primarily metal-metal bond trnasition at 552 nm is relatively unaffected, but the metal -ligsnd transition is strongly affected, shifting to 380 nm. This shift to lower wavelength may result from a strengthening of the Rh-0 bonds of the remaining butyrates caused by the higher relative charge on the metal dimer. This would lower the

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•rC7> O iCO +->

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21

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22 energy of the Rh-0 a bonding orbital s and raise the energy of the Rha* antibonding orbitals leading to the observed shift to higher energy. Addition of excess CF3SO3H (~10 equivalents) and allowing the solution to sit for one hour does not greatly change the spectrum. The main transitions are observed at roughly the same wavelengths. A large band extending into the ultraviolet region is observed which may result from rhodium dimer or solvent decomposition. Solvent decomposition is a definite problem when trifluoromethanesulfonic acid is used with organic solvents. For example, it catalyzes the decomposition of THF. 4 With acetonitrile, trimerization probably occurs to give 2,4,6-trimethyl1,3,5-triazine. This compound was not isolated, but when benzonitrile was used as a solvent in the above procedure, the analogous compound kyaphenine (2,4,6-triphenyl-l,3,5-triazine) was isolated and easily identified by elemental analysis, melting point and mass spectroscopy. Kyaphenine is normally synthesized by the addition of excess CCI3CO2H to benzonitrile. 65 Thus, the use of excess CF3SO3H should be avoided. Nevertheless, the UV-visible spectrum suggests that protonation of the bridging carboxylates is occurring with four equivalents of acid. The species generated in this manner can be identified by NMR spectroscopy. NMR data are summarized in Table 2-1. The 13 C{ 1 H} NMR spectra of j^-butyric acid and Rh 2 (but) 4 , both in acetonitrile-dj, are shown in Figures 2-2 and 2-3, respectively. Of particular importance is the signal for the carboxyl carbon which has a very different chemical shift in the two compounds. Addition to four equivalents of CF3SO3H leads to a spectrum as shown in Figure 2-4. The four peaks at 139.47, 126.87, 114.85, and 102.46 ppm relative to internal TMS correspond to the carbon in CF 3 S03(H) split by three equivalent fluorine nuclei ( 19 F,

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23 o U_ < -ri — C t— I Q.

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•rCM T3 •IX l-H •r-iQ CJ fo

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25

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-ol

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27 >*

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°?

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29

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30 1=1/2). The other signals correspond to free and Rh coordinated butyric acid, with the carboxyl carbon peaks occurring in the expected places, by analogy with Figures 2-3 and 2-3. Proton NMR spectroscopy gave similar results. Figure 2-5A shows the *H NMR spectrum of Rh 2 (but) 4 with the expected splitting patterns for an ^-propyl group. Figure 2-5B shows the spectrum after addition of four equivalents of CF3SO3H. Signals are observed for coordinated and free butyric acid. The poor resolution of some of these peaks may be due to the presence of acid, causing proton exchange and perhaps decomposition. Based on the peak intensities, the dominant species in solution has an average composition of Rh 2 (but) 2 . The area ratio of peaks corresponding to free and coordinated butyrate was 1:1 in several separately prepared solutions. The ratio of peak areas for the protons for both free and coordinated butyrate was 2:2:3 for H a :H g :H Y as expected. This solution gave no EPR signal at 77 K indicating that a Rh(II) monomer was not present. This does not prove that the dimer remains intact since disproportionation to dlagmetic Rh(III) and Rh(I) may have occurred. However, the NMR data suggest that the solution contains the dimer since the signals for coordinated butyrate, particularly Cj_, occur near those for Rh 2 (but) 4 . Also Rh(III) and Rh(I) complexes are generally orange or yellow. The NMR data, in conjunction with the UV-visible results, indicate that four equivalents of CF3SO3H generate Rh 2 (but) 2 2+ in acetonitrile solution. Attempts to isolate a solvated Rh 2 (but) 2 salt were unsuccessful. Evaporation of the acetonitrile solution left a dark red, water soluble oil. Previous workers^ 2, ^ reported that evaporation of the solution obtained by the titration of Rh 2 (0 2 CCH 3 ) 4 with aqueous CF3SO3H led to a deliquescent green oil which was similarly intractable. Attempts to

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32

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33 isolate a product using BPh^" and PFg" as counterions were unsuccessful. Some solids were obtained, but the results were not repeatable and the products could not be well characterized. Another approach that was taken to isolate a Rh 2 (but) 4 2+ species involved using a bridging dianionic ligand, Y 2 ~, to form a neutral compound Rh 2 (but) 2 Y. This type of compound has precedent in the A-frame series of complexes, which have been found to coordinate a wide variety of molecules to their exposed side. 66-69 The sulfide ligand was chosen since it is used in the A-frame complexes, * is readily available, has a high affinity for transition metals, and bridges easily. Anhydrous sulfide was generated directly in THF by addition of "Super-Hydride" (LiBH(CH 2 CH3) 2 ) to elemental sulfur. This solution was added to the Rh 2 (but) 2 solution leading to immediate formation of a black precipitate. The black compound was insoluble in all solvents so it could only be characterized by elemental analysis. Elemental analysis indicated a complex with 1-2 sulfurs and two butyrate groups. Mass spectroscopy was used to little avail. No molecular ion peaks were detected at m/e=412 for Rh 2 (but) 2 S or m/e=446 for Rh 2 (but) 2 (SH) 2 . Intense peaks corresponding to H 2 S and HS fragments were observed. The compound is possibly a sulfide or hydrosulfide bridged rhodium polymer which contains two butyrates per rhodium dimer. A similarly intractable compound was prepared using selenide. Rakowski Dubois and co-workers 7 ^ successfully converted the molybdenum sulfide polymer [(CgHgjMoS^., to the soluble binuclear complex [(C5H 5 )MoS(SH) 2 ] 2 by stirring the polymer for 5-7 days under 1 atm of H 2 . This was attempted with the rhodium sulfide polymer, but no dissolution was observed. The solid was also treated with 1-iodoheptane in the hope of alkylating any bridging SH

PAGE 40

34 groups to solubilize the complex. However, no reaction or dissolution was observed and the solid recovered should no increase in carbon or hydrogen content. The anion of 1,3-dithiopropane, generated in the same manner as the sulfide, was used in the hope of obtaining more soluble products, but gave only an oil. Other Y 2 ~ type ligands that could be considered are cis-l,2-dicyanoethene-l,2-d1thiolate (mnt) which forms complexes with many transition metals 71 and (HOPO) 2 2 ~ (pop) which forms bi nuclear complexes with platinum. 72,73 However, mnt reacts with Rh 2 (0 2 CCH 3 ) 4 to give a monomeric Rh(II) complex, 71 and would doubtless do the same with Rh 2 (0 2 CR) 2 2+ . In contrast to the results with platinum, 72 * 73 rhodium as both RhCl 3 and Rh 2 (0 2 CCH 3 ) 4 does not appear to react readily with pop or H3PO3 to give analogous P-bonded dimeric complexes. A final attempt at isolating a cationic rhodium carboxylate dimer involved the use of pyridine, a Lewis base far stronger than acetonitrile. Addition of excess pyridine to the acetonitrile solution of Rh 2 (but) 4 led to an immediate color change to orange. The Invisible absorption spectrum of this solution showed a band at 465 nm (e=481) presumably corresponding to the (Rh-Rh)ir* + (Rh-Rh) a* transition and a very large band extending into the UV region. This latter band may involve rhodium to pyridine tt* transitions. The order of addition of pyridine and acid is important. When pyridine (10 equivalents) is added to rhodium butyrate in acetonitrile, the purple Rh 2 (but) 4 (CH 3 CN) 2 solution immediately turns red, indicative of Rh 2 (but) 4 (pyr) 2 . The equilibrium constants for axial coordination of various Lewis bases to rhodium butyrate have been determined, 3 ~" and K eq for pyridine binding is several orders of magnitude larger than that

PAGE 41

35 for acetom'trile. However, when CF3SO3H (10 equivalents) is added, the purple color is restored indicating that the pyridine is completely protonated by the strong acid. This occurs even though some pyridine is coordinated to the Lewis acid Rh 2 (but) 4 . Adding more pyridine neutralizes the acid present and the red color of the axial pyridine adduct eventually develops. When excess acid is added to this, as with any acetonitrile solution of rhodium butyrate, the Rh 2 (but) 4 2+ species results and subsequent addition of pyridine leads to the orange color of what is presumably a pyridine adduct of Rh 2 (but) 4 with equatorial base coordination. Addition of excess acid to the orange solution restores the purple color indicating that the equatorial ly coordinated pyridines can also be protonated. Attempts were made to isolate solids from the orange solution by evaporation, cooling, and the use of various solvents such as water and methanol and various counter anions such as BPh 4 ~ and PFg". Oils were usually obtained; however a solid was isolated which analyzed approximately for Rh 2 (but) 2 (pyr) 4 (PF 6 ) 2 . With Rh 2 (0 2 CCH 3 ) 4 , less oiling occurred and what is presumably [Rh 2 (0 2 CCH 3 ) 2 (pyr) 4 ] (CF 3 S0 3 ) 2 was isolated. Based on this result and those from Ford's laboratory, 53,54 use of butyrate, while helpful in solution studies, is not recommended for isolation of solids. Some other reactivity studies were undertaken on the Rh 2 (but) 4 2+ solution. This solution showed no visible change upon exposure to air and the *H NMR spectrum was unchanged. On the basis of kinetic data, HRh 2 (0 2 CCH 3 ) 3 has been proposed as an intermediate in the hydrogenation of olefins catalyzed by rhodium acetate. Rhodium acetate itself shows no reactivity towards H 2 (1 atm) at temperatures up to 80 C. It was hoped that such a hydride species might be observed in the reaction of

PAGE 42

36 H 2 with the cationic rhodium dimer solution. This solution was sealed in an NMR tube under 1 atm of H 2 , but showed no visible or 1 H NMR spectral change. Furthermore, the solution shows no reaction with one or two equivalents of 1-hexene or CH30 2 CC=CC0 2 CH 3 , both of which might be expected to add oxi datively to the Rh-Rh bond. Thus, reactivity with organic molecules has not been enhanced by exposing the metal-metal bond. Molybdenum In contrast to the work with rhodium described above, it was possible to isolate stable, cationic acetonitrile coordinated derivatives of the molybdenum carboxylate dimer. Molybdenum acetate is completely insoluble in organic solvents, but when suspended in acetonitrile, addition of two equivalents of CF3SO3H leads to immediate formation of an intensely colored purple solution. Removal of solvent and recrystallization of the resulting solid from 1:1 acetonitrile/ toluene allows isolation in good yield of a purple crystalline complex. Elemental analysis suggests its formulation as [Mo 2 (0 2 CCH 3 ) 2 (CH 3 CN) 4 ] (CF 3 S0 3 ) 2 , (1). Use of more acid, up to 10 equivalents, leads to essentially the same product with greater solvent decomposition. The use of neat acid will be discussed below. This compound is air sensitive and very hygroscopic but is indefinitely stable under an inert atmosphere. Various methods were used to confirm that i is an acetonitrile coordinated Mo-Mo quadruply bonded species as formulated above. The oxidatio? state of molybdenum was found to be 2+ using Fe 3+ as oxidant using a reported method. 58 However, metal-metal bond cleavage can occur without oxidation state change. Examples include the photolysis of Re 2 Clg in acetonitrile to give

PAGE 43

37 Re(CH 3 CN) 3 Cl3 75 and the reaction of Mo 2 (0 2 CCH 3 ) 4 with t-BuNC to give Mo(t_-BuNC) 5 (0 2 CCH3)2. 76 The conditions required were more strenuous than those used here. Irradiation at 366 nm for 24-48 hours was needed for photolysis and in the second case, t^-BuNC is a far stronger ligand than acetonitrile. The UV-visible absorption spectrum of I is of interest and provides conclusive evidence that the Mo-Mo quadruple bond remains intact. In acetonitrile solution bands are observed at 535 (e=864), 390 (e=117) and 255 nm (e=7383). This resembles the results of Bowen and Taube 58 who found for Mo 2 (aq) and Mo 2 (en) 4 4+ absorption bands at 504 (e=337) and 478 nm (e=483), respectively and weaker bands at 370 (e=40) and 360 (e=36.4), respectively. A band at 235 nm (e=966) was also observed for Mo 2 (en) 4 2+ . Some controversy exists as to the assignment of the electronic transitions in the Mo-Mo quadruply bonded system. However, a very detailed single crystal polarized electronic absorption spectrum study by Martin and co-workers 77 indicated that the band observed at 435 nm corresponds to a (Mo-Mo)5 (Mo-Mo)6* transition. The second band at 377 nm was more tentatively assigned to a (Mo-Mo) 6* > (Mo-Mo) ** transition. A recent study by Manning and Trogler 78 of the electronic spectrum of matrix isolated Mo 2 (0 2 CCH3) 4 confirmed the assignment of the 6+6* transition although suggested that other, probably Mo-0 states, contribute to the observed band. At any rate, these two transitions are observed for 1. The UV-visible spectrum of 1 was also obtained in THF solution and gave qualitatively the same results. Bands at 490 (e=321), 335 (e=461), and 277 nm (e=3066) were observed. Dissociation of coordinated acetonitrile probably occurs which changes the absorption bands. The shift to shorter wavelengths may result from the replacement

PAGE 44

38 of the ir-acceptor CH3CN by the a-only ligand THF. Thus 1 in THF shows absorptions closest in wavelength and intensity to those of Mo 2 4+ (aq) and Mo 2 (en) 4 . In addition, X in THF is far more air sensitive than I in acetonitrile, changing color almost immediately upon air exposure, perhaps indicating poorer stabilization of the Mo 2 4+ unit. The IR spectrum of I (Nujol mull) is shown in Figure 2-6. Most of the absorption bands can be readily assigned. Very sharp bands corresponding to v(CN) of coordinated acetonitrile are observed at 2300 and 2285 cm" 1 . This shift to higher frequency, compared to 2266 cm" 1 for free acetonitrile, is indicative of end-on nltrile coordination with little ir-backbond stabilization. 79 Two v(CN) bands are seen because in addition to the v(CN) fundamental, there is a combination of the symmetrical CH3 deformation and the C-C stretch. These two bands are subject to Fermi resonance coupling which affects their frequencies and intensities. Unfortunately, no assignment can be made as to Mo-N stretches. Very few metal organonitrile complex M-N stretches have been conclusively identified and they usually are weak and of widely varying frequency. 80 Absorption bands corresponding to the acetate ligand are of interest. For I no band corresponding to v asy (C0 2 ) was observed. This is seen at 1578 cm" 1 in Na0 2 CCH 3 . 81 However, a strong band at 685 cm" 1 is observed which is most likely <5(C0 2 ). This occurs at 675 cm" 1 in Mo 2 (0 2 CCH 3 ) 4 60 and at 646 cm" 1 in Na0 2 CCH 3 80 and indicates the presence of bridging acetate in \. Finally, a weak band is observed at 410 cm" 1 which may correspond to a Mo-Mo stretch. In centrosymi-ctric metal carboxylate dimers this band is IR inactive. However, Raman spectroscopy studies 56 on a number of derivatives of the quadruply bonded Mo dimer show v(Mo 2 ) occurring at 383 to 404 cm" 1 with weak to

PAGE 45

39 30N»ii!l l lSN•Ml X

PAGE 46

40 medium intensities. It is possible that non-centrosymmetric isomers of 1 are present allowing observation of v(M02) ln tne ^ spectrum. Known molybdenum dimer complexes with this geometry in which the acetates are cis are Mo 2 (0 2 CCH 3 ) 2 ((Pz) 3 BH)2 82 and Mo 2 (0 2 CCH 3 ) 2 (CH 3 C0CHC0CH 3 ) 2 . 83 Infrared studies on these complexes were not reported; however these and an analogous isomer of \ t all with C 2v symmetry, would have an IR active Mo-Mo stretch. This would most likely be of low intensity due to the small dipole moment change involved. This possible structure and that of a centrosymmetric isomer are shown in Figure 2-7. The remaining IR bands can be assigned to the counterion, non-coordinated CF 3 S0 3 ~. Bands are observed at 1285, 1245, 1160, 1030, 755, 720, 635, 575, and 520 cm" 1 . The IR and Raman spectra of solid Na0 3 SCF 3 have been carefully analyzed by Miles and co-workers. The vibrations they observed and their assignments are as follows: 1280 (v asy (CH 3 )), 1232 (v s (CF 3 )), 1168 (v asy (S0 3 )), 1036 (v s (S0 3 )), 766 (5 S (CF 3 )), 630 (6 asy (S0 3 )), and 531 and 515 cm" 1 both 5 aS y(CF 3 )). These bands can be directly compared to those observed for 1. When CF 3 S0 3 " is coordinated, the IR bands for v(S0 3 ) change greatly. For example, Mo 2 (0 3 SCF 3 ) 4 has S-0 stretches at 1350, 1110, and 990 cm" 1 . 60 The band observed in I at 720 cm" 1 cannot be assigned to the CF 3 S0 3 ~ and is probably an acetate or acetonitrile vibration. Proton NMR spectroscopy was performed on I, but did not provide much insight into its structure. Signals were observed at 4.3 and 2.0 ppm relative to internal TMS in nitromethane^d-. The upfield signal is probably coordinated CH 3 CN since in CD 3 CN solution it broadened and decreased in intensity over time, disappearing after about one hour, indicating exchange with the solvent. The downfield signal is probably

PAGE 47

41 + CM + to X o o o ro X o

PAGE 48

42 CH3CO2" although it is rather far down-field for metal coordinated acetate. Paramagnetic impurities initially present or arising from complex decomposition would cause line broadening and unusual chemical shifts. 85 However, 1 does not show an EPR signal in 1:1 acetonitrile/toluene at 77K. A different synthetic approach was used to study the interconvertability of the Mo 2 derivatives. What is presumably the reported 60 Mo 2 (0 3 SCF3)4 complex was prepared but not characterized. To this was added acetonitrile to give an intensely colored blue solution. Addition of toluene led to formation of a bright blue precipitate. This complex did not give a satisfactory elemental analysis. The IR spectrum Indicated coordinated CH3CN, non-coordinated CF 3 S0 3~ and some residual bridging acetate as well as a strong v(0H) band. Slow evaporation of the filtrate led to formation of purple crystals. The IR spectrum and elemental analysis of these crystals coresponded to that of 1. The initially isolated blue complex is most likely one with less than two acetates giving a more highly charged species which 1s less soluble in organic solvents. Subsequent to this work, Mayer and Abbott 61 reported the synthesis of [Mo 2 (H 2 0)4(0 3 SCF3) 2 ] (CF3S03) 2 . This complex was synthesized from Mo 2 (0 2 CH) 4 and thus, in contrast to the previously reported Mo 2 (03SCF3) 4 , could be reproducibly prepared free from any carboxylate contamination since the formate decomposes to CO and H 2 0. Addition of acetonitrile to this complex led to isolation of blue [Mo 2 (CH 3 CN)g](CF3S03) 2 . The blue complex reported here is most likely impure [Mo 2 (CH3CN)g](CF3S03) 2 , indicating that the acetonitrile solvate of Mo 2 can also be prepared from molybdenum acetate, but much less successfully than by the method using molybdenum

PAGE 49

43 formate as starting material. What is interesting is that as found with the rhodium systems, the M 2 (02CR) 2 2+ species is very stable. Even following the extreme conditions of Abbott and co-workers, a considerable amount of the f^^CCf^^ species is isolated. Some reactivity studies on X were performed. As stated previously, the complex is air sensitive and quite hygroscopic as a solid. However, in acetonitrile solution, the complex is relatively stable. Dioxygen can be bubbled through this solution for at least 30 minutes without any visible change. Exposure to air does eventually decompose the dimer. This decomposition was monitored by UV-visible spectroscopy and is shown in Figure 2-8. The characteristic Mo-Mo quadruple bond absorption bands disappear and most likely a variety of monomeric molybdenum species result. Prolonged exposure to air gives a blue-green solution characteristic of high oxidation state Mo. It is likely that this decomposition is assisted by replacement of coordinated acetonitrile by water. Complex 1 dissolves in water to give a red solution similar to that of Mo 2 4+ (aq). This solution is very air sensitive, as 1s Moo (aq), in contrast to 1 in acetonitrile. Complex 1 reacts immediately with Et 4 N02CCH3 in acetonitrile to give a yellow solution from which yellow crystals of Mo2(02CCH 3 ) 4 precipitate. Complex I reacts readily in acetonitrile solution with stronger Lewis bases. Addition of excess (~10 equivalents) of nitrogen donors such as pyridine or N-methyl imidazole gave red solutions and phosphorus donors such as tricyclohexylphosphine gave blue solutions. These reactions were not investgated further; however, it is likely that a variety of derivatives

PAGE 50

44 350 400 450 500 X (nm) 550 600 Figure 2-8. UV-visible absorption spectrum of 1 in acetonitrile (6.0 x 10" M) showing changes on exposure to air.

PAGE 51

45 of the Mo 2 (0 2 CCH 3 ) 2 2+ unit with various ligands stronger than acetonitrile could easily be prepared. The electrochemistry of I was investigated to determine if stable Mo 2 ( 1 1, III) or other species could be generated. Previous electrochemical studies by Cotton and Pedersen 38 on Mo 2 Cl 8 4 " and Mo 2 (but) 4 indicated that these complexes could be quasireversibly oxidized at -0.4 V vs. see to short-lived Mo 2 (II.III) species that were not isolated. The Mo 2 (but) 4 + species was observed by EPR spectroscopy. Complex X in acetonitrile with 0.1 H (^-Bu) 4 NBF 4 as the supporting electrolyte showed no reversible redox waves over the range +2.0 to -2.0 V vs. Ag/AgCl,KCl(sat'd). A weak irreversible oxidation occurred at +1.5 V. Acetonitrile coordination may stablize the dimer towards oxidation, but does not facilitate Isolation of oxidized species. Another form of oxidation of the Mo 2 (II.III) unit could involve oxidative addition to the Mo-Mo quadruple bond. Such reactions are well known for carbon-carbon multiply bonded compounds. For example, Br 2 oxidatively adds to olefins to give dlbromo compounds. Of more relevance here are the studies by Chisholm and co-workers 86 " 88 who have achieved oxidative addition to the Mo-Mo triple bond in Mo 2 (0R) 6 complexes. For example, Mo 2 (v-Pr0) 6 reacts with (v-PrO) 2 to give Mo 2 (u-v-Pr0) 2 (v-Pr0) 6 , 85 with various alkynes in the presence of pyridine to give Mo 2 (y-Wr0) 2 (j^Pr0) 4 (pyr) 2 (u-C 2 R) 87 and with di methyl cyanamide to give Mo 2 (jj-PrO) 6 (u-HCMNe 2 ). 88 Such reactions might be expected for Mo 2 (0 2 CR) 4 complexes if the Mo-Mo bond were more exposed. Thus, complex J. is a likely candidate. Unfortunately, no reaction was observed between I and CH 3 I, (CH 3 CH 2 S) 2 and 1-hexene, all

PAGE 52

46 of which could ox1 datively add across the Mo-Mo quadruple bond. Complex 1 did react readily with dimethyl cyanamide (~10 equivalents) in acetonitrile to give a blue solution. From this a bright blue solid was isolated. The IR spectrum of this solid showed a very strong v(CN) band at 2260 cm" 1 Uujol mull) with no bands in the 1600 to 2200 cm" 1 range. This can be compared to free (Ch^^NCN, with v(CN) at 2205 cm" 1 and to complexes with side-on dimethyl cyanamide coordination such as [Ni(C0)(NCN(CH 3 ) 2 )]2 with v(CN) at 2008 cm" 1 89 and the above Mo(III) alkoxide dlmer with \>(CN) at 1582 cm" 1 . 88 The shift to higher frequency seen here indicates end-on nitrile coordination as seen with acetonitrile, with no evidence for side-on coordination involving the Mo-Mo bond. Complex 1 also showed no reaction with SnC1 2 or Vaska's compound (IrtCQHPPt^^CI). These complexes were hoped to add reductivity to 1 replacing acetonitrile to give clusters containing 4coordinate Sn or 6-coordinate Ir, respectively. A final approach towards investigating the reactivity of 1 was to use anionic metal fragments to generate clusters resembling the reactions attempted above to generate Sn or Ir containing clusters. The reaction of monomeric metal fragments to form clusters has been widely studied. 90 Of particular use is the reaction of anionic metal complexes with species containing a weakly bound ligand. An example is the reaction of Fe 5 C(C0) 14 2 " with W(C0) 3 (CH 3 CN)3 to give WFe 5 C(C0) 17 2 ". 91 An important point regarding the complexes synthesized in this manner is that the reactants are generally both metal carbonyl complexes or at least compounds containing metals in similar, low oxidation states with similar ligands. If 1 would react with these anionic species to form clusters, the result would be a cluster in which two of the metals, the

PAGE 53

47 molybdenum atoms, would be in a relatively high oxidation state with relatively electron-withdrawing ligands, carboxylates, while the other metal would be in a relatively low oxidation state with electrondonating ligands such as carbonyls. Complex I was reacted with Mn(C0) 5 " (C 5 H 5 )Mo(C0) 3 ~ and Fe(C0) 4 2 ". The first two can be easily prepared by reduction of the dimeric species Mn 2 (C0) 10 and (C 5 H 5 ) 2 Mo 2 (C0) 6 by Na/K alloy. 92 The iron complex is available commercially and is often referred to as Collman's reagent. 93 Unfortunately, these reduced species reacted with X via redox reactions. The metal carbonyl starting material was regenerated and could be identified by IR. Uncharacterized species from decomposition of the Mo dimer were also produced. Apparently, these anionic carbonyl complexes are too strongly reducing to form clusters. This problem often occurs in the reaction of anionic complexes even with other low oxidation state carbonyl compounds. For example, (C 5 H 5 )Fe(C0) 2 ~ and V(C0) 6 " are not usable in these reactions because they are such strong reducing agents. 90 Furthermore, some clusters are, like 1, easily reduced. For example, Fe 3 (C0) 12 , Fe 2 Ru(C0) 12 and FeRu 2 (C0) 12 are easily reduced and fragmented. 90 Thus, it appears that the reaction of higher oxidation state metal -metal bonded dimers with reduced organometallic species is not a facile means of synthesizing metal custers. In addition to 1, [Mo 2 (0 2 CCH 3 ) 2 (CH3CN) 4 ](CF 3 S03) 2 , the synthesis of other complexes containing the Mo-Mo quadruple bond was investigated. One approach would be to use a solvent other than acetonitrile. As discussed previously, the strong acid needed for carboxylate protonation precludes the use of many solvents. The problems with THF

PAGE 54

48 (polymerization) and nitriles (oligomerization) have already been mentioned. Solvents that would solvate the cationic species generated by carboxylate protonation but be only weakly coordinating are nitromethane, propylene carbonate and sulfolane (tetrahydrothiophene1,1-dioxide). The first two decompose readily upon addition of CF3SO3H; however sulfolane appears not to decompose. Addition of CF3SO3H (~4 equivalents) to suspensions of Mo 2 (0 2 CCH 3 ) 4 in these three solvents leads to a faint red color indicative of aquo-coordinated Mo dimer species. However, the bulk of the molybdenum acetate does not dissolve and addition of more acid does not lead to more dissolution, only to solvent decomposition. Clearly, the only reaction occurred because of the presence of water in these solvents. A reasonably good donor solvent, such as acetonitrile, is needed to stabilize any cationic molydenum complexes produced and so drive the carboxylate protonation reaction to completion. Another parameter that can be varied besides solvent is the acid used. It was desired in this work to avoid the use of aqueous solvent systems since those had been studied previously 58 and cationic Mo dimer complexes were not isolated except with strong ligands such as ethylenediamine. This solvent choice limits the variety of acids usable. Furthermore, acids containing halide ions are to be avoided since the Mo dimer readily coordinates halides. For example, Mo 2 (0 2 CCH 3 ) 4 reacts with Ph^AsCl in dilute HC1 to give [Mo 2 (0 2 CCH 3 ) 2 Cl 4 ] (Ph 4 As) 2 . Other complexing acids would produce similar species, resulting in a Mo dimer coordinatively saturated by strong, anionic ligands. A non-complexing, nonaqueous acid that is readily available, besides CF3SO3H, is fluoroboric acid as the diethylether adduct,

PAGE 55

49 C(CH 3 CH 2 )2°n HB|r 4This acid is very difficult to handle since it is very viscous and hygroscopic. Furthermore, it is difficult to purify and may be of varying composition, as will be shown below. Addition of approximately four equivalents of [(Et 2 0)]HBF4 to an acetonitrile suspension of Mo 2 (0 2 CCH3) 4 leads to formation of an intensely colored magenta solution. From this solution an air sensitive, hygroscopic magenta compound can be isolated that is best formulated as [Mo 2 (0 2 CCH 3 ) 2 (CH3CN) 5 ](BF 3 0H)2, (2). This complex was characterized in the same manner as 1. The oxidation state of Mo was found to be 2+. The UV-visible absorption spectrum of 2 in acetonitrile shows bands at 527 (e=890), 370 (e=205), and 269 nm (e=7000). This indicates that the Mo-Mo quadruple bond is present. Exposure to air leads to decomposition, as with 1, only it occurs more rapidly with X. This process is shown in Figure 2-9. The IR spectrum of 2 is of interest and supports the above formulation based on elemental analysis. The spectrum (Nujol mull) is shown in Figure 2-10. Three strong bands corresponding to v(CN) of coordinated acetonitrile are observed at 2308, 2282, and 2258 cm" 1 . Elemental analysis indicated that there were five acetonitriles in Z as opposed to four in 1. In I there are two v(CN) bands whereas in 2 a third band results from CH3CN in either a different coordination environment or from different isomers. Two possible isomeric structures for 2 are shown in Figure 2-11. As can be seen by comparison with Figure 2-8, in 1 the acetonitriles are equivalent while in 2 they are not. Comparison of the IR absorption bands corresponding to the acetate demonstrates again the difference between 1 and 2. Complex 1 showed no band corresponding to v aS y(C0 2 ). By contrast, Z shows bands at 1647,

PAGE 56

50 350 400 450 500 X (nm) 550 600 Figure 2-9. UV-visible absorption spectrum of 2 in acetonitrile (6.5 x 10" M) showing changes on exposure to air.

PAGE 57

51 33NVJ.1IHSNVM1 %

PAGE 58

52 .-1 1540, and 1500 cm" 1 . The first is most likely v asy (C0 2 ) for monodentate acetate, the latter two for bridging acetate. Comparison with known compounds with bridging acetate, such as Cr 2 (0 2 CCH 3 ) 4 (H 2 0) 2 which has v asy (C0 2 ) at 1575 cm" 1 94 and those with monodentate acetate, such as Ru(0 2 CCH 3 ) 2 (C0) 2 (PPh 3 ) 2 which has \> asy (C0 2 ) at 1613 cm' 1 , 95 shows that a band at this high frequency is characteristic of monodentate acetate. Very sharp, intense bands are observed at 680 and 685 cm" 1 corresponding to 6(C0 2 ). If one of the acetates is monodentate this would allow coordination of an additional acetonitrile as shown in Figure 2-11. It is possible that the fifth acetonitrile is axially coordinated; however this site in Mo carboxylate dimers is only weakly coordinating. Even a strong Lewis base such as pyridine only weakly binds to this position in Mo 2 (0 2 CCF 3 ) 4 , 96 which is a stronger Lewis acid than Mo 2 (0 2 CCH 3 ) 4 . A weak, but distinct, band at 405 cm" 1 may correspond to the Mo-Mo stretch. This would be IR allowed in Z since no centrosymmetric Isomers are possible as can be seen in Figure 2-11. A band is observed at 720 cm" 1 corresponding to an acetate or acetonitrile vibration as in I. The remaining bands correspond to the counterion and support its formulation as BF 3 0H". A strong band is seen at 1060 cm" 1 with weak, but distinct, bands at 950, 765, 520, 378, and 360 cm' 1 . Vibrational absorptions for BF 4 " are at 1070 (v 3 , v asy (BF)), 777 (v lt v s (BF)), 533 (v 4 , 5 asy (FBF)), and 360 cm" 1 (v 2 , 5 asy (FBF) ). 97 These same bands for B(0H) 4 " are at 945, 754, 533, and 379 cm" 1 . 98 All of these modes are Raman allowed, but only v 3 and v 4 are IR allowed in these tetrahedral complexes. The bands observed in Z at 1060 and 520 cm" 1 correspond to these two IR allowed vibrations. The band at 950 cm" 1 may be v 3 for B-0. The bands at 378 and 360 cm" 1 may correspond to v 2 for B-0 and B-F

PAGE 59

53 + CVJ to O CO

PAGE 60

54 bonds, respectively. In BF3OH", a complex with C 3v symmetry, all vibrations are IR allowed so these would be observed. Finally, two strong bands assigned to v(0H) are seen at 3600 and 3530 cm" 1 . Thus, the IR spectrum of Z supports the formulation of the counterion as BF3OH" presumably resulting from an impurity in the [(Et 2 0)]HBF 4 used. Support for this counterion formulation is also obtained by anion exchange. Complex Z can be dissolved in an acetonitrile solution of excess ( < n > -Bu) 4 NBF 4 or Ov-Bu) 4 PF 6 and addition of toluene leads to precipitation of primarily the BF 4 " or PF g " salt. This process can be repeated to effect complete exchange. The *H NMR spectrum of Z resembles that of 1 with signals observed at 3.0 and 2.1 ppm in CD3CN. Thus, NMR does not distinguish between different types of acetonitrile coordination. Due to the more difficult synthetic procedure for Z compared to 1, as well as more uncertainty as to the exact structure of 2, reactivity studies were not performed. Interestingly, a complex analogous to Z can be obtained using CF3SO3H. After recrystallization of 1, the filtrate is often magenta rather than purple. Addition of a small amount of toluene and allowing the solution to sit overnight leads to formation of a. crystalline magenta precipitate, (3J. The amount of 3 varies greatly from one preparation of 1 to the next. It is not clear as to the procedure for selectively preparing one or the other, although use of freshly distilled CF3SO3H leads to better yields of 1 over 3. A formula that can be proposed for 3 is [Mo 2 (0 2 CCH 4 ) 2 (CH3CN) 4 X](CF 3 S03)2 where X=CH 3 CN or H 2 0. The oxidation state of Mo in 3 is 2+. The elemental analysis of 3 favors X=H 2 0. This is also supported by the fact that 3 is more

PAGE 61

55 30NVillWSNVai %

PAGE 62

56 likely to be obtained with less pure, presumably water contaiminated CF3SO3H. However, the IR spectrum of 3, shown in Figure 2-12 (Nujol mull), has no band corresponding to v(0H). A shoulder on the Nujol band at 3250 cm" 1 might be from this vibration. The bands assignable to v(CN) at 2310, 2285, and 2255 cm" 1 are virtually identical in frequency and intensity pattern to those observed for Z. Furthermore, the bands assignable to the C0 2 vibrations are similar for Z and Z. A weak band Is seen at 1640 with stronger bands at 1530 and 1508 cm" 1 . The first can be assigned to v asv (C0 2 ) for monodentate acetate, the latter two to bridging acetate. Well resolved bands at 680 and 690 cm" 1 correspond to <5(C0 2 ). Strong, well resolved bands corresponding to all the vibrations of non-coordinated CF3SO3" are observed at 1280, 1230, 1150, 1030, 755, 635, 575, and 515 cm" 1 . The assignment of these bands has been discussed previously and are the same as those found in I. Without a structure determination by single crystal x-ray diffraction, the differences between complexes 1, Z, and Z cannot be definitively determined. Assuming that Z and Z contain monodentate and I bi dentate acetate, it is remarkable that these two types of carboxylate coordination lead to such different colors. The exact orientation of the monodentate acetate might give some clue to this. It is clear that different anions do not lead to different properties. In addition to the Mo 2 (0 2 CR) 4 system, the Mo 2 (S 2 CR) 4 system was investigated. The facile synthesis of Mo 2 (S 2 CCH 3 )4 nas Deen reported." Unfortunately, it shows no reaction with two to four equivalents of CF3SO3H in acetonitrile. Overnight stirring of Mo 2 (S 2 CCH 3 ) 4 in neat CF3SO3H leads to recovery of the starting material along with a small amount of decomposition products. The Cf^CS-?" species binds very

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57 strongly to Mo and is not readily protonated. Mo 2 (S 2 CR) 4 complexes could be used in calorimetric studies of Lewis base binding for comparison with RC0 2 ~ complexes. Mo 2 (0 2 CCH3) 4 1S soluble in THF and a complex such as Mo 2 (S 2 CCH 2 CH 2 CH 3 )4 might be soluble in more poorly coordinating solvents suitable for use in calorimetric work. Conclusion The addition of stoichiometric amounts of strong, non-complexing acids to metal -metal bonded carboxylate dimers leads to protonation of the bridging carboxylate and generation in solution of M 2 (0 2 CR) 2 2+ species. Spectroscopic evidence confirms that the metal-metal bond remains intact and that two carboxylates are retained. The choice of solvent is crucial since it must stabilize the resulting coordi natively unsaturated cationic complex, but withstand the strong acid. Acetonitrile fits these requirements and several acetonitrile coordinated complexes of the molybdenum dimer are reported here and elsewhere. *• With rhodium it was not possible to isolate such a complex as was previously found by workers using aqueous solvents. 32,52 using strong donors such as pyridine as described here, and related ligands as reported elsewhere, 53,54 it is possible to isolate a cationic rhodium carboxylate dimer. However, these ligands may not be sufficiently labile for subsequent reactivity studies on the rhodium system. It may be that even acetonitrile coordinates too strongly to the Mo dimer, since the complex reported here does not show reactivity towards oxidative addition in contrast to various organometallic metal -metal bonded complexes. Another interesting possibility is that only organometallic dimers, containing relatively electron donating ligands

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58 and with metals in a low oxidation state, can undergo these reactions which resemble those found in organic chemistry. The metal carboxylate dimer with acetonitrile coordination differs from organometallic complexes and undergoes reactions such as Lewis base coordination and ligand substitution resembling those found in classical coordination chemistry. Nevertheless, the photochemical and photophysical properties of the complexes described here may be of interest. Analogous systems studied by Gray and co-workers such as Mo 2 4+ (aq) 59 , the metal-metal bonded diphosphite bridged Pt(II)/(III) dimers 72 and the non-metal -metal bonded isonitrile bridged Rh(I) dimers 100 have shown interesting photochemical behavior. Furthermore, the ligand substitution reactions of the metal-metal bonded complexes described here which contain accessible equatorial sites could be investigated in a quantitative manner as was previously done for systems containing only axial coordination sites. Experimental Section Operations were carried out under nitrogen using Schlenk techniques or an inert atmosphere box except as otherwise noted. Solvents were distilled before use. Trifluoromethanesulfonic acid was distilled under reduced pressure. Tetrafluoroboric acid diethyletherate (Pfaltz and Sauer) was used without further purification. Rhodium acetate was synthesized from RhC^f^O^ by literature methods. 101 Tetrakis(n-butyrato)dirhodium(II) ^ h 2^ 02^^^3^4 (°*5 9» 1#1 rnm °l ) was refluxed for 6 h in jv-butyric acid (14 mL) and ^-butyric anhydride (1 ml_). The solution was concentrated to 3 mL and cooled at -20 C overnight. The resulting crude

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59 Rh 2 (but) 4 was recrystallized from hot toluene, washed with cold hexane and dried over P 2 5 overnight to yield 0.5 g (0.9 mmol, 80%). Anal. Calcd. for RH 2 C 16 H 28 8 : C, 34.68; H, 5.09. Found: C, 34.74; H, 4.99. RlMbut)? 2 " 1 " Solution Rh 2 (but) 4 (0.328 g, 0.59 mmol) was dissolved in CH3CN (5.00 mL) to give a purple solution. To this was added CF3SO3H (0.21 mL, 2.37 mmol) leading to an immediate slight color change towards dark red. Similar solutions using CD3CN were used for the NMR work. Sulfide Complex Elemental sulfur (0.0236 g, 0.74 mmol) was suspended in THF (1 mL). To this Super-Hydride (LiBH(CH 2 CH 3 ) 3 , 1.5 mL, 1 M_ in THF, Aldrich) was added dropwise. Gas evolution was vigorous and a pale yellow solution resulted. This solution was added to the above Rh 2 (but) 2 2+ solution (2 mL, 0.092 M_ in rhodium dimer). A black precipitate formed immediately. Filtration, washing with THF and drying under vacuum at 100 C afforded 0.8 g of a black, completely insoluble solid. Anal. Calcd. for Rh 2 (0 2 CCH 2 CH 2 CH 3 ) 2 S: C, 23.32; H, 3.43; S, 7.78; C:H, 6.80. Found: C, 24.39; H, 3.70; S, 12.53; C:H, 6.81. The high sulfur analysis results from SH units and bridging polysulfide. The selenium compound was prepared in the same manner and gave an even less satisfactory elemental analysis. Pyridine Complex To the above Rh 2 (but) 2 2+ solution (3 mL, 0.03 M_ in rhodium dimer) was added pyridine (0.16 mL, 2.0 mmol). An orange color immediately resulted. Attempts to obtain a solid by cooling and evaporation yielded only an oil. Addition of NH4PF6 (0.16 g, 1.0 mmol) dissolved in water

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60 (1 mL) and subsequent evaporation and cooling led to formation of an orange-red precipitate. This procedure was not always repeatable; oils often resulted. Furthermore, IR indicated the presence of CF3SO3" as well as PF 6 ". Anal. Calcd. for [Rh2(0 2 CCH 2 CH 2 CH3) 2 (C 5 H 5 N) 4 ](PF 6 ) 2 : C, 34.09; H, 3.47; N, 5.68. Found: C, 33.99; H, 3.87; N, 6.18. The above procedure using Rh 2 (0 2 CCH 3 )4 allowed isolation of an orange solid without addition of PF g ". Anal. Calcd. for [Rh2(0 2 CCH 3 ) 2 (C 5 H 5 N) 4 ] (CF 3 S0 3 ) 2 : C, 33.27; H, 2.79; N, 5.97. Found: C, 32.73; H, 2.98; N, 6.03. Tetrakis(acetato)dimolybdenum(II) This complex was synthesized following the procedure of Martin and co-workers 77 which gives much higher yields than the original method. 102 Mo(C0) 6 (1 g, 3.8 mmol ) was added to ^o-dichlorobenzene (30 mL). Acetic acid (8 mL) and acetic anhydride (1 mL) were added and the solution refluxed overnight during which time the solution turned almost black. The heating was stopped and the solution allowed to cool without removal of the heating mantle for 8 h. Filtration and washing with ethanol followed by diethyl ether led to isolation of beautiful yellow needle crystals of Mo 2 (0 2 CCH 3 ) 4 (0.65 g, 1.5 mmol, 80%). Anal. Calcd. for Mo 2 C 8 H 12 8 : C, 22.45; H, 2.83. Found: C, 22.45; H. 2.90. Molybdenum acetate should be used as soon as possible since it decomposes even under inert atmosphere or vacuum over a period of days to green and eventually black products. Tetrakis(acetonitrile)bis(acetato)dimolybdenum( II ) BisUrifluoromethyl sulfonate), (if Mo 2 (0 2 CCH 3 )4 (0.40 g, 0.93 mmol) was suspended in acetonitrile (4 mL). It is important that the acetonitrile be degassed using freeze-

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61 pump-thaw cycles with the final vacuum broken by nitrogen, otherwise decomposition of molybdenum acetate often occurs giving a brown solution. To this was added CF3SO3H (0.17 mL, 1.92 mmol). An intensely colored purple solution formed immediately and was stirred for 10 min. Removal of solvent by pumping left a dark purple solid which was dissolved in a minimum amount of acetonitrile (~2 mL) and filtered. Addition of toluene (~3 mL) led to formation of a purple precipitate after 1 h. The solid was recrystallized from 1:1 acetonitrile/toluene and washed with toluene followed by hexane to yield 0.5 g. Anal. Calcd. for [Mo2(02CCH3) 2 (CH 3 CN) 4 ](CF3S03)2: C, 21.77; H, 2.35; N, 7.25; S, 8.30; F, 14.76; Mo, 24.84; 0, 20.72. Found: C, 21.83; H, 2.38; N, 7.56; S, 8.28; F, 15.10; Mo, 24.00; (by dlff.), 20.85. From the filtrate obtained in the above recrystallization a magenta, rather than a purple, solution is often obtained. Addition of toluene (~1 mL) to this leads to formation of a magenta precipitate, Z. Anal. Calcd. for [Mo 2 (0 2 CCH3) 2 (CH 3 CN) 4 (H 2 0)](CF3S03) 2 : C, 21.27; H, 2.55; N, 7.09; S, 8.11; F, 14.42; Mo, 24.48; 0, 22.27. Found: C, 22.00; H, 2.65; N, 7.06; S, 8.08; F, 12.7; Mo, 22.59; (by diff.), 24.92. Pentakis(acetonitrile)bis(acetato)dimolybdenum(II) Bis(trifluorohydroxyborate) , (£) Mo 2 (0 2 CCH3)4 (0.71 g, 1.66 mmol) was suspended in acetonitrile as above. To this was added (Et 2 0).HBF 4 (0.8 mL, approx. 6 mmol). An intensely colored magenta solution immediately resulted. Removal of solvent by pumping left a magenta solid which was dissolved in acetonitrile (~4 mL) and filtered. A small amount of yellow needle crystals of unreacted Mo 2 (0 2 CCH 3 ) 4 remained. When less acid is used, more unreacted molybdenum acetate is recovered. To the filtrate was

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62 added die thy! ether (5 mL) which caused rapid formation of a magenta precipitate. The compound was recrystallized from 1:1 acetonitrile/toluene and washed with toluene followed by hexane to yield 0.9 g. Anal. Calcd. for [Mo 2 (0 2 CCH 3 ) 2 (CH 2 CN) 5 ](BF30H) 2 : C, 24.55; H, 3.38; N, 10.23; F, 16.65; Mo. 28.02. Found: C, 23.79; H, 3.32; N, 10.02; F, 17.03; Mo, 26.36. Anion Exchange Complex Z (0.3 g, 0.44 mmol) and (jr-Bu)4NBF 4 (1 g, 3.0 mmol) were dissolved in acetonitrile (5 mL). To this was added toluene (5 mL) leading to formation of a magenta precipitate. After two cycles of this procedure, IR of the magenta precipitate showed a greatly diminished v(0H) band and the other bands unchanged. Anal. Calcd. for CMo 2 (0 2 CCH3) 2 {CH 2 CN) 5 ](BF 4 )2: C, 24.41; H, 3.07; N, 10.17; F, 22.06; Mo, 27.86. Found: C, 24.49; H, 3.29; N, 11.77; F, 19.16; Mo, 38.13. Molybdenum Trifluoromethyl sulfate Complex To Mo 2 (0 2 CCH 3 ) 4 (0.2 g, 0.47 mmol) was added to CF3SO3H (10 mL). The suspension was heated at 100 C with stirring for 1 h, by which time all the solid dissolved. The acid was removed by pumping leaving a red solid which presumably corresponds to the Mo 2 (03SCF3)4(CF3S03H) complex described by Abbott and co-workers. 60 Further pumping with heating at 160 C led to formation of a tan solid which is presumably the Mo 2 (03SCF 3 ) 4 complex. 60 These intermediates were not isolated or characterized. Addition of acetonitrile (10 mL) to the tan solid led to formation of a bright blue solution. Addition of toluene (~7 mL) caused formation of a blue precipitate. Elemental analysis of this compound was not satisfactory, although it appeared to be an acetonitrile

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63 coordinated Mo(II) dimer. IR spectroscopy indicated strong v(CN) and v(0H) bands as well as bands corresponding to non-coordinated CF 3 S03~. Bands corresponding to residual acetate were observed at 1615 cm" 1 (v asy (C0 2 )) and 675 cm" 1 (5(C0 2 )). A band at 415 cm" 1 may be v(Mo 2 ). Slow evaporation of the filtrate obtained above resulted in formation of purple cyrstals of what is most likely Complex J.. The IR spectrumcorresponded to I as did the elemental analysis although the precipitate may have been contaminated with species such as CMo 2 (02CCH3)(CH3CN) x ](CF 3 S03)3 giving higher IS, IF, and 20. Anal. Calcd. for [Mo 2 (0 2 CCH 3 ) 2 (CH3CN)4](CF 3 S03) 2 : See above. Found: C, 21.33; H, 2.10; N, 6.23; S, 9.48; F, 15.48; Mo, 21.47; (by diff.), 23.91. Tetrakis(dithioacetato)dimolybdenum(II) This complex was synthesized following the procedure of Cotton and co-workers." CS 2 (0.77 mL, 0.013 mol) was added to CH 3 MgBr (5.63 mmol, as THF solution, Aldrich) in THF (10 mL). A pale yellow solution resulted which was stirred for 45 min. To this was added Mo 2 (0 2 CCH 3 ) 4 (0.60 g, 1.4 mmol). A dark red-brown solution formed immediately. After stirring 15 min, methanol (20 mL, N 2 purged) was added leading to formation of an orange-red precipitate. Filtration and washing with methanol afforded 0.44 g (561). This complex, in contrast to Mo 2 (0 2 CCH3)4, is indefinitely stable and can be recrystallized in air from THF. Anal. Calcd. for Mo 2 CgH 12 S 8 : C, 17.26, H, 2.17; S, 46.09; Mo, 34.48. Found: C, 17.46; H, 2.43; S, 45.93; Mo (by diff.), 34.18.

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64 Experimental Methods Elemental analyses were performed by the Microanalytical Laboratory of the University of Illinois, Urbana, IL, or by Galbraith Laboratories, Knoxville, TN. Ultraviolet-visible spectra were recorded on a Cary 14 spectrometer using matched quartz 1.0 cm cells. Infrared spectra were recorded on a Perkin-Elmer 599B instrument using KBr cells. Fourier transform 13 C{ 1 H} NMR spectra were recorded on a Varian Associates XL100 FT spectrometer operating at 25.2 MHz. The 13 C chemical shifts were measured with respect to the nitrile carbon of CD3CN (118.2 ppm relative to TMS). Proton NMR spectra were recorded using a Varian HR-220 NMR spectrometer equipped with a Nicolet Technology Corp. TT-220 Fourier transform accessory. Precision-grade tubes were used for the 220 MHz spectra so as to reduce spinning sidebands. The *H chemical shifts were measured with respect to internal TMS.

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CHAPTER III THE REACTIONS OF RHODIUM TRIFLUOROACETATE WITH VARIOUS LEWIS BASES Introduction As discussed in the previous chapter, it is possible to effect removal of the removal of the bridging carboxylate ligands in metal carboxylate dimers by reaction with stoichiometric amounts of strong non-complexing acids. This reaction allows Lewis bases and potentially, substrates for catalytic processes, to coordinate to equatorial as well as axial sites on the metal carboxylate dimer. An alternative approach to achieving this type of coordination is to use a carboxylate ligand with an electron-withdrawing group. This type of carboxylate would donate less electron density to the metal dimer subunit rendering the carboxylates more prone to displacement and the metals more susceptible to attack by Lewis bases. The effect of an electron-withdrawing carboxylate ligand, CF ? CF ? CF 2 Cn 2 " (hfb), has been quantitatively shown in earlier studies by Drago and co-workers. 25 The enthalpies of axial Lewis base adduct formation by Rh 2 (hfb) 4 versus Rl^fbut)^ were examined. The hfb Hgand greatly enhanced the Lewis acidity of the rhodium system towards electrostatic interactions and increased the acidity towards covalent interactions by almost as much. In addition to this greater reactivity towards Lewis bases, the metal fluorocarboxylate dimers have much greater solubility in non-coordinating organic solvents than do the corresponding alkylcarboxylate systems. This facilitates study of their solution chemistry. For example, since "02(Q2CCH3)4 i s 65

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66 completely insoluble in organic solvents and Rl^C^CCf^^ only sparingly so, a direct comparison of their solution properties is impossible. Use of the trifluoroacetate ligand makes such a study possible. The interest in a comparison of the solution chemistry of the rhodium and molybdenum carboxylate dimers stems from the large difference in their metal -metal interactions. As discussed earlier, the d^ Mo system has a strong, short, relatively unpolarizable quadruple bond. The d 14 Rh system has a longer, weaker, more polarizable single bond. Furthermore, since rhodium is more electronegative than molybdenum, the Rh-Rh molecular orbitals are overall lower in energy than the Mo-Mo bond orbitals. The result of all this is that in the rhodium dimer, the frontier MO's are the -n* HOMO and the a* LUMO while for molybdenum those metal -metal orbitals are vacant and high in energy while the 6 HOMO and the 6* LUMO are of main importance. This implies that the covalent interaction with axial bases should be strong for the rhodium carboxylate dimer and much less for molybdenum. This has been quantitatively confirmed by Drago and co-workers" in a comparison of the enthalpies of axial Lewis base adduct formation by Rh 2 (hfb) 4 versus Mo 2 (hfb) 4 . In addition, a ir-backbonding interaction was observed between the filled n* orbitals on the rhodium dimer and vacant u* orbitals on bases such as pyridine and acetonitrile. This interaction was not seen for the molybdenum dimer as expected from the MO scheme described above. Another implication of the MO scheme is that given the opportunity, Lewis bases should coordinate more readily to equatorial than to axial sites on molybdenum, while this would be less likely for rhodium. This type of reactivity has indeed been found with Mo when the

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67 trifluoroacetate dimer is used, since this ligand allows access to the equatorial sites. Girolami and co-workers 33 * 103 synthesized and characterized a number of adducts of molybdenum trifluoroacetate with phosphines and other Lewis bases. They found that Mo 2 (0 2 CCF 3 ) 4 not only formed adducts in which there was coordination along the Mo-Mo axis, but also some in which there was coordination in sites perpendicular to the Mo-Mo axis. All of these complexes were of general formula Mo 2 (0 2 CCF 3 ) 4 L 2 . Those with axial coordination were called Class I adducts, those with equatorial coordination, Class II. Only Lewis bases that are sterically small and good a-donors were reported to give isolable equatorial adducts. Examples are trimethylphosphine (PMe 3 ), triethylphosphine (PEt 3 ), and dimethylphenylphosphine (PMe 2 Ph). Andersen estimated steric bulk by cone angle and a-donor strength by v(C0) values as described by Tolman. 104 The assignment of complexes into the two classes was made on the basis of 19 F and 31 P MMR spectroscopy which showed different signals resulting from phosphines in different coordination sites. Infrared spectroscopy also showed different C0 2 stretches for the two types of CF 3 C0 2 " ligands. However some controversy exists over the assignment of IR and NMR peaks for these complexes. Cotton and Lay 105 also prepared phosphine complexes of Mo 2 (0 2 CCF 3 ) 4 and obtained spectra at variance with those of Girolami and Andersen and co-workers. 33 » 103 In addition, these two groups reported different structures for the complex Mo 2 (0 2 CCF 3 ) 4 (PMePh 2 ) 2 . Cotton and Lay 105 obtained a Class II (equatorial) adduct and Girolami and Andersen 103 a Class I (axial) adduct. Slight variations in synthetic procedure led to this difference since PMePh 2 is a phosphine intermediate on the size and donor strength scales.

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68 Other solution studies 106,107 have been performed on Mo 2 (0 2 CCF 3 ) 4 as well as a number of crystallographic studies. 96,103,104,108 j n contrast, the analogous rhodium system has not been as extensively investigated, particularly in solution. 5 * 6 Crystal structures have been determined for Rh 2 (0 2 CCF 3 ) 4 L2 where L=(CH 3 ) 2 S0 2 , 109 (CD 3 ) 2 $0, 110 PPh 3 , ni P(0Ph) 3 , in CH 3 CH 2 0H, 112 H 2 113 , 2,2,6,6-tetramethylpiperidinolyl-1-oxy 113 and (CH 3 ) 2 S0. 114 In all these cases, as in those with alkylcarboxylates, only Class I (axial) adducts were formed. However, a systematic study of the Lewis base reactivitiy of Rh 2 (0 2 CCF 3 ) 4 had not been performed. For the reasons discussed above, that is ligand effects and metal-metal bond effects, such a study was performed and is described below. Furthermore, it was hoped that this study would shed some light on the discrepancies in the interpretation of the spectroscopy properties of the molybdenum systems described above. Results and Discussion The 19 F NMR spectrum of Rh 2 (0 2 CCF 3 ) 4 was obtained in both nitromethane-^ and toluene-jig. All of the 19 F NMR data are summarized in Table 3-1. A sharp singlet was found in both room and low temperatures in both solvents which corresponds to the CF 3 groups on the four equivalent bridging trifluoroacetates. Nitromethane and toluene are very weak bases and thus should coordinate weakly, if at all, to the rhodium dimer. What is significant is that these signals occurred in the -73 to -75 ppm range (relative to internal CFC1 3 ). The signals were somewhat solvent and temperature dependent. Earlier workers 33,106,107 have assigned peaks in the -72 to -74 ppm range to monodentate CF 3 C0 2 " and peaks at -70 ppm to bi dentate CF 3 C0 2 " in Mo 2 (0 2 CCF 3 ) 4 complexes.

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69 The IR spectrum of Rh 2 (0 2 CCF 3 ) 4 shows a single v a$ y (C0 2 ) band in solution and in the solid state. All the major IR data are summarized in Table 3-II and the IR spectrum of Rh 2 (0 2 CCF 3 ) 4 is shown in Figure 31. However, this stretch occurs at a higher frequency (1650 to 1670 cm" 1 ) than v asy (C0 2 ) for bidentate CF 3 C0 2 " in Mo 2 (0 2 CCF 3 ) 4 complexes (~1600 cm" 1 ). Thus, there is no direct correspondence between the location of the 19 F NMR and IR signals for the rhodium and molybdenum systems. Nevertheless, monoand bidentate CF 3 C0 2 " give significantly different spectra in the rhodium complexes as will be shown below. Oxygen Donors Emerald green Rh 2 (0 2 CCF 3 ) 4 forms blue 2:1 complexes with oxygen donor bases such as tetrahydrofuran (THF), dimethylsulfoxide (DMSO), N,N-dimethylformamide (DMF), and trimethylphosphine oxide (0PMe 3 ). The THF adduct is quite stable but heating at 100 C under vacuum effects quantitative removal of THF to give base-free starting material. The 19 F NMR and IR spectra are characteristic of a Class I adduct. A singlet is observed in the 19 F NMR spectrum at -75 ppm and v asy (C0 2 ) occurs at about 1660 cm" 1 in both the solid adduct and in solution. The IR spectrum of Rh 2 (0 2 CCF 3 ) 4 (THF) 2 is shown in Figure 3-2. These results are similar to those for the free Lewis acid, Rh 2 (0 2 CCF 3 ) 4 . The crystal structure of Rh 2 (0 2 CCF 3 ) 4 (DMS0) 2 showed a Class I adduct, with 0-bonded DMSO. 109 There was nothing to indicate otherwise in solution since a single peak was observed in the 19 F NMR spectrum. Both axial S-coordination and equatorial 0or S-bonding would most likely lead to additional signals. The equivalence of the solution and solid state structures was confirmed by IR, which showed a single v asy(C02) band at 1662 cm-1 (Nujol mull) and at 1655 cm-1 (CHC13

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70 Table 3-1. 19 F NMR Data for Rh 2 (0 2 CCF 2 ) 4 Complexes 9 Complex

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71 Table 3-1. continued 1:1:2:1

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72 Table 3-II. Infrared Data for Rh 2 (0 2 CCF 3 ) 4 Complexes Complex

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73 30N»lllWSOTbl %

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74 MO 3DN»i.ilwSN»bi 1.

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75 solution) in agreement with the assignment as an axial adduct. The IR spectrum of Rh 2 (0 2 CCF 3 ) 4 (DMS0) 2 is shown in Figure 3-3. The DMSO bands are also of interest. In the solid state, two doublets were observed at 1005 (s) and 995 cm" 1 (s) and at 945 (s) and 937 cm" 1 (s). In CHC1 3 solution these occurred at 1020 (m) and 1000 cm" 1 (m) and at 948 (m) and 931 cm" 1 (w). Free DMSO in CHC1 3 solution has v(S0) at 1055 cm" 1 and a <5(CH 3 ) band at 946 cm. Oxygen coordination lowers v(S0) and sulfur coordination raises the frequency of this band. No bands were observed for Rh 2 (0 2 CCF 3 ) 4 in the 1050 to 1150 cm" 1 region where S-coordinated DMSO would obsorb. It should be noted that Rh 2 (0 2 CCH 3 ) 4 binds DMSO via the sulfur atom (v(S0) at -1090 cm" 1 ), 62 ' 115 further evidence of ligand effects on Lewis acidity of the rhodium carboxylate dimer. 115 Cotton and Felthouse 114 have reported bands for this complex at 943 and 939 cm" 1 (Nujol mull) which they assigned to v(S0) of 0-coordinated DMSO, while the higher frequency doublet was not mentioned. Their assignment was based on earlier work by Cotton and co-workers, 116 who proposed that the band at ~950 cm" 1 in DMSO complexes corresponds to v(S0) while that at ~1000 cm" 1 to 6(CH 3 ). However, Drago and Meek 117 reversed this assignment since the band at -1000 cm" 1 is more sensitive to the type of metal coordinated. The IR spectrum of Rh 2 (0 2 CCF 3 ) 4 (DMS0-d fi ) 2 was obtained here in the hope of clarifying the assignment of these two bands. The IR spectrum of this deuterated complex was identical to the original complex with respect to the bands related to CF 3 C0 2 ". Unfortunately, in the area of interest, there was also little change. Fairly strong, broad bands were seen at 1020 and 950 cm" 1 , with the latter more intense. A new band occurred at 825 cm" 1 which may

PAGE 82

76 30NVlll«SNVbl t.

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77 correspond to a 6(CD 3 ) band at 811 cm -1 in free DMSO-dg. Thus, a definitive assignment of these two bands cannot be made. When DMF was added to Rh 2 (0 2 CCF 3 ) 4 , a purple color initially appeared, but the solution then rapidly turned blue. The 19 F NMR spectrum of this complex showed a single peak at -74 ppm at room and low temperature. The IR spectrum was also characteristic of a Class I adduct (v asy (C0 2 ) at 1662 cm" 1 in CHC1 3 solution). In solution the amide v(C0) could be resolved from the v as y (C0 2 ) band (this was not possible in the solid) and was shifted from 1685 cm" 1 in free DMF (CC1 4 solution) to 1643 cm" 1 , indicative of O-coordination. 118 The IR spectrum of Rh 2 (0 2 CCF 3 ) 2 (DMF) 2 is shown in Figure 3-4. Addition of excess DMF did not change the 19 F NMR spectrum. Rh 2 (0 2 CCF 3 ) 4 was indefinitely stable in excess DMF. This is in contrast to DMSO. Kitchens and Bear 119 reported that addition of excess DMSO to Rh 2 (0 2 CCF 3 ) 4 led to formation of a yellow decomposition product, which was also observed here. This is probably due to eventual sulfur coordination. The reaction of Rh 2 (0 2 CCF 3 ) 4 with 10 equivalents of 0PMe 3 in 1:1 toluene/dichloromethane afforded a blue solid contaminated with crystalline, white, unreacted 0PMe 3 . The IR spectrum of this blue solid (Nujol mull) showed a strong, broad v as y (C0 2 ) band at 1650 cm" 1 and a band assignable to 6(C0 2 ) at 725 cm" 1 . A very strong, broad band at -1200 cm" 1 included v asy (CF 3 ) and v(P0). Thus, a Class I adduct is most likely formed as with the above oxygen donors. This is to be expected since using the E and C parameters, 27 " 29 0PMe 3 is a Lewis base roughly comparable to DMSO. Due to limited availability of 0PMe 3 , further studies were not performed.

PAGE 84

73 oj $ 3DN»lilHSNff«l%

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79 Nitrogen Donors A variety of nitrogen donor bases were reacted with Rh 2 (0 2 CCF 3 ) 4 with varying results. Isolable analytically pure complexes could not be obtained with piperidine and N-methyl imidazole (N-Helm). When these bases were added to toluene solutions of Rh 2 (0 2 CCF 3 ) 4 , a red color immediately resulted indicative of nitrogen base coordination. However, after several hours the solutions turned yellow and evaporation gave an intractable yellow tar in both cases. This indicates dimer decomposition forming Rh(I) and/or Rh(III) as was described with DMSO. Some 19 F NMR studies were performed on solutions of Rh 2 (0 2 CCF 3 ) 4 with these bases. A freshly prepared solution containing 10:1 NMeIm/Rh 2 (0 2 CCF 3 ) 4 showed single peaks at -74.6 ppm at 27 C and at -74.1 ppm at -61 C in CDC1 3 . Thus, a 2:1 Class I adduct was initially present and remained for a few hours. The spectrum became complex as the yellow color appeared. A freshly prepared solution of 10:1 piperidine/Rh 2 (0 2 CCF 3 ) 4 showed a major signal at -74.2 ppm and smaller peaks at -68.4 and -80.3 ppm indicating that rapid decomposition occurred. The major peak is presumably from axial ly coordinated dimer, the other two from decomposition products. It might be possible to prepare adducts with these two bases if only stoichiometric amounts were used. By contrast, use of excess triethylamine led to facile isolation of Rh 2 (0 2 CCF 3 ) 4 (Et 3 N) 2 . This complex had a singlet in the 19 F NMR spectrum, even with excess base, at -75 ppm at both room and low temperatures. This complex had an IR spectrum characteristic of bi dentate CF 3 C0 2 " in solution and in the solid state. The latter is shown in Figure 3-5.

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33Wi.xiftsmu>.'.

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81 With pyridine an interesting product was formed that is intermediate between the Class I adduct formed with Et 3 N and the decomposition products formed with piperidine and N-Melm. This complex is a stable red 4:1 adduct containing both axially (Class I) and equatorially (Class II) coordinated Lewis base and thus may be considered a new type of complex which will be called Class III. These three structures are shown in Figure 3-6. Only one of six isomers of Class II and III adducts are depicted. This behavior can be contrasted with the reaction of pyridine with Mo 2 (0 2 CCF 3 ) 4 96 and Rh 2 (0 2 CCH 3 ) 4 120 in which Class I adducts form. A precedent for this Class III compound exists. Webb and Dong 106 have performed solution studies on Mo2(0 2 CCF 3 )4 with varying amounts of pyridine and found 19 F NMR signals in the places predicted 33 for monoand bidentate CF 3 C0 2 " (-70.5, -75.3 ppm, respectively) and IR adsorption bands at 1713, 1617, and 1611 cm" 1 corresponding to v asy (C0 2 ) of monoand bidentate CF 3 C0 2 ". Only one MoMo stretch was observed in the Raman spectrum (343 cm" 1 ) indicating the presence of only one centrosymmetric isomer. The 19 F NMR spectrum of Rh 2 (0 2 CCF 3 ) 4 (pyr) 4 prepared here showed signals at -74.1 and -74.9 ppm in toluene-dg and at -74.7 and -75.4 ppm in CDC1 3 , both at -60 C. In both solvents the peak ratio was 1:1. Here monoand bidentate CF 3 C0 2 " are separated by less than 1 ppm, whereas in the molybdenum work they were separated by about 3 ppm. However, there are examples of monoand bidentate CF 3 C0 2 " with all resonances in the -74 to -76 ppm range. King and Kapoor 1 ^ have synthesized a large number of complexes such as (C 5 H 5 )Fe(C0) 2 (CF 3 C0 2 ) which has monodentate CF 3 C0 2 " and gives a 19 F NMR signal at -74.2 ppm in CDC1 3 . Creswell and co-workers 122 have prepared compounds such as 0s(C0)(PPh 3 ) 2 (CF 3 C0 2 ) 2 which has two 19 F NMR signals

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Figure 3-6. Possible structures for Lewis base adducts of Rh^tCLCCF.,). . Only one of the six isomers of both Class II and Class III adducts are shown.

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83 / CF 3 C :Rh\ \ . CF. .Rh V/° i CF, n o CF, CF, C-CF, .0 L Rh \ C i CF, m o CF 3 C-CF, / L' / Rh / \/ X C^ l CF,

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84 at -75.44 and -75.22 ppm in CDC1 3 assigned to monoand bidentate CF 3 C02~. Thus, not only do the locations of resonances in the rhodium dimer differ from molybdenum, but the chemical shift differences between CF3C02~'s in different environments do not correspond. The IR data for the pyridine complex are also in agreement with the Class III formulation. Absorption bands for v as y (C0 2 ) were observed at 1705 and 1642 cm' 1 (CHCI3 solution) and at 1705 and 1655 cm" 1 (Nujol mull) corresponding to monoand bidentate CF 3 C0 2 ~. Another characteristc IR band is S(C0 2 ) which occurs at 740 cm" 1 in Rh 2 (0 2 CCF 3 ) 4 . Free pyridine has bands at 740 and 693 cm" 1 . In the pyridine complex bands were observed at 760, 750, 738, 725, and 690 cm" 1 . It is likely that at least two of the first three bands correspond to 6(C0 2 ) for monoand bidentate CF3C0 2 ". The other absorption bands could be assigned to either pyridine or Rh 2 (0 2 CCF 3 ) 4 and the latter showed little change from the base-free rhodium dimer. The IR spectrum of Rh 2 (0 2 CCF 3 ) 4 (pyr) 4 is shown in Figure 3-7. Addition of excess pyridine, up to 20 equivalents, caused no change in the 19 F NMR spectrum. Two sharp signals of equal intensity were still observed at -74.7 and -75.3 ppm in the toluene-^ at 27 C. By contrast, in the molybdenum case 106 the two peaks coalecse at 30 C, indicating fast exchange. However, the slower exchange observed here is not unusual since in the M(C0)(PPh3) 2 (CF 3 C0 2 ) 2 complexes studied by Creswell and co-workers, 122 separate resonances corresponding to monoand bidentate CF 3 C0 2 ~ were observed at room temperature. As a final note, it should be mentioned that the synthesis of "Rh 2 (0 2 CCF3) 4 (pyr) 2 " was reported 123 a number of years ago, but the complex characterized only by C and H analysis. This procedure was repeated here and a compound was isolated that was most likely a mixture

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85 4O 33N\n.±msN*aj.*

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86 of pyridine adducts. This was the result of using ethanol as solvent rather than toluene, used here to obtain the pure 4:1 adduct. (See Experimental Section.) It is difficult to draw general conclusions from the above results based on criteria such as steric size, a-donor, and ir-acceptor abilities of the bases. Triethylamine was the strongest a-donor used; it is bulky and has no ir-acceptor ability. It formed axial adducts. Similarly, qui nucli dine (a Lewis base very comparable to Et 3 N) formed a Class I (axial) adduct with Mo 2 (0 2 CCF 3 )4 although its size and a-basicity would favor Class II. Pyridine, a base with less a-donor ability than Et 3 N, has ^-acceptor ability and formed a stable Class III (axial and equatorial) adduct. N-methylimidazole, a stronger a-donor but a poorer ^-acceptor than pyridine caused dimer cleavage although via a Class I adduct. Piperidine is a strong a-donor, but reactivity is most likely due to the protonic nature of the base. A final nitrogen donor base, acetonitrile, was used. It is a weak a-donor, but a ir-acceptor. Bear and co-workers 40 were unable to isolate a stable acetonitrile adduct of Rh 2 (0 2 CCH 3 ) 4 . These workers claimed that evaporation of a CH 3 CN solution of rhodium acetate gave only starting material. 40 It was found here, by contrast, that stable purple Rh 2 (02CCH 3 ) 4 (CH 3 CN) 2 was formed upon evaporation of an acetonitrile solution of the rhodium dimer. (See Experimental Section.) However, although Rh 2 (0 2 CCF 3 ) 4 (CH 3 CN) 2 can be similarly prepared, it readily loses acetonitrile and is hydrated to a blue-green material upon standing in air. The freshly prepared complex 19 F NMR showed a singlet at -74.1 ppm and a doublet at -74.5 ppm in CDC1 3 at -60 C. The area ratios were 2:1:1. Addition of excess CH 3 CN (-10 equivalents) led to

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87 signals at -74.7 and -75.4 ppm in equal area ratios. IR data snowed Class I bridging CF 3 C0 2 " bands. The solution structure of Rh 2 (0 2 CCF 3 ) 4 in the presence of acetonitrile is thus uncertain. However, the weaker coordination of CH3CN to the fluorocarboxylate as opposed to the alkylcarboxylate rhodium dimer is to be expected. This is due to irbackbonding interactions as discussed earlier and shown by Drago and coworkers. ^"^ Carbon Donors Reactions with the isoelectronic carbon donors _t-butylisonitrile and carbon monoxide were investigated. The reaction of t-BuNC with a variety of metal carboxylate dimers was studied by Girolami and Andersen. 76 They found that only monomeric complexes were obtained with Mo 2 (0 2 CCH 3 ) 4 , Mo 2 (0 2 CCF 4 ) 4 , Re 2 (0 2 CCH 3 ) 4 Cl 2 , and Ru 2 (0 2 CCH 3 ) 4 Cl. However, with Rh 2 (0 2 CCH 3 ) 4 only the Class I adduct Rh 2 (0 2 CCH 3 ) 4 U-BuNC) 2 was produced. It was of interest to determine what effect replacement of CH 3 C0 2 " by CF 3 C0 2 ~ would have in the dirhodium system. It was found here that reaction of Rh 2 (0 3 CCF 3 ) 4 with fr-BuNC (-10 equivalents) led to isolation of an air stable orange-brown complex best formulated as Rh 2 (0 2 CCF 3 ) 4 U-BuNC) 4 . Unfortunately, in contrast to the pyridine complex which had the same stoichiometry and easily interpretable NMR and IR spectra, _t-BuNC gave complicated results, as will be discussed below. This is most likely due to the presence in solution of a variety of species including more than one isomer of a Class III adduct and possibly monomeric species. Although fr-BuNC and pyridine have similar o-donor properties, the isonitrile is a better ir-acceptor and somehow this may lead to a variety of isomers of comparable stability. The 19 F NMR spectrum of this compound showed six peaks occurring between -73.0

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88 and -74.6 ppm in CDCI3 at -60 C. The X H NMR spectrum showed signals at 1.61 and 1.43 ppm in CDCI3 at -50 C. All NMR data for nuclei other than 19 F are summarized in Table 3-III. At room temperature the peaks occurred at 1.60 and 1.40 ppm, but instead of a 3:2 area ratio the ratio was 2:1. Thus, at different temperatures different isomers predominated, but specific assignment of the signals was not possible. The IR spectrum of this complex showed bands assignable to v (C0 2 ) at 1693 and 1658 cm' 1 in CHCI3 solution and at 1720 and 1660 cm" 1 in the solid state. A single strong 5(C0 2 ) band was observed at 725-730 cm" 1 (Nujol mull). There may have been more than one 6(C0 2 ) band, but resolution was not possible. Very strong absorption bands corresponding to v(NC) occurred at 2234 and 2167 cm" 1 (CHC1 3 solution) and at 2212 and 2132 cm" 1 (Nujol mull) as opposed to 2127 cm" 1 for free ^t-BuNC. This shift to higher frequency is expected for end-on isonitrile coordination. The other absorption bands were assignable to either tBuNC or Rh 2 (0 2 CCF 3 ) 4 . The IR spectrum of Rh 2 (0 2 CCF 3 ) 4 (t r BuNC) 4 is shown in Figure 3-8. Although the solution and solid state IR spectra were qualitatively the same, the fairly large difference for a given band such as v asy (C0 2 ) or v(NC) may indicate a different structure in solution. Further studies with this complex would be needed to unequivocally determine its structure. However, it seems clear that a Class I adduct is not formed in contrast to Rh 2 (0 2 CCH 3 ) 4 . 76 It is not surprising that a 4:1 complex is formed since _t-BuNC is a good a-donor and an excellent ir-acceptor. As found with pyridine, the CF 3 C0 2 " ligand was needed to allow coordination to the equatorial sites. The complex Rh 2 (0 2 CCH 3 ) 4 (C0) 2 has been isolated and structurally characterized by x-ray crystallography. 124 The v(C0) band occurs at

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89 +*l 3DN*±1II«ISN»H1 •

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90 Table 3-1 II . X H and 31 P{ 1 H} NMR Data for Rh 2 (0 2 CR) 4 Complexes a c , , Coupling TempComplex Nucleus Chemical Shift (ppm) Constant erature "" ~ [Hzj (%)_ Rh 2 (0 2 CCF 3 ) 4 (t-BuNC) 4 ! H X ' 61 S ' lA3 s (3:2) -50 27 Rh 2 (0 2 CCF 3 ) 4 (PPh 3 ) 2 100 MHz +32.81 d J=166.0 27 J= 92.7 100 MHz, CC1 4 solution +34.78 d J=153.0 27 J= 37 J=104.5 1 J=164.2 300 MHz +34.25 d of d h= 11.65 -50 ij= 47.4 fj= 33.8 2 J= 91.9 J= 11.7 (outer peaks) 15.1 (inner peaks) Rh 2 (0 2 CCF 3 ) 4 (P(c-Hx) 3 ) 2 31 P Jj=165.2 27 300 MHz Nucleus

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91 Table 3III. continued Complex Rh 2 (0 2 CCF 3 ) 4 (P(OPh) 3 ) 2 100 MHz 300 MHz 300 MHz 300 MHz Rh 2 (0 2 CCH 2 CH 2 CH 3 ) 4 (PPh 3 ) 2 Rh(0 2 CCF 3 ) 2 (P(0Me) 3 ) 3 (empircal formula) Nucleus

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92 2105 cm" 1 , below that of free CO (2143 cm' 1 ), indicative of irbackbonding. The mechanisn of this was discussed earlier. Rh 2 (0 2 CCF 3 ) 4 also forms a 2:1 adduct with CO although the CO is much more weakly bound. Indeed, it was not possible to isolate a CO adduct of Rh 2 (0 2 CCF 3 ) 4 , CO was too readily lost. However, other workers 125 reported isolation of this adduct as a light brown solid. The IR spectrum of this complex prepared as a KBr pellet under 1 atm of CO showed v(C0) at 2150 cm" 1 and v &sy (C0 2 ) at 1644 cm" 1 . 125 It was found here that bubbling CO through a solution of Rh 2 (0 2 CCF 3 ) 4 in CH 2 C1 2 led to appearance of a purplish blue color, resembling that formed with similar weak donors such as acetonitrile. The brown solid is surprising since this resembles complexes formed with strong donors such as phosphines and phosphites. The IR spectrum of this CH 2 C1 2 solution showed bands assignable to v(C0) at 2160 cm' 1 (m) and to v (C0 2 ) at 1660 (s) and 1760 cm' 1 (m). The former v asy (C0 2 ) band may correspond to CO free Rh 2 (0 2 CCF 3 ) 4 . This positive shift 1n v(C0) from free CO was taken as evidence of no Tr-backbonding in Rh 2 (0 2 CCF 3 ) 4 . 125 However, this is not a definitive argument. If there were no Tr-backbonding it is unlikely that CO would coordinate at all. As shown by Drago, 26 BF 3 , which using the E and C analysis, 27 " 29 is a stronger Lewis acid than Rh 2 (0 2 CCF 3 ) 4 , but does not bind CO since BF 3 cannot provide any -nbackdonation. The perturbation from o effects could cause an increase in v(C0) in Rh 2 (0 2 CCF 3 ) 4 (C0) 2 comparable to the decrease cause by n effects since both effects are small.

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93 Phosphorus Donors As mentioned previously, a large number of phosphine derivatives of Mo 2 (0 2 CCF 3 ) 4 have been reported. 33 ' 105 However, phosphites do not form adducts with Mo 2 (0 2 CCF 3 ) 4 presumably since they are not strong enough adonors. They do form axial complexes with Rh 2 (0 2 CCH 3 ) 4 since in contrast to the molybdenum system there is a significant ir-backbonding stabilization. It was of interest to extend this work to Rh 2 (0 2 CCF 3 ) 4 since only triphenylphosphine and triphenyl phosphite adducts of Rh 2 (0 2 CCF 3 ) 4 have been reported. 111 These complexes were studied by xray crystallography and found to be Class I adducts. However, their solution properties have not been investigated. The phosphorus donors used here were dimethylphenylphosphine (PMe 2 Ph), triphenylphosphine (PPh 3 ), tricyclohexylphosphine (P(c-Hx) 3 ), triphenyl phosphite (P(0Ph) 3 ) and trimethyl phosphite (P(0Me) 3 ). PMe 2 Ph forms a Class II adduct with Mo 2 (0 2 CCF 3 ) 4 due to its small size and strong basicity. 33 Thus, it would be a good candidate to form a Class III adduct with Rh 2 (0 2 CCF 3 ) 4 . Unfortunately, the reaction of Rh 2 (0 2 CCF 3 ) 4 with four equivalents of PMe 2 Ph yielded only an intractable orange oil indicating dimer decomposition. PPh 3 lies far outside the size and basicity range described by Andersen 33 for Class II adduct formation. Furthermore, in the solid state Rh 2 (0 2 CCF 3 ) 4 (PPh 3 ) 2 is a typical Class I adduct. 111 Thus, this complex would be unlikely to show unusual solution behavior and one would expect a simple 19 F NMR spectrum such as that found for the THF adduct. This was not the case. A freshly prepared solution of Rh 2 (0 2 CCF 3 ) 4 (PPh 3 ) 2 showed sharp 19 F NMR resonances at -74.4, -74.9, and -75.9 ppm in CDC1 3 at 27 c in area ratios of 1:1:2. There was also a

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94 small peak at -75.3 ppm. At -50 C there were still three sharp, major peaks only in an area ratio of 1:1:1.3. That there was little change over this temperature range indicates that the same species were present, although perhaps in differing amounts. Assignment of these peaks is difficult, presumably they corresond to monoand bidentate CF 3 C0 2 ~. However, the situation differs from that observed with the pyridine adduct and from the solution studies on Mo 2 (0 2 CCF 3 ) 4 with pyridine. 106 In those cases there were two peaks representing one Class III isomer with 1:1 monoand bidentate CF 3 C0 2 . The more complex spectrum observed here could be the result of a mixture of isomers containing axially and equatorial ly coordinated PPh 3 . That there would be anything other than axial coordination in solution is surprising. However, it is possible that in solution the dimer may dissociate to some extent. The molecular weight of Rh 2 (0 2 CCF 3 ) 4 (PPh 3 ) 2 in CH 2 C1 2 was found to be 590, half the expected value of 1183. This value could result from the existence of Rh2(0 2 CCF3) 4 (PPh 3 ) and free PPh 3 in solution. However, if these were the major solution species, then only one 19 F NMR resonance would be observed, although perhaps weak signals corresponding to 2:1 and base free species would be seen with similar chemical shifts. Furthermore, a singlet corresponding to free PPh 3 would be observed in the 31 P{ 1 H} NMR spectrum or a single broad peak coresponding to fast exchange between free and coordinated PPh 3 . Such behavior was found by Boyar and Robinson 6 who very recently reported the 31 P{ 1 H} NMR spectrum of Rti 2 (u 2 CCH 3 ) 4 (P(0Me) 3 )2 in dichloromethane-^ solution. These workers 126 observed a single broad peak at room temperature. The 31 P{ 1 H} NMR spectrum of Rh 2 (but) 4 (PPh 3 ) 2 in CDC1 3 at room temperature was obtained here and it also exhibited a single broad

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95 resonance. Thus, in both phosphine and phosphite coordinated rhodium alkylcarboxylate dimers rapid exchange occurs at room temperature between free and coordinated phosphorus ligands. However, Boyar and Robinson 1 " found that at 213 K exchange was slow enough to give an informative spectrum. Signals were observed that were assigned to Rh 2 (0 2 CCH) 3 ) 4 (P(0Me 3 ) 2 , Rh 2 (0 2 CCH 3 ) 4 (P(0Me) 3 ) and free P(0Me) 3 . The 1:1 adduct showed an AMX pattern and the 2:1 an AA'XX' pattern (A, A', M= 103 Rh; X, X'= 31 P). The AMX system was analyzed by a first-order approach, the AA'XX' by iterative computer simulation. Presumably, effective spin polarization occurs through the Rh-Rh bond (100% 103 Rh, 1=1/2) that allows extensive rhodium-phosphorus and phosphorusphosphorus coupling. By contrast, in the Mo 2 (0 2 CCF 3 ) 4 systems 33 ' 105 no molybdenum-phosphorus (25% Mo, 1=5/2) or phosphorus-phosphorus coupling was seen for either Class I or Class II adducts. However, the 31 P{ 1 H} NMR spectra obtained here for Rh 2 (0 3 CCF 3 ) 4 (PPh3) 2 were far more complex than those for the alkylcarboxylate systems. Using a 100 MHz instrument, two strong, sharp signals were observed in both CDC1 3 and CC1 4 solution. These signals had the same chemical shifts and coupling constants in the two solvents, indicating no effect of a hydrogen bonding solvent. A third, very weak signal was also observed and appeared to be a triplet in CC1 4 . However, use of a 300 MHz instrument which gave better resolution and required fewer scans revealed the true nature of the splitting. In addition, the 300 MHz spectrum was obtained at -50 C on a solution that had been frozen in an acetone/C0 2 bath immediately after preparation. When this precaution was not taken, the NMR spectra, both 19 F and 31 P{ 1 H}, showed some signs of decomposition since additional, very weak signals were observed. Three 31 P signals

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96 were observed for this freshly frozen solution at -50 C. Two consisted of a doublet of doublets, and the third was a doublet of quartets. These signals were in an area ratio of 3:1:3. Since ^3=ZJ for the second (weak) doublet of doublets, it closely resembled a triplet. True coupling constants cannot easily be obtained for spectra this complex. The two doublets of doublets could be either AMX or AA'XX' systems and the other signal could be something more complex, such as ABMX (or ABXY). Without definite knowledge of the solution species, it would be of little utility to attempt a computer simulation of the spectrum. Even 1f a set of coupling constants could be determined that would fit an observed signal, it might not be a unique solution. It should be noted that the descriptions "doublet of doublets" and "doublet of quartets" only roughly describe the observed signals since the splittings and intensities do not exactly correspond to what would be expected for first-order AMX, AMX 2 , A 3 MX, or ABMX systems. The X portion of both AMX and AMX 2 systems would show four peaks in 1:1:1:1 area ratios. The X portion of both A 3 MX and ABMX systems would have a doublet of four peaks in 1:3:3:1 area ratios for the former and 1:1:1:1 for the latter system. In the A 3 MX sysem, the four peaks would be equally separated, in the ABMX system that would be true only if J BX =2J AX* Tne latter system more accurately describes the observed signal since the peaks were roughly equal in inetnsity and were not equally spaced. The inner two peaks were nearer the outer peaks than to each other. Nevertheless, the 31 P{ 1 H} NMR spectrum of Rh 2 (0 2 CCF 3 ) 4 (PPh 3 ) 2 does allow some proposals to be made as to the solution behavior of this complex through a process of elimination. Although any intercon version between species was slow enough to give

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97 well resolved 19 F and 31 P{ 1 H} NMR spectra at room as well as low temperature, no signal for free PPh 3 was seen. This indicates that all PPI13 present was coordinated to rhodium and most likely no 1:1 adducts were present, in contrast to the results with the acetate and butyrate dimers. This is not surprising, since as will be shown below, Rh 2 (0 2 CCF3) 4 has a great affinity for phosphorus donors and of course is a much stronger Lewis acid than rhodium alkylcarboxylate dimers. Possible solution species are therefore those in which the rhodium dimer remains intact, but existing as more than one isomer, and monomeric rhodium complexes. A simple cleavage of the Rh-Rh bond would give Rh(0 2 CCF3) 2 (PPh3) 2 . Rhodium(II) complexes are uncommon, although species such as Rh(P(c-Hx) 3 ) 2 Cl 2 are known. 127 These Rh(II) monomers are EPR active as would be expected for a square planar d 7 complex. However, a Rh(II) monomer does not exist in the system described here since the NMR spectra showed no evidence of paramagnetic species (no line broadening or large isotropic shifts) and Rh(0 2 CCF 3 ) 4 (PPh 3 ) 2 gave no EPR signal in CH 2 C1 2 solution at 77 K. The possibility of species containing one Rh and one PPh 3 such as weakly associated [Rh(0 2 CCF 3 ) 2 (PPh 3 )]" and the Rh(III) cation of the same formulation can also be ruled out. Species containing one Rh and one PPh 3 would necessarily give AX signals. Although the 100 MHz 31 P{ 1 H} NMR spectrum gave support to this, the higher field spectrum clearly showed more complex splitting patterns and no simple doublets were observed. It is possible that in solution such complexes as Rh(0 2 CCF 3 )3 and Rh(0 2 CCF 3 )(PPh3) 2 are P resent « Tne latter complex has been previously reported. 128 The reaction of RhCl(PPh 3 ) 3 with CF 3 C0 2 H was reported to yield a yellow, very air-sensitive complex characterized only by

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98 elemental analysis and IR which showed bi dentate CF 3 C0 2 ~ ( v aS y( C0 2^ at 1660 cm" 1 ). 128 Thus, Rh(0 2 CCF 3 )(PPh 3 )2 is most likely a square planar, symmetrical complex. It would be an AX 2 system since it is difficult to imagine that the two PPh 3 ligands would be chemically or magnetically inequivalent. Furthermore, the solution would be expected to change color, which was not seen. Although the solution molecular weight favored monomeric species, the lower than expected value may have been the result of decomposition over the time period required for the procedure mainly due to oxidation. Previous workers^»128,129 also often obtained lower than expected molecular weights for analogous monomeric rhodium complexes. This leaves dimeric 2:1 adducts as possible solution species. Both axial (Class I) and equatorial (Class II) adducts as well as species containing both axially and equatorially coordinated PPh 3 (Class III) could exist. There are a total of nine possible isomers, one Class I, six Class II 33 and two Class III. These last two have either both PPh 3 ligands coordinated to one Rh, one axially the other equatorially, or one PPh 3 coordinated to each Rh, one axially the other equatorially. The relative amounts of these isomers is uncertain, but the presence of several of them would give rise to a variety of 19 F NMR signals as well as the complex 31 P{ 1 H} spectrum. The Class I and Class II isomers would most likely be AA'XX' systems since the two phosphine ligands are symmetry related. However, the Class III (axial and equatorial) isomers would probably be ABMX systems (A, B= 103 Rh; M, X= 31 P). This allows a tentative interpretation of the 31 P{ 1 H} NMR spectrum of Rh 2 (0 2 CCF 3 ) 4 (PR 3 ) 2 complexes which will be made after discussion of the other phosphorus donor adducts. As a final note, the coupling constants seen here are comparable to those

PAGE 105

99 previously reported for rhodium-phosphorus coupling in monomeric Rh(I) and Rh(III) complexes such as traru-RhCl (C0)(PPH 3 ) 2 for which J Rn . p =129 Hz 130 and mer-Rh(PMePhg) 3 C1 3 for which JR n _pi=36.0 Hz and J Rh-P2 =114,5 Hz Of course, the values obtained here (see Table 3III) are only first order approximations and do not accurately represent the true rhodium-phosphorus (or P-P and Rh-Rh) coupling constants. The IR spectrum of Rh 2 (0 2 CCF 3 ) 4 (PPh 3 ) 2 differed between solution and the solid state. In a Nujol mull a single v asy (C0 2 ) band was observed at 1665 cm" 1 consistent with the bridging carboxylate structure. The other absorption bands were assignable to PPho or Rh 2 (0 2 CCF 3 ) 4 . The IR spectrum is shown in Figure 3-9. However, in CHC1 3 solution v asv (C0 2 ) bands were observed at 1717 cm" 1 and at 1658 and 1648 cm" 1 . Thus, in solution some monodentate CF 3 C0 2 " coordination occurs which would be expected as a result of equatorial PPh 3 coordination in dimeric complexes. Some preliminary studies of the reaction of excess PPh 3 with Rh 2 (0 2 CCF 3 ) 4 were undertaken. Details are given in the Experimental Section. Two main products were isolated, an orange compound which was most likely the known 129 complex Rh(0 2 CCF 3 )(PPh 3 ) 3 and a yellow compound best formulated as Rh(0 2 CCF 3 ) 3 (PPh 3 ) 2 . The latter complex has not been previously reported, although yellow Rh(PR 3 ) 3 Cl 3 (where R=Me, Et, etc., but not Ph) is well known. 130,131 In ac | |i t i on> a sma n am ount of an orange, fairly insoluble complex was obtained which was best formulated as Rh 2 (0 2 CCF 3 ) 4 (PPh 3 ) 4 . It is important that air be excluded from the reactin or else triphenylphosphine oxide is produced. This was isolated as a crystalline compound, but it can also coordinate and complicate analysis of the products. Detailed investigation of these monomeric

PAGE 106

IOC (O i— o c\j

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101 rhodium complexes is beyond the scope of this work. It appears that given enough phosphine, cleavage of the Rh-Rh bond is possible, even by a bulky and relatively poor a-donor such as PPh 3 . Furthermore, there is strong evidence that in solution the Class I solid state structure does not remain intact. Both Class II and III complexes are also present and over time, monomeric Rh(I) and Rh(III) species may result. Interesting results were also found with tricyclohexylphosphine. The hope was that if any Rh-Rh bond cleavage occurred, Rh(II) species might be stabilized since, as described above, the only known Rh(II) phosphine complexes are those with P(c-Hx) 3 . 127 This ligand was reacted in excess (-10 equivalents) with Rh 2 (0 2 CCH 3 ) 4 in toluene and with Rh 2 (0 2 CCF 3 ) 4 in toluene and dichloromethane. In all cases, complexes of stiochiometry Rh 2 (0 2 CR) 4 (P(c-Hz) 3 ) 2 were isolated. The rhodium trifluoroacetate complex was brown and that for acetate was orange, as was found for the PPh 3 adducts. The IR spectrum of Rh 2 (0 2 CCF 3 ) 4 (P(cHx) 3 ) 2 is shown in Figure 3-10. However, use of 1:1 toluene/ acetonitrile and heating led to a yellow solution from which a pale yellow, presumably Rh(I) and/or Rh(III) complex was isolated. These results may be explained by the very large steric size of P(c-Hx) 3 (cone angle=170"). Although this phosphine is a good a-donor, its large size makes Rh-Rh bond cleavage reactions more difficult. The solution behavior of Rh 2 (0 2 CCF 3 ) 4 (P(c-Hx) 3 ) 2 greatly resembled that of the PPh 3 adduct. Complex 19 F and 31 P{ 1 H} NMR spectra were observed indicating the Class I structure was not maintained in solution. There was no evidence of Rh(II) species being present in solution since no EPR signal was observed for either the acetate or fluoroacetate adducts in toluene at both room temperature and 77 K. For Rh 2 (0 2 CCF 3 ) 4 (P(c-Hx) 3 ) 2 , four

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102 30NVlllWSNVyi %

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103 signals were observed in the ^F NMR spectrum over a 3 ppm range, indicating monoand bidentate CF 3 C0 2 ~. The 31 P{ 1 H} NMR spectrum showed three signals, two doublets of doublets and a doublet of quartets, in a 2:1:2 area ratio. The chemical shifts and estimated coupling constants for these signals were very similar to those seen for Rh 2 (0 2 CCF3) 4 (PPh3) 2 (see Table 3-III), although the chemical shift similarity may be coincidental since 31 P chemical shifts vary greatly. No signal for free P(c-Hx) 3 was seen. With the P(c-Hx) 3 adduct, it was not necessary to freeze the solution to obtain good NMR spectra. The greater stability of the tricyclohexylphosphine complex is also suggested by the value of 1060 obtained for the molecular weight in CH 2 C1 2 solution. This was lower than the expected value of 1219, but is much closer to the dimer molecular weight than found with PPh 3 . As with the PPh 3 adduct, an accurate analysis of this spectrum is not possible, however the signals observed most likely resulted from isomers with axial and equatorial P(c-Hx) 3 coordination. The solution IR spectrum supported this, since bands for v asy (C0 2 ) were seen at 1710 and 1660 cm" 1 indicating monoand bidentate CF 3 C0 2 " in solution in contrast to the solid state IR spectrum. With P(0Ph) 3 less unusual results were obtained. Triphenyl phosphite is a poor o-donor although it has better -rr-acceptor properties than PPh 3 . No complex of this ligand with Mo 2 (0 2 CCF 3 ) 4 exists and Rh 2 (0 2 CCF 3 ) 4 (P(0Ph) 3 ) 2 m as well as Rh 2 (0 2 CCH 3 ) 4 (P(0Ph) 3 ) 2 132 are typical Class I adducts in the solid state. Thus, it would seem very unlikely that this Rh 2 (0 2 CCF 3 ) 4 complex would show unusual solution behavior. This was found to be the case with one important proviso. Even in a sealed tube under a nitrogen atmostphere, a CHC1 3 solution of

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104 Rh 2 (02CCF3 )4(P(0Ph ) 3 )2 changed color over a period of days from orangeyellow to emerald green, characteristic of base free Rh 2 (0 2 CCF 3 ) 4 Addition of excess P(0Ph) 3 to a sample of this green solution restored the original orange color. Apparently, ligand oxidation occurred, similar to the 0PPh 3 formation discussed above. The mechanism for this phosphite decomposition is unknown. Presumably, if the reaction proceeds stoichiometrically only trace amounts of 2 or H 2 would be needed to effect complete oxidation with apparently little, if any, dimer decomposition. It should be noted that Kawamura and co-workers 133 have reported the frozen solution EPR spectrum of Rh 2 (0 2 CCF3) 4 (P(0Ph)3) 2 + generated from the neutral dimer by y-ray irradiation. In addition to the expected signal, a weak signal was detected but not discussed. It is possible that this arose from Rh 2 (0 2 CCF3) 4 + or some other species in which the phosphite had decomposed. The solid state IR spectrum showed a single v asy (C0 2 ) at 1670 cm" 1 and a fresh CHCI3 solution showed this band at 1665 cm" 1 . There were no differences between the two and all bands were assignable to P(0Ph) 3 and Rh 2 (0 2 CCF 3 ) 4 . The IR spectrum of Rh 2 (0 2 CCF 3 ) 4 (P(0Ph) 3 ) 2 is shown in Figure 3-11. P(0Ph)3 is too poor a a-donor and too good a ir-acceptor to cause other than axial coordination. The Class I solution structure of the P(0Ph) 3 adduct was confirmed with NMR. A freshly prepared solution of this complex showed a single sharp 19 F NMR resonance at -75.1 ppm in CDC13 at room temperature. However, by the time the low temperature spectrum was obtained, decomposition had occurred giving two major signals and several minor ones in the -74.5 to -75.5 ppm range. This rapid decomposition made 31 P NMR studies difficult. Using a 100 MHz instrument, which required a long data acquisition time and large NMR

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105 o o BONVilinSNVBl

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106 tubes (12 mm), the 31 P{ 1 H} NMR spectra that were obtained showed several signals presumably corresponding to coordinated phosphite and a sharp signal assignable to triphenyl phosphate. The 0P(0Ph) 3 signal increased over time. However, using a 300 MHz instrument (using 5 mm NMR tubes), and freezing the solution immediately after preparation prevented phosphate formation. The 31 P{ 1 H} NMR spectrum of Rh 2 (0 2 CCF 3 ) 4 (P(0Ph)3)2 obtained in this manner showed only one signal. At -50 C it was a doublet of doublets, but upon warming, the center two peaks collapsed so that by C, a 1:2:1 triplet was seen. This indicates that the second, weak doublet of doublets observed in the 31 P{ 1 H} NMR spectra of the PPh 3 and P(c-Hz) 3 complexes was most likely due to the Class I axial adduct. At higher temperatures the Class I adduct is an A 2 X 2 system (A= 103 Rh; X= 31 P) so that a triplet is seen. This suggests that the triplet seen in the room temperature spectrum of the PPh 3 adduct in CCl^ was probably real, and not an artifact of poor resolution. The separation between the outer peaks is 2J AX . At low temperatures, the Class I adduct is an AA'XX' system. The separation of the outer peaks is then |J AX + J AX , | and the separation of the inner peaks is either E((J AA . J XX .) 2 + (J AX J AX ') 2 ) 1/2 ± l J AA' J XX'f] or C((J AA . + J XX ,)2 + J AX " J AX ,)2)1/2 * l J AA' + JXX'HAn AA '*X' system has a total of ten lines, however very often they are not all observed since many are very broad and/or of low intensity. As A' becomes equivalent to A and X' to X, the inner peak separation becomes zero in all four possible combinations. All that can be determined here is that the rhodium-rhodium and phosphorus-phosphorus couplings are small compared to the rhodium-phosphorus coupling. Two signals are left to be accounted for in the PPh 3 and P(c-Hx) 3 spectra, the doublet of doublets

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107 and the doublets of quartets. These two signals were in equal area ratios in both spectra, suggesting they arose from two chemically different phosphine ligands on the same molecule. Using a first-order analysis, these signals correspond to an ABMX system (A, B= 103 Rh; M, X= 31 P). The doublet of quartets would be due to an axially coordinated phosphine coupled strongly to one rhodium ( JAX =lj Rh-P^ 90 Hz ^ and less strongly to the other rhodium (JBX =2j Rh-P^ 25 Hz ^ and tne otner phosphine (J MX Jp_ P =12 Hz), which would be equatorially coordinated. The doublets would then be due to the equatorially coordinated phosphine coupled strongly to one rhodium (JBM =lj Rh-P^ 165 Hz ^ and weakly to the other phosphine ( J MX = 3 J p _ p =12 Hz, as above) with the coupling to the other rhodium not observable (J AM = 2 J Rn _p=0). It is not unreasonable to assume that the axially coordinated phosphine would have a larger 2 JR n -p value than the equatorial phosphine, since the axial phosphine 1s along the Rh-Rh bond, allowing strong through-bond coupling. In the Class I P(0Ph 3 ) adduct and the signals assigned to the Class I complex in the phosphine spectra, JR n .p almost equals ^Rn-p. The above discussion fits the data reasonably well, although there are several difficulties. It is not clear why the Class I AA'XX' system becomes an A 2 X 2 system at higher temperature, this may have to do with easier rotation. Also, the 19 F NMR spectra are more complex than would be expected in the phosphine complexes, but this may be due to slight changes in CF 3 C0 2 ~ coordination that do not affect the 31 P signals. Finally, a higher order computer-assisted analysis is needed to fully analyze the 31 P{ 1 H} spectra and possibly obtain accurate coupling constants.

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108 Quite different results were obtained with P(0Me)3 although Rh 2 (0 2 CCH 3 ) 4 (P(0Me) 3 ) 2 has been reported and is a Class I adduct. 124 With this very small phosphorus donor the Rh-Rh bond was cleaved much more readily than with PPh 3 . Reaction of excess (10 equivalents) P(0Me) 3 with Rh2(0 2 CCF 3 ) 4 in toluene led to isolation of a pale yellow, air-sensitive, hygroscopic compound best formulated as Rh(0 2 CCF 3 ) 2 (P(0Me)3)3. Elemental analysis and molecular weight determination in CH 2 C1 2 supported this formula (see Experimental Section). However, since no EPR signal was observed for the complex in CH 2 C1 2 at 77 K and it gave a normal, diamagnetic NMR spectrum, monomeric Rh(II) was not present. Rather, the complex is most likely a mixture of equal amounts of Rh( I ) and Rh(III) species. The pale yellow color is characteristic of Rh(I) and Rh(II) phosphite complexes such as HRh(P(0Et) 3 ) 3 Cl 2 , 134 HRh(P(0Et) 3 ) 4 , 134 Rh(0P(0Me) 2 )(P(0Me) 3 ) 4 135 and [Rh(P(0Me) 3 ) 5 ] BPh 4 . 136 The 19 F NMR spectrum of the reaction product showed two sharp resonances in a 3:2 area ratio at both room temperature and at -50 C. The simplicity of the 19 F NMR spectrum is surprising since a variety of complexes could be present. One would expect an area ratio of 1:3 if the species present were Rh(0 2 CCF 3 )(P(0Me) 3 ) 3 and Rh(0 2 CCF 3 ) 3 (P(0Me) 3 ) 3 . The signals would then rise from monodentate CF 3 C0 2 " in either the square planar Rh(I) or octahedral Rh(III) complex. The observed area ratio most likely arises from different isomers. The principal species likely to be present in this case are [Rh(P(0Me) 3 ) 4 ] + and [Rh(0 2 CCF 3 ) 4 (P(0Me) 3 ) 2 r. These would also be square planar Rh(I) and octahedral Rh(II) complexes, respectively. The latter compound would have only monodentate CF 3 C0 2 ~ and could exist as both cis or trans

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109 isomers. These isomers could be present in virtually any ratio, such as 3:2, since steric constraints are minimal with this small posphite. Interconversion between the two isomers would not be expected and this accounts for the temperature independence of the 19 F NMR spectrum. As shown by Muetterties, 137 octahedral low oxidation state transition metal phosphite complexes are generally stereochemical^ rigid. The 31 P{ 1 H} NMR spectrum of the P(0Me) 3 reaction product was more complex than would be expected for the two ions given above. Multiplets were observed at +58 and +20 ppm and a smaller triplet at -72 ppm relative to external phosphoric acid in CDC1 3 at room temperature. The 31 P{ 1 H} NMR spectrum is shown in Figure 3-12. Since the 19 F NMR spectrum is simple, the complexity of the 31 P{ 1 H} NMR spectrum must arise from species without CF 3 C0 2 ~ ligands. In addition to [Rh(P(0Me) 3 ) 4 ] + , other Rh(I) phosphite complexes could exist in solution. In contrast to the octahedral complexes, lower coordination number phosphite complexes are generally stereochemical^ nonrigid. 134 " 137 Compounds such as Rh(0P(0Me) ? )(P(0Me)o) /1 135 a nd [Rh(P(0Me) 3 ) 5 ] + 136 have complex, fluxional 31 P{ 1 H} NMR spectra which nevertheless have been thoroughly analyzed. However, uncertainty about the exact products of the P(0Me) 3 reaction studied here and lack of variable temperature spectra makes such an analysis difficult. Most likely, the observed room temperature 31 P{ 1 H} NMR spectrum arises from a variety of Rh(I) phosphite complexes that are not stereochemical ly rigid combined with the two isomers of the Rh(III) trifluoroacetate phosphite complex. As a final note, the complex Rh(0P(0Me) 2 )(P(0Me) 3 ) 4 was originally reported as Rh 2 (P(0Me) 3 ) 8 . Subsequent work led to the new formulation but indicated that Rh 2 (P(0Me) 3 ) 8 could indeed be

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Q. r-H -h cn o CO

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Ill

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112 135 prepared. D It is possible that 0P(0Me) 2 is present in the complex reported here, although it is not supported by the analytical data. The IR spectrum of the P(0Me) 3 reaction product confirmed that only mondentate CF 3 C0 2 ~ was present. No bands were observed between 1600 and 1700 cm" 1 , only a single broad band at 1710 cm" 1 in CHCI3 solution and at 1725 cm" 1 in the solid state. Although further work is needed to characterize the reaction products, it is clear that P(0Me) 3 readily cleaves the Rh-Rh bond causing disproportionate into monomeric Rh(I) and Rh(III) complexes. This is in contrast to Rh 2 (0 2 CCH 3 ) 4 in which the acetates do not allow phosphite access to the equatorial coordination sites and dimer break up does not result. It appears that the action of phosphorus donors on Rh 2 (0 2 CCF 3 ) 4 leads to unusual reactivity. The normal air stable compounds PPh 3 and P(0Ph) 3 are easily oxidized. The rhodium dimer itself, which remains intact when reacted with strong a-donors such as Et 3 N or pyridine, the latter also having Tr-acceptor abilities, cannot stand up to reaction with phosphorus donors of comparable a-donor strength that are often sterically bulky. However, the failure of P(0Ph) 3 to effect Rh-Rh bond cleavage indicates that there are limits on donor ability beyond which only Class I adducts are formed. Nevertheless, the reason for the strong overall affinity of rhodium for phosphorus donors is not clear. Criteria such as ir-backbonding and certainly a-donor strength and ligand size are not enough to fully classify the Lewis base reactivity of Rh 2 (0 2 CCF 3 ) 4 .

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113 Conclusion The reactivity of Rh 2 (0 2 CCF 3 ) 4 with Lewis bases shows significant differences from the analogous Mo 2 (0 2 CCF 3 ) 4 and Rh 2 (0 2 CCH 3 ) 4 systems. Differences in the frontier MO's between the rhodium and molybdenum dimers can be used to explain the propensity for rhodium as opposed to molybdenum to form Class I adducts. For example, the poor a-donors but good ir-acceptors P(0Ph) 3 and CO form Class I adducts with Rh 2 (0 2 CCF 3 ) 4 and Rh 2 (0 2 CCH 3 ) 4 , but not with any molybdenum dimer. This is due to the strong ir-backbonding interaction between the filled tt* orbital s on Rh-Rh and empty ir* orbitals on these ligands. This interaction cannot occur in Mo-Mo which has empty it* orbitals. The a-bonding interaction between the ligand lone pair and the empty a* orbital on the metal carboxylate dimers is also important, but with weaker a-donors such as P(0Ph) 3 and CO it is not enough to allow isolation of molybdenum adducts with these ligands. Differences in electronegativity between CF 3 C0 2 ~ and CH 3 C0 2 " can be used to explain the ability to isolate Class III (4:1, axial and equatorial) adducts of Rh 2 (0 2 CCF 3 ) 4 with pyridine and _t-BuNC, but only Class I adducts of Rh 2 (0 2 CCH 3 ) 4 with these Lewis bases. The electronwithdrawing CF 3 group causes CF 3 C0 2 " to coordinate less strongly to the rhodium dimer than does acetate. This allows Lewis bases access to equatorial sites as well as the always available axial sites. When the Lewis base has the right combination of a-donor and u-acceptor properties, such as in pyridine and ^t-BuNC, the base is not labile, it binds permanently and Class III adducts can be easily isolated. When phosphorus donors are used, except when they are very poor crdonors (P(0Ph) 3 ), cleavage of the Rh-Rh bond can occur to give monomeric Rh(I) and Rh(III) products. The reason for this instability of the

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114 usually robust Rh-Rh bond towards phosphorus donors is not certain. Clearly, the CF 3 C02~ ligand is necessary to allow the P donor to attack at a kinetically viable rate. Then, perhaps, the thermodynamic stability of Rh(I) and Rh(III) phosphine and phosphite complexes drives these reactions to completion. Further work could involve the structural characterization of some of the complexes mentioned here. This would fully confirm the Class III structure. Another spectroscopic method that could prove useful is 103 Rh NMR, which has very recently been applied to Rh(II) dimers with bridging hydroxypyridine ligands. 138 This would assist in confirming the solution structure of many of the species described above, whether they are Class I, Class II or monomeric species. In addition, in 1:1 Lewis base adducts, the chemical shift of and coupling between the non-equivalent Rh nuclei could be used to understand electron polarization within the Rh-Rh bond as a result of coordination of a single base. It is also important that kinetic studies should be undertaken on the reactions of phosphorus donors with metal carboxylate dimers and analogous metal-metal bonded and monomeric complexes. This might shed some light on the unusual reactivity described here. These sorts of studies have been performed extensively on transition metal carbonyl complexes, often containing metal -metal bonds 139 and perhaps should be extended to other systems. Experimental Section All solvents were of reagent grade and were distilled from the appropriate drying agents before use. Bases were purified following established procedure. 140 Pyridine, N-methyl imidazole, piperidine, trithylamine, N,N-dimethylformamide, dimethyl sulfoxide, tetrahydrofuran,

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115 and acetonitrile were distilled from the appropriate drying agents before use. Trimethyl phosphite, triphenyl phosphite, dimethylphenylphosphine and _t-butylisonitrile were used as purchased without further purification. However, their purity was checked by IR. Triphenylphosphine was recrystallized from toluene before use. Operations were performed under nitrogen except as otherwise noted. Rhodium acetate was synthesized from RhCl 3 (H 2 0) 3 by literature methods. 101 Tetrakis(trifluororacetato)dirhodium(II) This compound was synthesized using a modification of the procedure of Cotton and Norman 108 for Mo 2 (0 2 CCF 3 ) 4 . Rh 2 (0 2 CCH 3 ) 4 (0.5 g, 1.13 mmol) was suspended in CF 3 C0 2 H (10 mL) and (CF 3 C0) 2 (1 mL). The mixture was refluxed for 2 h. The solvent was then removed by pumping and the procedure repeated with fresh acid. After removal of solvent the crude product, which was often a bluish green color, was recrystallized from 1:1 dichloromethane/toluene to give the bright green Rh 2 (0 2 CCF 3 ) 4 (0.60 g, 0.91 mmol, 81?). Anal. Calcd. for Rh 2 C 8 F 12 8 : C, 14.61; H, none; F, 34.65. Found: C, 14.65; H, none; F, 34.12. The compound decomposes under nitrogen in a sealed tube at 265 C. Bi s ( tetrahydrof uran ) tetraki s ( tri f 1 uoroacetato )dirhodi um( 1 1 ) Rh 2 (0 2 CCF 3 ) 4 (0.10 g, 0.15 mmol) was dissolved in THF (2 mL) to give a dark blue solution. Removal of solvent by pumping and recrystallization from boiling hexane in air afforded medium blue Rh 2 (0 2 CCF 3 ) 4 (THF) 2 (0.11 g, 0.14 mmol, 91%). Anal. Calcd. for Rh 2 C 16 H 16 F 12°10 : C » 23 92 ; H » 2.01; F, 28.39. Found: C, 23.61; H, 2.02; F, 28.22. The adduct loses THF quantitatively upon heating at 100

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116 C under vacuum. This makes it a convenient form for storing Rh 2 (0 2 CCF 3 ) 4 since the base-frea rhodium dimer is rather hygroscopic. Also the above procedure of THF adduct formation and hexane recrystallization is a convenient method for obtaining pure Rh 2 (0 2 CCF 3 ) 4 . Bi s ( di methy 1 sul f oxi de ) tetraki s ( tri f 1 uoroacetato )di rhodi um( 1 1 ) This compound was synthesized following the procedure of Cotton and Felthouse. 114 Rh 2 (0 2 CCF 3 ) 4 (0.050 g, 0.076 mmol) was dissolved in 1:1 benzene/chloroform (5 mL). DMS0 (0.2 mL) was added and a blue solution resulted. The solvent was removed by pumping and the resultant solid was washed twice each with toluene and hexane leaving a blue microcrystalline solid (0.059 g, 0.07 mmol, 95%). Anal. Calcd. for Rh 2 C 12 H 12 F 12 S 2 10 : C, 17.70; H, 1.49; F, 28.00; S, 7.88. Found: C, 19.05; H, 1.88; F, 28.32; S, 8.00. Bi s ( N, N-dimethylformamide) tetraki s(trifluoroaceta to )dirhodium( I U Rh 2 (0 2 CCF 3 ) 4 (0.030 g, 0.046 mmol) was dissolved in 1:1 dichloromethane/toluene (5 mL) in air. Addition of DMF (0.2 mL) led to an initial purple color which rapidly changed to blue. Evaporation led to formation of dark blue platelike crystals of Rh 2 (0 2 CCF 3 ) 4 (DMF) 2 (0.033 g, 0.041 mmol, 892). Anal. Calcd. for Rh 2 C 14 H 14 N 2 F 12 10 : C, 21.30; H, 1.76; N, 3.48; F, 28.35. Found: C, 21.30; H, 1.82; N, 3.30; F, 28.02. Bi s ( triethy 1 ami ne ) tetraki s ( tri f 1 uoroacetato )di rhodi um( I 1 ) Rh 2 (0 2 CCF 3 ) 4 (0.050 g, 0.076 mol) was dissolved in toluene (4 mL). Addition of Et 3 N (0.1 mL) caused an immediate color change to red. Concentration to 1 mL led to formation of a red precipitate.

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117 Filtration and washing with hexane afforded red, microcrystalline Rh 2 (02CCF 3 ) 4 (Et3N)2 (0.050 g, 0.058 mmol, 762). Anal. Calcd. for Rh 2 C 20 H 30 N 2 F 12 8 : C, 27.92; H, 3.52; N, 3.26; F, 26.50. Found: C, 28.33; H, 3.56; N, 3.12; F, 25.60. Tetrakis(pyridine)tetrakis(trifluoroacetato)dirhodium(II) Rh 2 (0 2 CCF 3 ) 4 (0.10 g, 0.15 mmol) was dissolved in toluene (5 ml_). Addition of 2 mL of a 10:1 toluene/pyridine solution caused an immediate color change to red. Concentration to 2 mL and cooling led to formation of a red precipitate. Filtration and washing with hexane afforded pinkish red microcrystalline Rh 2 (0 2 CCF 3 ) 4 (pyr) 4 (0.13 g, 0.13 mmol, 88%). Anal. Calcd. for Rh 2 C 28 H 20 N 4 F 12 8 : C, 34.52; H, 2.07; N, 5.75; F, 23.40. Found: C, 34.98; H, 2.14; N, 5.64; F, 22.22. The compound melts in a sealed tube under nitrogen at 169-170 C. The synthesis of Rh 2 (0 2 CCF 3 ) 4 (pyr) 2 was attempted by following the procedure of Stephenson and co-workers. 123 Rh 2 (0 2 CCF 3 ) 4 (0.03 g, 0.045 mmol) was dissolved in cold ethanol (2 mL). To this pyridine (-0.2 mL) was added dropwise. A red solution resulted and with further cooling a red precipitate formed. Filtration and washing with hexane afforded a red solid (0.025 g). Anal. Calcd. for Rh2 c 18 H 10 N 2 F 12°8 : C, 26.49; H, 1.24; N, 3.43. Found: C, 30.67; H, 2.05; N, 4.16. IR (CHC1 3 solution) v asy (C0 2 ), 1705 (m), 1688 (w), 1660 (s), 1650 cm -1 (m). 19 F NMR (CDC1 3 , 27 C) -75.0 (complex m), -75.8 (5). The reaction is most likely a mixture of 2:1, 3:1, and 4:1 pyridine adducts of Rh 2 (0 2 CCF 3 ) 4 . Tetraki s ( tert-buty 1 i soni tri 1 e ) tetrak i s ( tri f 1 uoroacetato )di rhodi um( 1 1 ) Rh 2 (0 2 CCF 3 ) 4 (0.10 g, 0.15 mmol) was dissolved in toluene (4 mL). To this solution was added _t-BuNC (0.10 mL, 0.89 mmol, Strem

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118 Chemicals). An orange solution immediately resulted. After 1 h, the solution was concentrated to 1 mL. Filtration of the resulting precipitate and washing with hexane afforded an orange-brown solid (0.12 g, 0.12 mmol, 80?). Anal. Calcd. for Rh 2 C 28 H 36 N 4 F 12 8 : C, 33.92; H, 3.66; N, 5.65; F, 23.00. Found: C, 33.67, H, 3.80; N, 5.39; F, 23.24. Bis(acetonitrile)tetrakis(trifluoracetato)dirhodium(II) Rh 2 (0 2 CCF 3 ) 4 (0.10 g, 0.15 mmol) was dissolved in air in acetronile (2 mL) to give a purple solution. Addition of water (3 mL) led to immediate precipitation of a purple solid. Filtration and drying under vacuum afforded Rh 2 (0 2 CCF 3 ) 4 (CH 3 CN 2 ) (0.09 g, 0.12 mmol, 80?). Anal. Calcd. for Rh 2 C 12 H 6 N 2 F 12 8 : C, 1945; H, 0.82; N, 3.78; F, 30.77. Found C, 25.18; H, 1.95; N, 3.79; F, 22.65. Synthesis of this compound using only organic solvents failed to give any purer a product. Furthermore, the compound is not indefinitely stable. It loses CH 3 CN even under inert atmosphere. In air, CH 3 CN is replaced over a period of 1 h by H 2 to give a blue-green solid. By contrast, evaporation in air of an acetonitrile solution of Rh 2 (0 2 CCH 3 ) 4 afforded a stable purple solid that is most likely the 2:1 acetonitrile adduct. Anal. Calcd. for Rh 2 C 12 H 18 N 2 8 : C, 27.50; H, 3.46; N, 5.34. Found: C, 27.54; H, 3.53; N, 5.02. Bi s ( tri phenyl phosphi ne ) tetraki s ( tri f 1 uoroacetato )di rhodi um( 1 1 ) This complex was synthesized following the procedure of Cotton and co-workers. 111 Rh 2 (0 3 CCF 3 ) 4 (0.050 g, 0.076 mmol) was dissolved in methanol (5 mL). Triphenylphosphine (0.040 g, 0.15 mmol) was dissolved in hot methanol (~5 mL). This solution was added to the blue Rh 2 (0 2 CCF 3 ) 4 (CH 3 0H) 2 solution to give an immediate dark brown color.

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119 The solution quickly became colorless and purplish brown needle crystals were deposited. Filtration and washing with methanol afforded 0.085 g (0.075 mmol, 942). Anal. Calcd. for Rh 2 C 44 H 30 P 2 F 12 8 : C, 44.66; H, 2.56; P, 5.23. Found: C, 44.18; H, 2.67; P, 5.18. Orange Rh 2 (but) 4 (PPh 3 ) 2 was synthesized in the same manner in 822 yield. Anal. Calcd. for Rh 2 C 52 H 58 P 2 8 : C, 57.89; H, 5.43; P, 5.74. Found: C, 58.07; H, 5.40; P, 5.88. Bis (tri phenyl phosphite)tetrakis(trifluoroacetato)dirhodium(II) Rh 2 (0 2 CCF 3 ) 4 (0.178 g, 0.286 mmol) was dissolved in methanol (10 mL). Triphenyl phosphite (0.150 mL, 0.572 mmol) was added dropwise to give a red-brown solution. The solution quickly became colorless and an orange-brown microcrystalline solid precipitated. Filtration, washing with methanol and drying under vaccum afforded 0.32 g (0.25 mmol, 87.5%). Anal. Calcd. for Rh 2 C 44 H 30 P 2 F 12 14 : C, 41.31; H, 2.35; P, 4.84. Found: C, 40.93; H, 2.25; P, 4.28. Bi s ( tri cycl ohexy 1 phosphi ne ) tetraki s ( tri f 1 uoroacetato )di rhodi um( 1 1 ) Rh 2 (0 2 CCF 3 ) 4 (0.053 g, 0.080 mmol) was dissolved in toluene (2.5 mL). Tricyclohexylphosphine (0.045 g, 0.160 mmol, Aldrich) was dissolved in toluene (2 mL) and added dropwise to the Rh 2 (0 2 CCF 3 ) 4 solution. A dark brown color immediately resulted. The solvent was removed by pumping to give a brown solid. Recrystallization from hot toluene afforded 0.08 g (0.07 mmol, 87.5%). Anal. Calcd. for Rh 2 C 44 H 66 P 2 F 12°8 : C » 43 -36; H, 5.46; P, 5.08. Found: C, 45.53; H, 5.49; P, 5.23. Use of the above procedure with 10 equivalents of P(cHx) 3 in CH 2 C1 2 solvent gave the same product as shown by IR and elemental analysis. Use of the above procedure with Rh 2 (0 2 CCH 3 ) 4 and 10

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120 equivalents of P(c-Hx) 3 and recrystallization from heptane afforded orange-brown Rh 2 (0 2 CCH 3 ) 4 (P(c-Hx) 3 ) 2 . Anal. Calcd. for Rh 2 C 44 H 78 P 2 8 : C, 52.70; H, 7.84; P, 6.18. Found: C, 52.54; H, 7.82; P, 5.00. Reaction of Rh ? (0 ? CCF 7 ) A with excess PPh-^ Rh 2 (0 2 CCF 3 ) 4 (0.162 g, 0.246 mmol ) was dissolved in toluene (5 idL). Triphenylphosphine (0.640 g, 2.44 mmol) was dissolved in toluene (3 mL) and added dropwise to the Rh 2 (0 2 CCF 3 ) 4 solution. A dark brown color characteristic of Rh 2 (0 2 CCF 3 ) 4 (PPh 3 ) 2 immediately resulted. The reaction mixture was stirred with heating for 1 h. During this time an orange precipitate formed. Filtration of the hot solution afforded 0.24 g. Thin layer chromatography using 2:1 chloroform/toluene indicated two components. Extraction of the orange product with hot 1:1 dichloromethane/toluene left behind a small amount (~0.05 g) of an orange solid which may be a 4:1 PPh 3 adduct of Rh 2 (0 2 CCF 3 ) 4 which precipitated before Rh-Rh bond cleavage could occur. Anal. Calcd. for Rh 2 c 80 H 60 p 4 F 12°8 : c s6 29 * H » 3 54 Found : C, 56.12; H, 3.87. Evaporation of the dichloromethane/toluene extract afforded an orange solid (0.15 g). This compound is most likely Rh(0 2 CCF 3 )(PPh 3 ) 3 . Anal. Calcd. for RhC 56 H 45 P 3 F 3 2 : C, 67.07; H, 4.52; P, 9.27. Found: C, 67.86; H, 4.71; P, 9.58. IR (Nujol mull) single v asy (C0 2 ) 1678 cm' 1 (lit. 130 1670 cm" 1 ). Addition of hexane (5 mL) to the filtrate from the original reaction mixture with cooling led to formation of a yellow precipitate. Filtration and washing with hexane afforded 0.12 g. This compound is most likely Rh(0 2 CCF 3 ) 3 (PPh 3 ) 2 . Anal. Calcd. for RhC 42 H 30 P 2 F 9 6 : C, 52.19; H, 3.13; P, 6.41. Found: C, 51.95; H, 3.10; P, 6.12. IR (Nujol mull) v asy (C0 2 ), 1710 cm" 1 . When the above procedure was repeated without rigorous exclusion of air, the reaction

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121 proceeded in qualitatively the same manner, but 0PPh 3 was isolated (checled by IR and elemental analysis) and the products gave less satisfactory analyses presumably due to 0PPh 3 coordination or possible side reactions. Reaction of Rh ? (0 9 CCF^) A with excess P(OMe)-, Rh 2 (0 2 CCF 3 ) 4 (0.169 g, 0.256 mmol ) was dissolved in toluene (3 mL). Trimethyl phosphite (0.30 mL, 2.54 mmol) was added dropwise to this solution. A red-brown solution initially resulted, presumably due to axial adduct formation. The reaction was fairly exothermic. After 1 h the solution had turned yellow with formation of a pure yellow precipitate. Addition of hexane (2 mL) with cooling followed by filtration and washing with hexane afforded a pale yellow solid (0.30 g). Anal. Calcd. for RhC 13 H 27 P 3 F 6 13 : C, 22.27; H, 3.88; P, 13.25; mol. wt., 701. Found: C, 22.50; H, 3.98; P, 13.40; mol. wt., 698 (in CHpCl p ) . Experimental Methods Elemental analyses were performed by the Microanalytical Laboratory of the University of Illinois, Urbana, IL. Fourier transform NMR spectra were recorded on a Nicolet Technology Corp. NT-360 spectrometer operating at 338.6 MHz for 19 F and 360.1 MHZ for h NMR spectra. All 19 F chemical shifts are with respect to internal CFC1 3 and all X H chemical shifts are with respect to internal TMS. 31 P{ 1 H} NMR spectra were recorded either on a Varian Associates XL-100 FT spectrometer operating at 40.5 MHz or on a Nicolet NT-300 spectrometer at 121.5 MHz. For the former instrument, samples were in 12 mm tubes with the 31 P chemical shifts previously set relative to 85% phosphoric

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122 acid. For the latter instrument, samples were in 5 mm tubes coaxial in 12 mm tubes containing trimethyl phosphite in chloroform-d as a 31 P chemical shift reference. However, all 31 P chemical shifts are reported with respect to 85% phosphoric acid. Phosphorus chemical shifts for reference were taken from the literature. 141 Infrared spectra were recorded on a Nicolet 7900 FTIR spectrometer for the CHC1 3 solutions and on a Perkin-Elmer 599B instrument for the Nujol mulls. The assistance of the staff of the Molecular Spectroscopy Laboratory, University of Illinois and of Professor Wallace Brey and Mr. James Rocca, both of the Department of Chemistry, University of Florida, is appreciated.

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CHAPTER IV SPECTROSCOPIC AND BONDING STUDIES OF RHODIUM CARBOXYLATE DIMER CATION RADICALS Introduction The qualitative MO scheme used in the previous two chapters was quite successful at explaining some general results obtained therein. Furthermore, this MO scheme has been used successfully to interpret quantitative results obtained from calorimetric studies of Lewis base binding to metal carboxylate dimers. 23 ' 25 This scheme has been helpful in understanding electrochemical data on the rhodium system. Electrochemical studies by Drago and co-workers 23 » 24 and Bear and coworkers 40 demonstrated that Rh 2 (0 2 CR)4 species are easier to oxidize when strong donors such as pyridine and DMSO are present. The stronger the rhodium-Lewis base a-bond, the higher in energy become the metal non-bondinq electrons. This allows easier oxidation of the metal dimer, since electrons are removed from these orbital s. When there is a ubackbondinq interaction between the metal and Lewis base, the metal anti-bonding orbitals are lowered in energy. This stablization increases the electrochemical potential for oxidation. Carboxylate ligand effects are also Important. With the electron withdrawing fluorocarboxylate ligand the rhodium dimer 1s virtually impossible to oxidize. There is some controversy as to the specific orbitals involved in this oxidation as will be discussed below. This qualitative MO scheme has also been used to explain UV-visible absorption 125 and EPR 123

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124 spectra 133 observed for [Rh2(02CR)4B2] + species generated either electrochemically or by y-ray irridiation. The chemical oxidation of the rhodium dimer and some UV-visible studies are described here. A number of theoretical studies have also been made on the metal carboxylate dimer. An MO scheme drawn from the calculations of Norman and co-workers 44 using the SCF-Xa scattered wave method is shown in Figure 4-1. This is the MO scheme they propose for the rhodium and ruthenium carboxlate dimers. The scheme differs for the molybdenum and rhenium (or technetium) dimers in that the 6* orbital is lower in energy than the degenerate it* orbital s. It is proposed that this occurs because the 6* orbital has significant carboxylate character while the n* orbitals are primarily metal based. Thus, for the less electronegative earlier transition metals such as molybdenum and rhenium, the metal only orbitals (such as tt*) are relatively higher in energy while for the more electronegative later transition metals such as ruthenium and rhodium, these metal only orbitals are lower in energy. However, the 6* orbital remains relatively constant 1n energy on going from Mo to Rh since the carboxylate ligands, which make a large contribution to this orbital, do not change. Naturally, for the ligand free M 2 n+ system, 6* is always lower in energy than tt*. This change in the relative energies of 6* and tt* most likely occurs, but it is not clear that a reversal occurs. As will be discussed below, it is possible that tt* is always above 6*. The above discussion of MO schemes does not include the effect of axial Lewis base coordination. A qualitative MO scheme which takes into account this effect is shown in Figure 4-2. The results of interaction between Rh 2 (0 2 CR)4 and two types of Lewis bases (B) are shown. The interaction between the two Lewis

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125 • • b b O ^ 6XD 60 fc= k ^ o ^ b o Q. D JQ o x x "O X

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126 major D4h level contribution abbreviation J 2U Rh-Rhcr*)
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127 base lone pair orbital s and the Rh-Rh a and a* orbital s leads to four molecular orbital s. These are represented as ai which is lowest in energy and is Rh-Rh and Rh-B a in character, a 2 which is Rh-Rh a* and Rh-B, a 3 which is Rh-Rh a and Rh-B a* in character and the a* antibonding orbital which is Rh-Rh and Rh-B a* in character. With weaker donor bases such as oxygen donors, the base lone pair orbital is lower in energy, so the rhodium-Lewis base interaction is not as strong and a 2 and a 3 are relatively close in energy with a 3 well below 6* and tt*. With strong donors with higher energy lone pairs, such as phosphorus bases, the rhodium-Lewis base interaction is strong. The result is that a 2 is low in energy and its anti-bonding counterpart, a 3 , is high in energy, above 5* and tt*. This gives a different HOMO for Rh 2 (0 2 CR) 4 with strong donors than with weak or no axial bases. The LUMO in all of these neutral complexes is a*, but the HOMO is a 3 in the former case and 6* or tt in the latter cases. When these species are oxidized, the resulting unpaired electron is in these different HOMO's (or SOMO's for semi-occupied molecular orbitals). Thus, with strong donors the electronic ground state is a 1 2 c 2 2 ii 4 6 2 6* 2 Tr* 4 a 3 1 and with weak donors o 1 2 o 2 2 Tr 4 6 2 6* 2 a 3 2 Tr* 3 . This leads to quite different EPR behavior as will be shown below. More recent calculations have lead to conclusions at variance with above MO scheme. Using ab initio methods, Nakatsuji and co-workers 47 proposed that [Rh 2 (0 2 CH) 4 B 2 ] + where B=H 2 or PH 3 both have an electronic ground state represented by (a 2 )a 2 6 2 Tr 4 Tr* 4 6* 2 a 1 , while [Rh 2 (0 2 CH) 4 ] + with no axial Lewis bases has a a<5 2 TT 4 Tr* 4 6* ground state. Using this proposal, the complexes represented as [Rh 2 (0 2 CR) 4 (0-donor ) 2 ] + and [Rh 2 (0 2 CR) 4 (P-donor) 2 ] + in Figure 4-2 would have the same appearance

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128 with the unpaired electron in a 3 in both cases. This is somewhat surprising and is in conflict with experimental results. Results and Discussion Chemical and UV-Visible Spectroscopic Studies As originally reported by Wilson and Taube, 52 it is possible to chemically oxidize the rhodium carboxylate dimer. Chlorine gas, lead dioxide or Ce(IV)(aq) all convert blue-green aqueous solutions of Rh 2 (0 2 CCH 3 ) 4 to orange solutions of Rh 2 (0 2 CCH 3 ) 4 + . Magnetic susceptibility by the Evans method gave u e ff=2.1 ± 0.4 per mole of Rh dimer, indicating one unpaired electron. The workers also isolated a solid from the oxidation product, but it was found to be unstable, reverting to Rh 2 (0 2 CCH 3 ) 4 and a Rh(III) product. The chemical oxidation of Rh 2 (0 2 CR) 4 where R=CH 3 and CH 3 CH 2 CH 2 was investigated here in organic solvents for comparison to the aqueous solution work and in the hope that it would be possible to isolate a more stable Rh 2 (II,III) species in this manner. Solutions of Rh 2 (0 2 CCH 3 )4 and Rh 2 (but) 4 in both ethanol and acetonitrile were oxidized by Cl 2 and Ce(IV). These orange solutions of Rh 2 (0 2 CR) 4 + were generated by bubbling through chlorine gas or by addition of one equivalent of (NH 4 )Ce(N0 3 ) 6 and are stable for about one hour. Unfortunately, a stable Rh 2 (0 2 CR) 4 + complex could not be obtained using ethanol or acetonitrile with either the acetate or nbutyrate. Some orange-brown solids similar to that described by Wilson and Taube 52 were obtained from these solutions, but they were not indefinitely stable. Nevertheless, the Rh 2 (II,III) species can be generated in solution relatively easily and used in spectroscopic studies. These workers also reported 52 the UV-visible spectrum of

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129 Rh 2 (02CCH 3 )4 and its cation radical, both in aqueous solution. Bands were seen at 585 (e=105) for the neutral complex. The UV-visible spectra of this complex in ethanol and acetonitrile were obtained here and are shown in Figures 4-3A and 4-4A, respectively. Bands were observed at 580 U=156) and 430 nm (e=75) in ethanol and at 543 (e=233) and 430 nm (e=l29) in acetonitrile. As discussed in Chapter II, these bands have been assigned to (Rh-RhM + (Rh-Rh)a* and (Rh-RhM (Rh0)o* transitions, respectively. 63 The band at longer wavelength is more strongly affected by solvent since it involves a transition to an orbital that contributes greatly to axial Lewis base bonding, while the shorter wavelength band involves orbitals that are relatively less affected by axial base coordination. The band at ~580 nm in ethanol and water is at much lower wavelength in acetonitrile. This is due to irbackbonding from the Rh-Rh it* orbitals lowering their energy. These effects have been discussed in detail elsewhere. 23 " 26 Wilson and Taube 52 reported that oxidation of rhodium acetate by Ce(IV) in 1 M CF3SO3H gave bands at 758 (e=330), 515 (e=316) and 217 nm (e=1.19 x 10 4 ). The results obtained here in ethanol solvent are in good agreement with those in aqueous solution. As shown in Figure 4-3B, bands were observed at 785 (e=191) and 510 nm (e=120). A large band at -300 nm includes Ce(III). In acetonitrile, as shown in Figure 4-4B, bands were seen at 815 (e=25) and 530 nm (e=180) as well as the large band extending into the UV region. It is proposed ^ that the band in [Rh 2 (0 2 CR) 4 ] + at -500 nm corresponds to the (Rh-Rhh* (Rh-Rh)a* transition and the band extending into the ultraviolet region is due to the ( Rh-Rh )tt* + (Rh-0)o* transition. This shift to higher energy is the result of oxidation. What is of interest is that the shift observed in

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130 C i— i O OJ CM ro

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132

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133 acetonitrile solvent is very small compared to the other solvents. This may be the result of Tr-backbonding effects. Neutral Rf^^CCf^J^Cr^CN^ has more Tr-backbonding than the corresponding cation since in the latter there is less tt* electron density to backbond. This decrease in backbonding raises tt* narrowing the energy gap between tt* and a* in the cation relative to the neutral complex. This compensates to some extent for the shift to higher energy transitions caused by oxidation. The last transition seen, that at the longest wavelength, does not occur in the neutral complex and based on MO calculations has been assigned to a (Rh-Rh)5 + (Rh-Rh)6* transition. This is a z-dipole allowed transition in D 4h symmetry. It could occur if the unpaired electron were in a 6* orbital. This would be the case if 6* were higher in energy than tt*. The opposite ordering may exist. Then the unpaired electron would be in tt* and the transition could be (Rh-Rh)Tr + (Rh-RhN*. This is an x,y-dipole allowed transition in D^. The energy of this transition would be affected by axial base coordination since these orbitals are involved 1n base binding. In contrast, 5+6* would be completely unaffected by the axial base since these orbitals are not at all involved in base binding. This could explain why in acetonitrile the transition occurs at lower energy and lesser intensity than in ethanol or water. Backbonding with acetonitrile lowers the tt* orbital energy relative to that in solvents incapable of this interaction. The above discussion is based on an earlier study 63 of the UV-visible spectrum of rhodium acetate. Gray and co-workers 142 have very recently reinvestigated the polarized electronic spectrum of this compound and disagree with the previous study. These workers have reassigned the band at -580 nm to a (Rh-Rhh* * (Rh-O)a*

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134 transition and that at -450 nm to a (Rh-Oh » (Rn-O)a* transition. 142 This is surprising since the band at ~530 nm is very sensitive to axial and not to equatorial ligation while the band at ~450 nm is sensitive to equatorial and not axial coordination. As discussed in Chapter II, these results would be expected based on the earlier 63 assignment. Since the Rh-Rh v* MO's are involved in axial base binding, it is possible that the 580 nm band would be sensitive to axial base even though it might not involve a transition to a Rh-Rh a* orbital. Furthermore, the ir-backbonding argument given above to explain the shift of this band upon oxidation would still be valid. Nevertheless, it appears that assignment of the electronic transitions of the rhodium carboxylate dlmer is not yet certain. If single crystal polarized electronic absorption spectra could be obtained for a Rh 2 (0 2 CR) 4 + species and for various Rh 2 (0 2 CR) 4 l_ 2 complexes, then perhaps the transitions could be assigned with greater certainty. EPR Studies EPR spectra for several metal carboxylate dimers have been observed. 35 " 39,133 In some cases the diamagnetic dimer can be converted to an S=l/2 system electrochemically or by chemical oxidation as discussed in the previous section. The EPR spectra of these paramagnetic dimers provide much information regarding their electronic structure. Of relevance here are the studies by Kawamura and coworkers 133 on [Rh 2 (0 2 CR) 4 B 2 ] + species where B=various phosphorus donors. These workers generated cationic rhodium dimers using electrochemical and y-ray irradiation methods. It was attempted here to study the EPR spectra of these species generated by simpler, chemical means such as chlorine oxidation. Unfortunately, EPR spectra could not

PAGE 141

135 be observed for any [Rh 2 (0 2 CR)4] + systems although the UV-visible absorption spectra indicated oxidation had occurred. Thus, all EPR spectra had to be obtained by electrochemical methods. Furthermore, spectra were only obtained when the electrochemical cell was active. Possible reasons for this difficulty of obtaining spectra are aggregation of the cation radicals or 2 binding to the rhodium complexes. Dioxygen binding to Rh 2 (aq) has been proposed^* 1 to give [(H 2 0) 5 Rh-0-0-Rh(H 2 0) 5 ] 4+ although no dioxygen bridged rhodium dimer has been isolated. Such complexes are known for cobalt. 143 Although attempts were made to keep out 2 > some was not doubt inevitably present. EPR spectra were observed for [Rh 2 (but) 4 B 2 ] + only when B=triphenylphosphine (PPh 3 ), pyridine (pyr) and N-methyl imidazole (NMelm). The spectra observed for the first two complexes are shown in Figures 4-5 and 4-6, respectively. These particular spectra were obtained by Mr. Richard Cosmano using an electrochemical cell designed by him. The complexes were in CH 2 C1 2 solution with U-Bu) 4 NBF4 as the supporting electrolyte. Computer simulations using a program for powder pattern spectra 144 are given below the experimental spectra. The simulations were performed by treating the Rh 2 5+ unit as an S=l/2, 1=1 system since there are two equivalent rhodium nuclei with one isotope ( 103 Rh, 1=1/2, u N =0.0884, 1002 natural abundance). Superhyperfine interactions from two equivalent phosphorus nuclei were included ( 31 P, 1=1/2, 100% natural abundance). In the pyridine adduct, nitrogen superhyperfine was not resolved and was not included in the simulations. The parameters obtained from these simulations are given in Table 4-1. The parameters obtained for the PPh 3 adduct, assuming

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136 -«n a;^

PAGE 143

1-4 1O <_> O-co 1 — 1

PAGE 144

138

PAGE 145

E

PAGE 146

140 o o m ro CD O O O C\J ro O O O" CD CM

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141 -4 -1 * cm x perfect axial symmetry, are g,. =1.998, g, =2.147, A„ p =202 x 10 Aj_ p =150 x 10" 4 cm" 1 and A 1so Rh =7 x 10" 4 cm" 1 . The value obtained for the rhodium hyperfine is very approximate. It is an upper limit based on the observed linewidths (40 MHz, hwhh). The EPR parameters obtained here are identical, within experimental error, to those reported by Kawamura and co-workers 133 for Rh 2 (0 2 CCH 2 CH3) 4 (PPh 3 )4 + . Their values were g |( =1.996, g 2 =2.148, A// P =205 x 10" 4 cm -1 , A x p =152 x 10" 4 cm" 1 , A./ Rh =13 x 10" 4 cm" 1 and Aj_ Rh was not resolved. The MO scheme given in Figure 4-2 can be used to explain the EPR spectra observed for the PPh 3 adduct. In this complex, since the axial base is a strong donor, the a 3 orbital is high in energy and lies above 6* and ir*. Thus, the unpaired electron generated by oxidation is in this orbital. Since a 3 is a non-degenerate orbital, g values close to the free electron value (g e =2.0023) are expected. However, contributions from excited electronic states can mix in orbital momentum effects which would give deviations from the free electron g value. Only states of the proper symmetry can contribute. Assuming idealized D 4n symmetry in the dimer, only electronic states with a 2q symmetry can contribute to g., since a 3 has a^ g symmetry and the z angular momentum operator, L z , transforms as a a 2g in D 4n (only a lg x a 2g x a 2g contains a lg ). Only electronic states with e g symmetry can contribute to g, since the x,y angular momentum operator, l_ x y , transforms as e q in D 4n (only a lg x e g x e g contains a lg ). Using Figure 4-1, it can be seen that no electronic states have a 2q symmetry so g., =g e . However, states involving electron promotion from the degenerate tt* orbitals which have e g symmetry can contribute to shift g. from g e . Since the u* orbitals are filled, a positive shift is observed. The phosphorus hyperfine

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142 coupling constants support this assignment of the unpaired electron being in a a type orbital. Values of A 1 so =(A / /+2A i _)(l/3)=502 MHz and ^dip = ^// "Aj_)(l/3)=52 MHz were observed. These can be compared to the values that would result in a system in which all the spin were localized on two equivalent sp 3 hybridized phosphorus orbitals. Using the tabulated 145 ' 146 atomic parameters, A iso =(13306)(l/2)=6653 MHz and A d1p =(S p )(P)(l/2)=(2/5)(917.0)(l/2)=183.4 MHz. Thus, a phosphorus s orbital contribution of (502/6653) =7. 54% and a p orbital contribution of (52/183. 4)=28. 17% is indicated. The ratio of these is 3.74:1 (p:s) versus 3:1 for true sp 3 hybridization. The above calculations indicate a substantial spin density on the phosphorus ligands, specifically on a phosphorus orbital which is largely of sp 3 hybridization. The additional p spin density, manifested by the large anisotropy in A p , most likely arises from phosphorus-rhodium it interactions. Thus, the EPR parameters for [Rh2(but) 4 (PPh3) 2 ] + as well as those of related complexes 133 are in agreement with the MO scheme shown in Figure 4-2. However, the EPR results for the adducts with the strong nitrogen donors pyridine and N-methyl imidazole cannot be easily explained since rhombic spectra were observed. Values of g x =1.990, g y =2.027, and g 2 =2.095 were obtained for the pyridine adduct. No rhodium or nitrogen hyperfine could be detected. However, the different linewidths (W x =W y =35 Hz and W 2 =45 Hz, hwhh) may indicate unresolved anisotropic hyperfine interactions. The positive shift of g z from g e and large difference between g x and g„ indicate that the pyridine adduct is very different from the phosphine complexes. This deviation from axial symmetry is most likely the result of Lewis base coordination to

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143 equatorial sites on the rhodium dimer as was observed with ^2(02^3)4 as discussed in the previous chapter. No EPR spectra were observed at 77 K for Rh 2 (but) 4 + alone or with any weak donors such as methanol or acetonltrile. This can be easily explained using the MO scheme in Figure 4-2. In Rh 2 (but) 4 or [Rh2(but) 4 B 2 ] + where B 1s a weak donor, the Rh-B interaction is low in energy and 03 lies below the <5* and tt* orbitals. Thus, the unpaired electron is in a degenerate pair of tt* orbitals. This leads to a great deal of spin orbit coupling which causes fast electron spin relaxation, preventing observation of an EPR spectrum. In contrast, the theorectical results of Nakatsuji and co-workers 47 would predict similar, and easily observable, EPR spectra for both [Rh 2 (0 2 CR)4(PR3) 2 ] and [Rh2(0 2 CR) 4 (R0H) 2 ] + since they claim that both have a Tf * 4 5* 2 a 1 electronic ground state. This clearly cannot be the case. It is also unlikely that the unpaired electron is in the <5* orbital. The theoretical results of Norman and co-workers 44 would suggest this. Their MO scheme, as shown in Figure 4-1, places 5* slightly above tt* in energy. Thus, oxidation would lead to a tt* 4 6* 1 electronic ground state for Rh 2 (but) 4 + alone or with weak donors. (Their predictions for the rhodium dimer with strong donors are the same as in the qualitative scheme shown in Figure 4-2 in which the unpaired electron is in a a-type orbital). If the unpaired electron were indeed in the non-degenerate 6* orbital, then the EPR spectrum would be observed. For example, in electrochemically generated Mo 2 (but) 4 + an EPR spectrum with g (( =g J _=1.941 was observed in CH 2 C1 2 at 77 K. 38 In this complex the unpaired electron is undoubtedly in a <5 orbital. This g value less than g e is to be expected since excited states involving transitions to empty (Mo-O)a*

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144 and (Mo-Mo )tt* orbital s are of the proper symmetry to affect g and g , respectively. These transitions are of b lg and e g symmetry, respectively and 5 is of b 2g symmetry, all in D 4h . Similarly, Re 2 (0 2 CC 6 H 5 )4Cl 2 was electrochemically reduced to a Re 2 ( 1 1 , 1 1 1 ) species whose EPR spectrum in CH 2 C1 2 at 77 K gave g. =1.713 and g Jr =2.136. 39 In this case, with a 5* 1 electronic ground state which has b lu symmetry, transitions involving empty (Re-O)a* and filled (Re-Re)ir orbitals are of the property symmetry (b 2u and e u , respectively) to affect g and g : , respectively. This leads to a negative shift in g., and a positive shift in g^.. Based on this extensive evidence, it appears that if the unpaired electron were indeed in a 6* orbital, an EPR spectrum similar to that seen for the rhenium complex would be observed. Since this was not the case, 6* must be either below or equal in energy to the it* orbitals. Further support for this proposal will be given in the following chapter in discussing the Ru 2 (0 2 CCR)4 + system. Conclusion Rhodium alkylcarboxylate dlmers can be easily oxidized using chemical oxidizing agents such as Cl 2 or Ce(IV) or by electrochemical methods to give formally Rh 2 (II,III) species. The UV-visible absorption spectrum of the resulting cation can be interpreted using a metal-metal bonding MO scheme. The effects of different solvents, which can axially coordinate to the dimer, can be seen in the UV-visible spectrum of the cation as well as the neutral dimer. These lend support to a irbackbonding interaction between rhodium and Lewis bases such as acetonitrile. EPR spectra for these cations can only be observed in active electrochemical cells and not in chemically generated species

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145 although they have the same UV-visible spectrum. This suggests an aggregation or dloxygen binding mechanism may be occurring. The EPR spectra that are observed for the rhodium dimer with phosphorus donors can be explained using the same MO scheme. No EPR spectra are observed for Rh 2 (but) 4 + with weak or no donors since the unpaired electron spin density is in degenerate Rh-Rh t\* orbitals. Theoretical studies 47 that propose identical electronic configurations for Rh 2 (0 2 CR) 4 + with both weak and strong donors are not in agreement with the experimental results. Furthermore, in contrast to other calculations, 44 it is unlikely that the unpaired electron Is 1n a <5* rather than tt* orbital. If this were so, then an EPR spectrum for Rh 2 (but) 4 + would be observed as seen 38 * 39 with other metal carboxylate dimer complexes with unpaired electrons in 5 or 6* orbitals. Experimental Section Synthesis Rh 2 (0 2 CCH 3 ) 4 , Rh 2 (but) 4 , and Rh 2 (but) 4 (PPh 3 ) 2 were synthesized as described in Chapters II and III. The other rhodium species were generated in solution by addition of stoichiometric amounts of the appropriate Lewis base to the rhodium dimer. Solvents (all reagent grade) and bases were distilled before use. Experimental Methods UV-v1sible spectra were recorded on a Cary 14 spectrometer using matched quartz 1.0 cm cells. Electrochemical procedures are described in detail elsewhere. 23,25 A PAR Model 173 potentiostat/galvanostat and a PAR Model 176 current-to-voltage converter were used. An electrochemical cell designed by Mr. Richard Cosmano was used.

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146 Electrochemical solutions for EPR spectroscopy were ~1 x 10~ 3 M in rhodium dimer and 0.1 M_ in (jv-Bu) 4 NBF 4 in CH 2 C1 2 . The reference cell consisted of a silver wire in a solution which was 0.42 M_ in (^-Bu) 4 NBF 4 and 0.05 M_ in (jv-Bu) 4 NI in CH 2 C1 2 saturated with Agl. A potential ~200 mY more positive than the redox couple involved was applied. During this process, EPR spectra could be observed. EPR spectra were recorded on a Varian E-9 X-band instrument. Computer simulations of the EPR spectra were performed using the program QPOW. 144 A copy of the program is given in Appendix E. In the simulations done here, the frame of reference was chosen so that the g tensor was diagonal and the A tensor was held in the same orientation as the g tensor. The nuclear g tensor was approximated as a isotropic g N =u^/I.

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CHAPTER V SPECTROSCOPIC AND REACTIVITY STUDIES OF RUTHENIUM BUTYRATE CHLORIDE Introduction As discussed earlier, almost all of the known metal -metal bonded complexes have an even number of d electrons. Although, as was shown in Chapter IV, it is possible to chemically or electrochemically generate paramagnetic metal-metal bonded complexes, thus containing an odd number of d electrons, and these species are often reasonably stable in solution. Nevertheless, normal synthetic procedure leads to even d electron metal carboxylate dimers for transition metals such as chromium, copper, molybdenum, tungsten, technetium, and rhenium. However, as was first discovered a number of years ago by Stephenson and Wilkinson, 48 when RuCl 3 (H 2 0) x is reacted with carboxylic acids a paramagnetic, odd d electron dlmer of formula Ru 2 (0 2 CR) 4 Cl results. This is formally a Ru 2 C II.III) complex. The electronic structure of this complex was originally explained using the MO scheme applied to other metal-metal bonded dimers. The eleven d electrons fill the a, 6, and it bonding orbitals and half fill the 5* and tt* antibonding orbitals. This gives a net Ru-Ru bond order of 2.5. A simplified version of this MO scheme is shown in Figure 5-1. Structural studies on Ru 2 (but) 4 Cl 147 and other Ru 2 (0 2 CR) 4 + derivatives 148 indicate that the two Ru atoms are crystallographically equivalent. Furthermore, a report by Cotton and Pedersen^ of the 147

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Figure 5-1. Qualitative MO scheme for metal -metal bonding in Ru 2 (0 2 CR) 4 + .

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149 a * 8 7T 4 1 3 +4 7T ±± FF O" ++

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150 magnetic properties and EPR spectra of Ru 2 (but) 4 Cl gave no support to a localized Ru 2 ( II, III) system. Evidence was found to support the description of Ru 2 (but) 4 Cl as an S=3/2 rather than S=l/2 system with the three unpaired electrons delocalized over both ruthenium atoms. Scattered-wave Xa calculations have been performed 44 on the Ru 2 (0 2 CH) 4 + species and they support this description of the electronic structure of the ruthenium carboxylate dimer. Qualitatively, the reason for this complex being a quartet rather than a doublet system is the stability of a half filled set of degenerate orbital s relative to other configurations. This is due to electron exchange interactions. Thus, the lowest energy configuration is for the 6* and degenerate tt* orbitals to be half filled, since the 6* orbital is very close in energy to the tt* orbitals. In the calculations by Norman and co-workers, 44 5* was proposed to be slightly higher in energy than tt*, but as discussed in the previous chapter, it is difficult to confirm this experimentally. If the 5* orbital were indeed higher in energy than tt*, it might be possible to prepare a Ru 2 (III,III) carboxylate dimer which would then have a Ru-Ru bond order of three and half filled tt* orbitals. Such a complex might be even more stable than the Ru 2 ( II , 1 1 1 ) dimer since it would have a stronger Ru-Ru bond and have Ru in a higher formal oxidation state. However, no such species has been reported and it appears that the Ru 2 ( 1 1, 1 1 1 ) complex cannot be oxidized without decomposition. In summary, the Ru-Ru 5* and tt* orbitals are close in energy with the relative ordering and energy difference uncertain. Nevertheless, this MO scheme has been used with success to explain resonance Raman 149 and single crystal polarized UV-visible spectra 150 of Ru 2 (0 2 CR) 4 + species. In order to further understanding of this

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151 interesting complex it was decided to examine the magnetic properties of Ru 2 (but)4Cl over the temperature range from 5 to 300 K. The original measurements were made only over the 60-300 K range. ^ In many cases, magnetic susceptibility measurements are necessary at low temperature to observe deviations from normal Curie-Weiss law behavior. It was also decided to repeat the EPR study since due to a poor signal-to-noise level in the original EPR experiments, a complete spectrum was not obtained and the conclusions are open to question. Complete solution EPR spectra of Ru 2 (but) 4 Cl and some derivatives thereof were obtained at 4 K. Far IR absorption spectra for the complex in the solid state at room temperature were also obtained. Another area of interest with the ruthenium carboxylate dimer, 1n addition to the nature of the Ru-Ru bond, is the extent of electron derealization since it is, formally at least, a mixed oxidation state complex. The well known Creutz-Taube ion, 151 [(Nf^^RudlMpyrazine) Ru( III ) (NH 3 ) 5 ] 5+ , and derivatives thereof represent another example of a formally Rt^dl.III) complex. This class of compound has been widely used to study electron transfer for 1t is possible to greatly vary both the bridging and non-bridging legands. 152 Furthermore, these complexes can frequently be easily converted to Ru 2 ( 11,11) or Ru 2 (III,III) species. Thus, there are many different parameters which can be varied to help in understanding the interaction between the two Ru atoms. By contrast, much less variation is possible in the ruthenium carboxylate dimer series. This formally Ru 2 ( II » 1 1 1 ) complex has thus far (with one exception described below) resisted efforts to be either oxidized or reduced to give stable Ru 2 ( III.III) or Ru 2 ( II, II ) species. In addition, less ligand variation is possible. There is no group between the two Ru

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152 atoms and there is less freedom in changing the other ligands so that the dimer is maintained. In contrast to the large number of rhodium and molybdenum dimers that are known with other than bridging carboxylate ligands, there are only two such examples with ruthenium. Mo-Mo bonded complexes exist with halide and carboxylate ligands and with ligands such as alkoxides, 4,86-88 amides, 4 dithiocarboxylates," sulfate, 58 and variously substituted 2-oxy-pridines. 153 With rhodium, complexes are known with 6-methyl-2-oxypyridine (mhp), 5,188 carbonate 154 and HNOCCF3". 42 With ruthenium, a Ru 2 (II,II) mhp complex has been recently reported. 155 However, it was obtained in only 8% yield. Complexes with complete trifluoroacetamidate substitution, 156 Ru 2 (HN0CCF 3 )4Cl, and partial oxalate substitution, 157 Ru 2 (0 2 CCH 3 ) 2 (C 2 04) 2 ~, have also been very recently reported. Both complexes have properties which greatly resemble the carboxylate dimer starting material. Finally, in contrast to the rhodium or molybdenum carboxylate dimers, the ruthenium dimer is very prone to decomposition into products no longer having the dimeric structure. For example, pyridine and trlphenylphosphine give adducts of general formula M 2 (0 2 CR)4B 2 with Mo and Rh, but these Lewis bases react with Ru 2 (0 2 CR) 4 Cl to give [Ru 3 0(0 2 CR) 6 (pyr) 3 ] + and [Ru 3 0(0 2 CR) 6 (PPh 3 ) 3 L 158 » 159 In these trimeric complexes, Ru-Ru bonds exist, but the complexes in no way resemble the carboxylate dimer starting material in either structure or type of metal -metal bond. The structure of these complexes is that of "basic iron acetate" which is well known 150 for Cr(III), Mn(III), Fe(III) and other metals in the 3+ oxidation state. This trimer also results upon treatment of the dimer with strong acid, 82 precluding a study of the type done in Chapter II. Perhaps as a result of this, the reactivity of the ruthenium carboxylate dimer towards Lewis

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153 bases has not been studied as extensively as the analogous rhodium and molybdenum systems. Some preliminary reactivity studies were performed on Ru 2 (but) 4 Cl and are described below. The work was undertaken in conjunction with a quantitative calorimetric study 161 of the enthalpies of Lewis base coordination to this representative ruthenium carboxylate dimer. Results and Discussion Magnetic Susceptibility The magnetic susceptibility of a powder sample of Ru 2 (but)4Cl was determined over the temperature range 5-300 K. Most data points were taken at low temperatures since the magnetic susceptibility of Ru 2 (but)4Cl had not been previously reported below 60 K. 36 A diamagnetic correction of -278 x 10" 6 cgsu was used, and it is simply the value obtained from Pascal's constants including the underlying diamagnetism of Ru(II) and Ru(III). 162 Initially, the data were fitted using a linear least-squares equation to a Curie-Weiss law behavior curve, l/x=a +a 1 T. The points above 35 K fitted well to this equation. An r 2 correlation of 0.99998 was obtained indicating that more points at high temperatures would not have been needed. The values obtained form this fit of the high temperature data agree closely with those reported previously by Cotton and Pedersen. 36 These values are summarized in Table 5-1. The value obtained here for x^ 300 (6.852 x 10~ 3 ) is much closer to the solution value obtained from both the Gouy and Evans methods (6.91 x 10" 3 ) than is the previously reported powder value (6.74 x 10~ 3 ). This agreement of the solution and solid state values is supported by computer simulations that show insignificant

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154 Table 5-1. High Temperature Powder Magnetic Susceptibility Data on Ru 2 (but) 4 Cl .300 x 10" cgsu Ref. 36 6.6 0.472 2.12 (60-300K) This work 6.984 0.4632 2.16 (350-300K) 14 2.13 6.74 ±0.03 6.91 ±0.05 in solutions 15.1 2.15 6.852 ±0.003 Table 5-1 I. Parameters obtained from Computer Simulation of the Powder Magnetic Susceptibility Data (Full Temperature Range) Using the Models Described in the Text "X 'avg zJ zJ c SE L Method r

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155 interdimer interactions (vide infra). Thus, at temperatures above 35 K, Ru 2 (but)4Cl exhibits normal paramagnetic behavior with a positive Weiss constant. The data below 35 K did not fit the Curie-Weiss law as well since high temperature approximations were no longer valid. In order to correctly explain these data, a full exponential treatment was needed. Several models are reasonable since in ^(but^Cl there may be both intramolecular and intermolecular effects. The latter are due to the polymeric nature of the solid state structure of Ru 2 (but) 4 Cl wherein Ru2(but)4 + units are bridged by chlorides to form approximately an infinite linear chain. 147 Thus, intermolecular antiferromagnetic exchange between ruthenium diiners is possible. Furthermore, as with all S > 1/2 systems, zero-field splitting within the S=3/2 ruthenium dimer is possible, which is an "intramolecular antiferromagnetic" effect. Therefore, five models were developed in an attempt to separate these effects and understand the magnetic behavior of Ru2(but) 4 Cl. These models (Methods 1-5) are described in detail in the Experimental Section. The first two zero-field splitting models (Methods 1 and 2) fit the data reasonably well. The parameters obtained by computer simulation of the magnetic data using Method 1 gave the best fit and g values of g„ =2.02 and g^_ =2.14 that are in good agreement with those obtained from the EPR spectra of Ru 2 (but) 4 Cl in various solvents (g,, =1.9465 and g, =2.200, vide infra). The experimental and theoretical curves for xm and v e ff using Method 1 are shown in Figure 5-2. The parameters obtained from all the simulations are summarized in Table 5-1 I. The value obtained for the zero-field splitting parameter, D, is fairly large, 77 cm" . In transition metal complexes, D is dominated by spin-

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fO •

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157 MAGNETIC MOMENT (/Li Bff /Ru 2 ) (iajx) AiniaiicGOsns oiibnovw

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158 orbit coupling effects. 145 These are expressed as D S0 =5 2 A where I is the spin-orbit coupling constant of the molecule and A is a tensor containing matrix elements of ground and excited electronic states connected by the orbital angular momentum operator, L. Using a simple LCAO-MO approximation, 5 depends on c, the atomic spin-orbit coupling constant which in turn is proportional to Z 4 , where Z is the atomic number. In a complex such as ^(but^Cl, one would expect ? to be large since there are two ruthenium atoms which have high atomic numbers. A large value for A would also be expected since ^(but^Cl has many, closely spaced electronic states. Thus, a large value for D is not surprising. Few calculations have been performed to theoretically determine D values 145 and Ru2(but) 4 Cl is no doubt far too complex. There also are no analogous compounds with which to compare this value to determine how meaningful it is. Conventional EPR spectroscopy has been used to measure D for a number of high spin molecules. 145,1 ^ However, commonly used microwave frequencies do not exceed ~3 cm", far too small to determine D in this complex. Magnetic resonance using far-infrared sources which can go up to several hundred cm" 1 would allow an independent measurement of D to compare with the above value. This method has been used successfully to study metal! ©porphyrins with large zero-field splitting. 164 Method 2, the exponential form for the zero-field susceptibility, fitted the data well, but gave g.. =3.03, in poor agreement with the EPR data. One would expect use of the full spin Hamiltonian with the experimental magnetic field to determine the energy more accurately than the zero-field exponential model. Thus, Method 2 is qualitatively correct, but Method 1 is quantitatively better.

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159 By contrast, use of Method 3, the Ising model, gave a very poor fit to the data. The experimental and theoretical curves using this model are shown in Figure 5-3. This model only considers anti ferromagnetic interactions between S=3/2 units in an infinite linear chain. 16i > A q,-,.^ j i so value of 1.93 was obtained with J=-0.32 cm -1 . Since the fit was so poor, these values have little meaning. In addition, a model was used which contained the exponential form of the zero-field susceptibility for an S 1 =S 2 =3/2 dimer experiencing magnetic exchange. This dimer version was less successful than Method 3, giving J=-0.48 cm" 1 and 9iso =1,37 and a P° or flt * Use of Method 4 which contained zJ parameters to include both zerofield splitting and exchange effects was also unsuccessful. These parameters did not improve the fit and gave unreasonable values. Method 5, a more exact treatment in which the full spin Hamiltonian for a dimer of S=3/2 units experiencing both anti ferromagnetic exchange and zerofield splitting was used. Although the fit was quite good, the parameters obtained were unrealistic. Values for g., of 1.50 and g, of 1.48 were obtained, quite different from the g values determined from EPR. Values for D of 68.8 cm" 1 and J of +0.032 cm" 1 were also obtained. This D value is not inconsistent with that obtained by Method 1 and the very small, surprisingly positive, J value indicates again that zero-field splitting and not magnetic exchange interactions are dominant in Ru 2 (but) 4 Cl. In an attempt to restrain the fitting procedure to more reasonaoie values, Method 5 was repeated holding g. =1.95 and g =2.20, the g values obtained from EPR. This gave 0=250.0 cm" 1 and J=-2.00 cm" 1 and a very poor fit. The failure of Method 5 is not surprising since this model assumes that anti ferromagnetic exchange

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fO T— I— •r0} (U •rO <+-

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161 MAGNETIC MOMENT (^. eff /Ru 2 : UJ cr => h< or LU CL LJ (iaix) AiniaiicGOsns oiibnovw

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162 is the dominant term in the spin Hamiltonian, whereas in Ru 2 (but) 4 Cl it is zero-field splitting that is dominant, if not the sole field independent term in the Hamiltonian. There are of course problems inherent in applying this dimer model to the polymeric Ru 2 (but) 4 Cl. Also, the validity of the use of the Heisenberg Hamiltonian has recently been questioned. 166 However, it was found that for systems in which the oxidation states are localized, the Heisenberg Hamiltonian is still valid. This is most likely the case for Ru 2 (but) 4 Cl since the Ru-Ru units are quite widely separated and the interaction 1s weak, if it exists at all. The conclusion that can be drawn from the magnetic susceptibility data is that Ru 2 (but) 4 Cl, in spite of its polymeric structure, 1s a complex in which the Ru 2 (but) 4 + unlts can be treated as Isolated S=3/2 systems. This 1s In agreement with the crystal lographic data. In Ru 2 (but) 4 Cl the Ru-Cl bond is extremely long, 2.587 A 147 versus 2.35 A in Ru(III) chloride compel xes, 167 indicating a weak interaction. This is also in agreement with the EPR data as discussed below. The experimental and calculated values for x\/\ and u e ^ are given in Appendix A. EPR Spectra The EPR spectrum of Ru 2 (but) 4 Cl in various solvent systems was obtained at liquid helium temperature. No spectrum could be observed at liquid nitrogen temperature, although Cotton and Pedersen 36 reported a broad signal at this temperature. No EPR spectrum was observed for pure powder Ru 2 (but) 4 Cl at 4 K, presumably because of magnetic exchange interactions leading to fast electron spin relaxation. The following spin Hamiltonian was used to interpret the EPR spectra.

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163 M = gH.a.S + I.A.S 3 N H.£ N .I + S.D.S Since the value for D is large (-77 cm" 1 ) only the M s =±l/2 states are populated at 4K and the microwave frequency is too small (~0.3 cm" 1 ) to effect any transitions to the M s =±3/2 states. Thus, a computer simulation of the frozen solution spectra could be performed using a program for powder pattern spectra of S=l/2 systems, 144 as was used in the previous chapter. Ruthenium has five zero-spin nuclei ( 96 Ru, 98 Ru, 100 Ru, 102 Ru, and 104 Ru) and two nuclei with 1=5/2: 99 Ru, u N =-0.63, 12.72% natural abundance and 101 Ru, y N =-0.69, 17.07% natural abundance. The simulations done here treated the 1=5/2 nuclei Individually using their own g N values (the same g and A values) and the two were added in the correct isotopic ratio. The spectrum for the zero-spin nuclei (including only electronic Zeeman terms) was determined independently and could then be added to the 1=5/2 spectrum in the desired ratio. The EPR spectrum of Ru 2 (but) 4 Cl in 1:1 toluene/ dichloromethane with 12 v/v acetone is shown in Figure 5-4. The perpendicular and parallel regions are shown independently on an expanded scale in Figures 5-5 and 5-6, respectively. The EPR spectrum of Ru 2 (but) 4 Cl in 9:1 methanol /ethanol is shown in Figure 5-7. The perpendicular and parallel regions are shown on an expanded scale in Figure 5-8 and 5-9, respectively. Simulations are shown below each experimental spectrum. The values obtained by computer simulation of the spectra are given in Table 5-III. The simulations gave g x =4.400 for an S=l/2 system. For an S=3/2 system with D » gSH. one can refer to effective g values, g eff =hv/SH, such that for the M s =±l/2 Kramers doublet: g,. effs g„ and g^ eff =2 gj _[l-(3/16)(g x eH/D) 2 ]. 145 For D as large

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164 Table 5-1 II . Parameters Obtained from Computer Simulation of Frozen Solution EPR Spectra of Ru 2 (but) 4 Cl h 9avg A // A I Ref. 36 2.03 2.18 2.13 9 ± 3 x 10~ 4 31 x 10" 4 (methanol 4.2K, 9.186 GHz) This work 1.9465 2.200 21.7 ±.5 x 10" 4 26.7 ±.5 x 10" 4 (1:1 toluene/ ±.0005 ±.001 CH 2 C1 2 , 3.4K, 9.4450 GHz) a,. , . -1 Values in cm ,

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rt3

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166 C3 O

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+J CO £= O QJ i— I OO I/O CD

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168

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0) OJ •<-

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170

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•rE fro •<— i—

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172

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0) CT> CT> CO -rCO

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174

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— o
PAGE 182

176

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177 as it is in this complex, gj. ef ^=2g,. Thus, g =2.200 which is close to the value of 2.18 obtained by Cotton and Pedersen. 36 The value for g.. of 1.9465 differs from theirs (2.03), but they did not actually observe the parallel signal at 4 K. The value obtained here for Aj_ was 26.7 x 10" 4 cm" 1 and for Aj, was 21.7 x 10~ 4 cm" 1 . The latter value differs considerable from the previously reported value of 9 x 10" 4 cm" 1 . However, the value reported here is based on an observed signal. The EPR parameters and relative intensities of the zero-spin to 1=5/2 signals were solvent independent. The linewidths did vary somewhat with solvent. The narrower linewidths in 1:1 toluene/dlchloromethane (Wj_=40 MHz and W w =10 MHz, hwhh) allowed better resolution of the perpendicular region, but led to extensive noise in the parallel region. The broader linewidths in 9:1 methanol/ethanol (W^=90 MHz and W /y ,=10 MHz) gave less noise in the parallel region. The relative intensities of the zero-spin to 1=5/2 signals in all solvent systems corresponded to 54.09% with 1=0 and 45.91% with 1=5/2. This is the ratio that would be expected for derealization over both Ru atoms. For a ruthenium dimer, 42.29% of the dimers will have two zero-spin nuclei, 41.83% will have one 1=5/2 Ru nucleus and 8.87% will have two 1=5/2 nuclei. The last type will give a signal of very low intensity since not only will there be few such dimers, the transitions will be spread out over 11 lines. The high nuclear spin species was not considered in the simulations. Derealization was proposed 36 earlier for Ru 2 (but)4Cl, but since only a rather broad signal in the perpendicular region and none in the parallel region was observed, it could not be claimed with complete certainty. The observation here of the parallel signal which had much narrower linewidths and larger hyperfine splittings (in G) than the perpendicular

PAGE 184

178 signal allows this derealization to be unequivocally determined. Furthermore, in the toluene/dichloromethane glass the perpendicular linewidths were much narrower than in the previous work. This allowed the relative intensities in that area of the spectrum to be more clearly determined. To investigate this derealization as a function of solvent, anion and added Lewis bases, other spectra were obtained. A totally symmetric species, for example, [Ru2(but)4(CH30H) 2 ](CF 3 S03), would be expected to contain equivalent Ru atoms, but an asymmetric species such as Ru 2 (but) 4 (B)Cl where B=Lewis base, might not. The effect of chloride coordination was investigated by generating [Ru2(but) 4 (CH 3 0H) 2 ](CF3C03) in solution by addition of one equivalent of Ag(CF 3 S03) to a solution of Ru 2 (but) 4 Cl in 9:1 methanol /ethanol leading to precipitation of AgCl. The species in solution 1s presumably [Ru2(but)4(CH30H) 2 ](CF 3 S03) since CF3SO3" 1s such a poorly coordinating anion. The EPR spectrum of this species was identical to that obtained for Ru 2 (but) 4 Cl in 9:1 methanol /ethanol indicating extensive chloride dissociation in agreement with conductivity results. 48,161 j ne parameters and relative signal intensities were the same for the CF3SO3" species as for Ru 2 (but) 4 Cl in 1:1 toluene/dichloromethane with 1% v/v acetone in which the complex exists most likely as Ru 2 (but) 4 ( (Ct^^COjCl with axially coordinated acetone and chloride. Acetone, even in excess, would not be expected to displace chloride in such a low dielectric constant medium. 168 Furthermore, a solution of Ru 2 (but) 4 Cl in 1:1 toluene/dichloromethane with exactly one equivalent of pyridine present gave an EPR spectrum similar to that for acetone. In this low dielectric solvent the predominant species is most likely Ru2(but) 4 (pyr)Cl. The main difference in the EPR spectra occured when the

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179 solvent was changed from 1:1 toluene/dichloromethane to 9:1 methanol/ ethanol. The linewidths in the former solvent were narrower because it forms a better glass and has a lower dielectric constant. EPR spectroscopy can provide information regarding equivalence of the Ru atoms. If complete localization of unpaired electron spin density occurred, one would observe an intensity ratio of 70.21% for the signal arising from spin on an 1=0 nucleus to 29.79% for that of an 1=5/2 nucleus. As expected, this result was never observed since it is unreasonable to expect localization to this extent in a strongly metalmetal bonded complex. Derealization of unpaired electron spin density over both metal atoms has been found unequivocally in analogous S=l/2 carboxylate dimers of Mo, 37 » 38 Re, 35,39 and Rh, 133 as discussed in the previous chapter. If complete electron derealization existed, the relative intensities of the zero-spin to 1=5/2 signals would be 54.09% to 45.91%. This was the observed result. However, this does not prove that the two ruthenium atoms are chemically equivalent. For nonequivalent nuclei, the hyperfine pattern would show different A values for the chloride-coordinated Ru atom versus the pyridine-coordinated Ru in Ru4(but) 4 (pyr)Cl. Given the experimental linewidths in the parallel region of 3.34 x 10" 4 cm" 1 , the difference in A values must be considerably less than this since only one A value could be resolved. Thus, the question of the equivalence of electron derealization over the Ru atoms cannot be completely answered without the use of isotopically pure ruthenium. Natural abudance ruthenium is dominated by the many zero-spin isotopes which give no information on chemical equivalence and the low abundance of the two 1=5/2 nuclei makes resolution of slight changes in A values impossible. In contrast,

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130 isotopically pure complexes would show either an eleven line spectrum in a 1:2:3:4:5:6:5:4:3:2:1 pattern if the Ru atoms were exactly equivalent or a sextet of sextets if they were not. Unfortunately, the high cost and limited avilability of isotopically pure ruthenium makes definitive work on this matter prohibitive. Infrared and Raman Spectroscopy Stephenson and Wilkinson " reported the Far IR spectrum of Ru 2 (0 2 CCH 3 )4Cl. Absorption bands were observed at 403 and 341 cm" 1 which they assigned to Ru-0 and Ru-Cl stretching modes, respectively. The latter is where a metal terminal chloride stretch would normally occur. 169 However, in Ru 2 (0 2 CR)4Cl the chlorides are bridging with a very long and thus weak Ru-Cl bond. Therefore, one would expect v(RuCl ) to occur at a much lower frequency. For example, the chloride bridged polymeric complexes N1(pyr) 2 Cl 2 170 and Co(pyr) 2 Cl 2 171 have v(MCl ) at 186 and 193 cm" 1 , respectively. Much later, Clark and Ferris 149 performed an extensive resonance Raman study on a series of ruthenium carboxylate dimers as KC1 pellets. No bands were assigned to a Ru-Cl stretch. Strong bands assigned to v(Ru-Ru) and v(Ru-O) were observed at room temperature at 327.3 and 369.2 cm" 1 , respectively for Ru 2 (0 2 CCH 3 ) 4 Cl and at 330.8 and 376.5 cm" 1 , respectively for Ru 2 (but)4Cl. These Ru-Ru and Ru-0 bands have a^,, symmetry in D^^ and are thus Raman allowed and IR forbidden. A large number of progressions of these bands was also seen. The Far IR spectrum of Ru 2 (but)4Cl was obtained here as a Csl pellet and is shown in Figure 5-10. A strong band at 195 cm" 1 was observed. This band is very likely v(Ru-Cl) due to Its Intensity and low frequency. A strong band was also seen at 460 cm" 1 which could be the asymmetric Ru-0 stretch with a2u symmetry in D4 n .

PAGE 187

«3+J

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182 33NVlilWSNVdl %

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183 Medium bands were observed at 342 and 375 cm" 1 . The assignment of these bands is uncertain. The former is analogous to the band at 341 cm" 1 reported for Ru 2 (0 2 CCH 3 ) 4 Cl. It is conceivable that distortions from idealized D 4h symmetry occur on the fast IR time scale that are averaged out using the much slower method of x-ray crystallography. These distortions could lower the symmetry allowing observation of the normally IR forbidden a lg modes. Due to instrumental difficulties, it was not possible to obtain a good Raman spectrum of Ru 2 (but) 4 Cl for comparison to previous work. A low resolution Raman spectrum of Ru 2 (but) 4 Cl in methanol solution showed a broad band at 360 cm" 1 which presumably arose from the v(Ru-Ru) and v(Ru-O) vibrations. No band was observed at -200 cm" 1 since Ru 2 (but) 4 Cl Ionizes in methanol. MO Schemes and Theoretical Calculations The short Ru-Ru distance in Ru 2 (but) 4 Cl of 2.281 A versus 2.65 A in Ru metal, 147 implies a strong interaction. Thus, some sort of metalmetal bonding model is needed and various MO schemes have been proposed. The MO scheme of Norman and co-workers, 44 shown in Figure 4-1, is in reasonably good agreement with the experimental results. They propose that in the ruthenium carboxylate dimer system there are singly occupied 6* and ** orbital s that are very close in energy for both Ru 2 (0 2 CH) 4 + and Ru 2 (0 2 CH) 4 Cl 2 ". In addition to justifying the quartet electronic ground state of Ru 2 (but) 4 Cl, this MO scheme can successfully explain the EPR parameters observed. The arguments used to interpret the EPR spectra of the rhodium systems described in the previous chapter can be used again here. However, in the ruthenium system, transitions involving both the 5* orbital (b lu in D 4h ) and the it* orbital s (e q in Q 4n ) must be considered. In this system, there is no concern over the

PAGE 190

184 relative order of these two sets of orbital s, since both are semioccupied. Since L z transforms as a2q, only excited states with e q or b 2tl symmetry can contribute to shifts in g„ from g e ( since only b lu x a 2q x ^u anc * e q x a 2q x e q coirta i n a lg)« There are no excited states of accessible energy with e g symmetry, however there are several with b 2u . A transition of the unpaired electron in 6* to an empty Ru-0 a* orbital with b 2u symmetry would give a negative shift in g.. . Norman and co-workers 44 calculated this contribution to be -0.042. However, since a g shift of +0.03 was originally reported, ° Norman and co-workers also included promotion of electrons from filled Ru-0 a and it orbital s with b 2u symmetry to obtain a g,j shift of +0.013 leading to a total of -0.029. Since an accurate g„ shift of -0.056 was observed here, it appears that only the former mechanism applies and was perhaps slightly underestimated. The situation for g^ is more complicated. Since l_ x transforms as e g in D 4h , excited states of e u , a lqf a 2g , b lg , and b 2q symmetry all can contribute to shifts in g, from g e (since b^ u x e q x e u and all g x g x g states contain a lg ). Almost all of these states arise from transitions involving filled orbital s, such as Ru-Ru it (e u ) or RuRu 5 (b 2g ), so a positive shift in g^ is expected. Norman and coworkers were able to rougKly calculate g^ including ten excited states to obtain a g value of 2.18, in good agreement with the observed value of 2.200. One can also attempt to obtain information from A values. Values of A iso =(A // +2A_ I )(l/3)=25rlO~ 4 cm" 1 and A dip =(A 7/ -A x ) (1/3)— 1.67xl0~ 4 cm~ * were observed. A simple method for relating these values to a bonding scheme is to use atomic hyperfine parameters and disregard the ligand effects. These methods to relate A values with types of bonding have been used

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185 successfully in ligand free, matrix isolated metal dlmers. 1*5,163 y do this for Ru 2 (but)4Cl, one must approximate the complex as Ru 2 with a d6 1 (xy)diT 2 (xz,yz) electronic ground state. This approximation is inaccurate since it would give Aj so =0 due to the assumption that these are pure d states and thus with no s electron density at the nucleus. It would also give A dip =[(l/3) (5 dxy )+(2/3)(S dxz )](P)(l/2)=0 since 3 dxy = -2/7 and ci dx2 yz =+l/7. It is necessary to use a more sophisticated approach that would take into account the fact that the Ru-Ru bond orbitals are not pure d states and would include spin polarization effects. Norman and co-workers 44 have performed this sort of calculation and obtained A values for Ru 2 (0 2 CH) 4 + of A 1 so =9 x lO'^cm" 1 and A dl p =-0.6 x 10" 4 cm _1 . As these workers point out, these theoretical values are very crude. Ideally, inclusion of a very large number of higher order terms is needed. This would lead to greater electron spin density at the nucleus. The value reported here for A,, (21.7 x 10" 4 cm _1 ) is much larger than the previously reported 36 value (9±3 x 10" 4 cm _1 , also written as 93, presumably a typographical error) which causes A d1 D to be in much better agreement with the theoretical value. A different theoretical approach towards developing an MO scheme for metal carboxylate dimers was recently proposed by Sowa and coworkers. 125 They combined the d orbitals of monotneric Rh(0 2 CR) 2 L units to obtain a metal -metal bonded system. This method was applied here to Ru 2 (0 2 CR) 4 L 2 where L=C1" as in the chloro-bridged solid or CH3OH as in solution. The results are shown in Figure 5-11. It can be seen that it is very difficult to use this MO scheme consistently to obtain a reasonable S=3/2 electronic ground state for the ruthenium carboxylate dimer. Disregarding the effect of the axial ligand L, it is possible to

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Figure 5-11. Formation of metal -metal bond orbital s for Ru ? (CLCR)»L ? using the method of Sowa and 125 co-workers. (A) D 4h Ru(0 2 CR) 2 as basis set, xy > z ; (B) as in A, but with z 2 > xy; (C) C 4v Ru(0 2 CR) 2 as basis set, xy > z ; (D) as in C, but with z > xy. The ordering 2 xy < z is more likely for alkyl as opposed to fluorocaboxylates.

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137 xz.yz xz,yz xz.yz Ru I ,0 I ,o I ' I ' Ru — Ru o I o I L Ru /I 1 I L — Ru — Ru' — L o 1 I '4h '4v

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188 obtain a quartet ground state, particularly with d x 2 > d xy in energy. i or This is proposed to be the case with alkylcarboxylate Hgands. " However, when L is included, the very high energy a orbital must be populated to give an S=3/2 state. This seems unlikely so this MO scheme would suggest a doublet electronic ground state for Ru 2 (0 2 CR) 4 L 2 . This is clearly not the case. The problem with the MO scheme of Sowa and coworkers 125 is that it treats the metal-ligand interactions as being of primary importance with the metal-metal interaction included afterwards. This approach is not valid, the metal dimer is a distinct unit with the metal-metal bond playing a major, if not dominant, role. The qualitative MO scheme used is much more satisfactory at explaining the properties of the ruthenium carboxylate dimer and is in agreement 44 • with the sophisticated calculations of Norman and co-workers. As a final note, it is possible that deviations from D 4n symmetry, which would remove the degeneracy of the ir* orbitals, would lead to an S=l/2 electronic ground state. The oxalate complex mentioned above, Ru 2 (0 2 CCH 3 ) 2 (C 2 4 ) 2 ~, fits this requirement, but 1s nevertheless an S=3/2 system (u eff =4.22 by the Evans method). 157 This is not surprising, since the oxalate and carboxylate Hgands are similar and the coordination of the Ru 2 5+ core is 8 in both casees. If a ruthenium dimer with two sets of very different Hgands could be prepared, then one ** MO or quite possibly the <5* MO might be low enough in energy to be filled and give a doublet ground state molecule. Reactivity As described previously, in contrast to rhodium or molybdenum, no complexes of general formula Ru 2 (0 2 CR) 4 BCl or [Ru 2 (0 2 CR) 4 B 2 ]Cl have been reported. Rather, strong Lewis bases such as pyridine or PPh3 react to

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189 form complexes such as [Ru 2 0(0 2 CR) 6 (pyr)3] + and Ru 2 0(0 2 CR) 6 (PPh3)3. 158,159 It was found here that upon exposure to air of a solution of Ru 2 (but) 4 Cl in CH 2 C1 2 with excess pyridine (-10 equivalents), the dark blue-green color of the oxo-bridged trimer rapidly developed. Similar dark blue-green decomposition products were observed with N-methylimidazole, 4-picoline-N-oxide and triethylamine. By contrast, a red color was observed with primary amines such as propylamine which most likely resulted from formation of "ruthenium red" species by analogy with the known 172 complex [Ru 3 2 (NH3) 14 ]Cl 6 .4H 2 0. However, when air was rigorously excluded a dark brown hygroscopic solid could be isolated from the pyridine solution which was best formulated as Ru 2 (but) 4 (pyr) 2 Cl. This complex can be prepared by addition of excess pyridine (5-10 equivalents) to Ru 2 (but) 4 Cl in CH 2 C1 2 followed by removal of solvent and washing with hexane. The EPR spectrum of this complex in CH 2 C1 2 at 4 K showed signals at g e -4.4 and 1.95 as with Ru 2 (but) 4 Cl Itself, indicating the S=3/2 dimer remained intact. As far as can be determined, this represents the first Lewis base adduct of the ruthenium carboxylate dimer to be isolated. It was not possible to isolate a similar complex with triphenylphosphine. Despite careful exclusion of air and use of only two equivalents of PPh3» small amounts of the purple oxo-bridged trimer were obtained along with unreacted Ru 2 (but) 4 Cl. In contrast to the formally RU3 (111,111,111) species formed with pyridine and water, the PPh 3 complex is formally a £113(11, III, III) system. Since the complex is normally synthesized using a large excess of phosphlne, it is possible that some PPh3 reduces a RU3 (111,111,111) species with the remainder coordinating to form Ru 3 ( II,III,III)0(0 2 CR) 6 (PPh 3 )3. Ligand reactivity would make it very

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190 difficult to isolate any ruthenium carobxylate dimer phosphine product. In reactions with weaker Lewis bases, ^(but^Cl shows no tendency to decompose. Solutions of ^(but^Cl in acetone, acetonitrile, DMSO, and tetrahydrothiophene (THTP) in air showed no visible change over prolonged periods. However, attempts to form adducts with these Lewis bases let only to recovery of starting material. Unlike these others, THTP is a strong base towards covalent interactions (C B =7.9 vs. 6.4 for pyridine), 27 "* 29 but is weak towards electrostatic interactions (E B =0.341 vs. 1.17 for pyridine). ~ 29 This indicates that, as is often the case, a combination of electrostatic and covalent properties are necessary for a strong Lewis acid-base interaction. Conclusion ^(but^Cl, a typical example of the ruthenium carboxylate dimer series was examined by a variety of physical methods. Variable temperature magnetic susceptibility on a powder sample in conjunction with frozen solution EPR spectroscopy demonstrated that the complex is an S=3/2 system as was originally proposed. 48 In contrast to earlier suggestions, 36 there are no noticeable interdimer magnetic effects despite the polymeric solid state structure of the complex. ^(but^Cl does exhibit large zero-field splitting interactions due to spin-orbit coupling phenomena. Unpaired electron spin density is delocalized over both Ru atoms as with other S=l/2 metal carboxylate dimer radicals. It is possible that the two Ru atoms are not chemically equivalent, but this difference cannot be resolved without the use of isotopically pure ruthenium. Far IR spectroscopy of solid Ru 2 (but)4Cl showed a previously

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191 unreported band which is assigned to v(Ru-Cl). The results obtained from experiments here are in good agreement with theoretical studies by Norman and co-workers. In contrast, other MO schemes 125 could not be satisfactorily applied to the ruthenium carboxylate dimer system. Reactivity studies on Ru 2 (but) 4 Cl indicate that although strong Lewis bases readily decompose the metal -metal bonded dimer system, it is possible to isolate an axial Lewis base adduct of the type more easily obtained with the rhodium or molybdenum carboxylate dimers. With fairly weak bases it was not possible to isolate adducts, but as no decomposition occurred, studies can be performed on the solution chemistry of Ru 2 (but) 4 Cl in the presence of these bases. Thus, it appears that although the electronic structure of the ruthenium carboxylate dimer can be reasonably well explained, the Lewis base reactivity of this complex is less clear. As was found with Rh 2 (0 2 CCF3) 4 , the metal-metal bonded dimer is generally quite stable, but often under mild conditions can be converted to greatly different species. In the case of Rh 2 (0 2 CCF 3 ) 4 , monomeric Rh(I) and Rh(III) complexes were formed. With Ru 2 (but) 4 Cl trimeric oxo-bridged species resulted. In both cases the products are thermodynamically very stable species to which the metal carboxylate dimer converts when given the opportunity. Experimental Section Magnetic Susceptibility Magnetic susceptibility measurements were performed on an S.H.E, Corporation (San Diego, CA) VTS-50 SQUID magnetometer. Ten measurements were recorded at each temperature at a field of 10.0 kG with the mean

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192 and standard deviation at each point directly calculated. Hg[Co(NCS) 4 ] was used to check the instrument and the susceptibility value obtained agreed with the literature value. 162,173 j ne assistance of Dr. Michael Weissman and Dr. Apurba Roy, both Department of Physics, University of Illinois, Urbana, IL, is appreciated. EPR Spectroscopy EPR spectra were recorded on a Bruker ER-200D X-band instrument equipped with an Oxford liquid helium cryostat. The magnetic field was previously calibrated and the microwave frequency measured by a Systron Donnor Model 6245A instrument. Samples were ~1 x 10" 2 M in sealed, degassed quartz tubes. The assistance of Dr. Peter Debrunner and Mr. Michael Hendrich, both Department of Physics, University of Illinois, is appreciated. IR and Raman Spectroscopy Far IR spectra were recorded on a Digilab Fourier transform IR spectrometer. Ru2(but) 4 Cl was prepared as a Csl pellet (1% w/w). The assistance of Dr. David Tanner and Mr. Richard McCall, both Department of Physics, University of Florida, Gainesville, Florida, is appreciated. Raman spectra were recorded on a Spex Raman spectrometer using an argon ion laser at 488.0 nm. Ru 2 (but)4Cl was prepared as a methanol solution (-5 x 10~ 2 M.). The assistance of Dr. Willis Person and Mr. Luis Hernandez, both Department of Chemistry, University of Florida, is appreciated. Computer Simulations Computer simulations were performed using a DEC VAX 11/780 computer. For the magnetic susceptibility data the master program

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193 DSUSFIT was used. 174 " 177 The program uses the non-linear least-squares fitting program DSTEPIT. 178 Copies of the programs are given in Appendix F. The assistance of Dr. David Hendrickson and Mr. Mark Timken, both Department of Chemistry, University of Illinois, is appreciated. For the EPR data the program QPOW was used. 144 Copies of the EPR programs are given in Appendix E. In the simulations done here, the frame of reference was chosen so that the g tensor was diagonal (with g x =g y =g,) and the A tensor was held in the same orientation as the g tensor. The nuclear g tensor was approximated as an isotropic g N =y N /I. The assistance of Dr. R. Linn Belford and Mr. Jeffrey Cornelius, both Department of Chemistry, University of Illinois, is appreciated. Synthesis Tetraki s ( n-butyrato )di rutheni um( 1 1 , 1 1 1 ) Chi ori de Ru 2 (but) 4 Cl was synthesized following the procedure of Stephenson and Wilkinson. 48 An alternative method 179 which uses LiCl as an additional chloride source was not as successful. RuCl3(H 2 0) x (1 g, Aldrich) was refluxed in a solution of _n_-butyric acid (35 mL) and nbutyric anhydride (7 mL) for 6 h. The reaction was run under an oxygen atmosphere. It is important that 2 be bubbled vigorously through the reaction mixture and not just passed over the solution. Unless this is done, large amount of black, insoluble reduced Ru carbonyl species are produced. These complexes were observed by the original workers. 48 After 6 h (and no more), the solution was filtered while hot and cooled at 10 C overnight. Filtration and washing with diethylether yielded crude Ru 2 (but)4Cl which was then recrystallized twice from hot butyric acid. It is important that the recrystallizations be done fairly

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194 quickly since Ru 2 (but) 4 Cl is converted to the oxo-bridged trimer in hot butyric acid. Anal. Calcd. for Ru 2 C 16 H 28 8 Cl: C, 32.79; H, 4.82; CI, 6.05. Found: C, 32.65; H, 4.80; CI, 5.98. Bis(pyridine)tetrakis(n-butyrato)diruthenium(II,III) Chloride Ru 2 (but) 4 Cl (0.20 g, 0.34 mmol ) was suspended in CH 2 C1 2 (3 mL) under nitrogen. To this was added pyridine (0.20 mL, 2.5 mmol). A dark brown solution immediately resulted. After stirring 15 min, the solvent was removed and washed several times with hexane. Anal. Calcd. for Ru 2 C 26 H 38 N 2 8 Cl: C, 41.96; H, 5.15; N, 3.76; CI, 4.76. Found: C, 41.61; H, 5.14; N, 4.01; CI, 4.36. Magnetic Susceptibility Models Method 1. This model used the full spin Hamiltonian for an octahedral S=3/2 system as follows: X = 3{g xVx + g y^y + g z H zV + DC *z " ( 1/3 > s < s + ™ + E( ^ " §) D and E are scalar zero-field splitting parameters. With only axial distortion, E=0 and g x =g y =g , . The matrix elements for this spin Hamiltonian are given in Appendix B. Method 2. This model used the exponential form for the zero-field susceptibility of an octahedral S=3/2 complex with axial zero-field splitting. The equations were taken from O'Connor 173 and are as follows: 2 2 2 2 Ng /| 8 1 + 9 exp(-2D/kT) Hg ^ 3 4 + (3kT/D)(l exp(-2D/kT)) y = — — — ———————— )( = ————— i " kT 4(1 + exp(-2D/kT)) M kT 4(1 + 2 exp(-2D/kT))

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195 An orientational average, x-j so = (x,, + 2x^)(l/3) was used. Method 3 . This model used the Ising model which considers a onedimensional infinite chain of antiferromagnetically coupled spins. The full exponential form for the zero-field susceptibility for S=3/2 (and S=l) has been worked out by Suzuki, Tsujiyama, and Katsura. 5 The equations are quite lengthy and will not be reproduced here. No provisions are made for effects other than an anti ferromagnetic interaction along the linear chain. Based on the crystal structure of Ru 2 (but)4Cl, J 47 this model is not unreasonable since there is an infinite approximately linear chain of chloro-bridged Ru2(but)4 + units. ilethod 4 . This model attempted to include both intramolecular zero-field splitting and intermolecular anti ferromagnetic exchange. This was done using the molecular field approximation. 173 The parameter zJ was included to account for weak magnetic interactions between S=3/2 units. The equation is as follows: ' x i X = CT 1 1 ^zJ/Ng.Vh.,. Here x-j=x )( or x,» 9i = 9// or 9_l » and tne equations for xj are those given in Method 2. Method 5. This model used a dimer of $^=$2=3/2 units that are antiferromagnetically coupled with both Sj and S 2 undergoing the same axial zero-field splitting. This model treats only interactions between a pair of Ru 2 (but) 4 + units and ignores any longer range interactions. To develop a model including long range interactions by using a trimer (either linear or joined) or higher polymers and including zero-field

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196 splitting on all the units would be very complex. Laskowski and Hendrickson 175 have studied an S 1 =S 2 =5/2 dimer with axial zero-field splitting on both Sj and S 2 using the following spin Hamiltonian: M = g /| 6H z .s z + g x s(H x .s x + Hi) + DCS 2 -(1/3)S(S + 1)] 2JS r $ 2 In this equation a coupled basis set, $=$^$2, is used. 180 This basis set derived for an S=3/2 dimer is given in Appendix C. D is the axial zero-field splitting parameter. J is the isotropic exchange parameter (Heisenberg-Dirac-Van Vleck form). Only an isotropic J is needed since Si and S 2 are symmetry related. •* The matrix elements for this spin Hamiltonian are given in Appendix D.

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CHAPTER VI GENERAL CONCLUSIONS There are several interesting conclusions that can be drawn from the work described in this thesis. One is that the metal carboxylate dimer is a relatively stable species even though metal-metal bonds, such as the one existing in the molybenum dimer, are rarely found in inorganic complexes and have no analogy in organic compounds. However, in most cases, particularly those involving interpretation of spectroscopic results, the metal dimer can be treated as a single unit using a simple MO scheme. The metal-metal interaction is strong enough that the complex is no longer a species containing two metals, but can be best thought of as a complex containing a single metal, but with twice the normal size and coordination number. The reactivity of the metal carboxylate dimer can also be explained by this MO scheme, but it is not always sufficient. In many cases, the reaction products are the same as would be obtained using monomeric complexes of the metal as reactants, and not carboxylate dimers of a different metal, even though the two dimers might have the same MO formulation. Furthermore, the preference of certain dimers for specific oxidation states is not always fully rationalized by the MO scheme. It also depends on which oxidation states are commonly found for monomeric complexes of the metal. This is particularly true for ruthenium. Another important point is that the nature of the carboxylate ligand is crucial in determining the reactivity of these dimers. There is often the tendency in inorganic 197

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198 chemistry to emphasize comparisons between different complexes based solely on the metals involved, but it is no less important to study the effects of different ligands and hold the metal constant. This can be seen in the reactivity of the rhodium carboxylate dimer. This kind of systematic investigation can then be applied to more complex multi-metal systems such as those in biological systems or of industrial importance.

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CO O CTl CTl ^J" i^ lo r-^ o ct> ct> r-. CTl CO CTi CO 10 10 to in m K) (D W ID H O O CO «x> CO CO CvJ CM C\J CvJ CM co co co co co oo oo oooooooooooooooooooooo lo

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APPENDIX B. UPPER RIGHT HAND USED IN METHOD 1 -ZERO MATRIX ELEMENTS FOR SPIN HAMILTON IAN

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APPENDIX C. COUPLED BASIS SET FOR S = Sj + S 2 WHERE S 2 = 3/2, USED IN METHOD 5 (DERIVED USING REF. 180) |S, M >=|M , M_ > s s 1 s 2 |3, ±3>=|±3/2, ±3/2> 1 3, ±2>=(l//2) 1+3/2, ±l/2> + (l//2)|±l/2, ±3/2> |3, ±l>=(l//5)|±3/2, ±l/2> + (1//5) |±l/3, ±3/2> + (/375) ±1/2, ±l/2> |3, 0>=(l//20)j+3/2, -3/2> + (1//20) |-3/2, +3/2> +(/5720) |+l/2, -l/2> + (•'9720)1-2/1, +l/2> |2, ±2>=±(l//2)|±3/2, ±l/2> (1//2) |+l/2, ±3/2> |2, ±l>=±(l//2)]±3/2, l/2> (1//2)| 1/2, ±3/2> |2, 0>= (1/2)^3/2, -3/2> (l/2)|-3/2, +3/2> +(l/2)K/2, -l/2> (l/2)|-l/2, +l/2> |1, ±1>= (/37T0)|±3/2, l/2> + (/3/10)| 1/2, ±3/2> (/4/To) l±l/2, ±l/2> |1, 0>= (^9720)1+3/2, -3/2> + (/9720)| -3/2, +3/2> -(l//20)|+l/2, -l/2> (1//20)| -1/2, +l/2> |0, 0>= (l/2)|+3/2, -3/2> (l/2)|-3/2, +3/2> -(1/2)1+1/2, -l/2> + (l/2)|-l/2, +l/2> 201

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APPENDIX D. UPPER RIGHT HAND NON-ZERO MATRIX ELEMENTS FOR SPIN HAMILTONIAN USED IN METHOD 5 = < 3, ±3 < 3, ±2 < 3, ±1 < 3, < 2, ±2 < 2, ±1 < 2, < 1, ±1 < 1, < 0, < 3, ±1 < 3, < 2, < 3, 3 < 3, 2 < 3, 1 < 3, -1 < 3, -2 < 2, 2 < 2, 1 < 2, < 2, -1 < 1, 1 < 1, |M|3,

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APPENDIX E COMPUTER PROGRAMS USED FOR EPR SPECTRAL SIMULATIONS This appendix contains the computer programs used for EPR spectral simulations of both powder pattern and single crystal S=l/2 systems. The original versions of the programs titled XPOW, XTAL, XCAL, and EPRLIBS can be found in Reference 144. XPOW calculates a powder pattern spectrum; XTAL a single crystal spectrum, and XCAL calculates field positions and intensities for a series of single crystal spectra. EPRLIBS contains subroutines which set up the spin Hamiltonian matrices which are diagonalized to give eigenvalues and eigenvectors from which the transition fields and Intensities are calculated. EISPACK subroutines, developed at Argonne National Laboratory, are used for the matrix operations. Further details can be obtained by inspection of the programs and from the literature. 144 The program titled DXTLFIT calculates EPR parameters (g and A values) for single crystal spectra by fitting the experimental field positions to calculated transitions using the DSTEPIT non-linear least-squares curve fitting program. 178 203

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7

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205 71 C LINE *1: 72 C 73 C KRYSTL.NUCLQ.NZB.NZC, IPHASE, ISPECP, MARKTR 74 C 75 C KRY5TL: =0 FOR INPUT A5 PRINCIPAL VALUES AND EULER ANGLES 76 C (OBTAINED FROM POWDER PATTERN SPECTRUM). 77 C KRY5TL: =1 FOR INPUT A5 FULL MATRICES (TENSORS, OBTAINED 79 C FROM SINGLE CRYSTAL SPECTRUM). 7? C NUCLQ: =0 IF NO QUADRUPOLAR PARAMETERS ARE TO BE READ IN 80 C NUCLQ: =1 IF QUAORUPOLAR PARAMETERS ARE TO BE READ IN FROM 81 C THE DATA FILE (UNIT 8). 82 C NZB, NZC: =0 FOR "NORMAL" USE OF HYPERFINE-5QUARED MATRIX 83 C PROJECTIONS FOR 5UPERHYPERFINE NUCLEI B AND C RESPECTIVELY 84 C =1 FOR USE OF FIRST-POWER PROJECTIONS SUITABLE FOR THE 85 C CA5E OF A NUCLEAR ZEEMAN TERM DOMINANT OVER THE HYPERFINE 86 C TERM. 87 C IPHASE: =»0 SPECTRUM IS MULTIPLIED BY 1. IPHA5E NONZERO 88 C CALCULATED SPECTRUM IS MULTIPLIED BY -1 SO THE RESULT 89 C IS 180 DEGREES OUT OF PHASE WITH THE ORIGINAL (IPHASE0) 90 C ISPECP: A NONZERO VALUE FOR ISPECP WILL PRINT INTO A FILE 91 C (LOGICAL UNIT 12) A DIGITIZED RECORD OF THE SPECTRUM. 92 C MARKTR: A NONZERO VALUE FOR MARKTR WILL CAU5E THE PROGRAM 93 C TO COMPUTE THE FIELD POSITIONS OF THE TRANSITIONS ALONG 94 C THE PRINCIPAL AXES. THEY ARE PLOTTED OUT ALONG THE BOTTOM 95 C OF THE SIMULATION IN THE ORDER X,Y,Z (TOP TO BOTTOM). 96 C THI5 FEATURE 15 AUTOMATICALLY TURNED OFF WHEN 97 C THE THETA RANGE IS NOT THE DEFAULT, I.E., WHEN THETA1 IS 98 C NOT ZERO AND/OR THETA2 IS NOT 90 OR 180 DEGREES. 99 C 100 C LINE #2: 101 C 102 C FREQ,IDERIV,IFORBD,BZEMN 103 C 104 C FREQ: THE EXCITATION FREQUENCY IN GHZ. 105 C IDERIV: =»2 FOR A 5ECOND DERIVATIVE SPECTRUM. OTHER THAN 106 C 2 GIVES A FIRST DERIVATIVE SPECTRUM. 107 C IFOR80: »0 FOR NORMAL SPECTRUM. WHEN IFORBD IS NONZERO 108 C THE INTENSITIES OF THE ALLOWED TRANSITIONS WILL BE SET 109 C TO ZERO. THE SPECTRUM WILL THEN CONTAIN ONLY FORBIODEN 110 C CONTRIBUTIONS. 111 C BZEMN: THE FIELD AT WHICH THE HAMILTONIAN WILL BE 112 C DIAGONALIZED. A ZERO WILL GIVE THE SAME CALCULATION 113 C A5 WITH THE ORIGINAL QPOW PROGRAM. THIS FEATURE ALLOWS 114 C THE ACCURACY OF THE FREQUENCY-SHIFT PERTURBATION FORMULA 115 C TO BE TESTED. (USEFUL ESPECIALLY AT LOW FIELDS). 116 C 117 C LINE *3: 118 C 119 C SPINA, 5PINB,SPINC, NEB, NEC 120 C 121 C SPINA: THE SPIN OF THE MAJOR NUCLEUS 122 C SPINB, 5PINC: SPINS OF THE SUPERHYPERFINE NUCLEI B AND C 123 C NEB, NEC: NUMBER OF EQUIVALENT NUCLEI FOR SPINB AND 124 C 5PINC, RESPECTIVELY 125 C 126 C LINE *A: 127 C 128 C VERTSF.SCLPK 129 C 130 C VERTSF. SCALING FACTOR FOR INTENSITY. THE DEFAULT VALUE 131 C IS 100. VERT5F MAY BE GREATER THAN 100, IN WHICH CASE 132 C ANY PEAK OVER 100.0 WILL BE OFF-SCALE (TR'iwrATED) . 133 C 5CLPK: A NONZERO VALUE FOR SCLPK INDICATES THAT THE VALUE 134 C IS TO BE USED A5 AN ARTIFICIAL MAXIMUM INTENSITY. 135 C THIS ALLOWS THE U5ER TO COMPARE RELATIVE INTENSITIES OF 136 C VARI0U5 PLOTS. A ZERO VALUE DIRECTS THE PROGRAM TO FIND 137 C THE MAXIMUM INTESITY OF THE SPECTRUM AND USE THIS A5 A 138 C SCALING PARAMETER. 139 C 140 C LINE *3:

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206 141 C 142 C NTR,NTH,NPH,LPH,THETA1,THETA2 143 C 144 C NTR: NUMBER OF HYPERFINE TRANSITIONS FOR SPINA; CALCULATES 145 C THE PRIMARY TRANSITIONS FIRST (DELTA MI-O), THEN 146 C /DELTA MI-1/, /DELTA MI-2/ ,..., /DELTA MI-2*MI / . BECAUSE 147 C OF SIZE LIMITS ON P AND TM ARRAYS, NTR MAX-64 (1-7/2). 148 C FOR A GIVEN SPINA. NTR MAX<2*MI+1 )**2 50 THE DEFAULT VALUE 149 C IS SET TO THIS NUMBER IN THE DEFAULT ASSIGNMENT SECTION. 150 C NTH: -NUMBER OF THETA DIVISIONS (VERTICAL GRID) 151 C NPH: -NUMBER OF PHI DIVISIONS (HORIZONTAL GRID) AT THE 152 C EQUATOR. 153 C THERE ARE SIZE LIMITS ON NTH AND NPH BECAUSE OF THE 5IZE 154 C OF THE ARRAYS CT,5T,CP,SP. NTH MUST BE SMALLER THAN 180. 155 C THE LIMIT FOR NPH VARIES WITH NTH. IN PRACTICE, IT 156 C SHOULD NOT BE NECESSARY TO EXCEED NTH-50 OR NPH-20 . 157 C LPH INDICATES THE PHI (HORIZONTAL) RANGE USED. 158 C LPH-1 FOR PHI RANGE OF TO 90 DEGREES 159 C LPH-2 FOR PHI RANGE OF TO 180 DEGREES 160 C THETA1 AND THETA2 INDICATE THE THETA (VERTICAL) RANGE USED. 161 C THETA1-INITIAL THETA (0 TO CALCULATE THE ENTIRE SPECTRUM, 162 C ABOUT 40 DEGREES TO CALCULATE ONLY THE PERPENOICULAR PART) 163 C THETA2-FINAL THETA 164 C**** RULES ON THETA AND PHI RANGES: 165 C A IS U5ED AS AN EXAMPLE. THE RULES ALSO APPLY TO B,C AND Q 166 C IF THE GX,Y,Z AXES ARE COINCIDENT WITH THE AX,Y,Z AXES, 167 C THEN ALPHA, BETA, GAMMA-0 AND THETA RANGE IS TO 90, 168 C PHI RANGE 15 TO 90 . (LPH-1) 169 C IF ONLY THE GZ AND AZ AXES ARE COINCIDENT, 170 C THEN BETA-0 AND ALPHA AND/OR GAMMA ARE NONZERO AND 171 C THETA RANGE IS TO 90, PHI RANGE IS TO 180. (LPH-2) 172 C IF ONLY THE GY AND AY AXES ARE COINCIDENT 173 C THEN ALPHA, GAMMA-0 AND BETA 15 NONZERO AND THETA RANGE 174 C 15 TO 180, PHI RANGE IS TO 90. (LPH-1) 175 C IF NO AXES ARE COINCIDENT, 176 C THEN BETA 15 NONZERO AND ALPHA AND/OR GAMMA ARE NONZERO 177 C AND THETA RANGE IS TO 180. PHI RANGE IS TO 180. 178 C VALUES FOR LPH AND THETA1 AND THETA2 WILL BE AUTOMATICALLY 179 C COMPUTED BY THE PROGRAM WHEN THEIR INPUT VALUES ARE 5ET-0 . 180 C THE ECHO OF THE INPUT PARAMETERS INDICATES THE RANGE USED. 181 C 182 C LINE *6: 183 C 184 C W(I) 1-1,3; CUTOFF, L5 185 C 186 C W(I): HALF-WIDTH AT HALF-HEIGHT, A55UMED COAXIAL WITH 187 C G-MATRIX. WIDTHS IN MHZ. READ IN ORDER WX.WY WZ. 188 C CUTOFF: CONTRIBUTIONS TO THE SPECTRAL LINESHAPE ARE 189 C CALCULATED ONLY UP TO A DISTANCE OF CUTOFF* W (THE PRODUCT 190 C OF THE LINESHAPE AND CUTOFF) FROM EACH RESONANCE FIELD 191 C POSITION. 192 C L5: LINESHAPE FUNCTION. LS-0 FOR LORENTZIAN, NONZERO 193 C FOR GAUSSIAN. 194 C 195 C LINES 7-8: 196 C 197 C CONE(I) 1-1,3; CTWO(J) J-l ,3 198 C EPSILN(I) 1-1,3 199 C 200 C LINEWIDTH VARIES A5 THE MAGNETIC QUANTUM NUMBER, MI, AND 201 C THE FREQUENCY, AS DESCRIBED BY FRONCI5Z AND HYDE. SEE: 202 C FR0NCI5Z, W.; HYDE, J. 5. J. CHEM . PHY5. 1980, 73, 3123. 203 C THE LINEWIOTH FORMULA IS: 204 C 205 C U**2= WO**2 +
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208 281 IMPLICIT REAL*4 (A H, Z) 282 EXTERNAL PL2CA 283 C 284 " DATA ZER , ONER, TUOR , THRER , FOUR, 5IXTN /O , 1 , 2,3 , 4 , 16/ 285 DATA ZERO, ONE, TWO, THREE /O . , 1 . .2 . ,3 . 0/ 286 DATA W0NPT3, PNT5 , NINETY, HUND /l. 4,0.8,90.0 ,100 . 0/ 287 DATA HUND80 , ATEY , ATEY3 / 180 . ,80 . ,85 . 0/ 288 DATA PT0H1 , PNT31 /O. 01, 0.31/ 289 DATA GELEC /2 . 0023193134/ 290 DATA BETA, PI / 1 . 399612386 , 1 . 743329232E-2/ 291 C 292 C*** GELEC FREE ELECTRON G VALUE. 293 C*** BETA = (BOHR MAGNETON / PLANCK ' 5 CONSTANT) MHZ/GAUSS 294 C*** PI = PI/180 CONVERTS DEGREE5 TO RADIANS. 295 C 296 COMPLEX V(16,16) 297 COMPLEX 5UM(3) , SII , SIJ , YINT 298 C 299 DIMENSION ANGSAO) , ANGSBO) , ANG5CO) , ANGSQO) 300 DIMENSION A (3 ) , B ( 3 ) , C t 3 ) , G ( 3 ) , Q ( 3 ) , R ( 3 > , S ( 3 ) , W < 3 I 301 DIMENSION GXTALO ,3) , AXTALO ,3) ,BXTAL< 3 ,3) , CXTALO ,3) , 302 X QXTAH3.3J 303 DIMENSION 82(3) , C2< 3 ) , G2< 3 ) , WG < 3 , 32) , GBETA (3 ) 304 DIMENSION AA (3 ,3) , BB (3 ,3 ) ,CC ( 3 ,3 ) , QQ ( 3 , 3) 305 DIMENSION EULERO) ,ZRTN< 3 ,3) ,ZRU3 ,3) 306 DIMENSION CONEO) .CTU013 ) ,EPSILN(3 > 307 DIMENSION AR( 16 , 16> , AI ( 16 . 16) ,ZR( 16 , 16 > , ZI ( 16 16) 308 DIMENSION D ( 16) . E( 16 ) , TAU(2 , 16) ,GP( 4 4) GPK4 ) E2 t 16) 309 DIMENSION ITB<26 ) , ITC(20 > , 5PECTR<4000 ) . GWT ( 2) ,TABLS ( 1000 ) 310 DIMENSION ST ( 181 , 4 ) ,CT ( 181 ,4) , SP( 181 ,4) ,CP( 181 .4) 311 DIMENSION P( 193 ,32) , TM( 195) , AQ( 16 , 16 ,2) IUL( 2. 64) 312 DIMENSION AQ1 ( 16 , 16) , AQ2C16 , 16 ) ,GB1 ( 3 , 16 ) ,GB2(3 , 16 ) , 313 X GBN(3,16,2) 314 DIMENSION POINTX ( 2000 >, POINTY(2000 ) .XPLOT (3000 ) , 315 X YPLOTI3000) , 5CRCH1 (3000 ) , SCRCH2( 3000 > 316 C 317 EQUIVALENCE ( AQ( 1 ) , AQ1 ( 1 ) ) , ( AQ ( 1 , 1 , 2) , AQ2( 1 ) ) 318 EQUIVALENCE (GBN( 1 ) ,GB1 ( 1 ) ) , (G8N( 1 , 1 ,2) ,GB2( 1 ) ) 319 C 320 DATA MAXEIG /16/ 321 C 322 C**** MAXEIG-2*(2*SPINA+1> IS ORDER OF SPIN-HAMILTONIAN MATRIX 323 C TO BE DIAGONALIZEO . AT PRESENT, DIMENSION MAXEIG IS SET 324 C FOR SPINA-7/2. IF MAXEIG IS CHANGED, DIMENSIONS MUST 325 C CORRESPONDINGLY BE CHANGED: (Z-MAXEIG) 326 C GBN(3,Z,2) , P( 3+3*Z*Z/4 .32) , TM(3+3*Z*Z/4) AQ( Z ,Z ,2) ,AQ1(Z,Z) AQ2(Z,zi ,GB1(3,Z) ,G82(3,Z) , AR(Z.Z) ,AI (Z ,Z ) ,ZR(Z ,Z) ,D(Z) , IUL(2,Z*Z/4) ,E(Z) ,E2(Z),TAU(2,Zi , V (Z , Z) ,NTRD«(Z/2)**2. 329 C 330 DATA GPI /. 91500474, .38499526, .41500474, .08499326/ 331 C 332 C**** ARRAY GPI CONTAINS COEFFICIENTS WHICH DETERMINE 333 C POSITIONS OF DIAGONALIZATION POINTS AT WHICH 334 C SPIN HAMILTONIAN 15 DIAGONALIZED . 335 C 336 DATA GPF /0. 53340094/ „„»„,.-,, 337 DATA GP / 0.3772513, 1.201637, -0.649133 0.0702477, 33a X 0.1800498, 1.3476184, -0.5847209, 0.0570527, 339 X 0.0370327, -0.3847209, 1.3476184, 0.1800498, 340 X 0.0702447, -0.649133, 1.201637, 0.3772313 / 342 C*** ARRAY GP CONTAINS COEFFICIENTS FOR COMPUTING INTERPOLATED 343 C VALUES OF THE FUNCTION TO BE INTEGRATED NUMERICALLY. THESE 344 C INTERPOLATION POINTS ARE OF LE55ER WEIGHTS COMPARED TO 345 C DIAGONALIZATION POINTS. 346 C*** GPF IS THE RELATIVE WEIGHT FOR THE POINTS. SEE: 347 C CONTE, 5.D.; OE BOOR, C. "ELEMENTARY NUMERICAL ANALYSIS"; 348 C MCGRAW-HILL: NEW YORK, 1972; P 304. 349 C 350 DATA G.A.B.C.Q.ANGSA.ANGSB.ANGSC.ANGSQ.QD.QE /29*0.0/ 327 C 328 C

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209 351 C 352 C**** READ IN PARAMETERS AND WRITE OUT TO OUTPUT LISTING. 353 C 354 " READ<8,*>KRY5TL,NUCLg,NZB,NZC,IPHA5E,ISPECP,MARKTR 355 READ (B,ll FREQ , IDERI V , IFORBD , BZEMN 356 READ ( 8 , * ) SPINA .5PINB , SPINC ,NEB , NEC 357 REA0(8,*)VERTSF,SCLPK 358 READ ( 8 , * ) NTR . NTH , NPH , LPH , THETA1 , THETA2 359 READ18,*) ( ( U( I ) , 1-1 , 3) .CUTOFF , LS > 360 READ(8,«) <(CONE, 1-1 . 3) , (CTUO < J) , J-l,3)> 361 READ(8,») (EPSILN(I>, 1-1,3) 362 READ(8,*)GN,GR,QR,GWT(1) ,NIS 363 READ (8 , * I BCNTR , BTOTAL , HINT , BANK 364 IF(KRYSTL.NE.ZER) GO TO 50 365 READ(8,*) (G(I),I-1,3) 366 READ<8.*) ( < A( I ) , 1-1 , 3) , < ANG5A( J) , J-l , 3> > 367 READ<8,») ( (B( I ) , 1-1 ,3) , < ANGSBI J ) , J-l ,3) I 368 READ<8,*> ( , 1-1 .3) , ( ANGSCl J) , J-l ,3) ) 369 IF(NUCLQ.NE.ZER) READ«8,*> (QD ,QE , ( ANGSQd ) , 1-1 , 3) I 370 GO TO 100 371 C 372 C ALTERNATIVE INPUT WHEN KRY5TL IS NONZERO. 373 C G,A,B,C AND Q READ IN AS TENSOR5 BY ROW SO THE FIRST 374 C VALUE IS GXX THEN GXY THEN GXZ THEN GYX ETC. 375 C 376 50 CONTINUE 377 DO 80 1-1 ,3 378 READ<8,*)(GXTAL(I,J) , J-l, 3) 379 80 CONTINUE 380 CALL PREP(GXTAL,ZRTN,G,EULER) 381 G21»AB5(GITU0R)-G(0NER) » 382 G32=AB5 383 IF(G21 LT. G32) GO TO 82 384 SCRAM-G(ONER) 385 G(ONER)-G(TUOR) 386 G 392 ZRTN(AXTALII,J) , J-1,3) 396 84 CONTINUE 397 CALL TRNFMCAXTAL.ZRTN.AXTAL) 398 CALL PREP(AXTAL,ZR1,A,ANGSA> 399 DO 86 1-1,3 400 READ(8,*)(BXTAL(I,J) , J-1,3) 401 86 CONTINUE 402 CALL TRNFM(BXTAL,ZRTN,BXTAL) 403 CALL PREP(BXTAL,ZR1,B,ANGSB) 404 DO 88 1-1,3 405 READ{8,*)(CXTAL(I,J) , J-1,3) 406 88 CONTINUE 407 CALL TRNFH(CXTAL,ZRTN,CXTAL> 408 CALL PREP(CXTAL,ZR1,C,ANG5C) 409 IF(NUCLQ.EQ.ZER) GO TO 100 410 DO 90 1-1,3 411 READ ( 8 , * ) < QXTAL ( I , J ) , J-1,3) 412 90 CONTINUE 413 CALL TRNFMJ QXTAL. ZRTN , QXTAL) 414 CALL PREP(QXTAL,ZR1,Q,ANGSQ) 415 QD-1.3*Q 416 QE=0.5*(Q(0NER)-Q(TU0R) ) 418 C*##***#****# END OF PARAMETER READ-IN SECTION. ************ 420 C *******START OF PARAMETER PRINT-OUT**»******

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210 421 423 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 1UC [ 7 , 102 ) KRYSTL , NUCLQ , NZB , NZC , I PHASE , I5PECP , MARKTR r ( 11X , ' KRYSTL , NUCLQ , NZB , NZC , IPHASE , I5PECP , HARKTR ' , 100 CONTINUE WRITE! 102 FORMAT , X 12X. II. IX ,11, IX ,11, IX ,11, IX, II, IX, II, IX ,11) WRITE (7 , 112)FREQ , IDERIV , IFORBD , BZEMN 112 FORMAT ( 12X , ' FREG IDERIV IFORBD X 10X,F8.S,2I8,F8.21 WRITE (7 , 122 ) SPINA , SPINB , 5PINC , NEB , NEC 122 FORMAT (13X, 'SPINA SPINB SPINC X /10X,3F8.1 ,218) WRITE(7 1 132)VERT5F,SCLPK 132 FORMAT ( 12X , ' VERTSF SCLPK ' , / 10X , F8 . 4 ,E16 . 8) WRITE ( 7 . 142 ) NTR , NTH , NPH , LPH , THETA1 , THETA2 BZEMN NEB NEC , NTH 142 FORMAT! {5X, 'NTR X /10X,4I8,2F8.2) WRI TE( 7, 152 )W, CUTOFF ,LS NPH LPH THETA1 THETA2' WX WY WZ CUTOFF LS' ,/lOX, CONEY CONEZ CTWOX CTWOY CTWOZ' , /10X.3F8.2) GWT(l) NIS' ,/BX, BANK' ,/10X,4F8.2) 152 FORMAT (15X, ' X 4F8.2.7X.I2) WRITE(7,136) CONE,CTWO 156 FORMAT ( 12X , ' CONEX X /10X.6F8.4) WRITEI7.158) EP5ILN 158 FORMAT (12X, 'EP5ILNX EP5ILNY EPSILNZ' WRITE!7.162)GN,GR ( QR I GWT(1> ,NI5 162 FORMAT ( 13X , ' GN GR QR 1 F8.4,3F8.2,1I8> WRITE ( 7 , 172 i BCNTR , BTOTAL .HINT , BANK 172 FORMAT 1 12X , ' BCNTR BTOTAL HINT WRITE!7,262)G 262 FORMAT (14X ' GX GY GZ' , / 10X , 3F8 . 5) 290 WRITE17.330) 330 FORMAT! J//13X.17H PRINCIPAL VALUES , 18X , 13H EULER ANGLES, 1 //13X, 'X' ,11X, 'Y' ,11X, 'Z' ) WRITE(7,340)G WRITE(7,350)A,ANGSA WRITE(7,360)B,ANG5B WRITE(7,370)C,ANGSC WRITE(7,380)Q,ANG5Q WRITE(7,390)W WRITE!7,400)Q0,QE IF(LS.EQ..ZER)WRITE!7,410) IF ( LS . NE . ZER > WRITE ! 7 , 420 > 340 FORMAT (6H G ,3F12.3) 350 F0RMATI6H A/MHZ , 3F12 . 3 ,3X , 3F10 . 2) 360 FORMAT (6H B/MHZ , 3F12 . 3 ,3X , 3F10 . 2) 370 F0RMATI6H C/MHZ , 3F12 . 3 ,3X , 3F10 . 2) 380 FORMAT<6H Q/MHZ , 3F12 . 3 ,3X , 3F10 . 2) 390 FQRMAT(6H W/MHZ , 3F12 . 3) 400 FORMAT(//10X,4H QD-,F12.3,4H QE-,F12.3> 410 FORMAT! /1H ,'LINESHAPE LORENTZIAN') 420 FORMAT! /1H ,'LINESHAPE GAUSSIAN') C C*****#****** END OF PARAMETER PRINT-OUT *******#•*# C Q C******** SET UP DEFAULT VALUES FOR VARIABLES ****** C IDERIV , VERT5F , NTR , LPH , THETA1 , THETA2 C IF! IDERIV. NE.TWOR) IOERIV-ONER DRV5YM! -ONE ) **IDERIV IF! VERT5F.EQ.ZER0) VERT5F-HUND NTRO=! (5PINA*TU0)+0NE)**TW0 IF(NTR.GT.NTRD) NTR="NTRD IF(LPH.EQ.TWOR)GO TO 391 LPH«ONER .NE.ZER0.0R.ANG5QO) NE.ZERO.QR.ANGSAO) NE.ZER0.0R.ANG5BO) IF(ANG5Q(1) IF(ANGSA(1) IF(ANG5B(1) IF(ANGSCil) NE.ZERO.OR.ANGSCO) NE.ZERO) NE.ZERO) NE.ZERO) NE.ZERO) LPH-TWOR LPH-TWOR LPH-TWOR LPH-TWOR

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211 491 391 CONTINUE 492 JPH(NPH/TW0I+PNT31 493 LTH= ONER 494 IFITHETA1 . LT . ZERO ) THETA1-ZERO 495 IF(THETA2.GT.HUND80> THETA2-HUND80 496 IF ( THETA1 . EQ . ZERO. AND. THETA2 . EQ . ZERO) THETA2-NINETY 497 IF(THETAl.NE.ZERO> MARKTR-ZER 498 IF (THETA2.NE. NINETY. AND. THETA2 . NE .HUND80 ) MARKTR-ZER 499 IF(ANG5Q(2) .NE. ZERO. OR. ANG5A(2) . NE . ZERO) THETA2-HUND80 500 IF(ANGSB(2) . NE . ZERO. OR. ANGSC(2> . NE . ZERO) THETA2-HUND80 501 IF(THETA2.EQ.HUND80> LTH-TWOR 502 392 CONTINUE 503 JTH +W < TWOR ) +W ( THRER ) ) / ( GELEC*BETA ) 537 BMAX BHI + BDELTA 538 BMIN BLO BDELTA 539 KLOT«(BOELTA/HINT)+PTOHl 540 KLOTl«KLOT+ONER 541 KMOT« ( BTOTAL+BOELTA ) /HINT+PTOH1 542 KMOT1-KMOT+ONER 543 KTOT-KMOT+KLOT+ONER 544 TYPE *, 'KTOT-' ,KTOT 545 C 546 C A LINESHAPE TABLE (TABLS) IS CONSTRUCTED. 547 C THIS ARRAY CONTAINS 1/2 OF A LORENTZIAN OR GAU55IAN 548 C 15T OR 2ND DERIVATIVE LINESHAPE WITH AN ARBITRARY 549 C WIDTH. IN THE LINESHAPE CALCULATION SECTION, THESE 550 C VALUES WILL BE SCALED TO FIT THE WIDTHS OF THE 551 C PARTICULAR LINES. 552 C 533 CUTHIN-CUTOFF/HINT 554 KUTOr* CUTOFF+ONE 555 KP=KUTOF*100 556 DO 428 KC-1 , KP 557 XK=(KC-0NER>/100 558 IF(LS.NE.ZER) GO TO 424 559 IFdDERIV EQ.TWOR) GO TO 422 560 TABLS(KC)=»XK/(XK*XK+ONE)**2

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212 561 GO TO 428 562 422 TABL5(KC)-<0NE-THREE*XK*XK>/(XK*XK+0NE)**3 563 GO TO 428 564 424 IF( IDERIV.EQ.TUOR) GO TO 426 565 TABL5(KC)-XK*EXP(DLN2*XK*XK> 566 GO TO 428 567 426 TABL5(KC)=(QNE+TU0*0LN2*XK*XK)*EXP(DLN2*XK*XK) 568 428 CONTINUE 569 C 570 C INITIALIZE ARRAY "5PECTR" FOR LATER DEPOSITION OF 571 C LINESHAPE DATA. 572 C 573 DO 430 NZ3-1.KT0T 574 5PECTR(NZ3)-ZERO 575 430 CONTINUE 576 C 577 C OPTIONAL ADDITION OR SUBTRACTION OF A PREVIOUS SPECTRUM 578 C PREVIOUS SPECTRUM IS READ OFF UNIT 13, AND IS ADDED TO 579 C (BANK > 0) OR SUBTRACTED FROM (BANK < 0) THE PRESENT 380 C SPECTRUM. 581 C 582 IF (BANK) 440, 480, 440 583 440 CONTINUE 584 DO 470 N-l.NTOT 585 READ! 13 , 450 > SPECTR( KL0T1+N-1 ) 586 450 F0RMAT(13X,E23.16I 587 SPECTR( KLOT1+N-1 >-BANK*SPECTR( KLOT1+N-1 ) 588 470 CONTINUE 589 480 CONTINUE 590 C 591 C*** FIRST ISOTOPE OF THE MAJOR NUCLEUS, AND NUCLEI B,C • 592 C 593 CALL BINOISPINB.NEB.NSPB.ITB) 594 CALL BINO(SPINC,NEC,NSPC,ITC) 595 C 596 DO 490 1=1,3 597 G2(I)=G(I)*G(I) 598 GBETA(I>«Gm*BETA/TUO 599 B2(I)-B(I)*B(I> 600 C2(I)-C(I»*C(I) 601 490 CONTINUE 602 AMI-5PINA 603 IF(SPINA.EQ.ZERO) AMI-ONE 604 C 605 C CALCULATE LINEUIDTHS FOR ALL MI VALUES OF 606 C EACH OF THE X,Y,Z COMPONENTS. 607 C 608 DO 492 J-l.NSPA 609 DO 491 1-1,3 610 UG(I,J)-(U(H*U(I) + ( CONE ( I ) *CONE ( I ) / 4 . ) *AMI*AMI 611 X +/4.0>*FREQ*FREQ 612 X +(EPSILN(I) /TUO)*CONE(I)*CTUO(I)*AMI*FREQI 613 X *G(I)*G 614 WG(I ,NEIGP1-J)-WG(I ,J> 615 491 CONTINUE 616 AMI-AMI-ONE 617 492 CONTINUE 618 C 619 Q(ONER>QE-QO/THREE 620 Q(TWOR)-QE-QD/THREE 621 Q(THRER)-TUO*QO/THREE 622 CALL TRANS(ANGSA,A,AA) 623 CALL TRANS (ANGSQ.Q.QQ) 624 IF(NZB .EQ. ZERIGO TO 500 625 CALL TRAN5(ANG5B,B,BB) 626 GO TO 510 627 500 CALL TRAN5 ( ANG5B , B2 , BB ) 628 510 IFINZC . EQ . ZERJGO TO 520 629 CALL TRAN5(ANGSC,C,CC) 630 GO TO 530

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213 631 520 CALL TRAN5 ( ANG5C , C2 ,CC > 632 530 CALL QUA01 ( AA , 3Q ,CN , NEIGST , MAXEIG , AQ1 , GB1 ) 633 DO 540 J-1,3 634 DO 540 I-l.J 635 GG*G(I)*G(J) 636 BB(I ,J)«BB(I,J>*GG 637 CC(I,J>-CC 648 550 FORMAT I ///lSHOSECOND ISOTOPE) 649 DO 560 1-1,3 650 A(I)=A(I)*GR 631 Q(I)-q(I)*QR 652 560 CONTINUE 633 QD-QD*QR 634 QE=QE*QR 635 GN=GN*GR 656 GUT (TUOR) -ONE-GUT (ONER) 657 URITE(7,330)A,ANG5A 658 URITE(7,400)Q0,QE 659 CALL TRAN5(ANG5A,A,AA) 660 CALL TRANS (ANGSQ.q.QQ) 661 CALL QUAD1(AA,QQ,GN I NEIG5T,MAXEIG,AQ.2,GB2> 662 570 CONTINUE 663 C 664 CM*** DETERMINE (THETA. PHI) GRID FOR INTEGRATION ***** 665 C THE SPHERICAL SURFACE 15 DIVIDED INTO 5UB-REGI0NS OF 666 C (ZIG)*(ZEP>. 667 C 668 KPHZER 669 THETA1PI * THETA1 670 THETA2PI * THETA2 671 ZIG(THETA2-THETA1) /JTH 672 DO 580 J-1,4 673 DO 580 I-l.JTH 674 TH=THETA1+(I-GPI< J))*ZIG 675 CT(I,J)-C05(TH) 676 ST(I,J)»SIN(TH) 677 580 CONTINUE 678 C 679 C********* 8EGIN THETA-INTEGRATION LOOP. ****** 680 C LATITUDINAL (THETA) RANGE IS COVERED BY MT-1 ,2 ,3 , . . . . , JTH . 681 C LONGITUDINAL (PHI ) RANGE IS COVERED BY MP" 1,8.3, , MPH . 682 C THERE ARE 16 DIAGONALIZATION AND 16 INTERPOLATION POINTS 683 C UITHIN EACH SUB-REGION. INDICES ( MT , MP) IDENTIFY A 5UB684 C REGION, INDICES (LT, LP) IDENTIFY A DIAGONALIZATION POINT 685 C IN THE SUB-REGION. 686 C 687 DO 900 MT-1 ,JTH 688 C 689 MPH=JPH*5T(MT.ONER)+ONER 690 IF(MPH.EQ.KPH) GO TO 600 691 MPHL-MPH/LPH+PNT31 692 C 693 C RANDOM DISTRIBUTION OF POINTS ON THE SURFACE OF UNIT SPHERE 694 C UILL RE5ULT IN THE NUMBER OF POINT5 AT A GIVEN LATITUDE 695 C PROPORTIONAL TO SIN(THETA). THE VALUE OF MPH IS WEIGHTED 696 C ACCORDINGLY. 697 C 698 ZEP=PI*NINETY*LPH/MPH 699 DO 590 J-1,4 700 DO 590 I-l.MPH

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214 701 PH=(I-GPI(J) )*ZEP 702 CP(I , J)-C05(PH) 703 SP(I , J)-SIN(PH) 704 590 CONTINUE 705 KPH=MPH 706 600 CONTINUE 707 C 708 C*#***#***# BEGIN PHI-INTEGRATION LOOP. *#**# 709 C 710 DO 890 MP-1 ,MPH 711 C 712 DO 880 NT-1 ,NI5 713 C 714 DO 730 JN-1,16 715 C 716 LI» (JN-ONER)/FOUR + PTOH1 717 LTJN FOUR*LI 718 LPLI + ONER 719 C 720 C : JN 12 3 4 3 6 7 8 9 10 11 12 13 14 13 16 721 C :::::LT 12341234 1234 12 3 4::::: 722 C ::::: LP 11112222 3333 4444::::: 723 C UNIT VECTOR DC( DCX , DCY.DCZ) REPRESENTS MAGNETIC FIELD 724 C DIRECTION ALONG WHICH THE 5PIN-HAMILT0NIAN WILL BE 725 C DIAGONALIZED. (I.E. A DIAGONALIZATION POINT) 726 C DC STANDS FOR DIRECTION COSINE 727 C 728 DCX5T(MT,LT)*CP 729 DCY5T(MT,LT»*5P(MP,LPI 730 OCZ= CT(MT.LT) 731 DCXX-OCX*DCX 732 DCYY=DCY*DCY 733 DCZZ=DCZ*OCZ 734 DCXY=DCX*DCY 735 DCYZ-DCY*DCZ 736 DCZX-DCZ*DCX 737 C 738 C***5ET UP MAGNETIC FIELDS H AT WHICH HYPERFINE MULTIPLETS 739 C OCCUR FOR FIXED FREQUENCY "FREQ" . H IS THE MAGNETIC FIELD 740 C MAGNITUDE FOR CALCULATION OF THE ENERGY LEVELS AT EACH 741 C ORIENTATION. JGEFFG EFFECTIVE) 743 L GEFF-5QRT(G2<0NER)*DCXX+G2(TW0R)*DCYY+G2«THRER)*DCZZ) 744 GB-GEFF*BETA 745 GGB-GEFF*G8 746 H-FREQTH/GB 747 HZEMN-BZEMN 748 IF(HZEMN.EQ.ZERO) HZEMN-H 749 TWOH-H+HZEMN 730 HDCX-HZEMN*DCX 751 HDCY»HZEMN*DCY 752 HDCZ=HZEMN*DCZ 753 STGMPH-GWT ( NT > *5T ( MT , LT ) / ( GB*MPH ) 754 DCXXM1-ONE-DCXX 755 DCYYM1-ONE-DCYY 756 DCZZM1-ONE-OCZZ 757 C 758 C***SET UP MAJOR STORAGE ARRAY P 759 C IN COLUMNS 1-16: THE TOP 2 ROWS STORE MATRIX PROJECTIONS OF 760 C BB AND CC ( SUPERHYPERFINEI , THE THIRD ROW STORES PROJECTIONS 761 C OF WIDTH ALONG THE 16 DIAGONALIZATION POINTS OF A 4 X 4 762 C BLOCK. THE NEXT NTR ROWS STORE THE TRANSITION ENERGIES. 763 C THE NEXT NTR ROUS STORE INTENSITIES WEIGHTED TO THEIR rmkitftuf 764 C RELATIVE IMPORTANCE DUE TO THEIR LOCATION ON THE UNIT SPHERE 765 C THE FINAL NTR ROWS STORE THE TRANSITION WIDTHS. 766 C 767 IFINZB .EQ. ZER ) GO TO 610 768 P ( ONER . JN ) =AB5 ( BB ( ONER , ONER ) *DCXX+BB ' TWOR , TWOR ) *DCYY+ 769 X BB(THRER,THRER)*DCZZ 770 X +TUO*(BB(ONER,TUOR)*DCXY+BB
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215 771 X BB(ONER.THRER)*DCZX ) ) /GGB 772 GO TO 620 773 610 P( ONER, JN> -SQRT ( 8B( ONER, ONER ) *DCXX+BB ( TUOR , TUOR) *DCYY+ 774 X BB(THRER,THRER)*OCZZ 775 X +TUO*(BB(ONER,TUOR>*DCXY+BB(TUOR,THRER)»OCYZ+ 776 X BB(ONER,THRER)*OCZX) ) /GG8 777 620 IF(NZC . EQ . ZER)GO TO 630 778 P ( TUOR , JN I -ABS (CC ( ONER , ONER ) *OCXX+CC ( TUOR , TUOR ) »0CYY+ 779 X CC(THRER,THRER)*DCZZ 780 X +TWO*(CC (ONER, TUOR )*0CXY+CC( TUOR, THRERXDCYZ+ 781 X CC(ONER,THRER)*DCZX) )/GGB 782 GO TO 640 783 630 P ( TUOR, JN) =»SQRT < CC( ONER, ONER >*0CXX+CC( TUOR, TUOR )*OCYY+ 784 X CC(THRER,THRER)*DCZZ 785 X +TUO*(CC(ONER,TUOR>*DCXY+CC(TUOR,THRER)*DCYZ+ 786 X CC(ONER,THRER)*DCZX) ) /GGB 787 640 CONTINUE 788 C 789 C***SET UP 5PIN-HAMILTONIAN MATRIX: REAL PART-AR, IMAGINARY PART 790 C =AI. SET UP UNIT MATRIX ZR (INPUT FOR TQL2) 791 C AQ KNOUN VIA EQUIVALENCE UITH AQ1 , OBTAINED IN QUAD1 . 792 C 793 DO 660 I=2,NEIGST 794 JJI ONER 795 DO 650 J-l.JJ 796 ZR(I,J)»ZERO 797 ZR(J,I)»ZERO 798 ARd , J)-AQ(I,J,NT> 799 AI(I,J)«AQ(J,I,NT) 800 650 CONTINUE 801 660 CONTINUE 802 C 803 00 680 I-l.NEIGST 804 N» ONER 805 IF (I.GT.N5PA) N-ONER 806 ARII ,I)-AQ(I,I ,NT)+HDCZ*(GBN(THRER,I,NT)+GBETA(THRER)*N) 807 ZR(I,I>-ONE 808 AI(I,I)-ZERO 809 IFd.EQ.ONER .OR. I.EQ.N5PA1) GO TO 670 810 J= I ONER 811 AR( I ,J)-AR(I ,J)+HDCX*GBN(ONER,I,NT) 812 AI(I,J)-AI(I.J)+HDCY*G8N(TUOR,I ,NT) 813 670 IF(I.LT.NSPAl) GO TO 680 814 J=NEIGP1-I 815 AR( I ,J)-AR(I ,J)+HDCX*GBETA(ONER) 816 Aid. J) -Aid, J) +HDCY*GBETA ( TUOR J 817 680 CONTINUE 818 C 819 CM******* DIAGONALIZATION OF SPIN-HAMILTONIAN MATRIX ********** 820 C 821 CALL HTRIDI(MAXEIG.NEIGST,AR,AI,D,E,E2,TAU) 822 CALL TQL2(MAXEIG,NEIGST,D,E,ZR,IERR) 823 IF(IERR.NE.ZER) GO TO 930 824 C 825 C 15 THE SET OF M PRINCIPAL ENERGY VALUES, IN ASCENDING 826 C ORDER. 827 C 828 CALL HTRIBK(MAXEIG,NEIG5T,AR,AI,TAU,NEIG5T,ZR,ZI> 829 C 830 C THE COMPLEX NUMBER ARRAY V 15 PARTITIONED INTO 2 BLOCKS OF 331 C NSPA COLUMNS EACH, INTO UHICH ARE DEPOSITED EIGENVECTORS 832 C (ZR.ZI) OF 5PIN HAMILTONIAN AND COMPLEX CONJUGATES OF THOSE. 833 C 834 DO 700 K-l.NSPA 835 K4=K+NSPA 836 DO 690 J*1,NEIG5T 837 5IPR3»ZR(J,K4) 838 5IPR4=ZI(J,K4) 839 5IPR1«ZR(J,K> 340 SIPR2-ZI(J,K)

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216 841 V(J,K4)=CMPLX(SIPR3,5IPR4) 842 V(J,K)=CMPLX(5IPR1,-5IPR2> 843 690 CONTINUE 844 700 CONTINUE 846 C TRANSITION FIELDS DETERMINED FROM SPECTROMETER FREQUENCY 847 C AND EIGENENERGIES USING 1ST ORDER FREQUENCY-SHIFT 848 C PERTURBATION FORMULA. STORE TRANSITION FIELDS IN ARRAY P. 849 C 850 DO 740 JA-1 , NTR 851 IU-IULIONER, JA) 852 IL-IUL(TUOR.JA) 853 JVTHRER + JA 854 P(JV, JN)-TUOH+(D(IL)-D(IU) ) /GB 855 C 856 C***CALCULATE TRANSITION INTENSITIES FROM THE EIGENVECTORS*** 857 C STORE RELATIVE TRANSITION INTENSITIES ( TI t IN ARRAY P 858 C 859 SUM (ONER)ZERO 860 5UM(TUOR)ZERO 861 5UM(THRER)-ZERO 862 C 863 DO 720 1-1 .NEIGST 864 J-NEIGP1-I 865 SII-Vd.IUXVd.IL) 866 SIJ-V(I ,IU>*V(J,IL> 867 SUM(ONER)5UM(ONER)+5IJ 868 IFd.GT.N5PA) GO TO 710 869 SUM(TUOR)SUM(TUOR)+SIJ 870 5UM(THRER)-5UM(THRER)+5II 871 GO TO 720 872 710 CONTINUE 873 SUM(TUOR)5UM(TW0R)-SIJ 874 5UM(THRER)-5UM(THRER)-5II 875 720 CONTINUE 876 SUM(TWOR)5UM( TUOR) *( . , 1 . ) 877 DO 730 J-1,3 878 YINT=G(J)*SUM(J) 879 R(J)-REAHYINT) 880 S(J)-AIMAGIYINT) 881 730 CONTINUE 882 C 883 R1P51-R(0NER)**2 + 5(ONER)**2 884 R2PS2-R(TU0R>**2 + 5 ( TUOR ) **2 885 R3P53-R( THRER )**2 + S( THRER )**2 88 6 CROTRM-TUO* ( ( R ( ONER ) *R ( TUOR 1+5 ( ONER )*S ( TUOR ) ) *DCXY+ 887 X (R(TUOR)*R(THRER)+S(TUOR)*S(THRER>) 888 X *DCYZ+(R(THRER)*R(ONER)+S(THRER)*S(ONER) XOCZX) 889 890 TIR1PSKOCXXM1 + R2P52*DCYYM1 + R3PS3*DCZZM1 CROTRM 891 JV-JV+NTR 892 P(JV,JN)-TI*STGMPH 893 C 894 C***5TORE THE WIDTH FOR EACH TRANSITION IN THE P ARRAY 895 C S97 P(jy JN)-PNT3*( SQRT*DCXX+UG+ SQRT (UG (ONER , IL ) *0CXX+UG( TUOR , IL )* 899 X DCYY+UG ( THRER, IL ) *DCZZ ) 1/GGB 900 C 901 740 CONTINUE 902 750 CONTINUE 9P4 C INTERPOLATION POINTS ARE DETERMINED USING LAGRANGIAM FORMULA Hi C INTERPOLATED VALUES OF ENERGIES, INTENSITIES AND UIDTH5 ARE 906 C STORED IN COLUMNS 17 32 OF THE P ARRAY. 907 C 908 DO 770 1-1,4 909 JI + FOUR 910 K= J + FOUR

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217 911 L= K + FOUR 912 DO 770 N»l,4 913 JM=L + FOUR*N 914 00 760 JU«1,NTR3P3 915 P ( J V , JM ) -GP ( ONER , N ) *P ( JV , I ) +GP ( TUOR , N ) *P ( JV . J ) 916 X +GP(THRER,N)*P( JV , K ) +GP< FOUR , N UP ( JV ,L ) 917 760 CONTINUE 918 C 919 C INTENSITIES AT INTERPOLATED POINTS ARE SCALED BY GPF . 920 C 921 DO 770 JV-NTR4.NTR2P3 922 P(JV,JM)-P(JU,JM)*GPF 923 770 CONTINUE 924 C 925 C 926 C 927 C IF ONLY FORBIDDEN TRANSITIONS ARE WANTED, 928 C THIS SECTION ARBITRARILY SETS THE INTENSITIES OF THE 929 C ALLOWED TRANSITIONS EQUAL TO ZERO. 930 C 931 IF(IFORBO.EQ.ZER) GO TO 780 932 NTR3AL-NTR3+NSPA 933 C 934 DO 784 JH«1 ,32 935 DO 784 JUNTR4 , NTR3AL 936 P(JU .JNJ-ZERO 937 784 CONTINUE 938 780 CONTINUE 939 C 940 C***#*#*******#* BEGIN LINE5HAPE CALCULATION *#•#*#*#** 941 C 942 DO 810 N-1,32 943 BNG-P(ONER,N) 944 CNG*P(TWOR,N) 945 C 946 DO 810 JA-1 ,NTR 947 HA=P(3+JA,N) 948 WIDTH-PI NTR2P3+JA.N) 949 W2=WIDTH*WIDTH 950 IF(IDERIY.EQ.TUOR) W2-W2*WIDTH 951 N55»CUTHIN*WIDTH+PT0H1 952 5S=P(NTR3+JA,N)/W2 953 DO 810 JB-1.N5PB 954 HB«HA-BNG*(SPBNEB-JB> 955 DO 810 JC-1.N5PC 956 HC=»HB-CNG*(SPCNEC-JC) 957 IF(HC.LT.BMIN.OR.HC.GT.BMAX) GO TO 810 958 C 959 C IF TRANSITION MARKS ARE WANTED (MARKTR NONZERO), 960 C PUT X,Y AND Z MARKS AT TRANSITIONS (HO. 961 C 962 IF ( MARKTR. EQ.ZER) GO TO 788 963 IF1MT.NE.ONER.OR.MP.NE.ONER.OR.N.NE.ONERIGOTO 786 964 IF(JA.GT.N5PA)GO TO 788 965 KZERO=KZERO+ONER 966 POINTXt KZERO 1-HC 967 POINTY (KZERO)— 80.0 968 GO TO 788 „.,, 969 786 IF-HC 979 POINTY (KZERO)— 70 .0 980 788 CONTINUE

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218 981 W5=55*ITB(JB)*ITC(JC) 982 WSDVSM= -US*DRV5YM 983 KH=(HC-BMIN> /HINT 984 C0N1=U0NPT5+(HC-BMIN)*HUND/WIDTH 985 C0N3=W0NPT5-(HC-BMIN>*HUND/ WIDTH 986 C0N4-HINT*HUND/UI0TH 987 C0N2=-C0N4 988 NI = KH-NS5 989 NJ= KH+N55 990 NK1=KH + ONER 991 IF(NI LT.ON£R>NI=ONER 992 IF(NJ.GT.KTOT)NJ=KTOT 993 DO 790 KL=NI , KH 994 LSPTR=C0N1+C0N2*KL 995 SPECTR(KL)=SPECTR(KL)+W5DV5M*TABL5(L5PTR1 996 7V0 CONTINUE 997 C 998 DO 800 KL=NK1 , N J 999 L5PTR=C0N3+C0N4*KL 100 5PECTR(KL)=SPECTR *P ( JV , J ) 1011 X +GP(THRER,N)*P(JV,K)+GP(FOUR 1 N)*P 1018 UIDTH«TM(NTR2P3+JA) 1019 W2=WIDTH*UIDTH 1020 IF(IDERIU.Eq.TUOR> W2=W2*UIDTH 1021 NSS=CUTHIN*WIDTH+PT0H1 1022 55=TM(NTR3+JA)*GPF/U2 1023 DO 860 JB=»1 ,N5PB 1024 HB=HA-BNG*(JB-5PBNEB) 1025 DO 860 JC=1,NSPC 1026 HC"HB-CNG*(JC-5PCNEC) 1027 IF(HC.LT.BMIN.OR.HC.GT.BMAX) GO TO 860 1028 W5=5S*ITB«JB)*ITC< JO 1029 W5DV5M* -US*0RV5YM 1030 KH«(HC-BMIN)/HINT 1031 C0N1=W0NPT5+ 1044 825 CONTINUE 1045 C 1046 DO 830 KL=NK1 , N J 1047 LSPTR-C0N3+C0N4*KL 1048 SPECTR ( KL ) =5PECTR{ KL ) -WS*TABL5 ( LSPTR) 1049 830 CONTINUE 1050 860 CONTINUE

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219 1051 870 CONTINUE 1052 880 CONTINUE 1053 890 CONTINUE 1054 900 CONTINUE 1055 C 1056 C***#**#*#*#* END OF INTEGRATION & INTERPOLATION. ##******** 1057 C 1058 C 1059 C *******SCALE, PLOT AND STORE SPECTRA******* 1060 C 1061 C DETERMINE MAXIMUM SPECTRUM INTENSITY 1062 C 1063 904 PEAK=ZERO 1064 DO 910 N=l,NTOT 1065 TE5TPK=ABS(5PECTR(KL0T1+N-1) ) 1066 IF(PEAK.LT.TESTPK) PEAK-TE5TPK 1067 910 CONTINUE 1068 WRITE(7,912) PEAK 1069 912 FORMAT (/10X, 'PEAK «',2X,E16.8> 1070 IF(SCLPK.NE.ZERO) PEAK=SCLPK 1071 IF ( PEAK. NE. ZERO) WGF-UERTSF/PEAK 1072 IF < PEAK. EQ. ZERO) UGF-ONE 1073 PHA5E»ONE 1074 IF(IPHASE.NE.ZER) PHASE— PHASE 1075 C 1076 DO 920 N-1.NT0T 1077 XPLOT(N)=BLO+(N-l>*HINT 1 078 YPLOT ( N ) -SPECTR < KLOT1+N-1 ) *UGF*PHA5E 1079 C 1080 C THESE IF STATEMENTS TRUNCATE PEAKS WHEN VERTSF > 100.0 1081 C THIS PERMITS BASELINE TO BE BLOWN UP U/OUT GOING OFF SCALE 1082 C 1083 IF(YPLOTIN) .GT.HUND) YPLOT ( N)-HUND 1084 IF(YPLOT(N) .LT.-HUND) YPLOT(N ) — HUNO 1085 C 1086 C IF DESIRED ( ISPECP NONZERO), THEN CONTENTS OF 5T0R ARRAY 1087 C ARE WRITTEN TO UNIT 12 FOR FUTURE USE. 1088 C 1089 IF ( ISPECP. EQ.ZER) GO TO 920 1090 WRITE112.919) XPLOT 1091 919 FORMAT(1X,F10.3,2X 1 E23.16,2X,F10 .3) 1092 920 CONTINUE 1093 C 1094 C*+******#****** BEGIN PLOTTING SECTION **#*#*##*#*#** 1095 C 1096 C FILL UP THE SCRATCH ARRAYS 1097 C 1098 DO 925 I-l.NTOT 1099 SCRCHim-XPLOTdl 1100 SCRCH2(I)-YPL0T(I) 1101 925 CONTINUE 1102 C 1103 C *** USE PL0T79 ROUTINES ON UF/QTP UAX *** 1104 C 1105 C INITIALIZE THE PLOT SYSTEM 1106 C 1107 926 CALL PLTOO Hq9 C 5ET PLOT SIZE TO 25.0 CM LONG, 20 CM WIDE. 1110 C 1111 CALL SET5Z(25. ) 1112 C 1113 CALL SETDS2(1. , .8) 1114 C 1115 C PLOT THE AXES USING THE ROUTINE PLTAX 1117 C CALL PLTAX(X,Y,TITLE,NCHAR, SIZE, THETA , VMIN , DV , VMAX , TICK, MODE) 1118 C 1119 C X X COORDINATE OF ORIGIN U20 C Y Y COORDINATE OF ORIGIN. (X,Y) IN WORLD UNITS

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220 1121 C TITLE HOLLERITH CHARACTER STRING AS AXI5 LABEL 1122 C NCHAR LENGTH OF STRING 1123 C SIZE LENGTH OF AXIS IN WORLD UNITS 1124 C THETA ROTATION ANGLE OF AXIS: FOR HORIZONTAL, 1125 C 90 FOR VERTICAL 1126 C VMIN MINIMUM VARIABLE ON AXIS 1127 C DV DIVISIONS TO BE MARKED ON AXIS 1128 C VMAX MAXIMUM VARIABLE ON AXIS 1129 C TICK LENGTH OF TICK MARKS, 0.005 TO 0.015 IS GOOD 1130 C < CLOCKWISE FROM AXI5, > COUNTERCLOCKWISE 1131 C MODE ORIENTATION OF TITLE WITH RESPECT TO AXIS 1132 C -1 FOR BOTTOM HORIZONTAL AXIS, +2 FOR LEFT 1133 C VERTICAL AXIS 1134 C 1135 C PLOT AND LABEL THE X-AXIS 1136 C 1137 CALL PLTAXO./23. ,3./25. , 18HFIELD STRENGTH ,18, 1138 1 20. /25. ,0. ,BLO, 20. ,BHI, .015,-1) 1139 C 1140 C PLOT AND LABEL THE Y-AXIS 1142 ^ CALL PLTAXJ3./23. , 3./2S. . 9HINTENSITY , 9, 1143 1 15./23. ,90. ,-100. ,20. ,100. ,-.013,21 1144 C 1145 CALL 5ETVP2(3./23. ,23. /25. ,3./23. ,18. /2S. ) 1147 C DRAW THE LINE FOR THE SPECTRUM 1148 C 1149 C CALL GRFGI ( XI , X , X2 , Yl , Y , Y2 , N , WORK1 , W0RK2 , NINT , SIGMA , PL2 ) 1150 C 1151 C XI X LOWER LIMIT 1152 C X(N> ARRAY OF X VALUES IN ASCENDING ORDER UITH MO 1153 C TWO VALUES EQUAL 1154 C X2 X UPPER LIMIT 1155 C Yl Y LOWER LIMIT 1156 C Y(N) ARRAY OF Y VALUES N ELEMENTS LONG 1157 C Y2 Y UPPER LIMIT 1158 C N NUMBER OF POINTS U59 C UORKKN) 5CRATCH ARRAY OF N ELEMENTS 1160 C U0RK21N) SCRATCH ARRAY OF N ELEMENTS U61 C NINT NUMBER OF POINTS TO INTERPOLATE BETWEEN X(l) 1162 C AND X(N) 1163 C SIGMA TEN5I0NED SPLINE PARAMETER 1164 C PL2 2-0 PEN MOVEMENT SUBROUTINE, USUALLY PL2CA 1165 C MUST BE DECLARED EXTERNAL 1166 CALL GRFGI ( BLO . XPLOT . BHI , -100 . , YPLOT 100 . ,NTOT , 1167 1 5CRCH1,SCRCH2,NT0T,1. ,PL2CA) 1168 C 1169 C MARK THE TRANSITIONS WITH PLUS SIGNS 1170 C 1171 C CALL GRFGP (XI ,X ,X2 , Yl , Y , Y2 , N , MARK , PL2 ) 1172 C 1173 C XI X LOWER LIMIT 1174 C X(N) ARRAY OF N X VALUES 1175 C X2 X UPPER LIMIT 1176 C Yl Y LOWER LIMIT 1177 C Y(N) ARRAY OF N Y VALUES 1178 C Y2 Y UPPER LIMIT 1179 C N NUMBER OF POINT5 U80 C MARK SYMBOL NUMBER (1,2,...) ACCORDING TO MARKS CODE 1181 C PL2 2-D PEN MOVEMENT ROUTINE NAME E.G. PL2CA 1182 C MUST BE DECLARED EXTERNAL TYPE. 1 1 83 C 1184 " IF(MARKTR.EQ.ZER) GO TO 929 1185 CALL GRFGP ( BLO , POINTX , BHI , -100 ., POINTY , 100 ., KZERO , 1186 1 2.PL2CA) 1187 C 1188 C EJECT THE FRAME 1189 C 1190 929 CALL PLTEJ

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221 1191 1192 1193 1194 930 URITE(7,940)IERR 940 F0RMAT(/2X,5HIERR» STOP END 13) $ FOR R5D*0I5K:CJT:XP0W * FOR R5D$DISK:CJT.ILL1EPRLIBS t LINK XPOU.EPRLIBS.UTILtDISKtCEISPACKDEISPACK.OLB/LIB,3PLT:PTIGERLIB IF PI .EQ5. ON CONTROL Y THEN * GOTO DONE THEN INQUIRE PI "Na«e of fill with XPOU data (NO .ext!> A55IGN ASSIGN A55IGN 'PI 'PI' 'PI .DAT .LST PTI FOR008 FOR007 FOR021 RUN RSD*DISK: CJT3XPOU.EXE DONE: 0EA55IGN FOR008 DEA55IGN F0R007 DEAS5IGN F0R021 „ WRITE 5Y5*OUTPUT "Your output lilting i« in PI .L5T. URITE SYSSQUTPUT "Your plot file ii in ''PI '.PTI.' INQUIRE PLOTIT "Do you want it plotted at the printer on your teremal i IF PLOTIT THEN 0PLT : PLOTTIGER .COM 'PI'. PTI TT :

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222 i c*********t**ttt**tt*****tt*tt****t***t********t**t**t****ttt*t* 2 c*********************** XTAL ******************************* 3 C 4 C XTAL VERSION OF QXTAL EPR SIMULATION PROGRAM A5 MODIFIED 5 C FOR USE AT THE UNIVERSITY OF FLORIDA (J. TELSER 3/15/84). 6 C 7 c*********<***************************************************** 8 C 9 C "QXTAL" EPR SIMULATION PROGRAM. 10 C (J COPYRIGHT 1980 BY R. L. BELFORD AND COWORKERS 11 C 12 C WHEN PUBLISHING MATERIAL USING THIS PROGRAM, PLEASE 13 C USE THE FOLLOWING REFERENCES: 14 C 15 C 1. BELFORD, R.L.; NILGE5, M.J. "COMPUTER SIMULATION 16 C OF POWDER SPECTRA", EPR SYMPOSIUM, 21ST ROCKY 17 C MOUNTAIN CONFERENCE, DENVER, CO; AUGUST, 1979. 18 C 2. NILGE5, M.J. PH.D. THESIS, UNIVERSITY OF ILLINOIS, 19 C 1981. ALTMAN A T L E. IBID. 1981. MAURICE, A.M 20 21 C 22 C IBID! 1982. 6ULIBA, E . P .' IBID! 1983. 24 C THIS PROGRAM SIMULATES ELECTRON PARAMAGNETIC RESONANCE 25 C SINGLE CRYSTAL SPECTRA FOR SYSTEMS WITH ELECTRON SPIN EQUAL 26 C 1/2 AND NUCLEAR SPIN OF THE MAJOR NUCLEUS (SPINA) LESS THAN 27 C OR EQUAL TO 7/2. NUCLEUS A MAY HAVE ONE OR TWO ISOTOPES. 28 C THE TWO MUST HAVE THE SAME SPIN. 29 C THE ZEROTH ORDER HAMILTONIAN, INCLUDING ELECTRONIC 30 C ZEEMAN AND NUCLEAR ZEEMAN , HYPERFINE AND QUADRUPOLAR 31 C TERMS, 15 DIAGONALIZED BY MEANS OF EISPACK ROUTINES. THE 32 C TRANSITION FIELDS ARE OBTAINED FROM THE EIGENENERGIES WITH 33 C A FIRST ORDER FREQUENCY-SHIFT PERTURBATION FORMULA. THE 34 C EIGENVECTORS ARE USED TO OBTAIN THE TRANSITION INTENSITIES. 35 C THE HYPERFINE AND QUADRUPOLE MATRICES MAY BE ROTATED 36 C TO THE G TENSOR BY COORDINATE TRANSFORMATIONS ABOUT EULER 37 C ANGLES ALPHA, BETA, GAMMA, AS OEFINED BY ROSE. SEE: 38 C ROSE, M.E. "ELEMENTARY THEORY OF ANGULAR MOMENTUM"; 39 C WILEY: NEW YORK, 1963. 40 C SUPERHYPERFINE CONTRIBUTIONS FROM AS MANY AS 2 SETS OF 41 C EQUIVALENT NUCLEI (5PINB AND SPINC) CAN BE COMPUTED FOR THE 42 C CONDITIONS WHERE THE NUCLEAR ZEEMAN TERM (GN*BN*B*I) IS 43 C EITHER VERY LARGE OR VERY SMALL COMPARED TO THE HYPERFINE 44 C TERM. THE NUCLEAR G VALUE IS ASSUMED TO BE ISOTROPIC. 45 C THE PROGRAM AL50 TAKES INTO ACCOUNT ANISOTROPIC LINE 46 C BROADENING DUE TO CRYSTAL IMPERFECTIONS. 47 C 48 C 49 C 50 C INPUT QUANTITIES 51 C IN THIS VERSION ALL DATA ARE READ IN USING FREE FORMAT 52 C THE PARAMETERS NEED ONLY BE SEPARATED BY BLANKS. 53 C ALL PARAMETERS MUST BE SPECIFIED (CAN BE-O) AND MUST 54 C BE ON THE CORRECT LINE. 55 C 56 C LINE #1: 57 C 58 C FREQ 59 C 60 C FREQ: THE EXCITATION FREQUENCY IN GHZ. 61 C 62 C LINE #2: 63 C 64 C SPINA, 5PIHB, SOTNC, NEB, NEC 66 C SPINA: THE SPIN OF THE MAJOR NUCLEUS 67 C 5PINB, SPINC: SPINS OF THE SUPERHYPERFINE NUCLEI B AND C 68 C NEB, NEC: DUMBER OF EQUIVALENT NUCLEI FOR SPINB AND SPINC 69 C 70 C LINE #3:

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223 71 c 72 C VERT5F,SCLPK 74 C VERT5F: SCALING FACTOR FOR INTENSITY. THE DEFAULT VALUE 75 C 15 100. VERTSF MAY BE GREATER THAN 100, IN WHICH CASE 76 C ANY PEAK OVER 100.0 WILL BE OFF-5CALE (TRUNCATED). 77 C SCLPK: A NONZERO VALUE FOR 5CLPK INDICATES THAT THE VALUE 78 C 15 TO BE U5ED AS AN ARTIFICIAL MAXIMUM INTENSITY. 79 C THIS ALLOWS THE USER TO COMPARE RELATIVE INTENSITIES OF 80 C VARIOUS PLOTS. A ZERO VALUE DIRECTS THE PROGRAM TO FIND 81 C THE MAXIMUM INTESITY OF THE SPECTRUM AND USE THIS AS A 82 C SCALING PARAMETER. §3 6 LINE *4: 85 C 86 C NTR, NOR 87 C 88 C NTR: NUMBER OF HYPERFINE TRANSITIONS FOR SPINA; CALCULATES 89 C THE PRIMARY TRANSITIONS FIRST (DELTA MI-0). THEN 90 C /DELTA MI-1/, /DELTA MI-2/ ,..., /DELTA MI-2*MI / . BECAUSE 91 C OF SIZE LIMITS ON THE ARRAYS, NTR MAX-64 (1-7/2). 92 C FOR A GIVEN SPINA, NTR MAX( 2*MI+1 >**2 SO THE DEFAULT VALUE 93 C IS SET TO THIS NUMBER IN THE DEFAULT ASSIGNMENT SECTION. 94 C NOR: NUMBER OF ORIENTATIONS FOR WHICH SPECTRA ARE TO 95 C BE CALCULATED. 96 C 97 C LINE #5: 98 C 99 C CUTOFF, OMECA , L5 101 C CUTOFF: CONTRIBUTIONS TO THE SPECTRAL LINE5HAPE ARE 102 C CALCULATED ONLY UP TO A DISTANCE OF CUTOFF* W (THE PRODUCT 103 C OF THE LINE5HAPE AND CUTOFF) FROM EACH RESONANCE FIELD 104 C POSITION. 105 C OMEGA: HALF-WIDTH AT HALF-HEIGHT OF THE ANGULAR 106 C MISALIGNMENT DISTRIBUTION FUNCTION. OMEGA IN DEGREES. 107 C L5: LINESHAPE FUNCTION. L5-0 FOR LORENTZIAN , NONZERO 108 C FOR GAUSSIAN. 109 C 110 C LINE #6: 111 C 112 C W(I) 1-1,3; ANGSW(J) J-1,3 111 C U(I): PRINCIPAL VALUES OF THE LINEWIDTH MATRIX, 115 C HALF-WIDTH AT HALF-HEIGHT. WIDTHS IN MHZ. 11 6 c ANGSW(J): EULER ANGLES WHICH ROTATE THE W MATRIX FROM U7 C THE COORDINATE SYSTEM WHERE G*G IS DIAGONAL TO THE ONE 118 C WHERE W IS DIAGONAL. 119 C 120 C LINE #7: 121 C 122 C GN,GR,QR,GWT(1) ,NIS III e c ttacLBl? L B!Mnfih u S 5 iBREl H fo F il 5 I s fi?a5WE»? F THE MAJ0R 126 C GR. -RATIO OF GN (2ND I50TOPE / 1ST ISOTOPE). „„.-„-_, 127 C QR=RATIO OF QUADRUPOLE MOMENT (2ND ISOTOPE / 1ST ISOTOPE) 128 C GUT(l): -(PERCENT ABUNDANCE OF 15T ISOTOPE) / 100 . 129 C NIS: -NUMBER OF ISOTOPES TO BE CALCULATED. ( 1 OR 2). 130 C 131 C LINE *8: 132 C 133 C 8CNTR,BT0TAL,BZEMN,HINT } 3S C BCNTR: CENTER OF SPECTRUM (GAUS5). IF BCNTR0.0, lii C THEN THE PROGRAM WILL CALCULATE A CENTER OF THE PLOT. 137 C BTOTAL: FIELD SWEEP (GAU55). MUST BE SPECIFIED, lie C BZEMN: THE FIELD AT WHICH THE HAMILTONIAN WILL BE 139 c DIAGONALIZED. A ZERO WILL GIVE THE 5AME CALCULATION 140 C AS WITH THE ORIGINAL QP0W PROGRAM. THIS FEATURE ALLOWS

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225 211 212 213 214 213 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 C C*** c*** c IMPLICIT REAL*4 ( A-H , 0-Z) EXTERNAL PL2CA DATA BETA, PI / 1 . 399612386 , 1 . 743329252E-2/ BETA(BOHR MAGNETON/PLANCK'S CONSTANT) MHZ/GAUSS PI= PI/ 180 CONVERTS DEGREES TO RAOIANS. COMPLEX V(16,16),SUM(3),SII ,5IJ,YINT DIMENSION ANG5AO) ,ANG5B(3) ,ANGSC(3) ,ANGSQ(3) ,ANGSU(3) DIMENSION SPECTRMOOO) ,UGU(64> .TABLSI 1000) DIMENSION XPLOTI3000) ,YPL0T(3060) .SCRK3000) ,5CR2(3000) DIMENSION A (3) ,B(3> ,C(3) ,G(3) ,Q(3l ,R(3> ,5(3) ,W(3) , X A2(3> ,B2(3) ,C2(3) mmm „ „, DIMENSION G2<3) ,W2(3> .AA(3,3) , BB (3 ,3 > .CC < 3 ,3) , QQ<3 , 3) DIMENSION AAA<3,3> , GUT < 2) . ITB<20 ) ITC (20 > WU( 3 3) DIMENSION AQ<16,16,2) ,IULt2,64) ,GBN(3,16,2) ,GBETA(3) DIMENSION AQ1<16,16> ,AQ2<16,16> ,GB1(3,16> , GB2(3,16) DIMENSION AR(16,16) ,AI( 16,16 ) ,ZR( 16,16 > ,ZI( 16, 16) DIMENSION D(16) ,E(16) ,E2(16) ,TAU(2,16) EQUIVALENCE (AQ<1> ,AQ1(1) ) , (AQ(1,1,2) ,AQ2(1) > EQUIVALENCE (GBN( 1 ) ,GB1 ( 1 ) ) , (GBN(1,1,2) ,GB2(1) ) DATA MAXEIG /16/ C C**** c c c c c c c c**** c MAXEIG-2*(2*5PINA+1) 15 ORDER OF 5PIN-HAMILT0NIAN MATRIX TO BE DIAGONALIZEO. AT PRESENT, DIMENSION MAXEIG 15 SET FOR 5PINA-7/2. IF MAXEIG IS CHANGED, DIMENSIONS MUST CORRESPONDINGLY BE CHANGED: (Z-MAXEIG) G8NO Z,2) ,P(3+3*Z*Z/4,32) ,TM(3+3*Z*Z/4) AQ(Z Z,2) ,AQ1(Z,Z) AQ2(Z Zi ,GB1(3,Z) ,GB2(3,Z) ,AR(Z,Z) ,AI(Z,Z) ,ZR(Z,Z) ,D(Z) , IUL(2,Z*Z/4> ,E(Z) ,E2(Z> ,TAU(2,Z) , V ( Z , Z ) ,NTRD» ( Z/2 )**2 . READ IN PARAMETERS AND WRITE TO OUTPUT LISTING. READ(5,*)FREQ READ (5,*) SPINA, SPINB.5PINC , NEB, NEC READ(5,*)VERTSF,5CLPK READ(3,*)NTR,NOR READ ( 5 , * ) CUTOFF , OMEGA , L5 REA0(5,*I ((U(I), 1-1 ,3) , (ANGSU(J) READ(5,*)GN,GR,QR,GUT(1) .NIS J-l ,3) ) READ ( 5 ' * ) BCNTR ', BT6TAL , BZEMN , H INT READ (5 READ (5 READ I 5 READ (5 READ (5 READ(5 READ (5 (G(I) *) ( (A(I) *) ( (BID *l ( (C(I) *) (QD.QE *)TH1 ,PH1 *)TH2,PH2 1-1,3) I-i ,3) , (ANGSA(J) , 1-1 ,3) , (ANGSB(J) , 1-1 ,3) , (ANGSC(J) , (ANGSQ(I), 1-1,3)) DL1 DL2 J-l J-l J-l ,3) ) 3) > ,3) * C c**** c WRITE OUT PARAMETERS WRITE(6,11)FREQ 11 F0RMAT(13X, ' FREQ ' /10X.F8.5) WRITE ( 6 , 12) SPINA , SPINB , SPINC , NEB , NEC 12 FORMAT (i3X, 'SPINA 5PIN8 SPINC 1 /10X.3FB. 1 ,218) WRITE (6,13) VERT5F , 5CLPK 13 FORMAT (12X, ' VERT5F SCLPK URITE(6,14)NTR,N0R 14 FORMAT (13X, 'NTR N0R',/13X WRITE (6, 13) CUTOFF, OMEGA, L5 15 FORMAT (12X, 'CUTOFF OMEGA URITE(6,16)GN.GR,QR,GWT(1) ,NI5 16 FORMAT (12X, ' GN GR QR 1 F8.4,3F8.2,1I8) NEB NEC 13 ,/10X,F8.2,E16.8) 3X.I3) LS' , /10X,2F8.2,7X,I2) GUT(l) NIS' ,/8X,

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226 281 WRITE (6,17) BCNTR , BTOTAL , BZEMN , HINT 282 17 FORMAT (12X, 'BCNTR BTOTAL BZEMN HINT ', 283 1 /10X.4F8.2) 284 URITE(6,18)G 285 18 F0RMAT(14X,' GX GY GZ ' , / 10X , 3F8 . 5 1 286 URITE(6,20) 287 20 F0RMAT1///13X.17H PRINCIPAL VALUES , 18X , 13H EULER ANGLES, 288 1 / /13X, 'X' ,11X, 'Y' , 11X, 'Z' ) 289 URITE(6,21)G 290 URITE(6,22)A,ANGSA 291 URITE(6,23)B,ANG5B 292 WRITE(6,24)C,ANGSC 293 URITE<6,23)Q,ANG5Q 294 URITE(6,26)U,ANGSU 295 URITE(6,27»QD,QE 296 IF(LS.EQ.0)URITE(6,28) 297 IF(LS.NE.0)WRITE(6,29) 298 21 FORMAT(6H G .3F12.3) 299 22 F0RMAT(6H A/MHZ , 3F12. 3 , 3X , 3F10 . 2» 300 23 FORMAT (6H B/MHZ , 3F12 . 3 ,3X , 3F10 . 2) 301 24 F0RMAT16H C/MHZ ,3F12 . 3 ,3X , 3F10 . 2) 302 25 FORMAT (6H Q/MHZ , 3F12 . 3 ,3X , 3F10 . 2) 303 26 F0RMATI6H W/MHZ ,3F12 . 3 .3X , 3F10 . 2> 304 27 F0RMAT(//10X,4H QD-,F12.3,4H BE-,F12.3) 305 28 FORMAT (/1H , 'LINE5HAPE LORENTZIAN') 306 29 F0RMAT(/1H ,'LINESHAPE GAUSSIAN') 307 WRITEI6.30) 308 URITE(6,31)TH1 ,PH1 , OL1 309 URITE(6,31)TH2,PH2,DL2 310 30 FORMAT! /10X, ' THETA PHI DELTA') 311 31 FORMAT (8X.3F8. 2) IJ§ 8****** INITIALIZATION SECTION ****** 314 C 315 NTRD-I (2.0*SPINA>+1.0)*< < 2 . 0*SPINA ) +1 . ) 316 IF(NTR.GT.NTRO) NTR-NTRD 317 IF(UERTSF.EQ.O.O) VERTSF-100.0 313 DLN2-LOG<2.0) 319 N5PA-2.0*SPINA+1 .1 320 N5PA1=»N5PA+1 321 NEIG5T=2*N5PA 322 NEIGP1=NEIGST+1 323 SPBNEB=5PINB*NEB+1.0 324 SPCNEC»5PINC*NEC+1.0 325 C 326 C OETERMINE NUMBER OF POINTS FOR PLOT (NTOT) AND FOR 327 C CALCULATION (KTOT). 328 C 329 NTOT»(BTOTAL/HINTI+l .01 330 TYPE *. 'NTOT' , NTOT 331 IF ( NTOT. GT. 3000) STOP 'NTOT OUT OF RANGE' 332 BHALF-BTOTAL/2.0 333 BDELTA2 . 0* ( U( 1 ) +U ( 2 ) +U ( 3 ) ) + . 01 334 KLOT«