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Electrochemical and intervalence transfer properties of new mononuclear and binuclear ruthenium complexes

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Title:
Electrochemical and intervalence transfer properties of new mononuclear and binuclear ruthenium complexes
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Montague, Skiles Albert, 1956-
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English
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xi, 98 leaves : ill. ; 28 cm.

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Subjects / Keywords:
Breathing ( jstor )
Dimers ( jstor )
Electron transfer ( jstor )
Electronics ( jstor )
Electrons ( jstor )
Infrared spectrum ( jstor )
Ligands ( jstor )
Oxidation ( jstor )
Ruthenium ( jstor )
Solvents ( jstor )
Electrochemical analysis ( lcsh )
Ruthenium ( lcsh )
Valence (Theoretical chemistry) ( lcsh )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Thesis:
Thesis (Ph. D.)--University of Florida, 1984.
Bibliography:
Includes bibliographical references (leaves 94-97).
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Skiles Albert Montague.

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University of Florida
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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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ELECTROCHEMICAL AND INTERVALENCE TRANSFER PROPERTIES
OF NEW MONONUCLEAR AND BINUCLEAR RUTHENIUM COMPLEXES












BY

SKILES ALBERT MONTAGUE


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


UNIVERSITY OF FLORIDA


1984































to my family














ACKNOWLEDGMENTS


I would like to thank those who made my stay in

Gainesville some of the best years of my life.


iii















TABLE OF CONTENTS

Page

ACKNOWLEDGMENTS..........................................iii

LIST OF TABLES .......................................... vi

LIST OF FIGURES ........... ..............................vii

ABSTRACT ................................................ x

CHAPTER


GENERAL INFORMATION ...........................

PHYSICAL MEASUREMENTS .........................
Materials ................................
Apparatus and Technique ..................

PREPARATIONS ..................................
Notes on Preparations ....................
Ligands ..................................
Ruthenium Complexes ......................

ELECTROCHEMISTRY OF THE MONOMERS ..............
Introduction ........ ................... ..
Experimental ....... .......................
Discussion ...............................

ELECTROCHEMISTRY OF THE DIMERS ................
Introduction.. .............................
Experimental and Results .................
Discussion ...............................

THEORY OF INTERVALENCE TRANSFER ...............
Simple Model ..............................
Classification of Mixed-Valence Complexes
Hush Theory...............................
PKS Theory ...............................
Discussion ...............................

INTERVALENCE TRANSFER OF DIMERS ...............
Introduction ..............................
Experimental..... ..........................


1

5


I

II


III





IV





V





VI







VII









CHAPTER

VII


VIII


IX

REFERENCES

BIOGRAPHIC


Page

Hush Treatment ........................... 62
PKS Treatment............................ 64

NEAR INFRARED STUDIES OF MONOMER MONOCATIONS.. 89
Introduction ............................. 89
Experimental ............................. 90
Discussion................................ 90

SUMMARY ....................................... 92

.............................................. 94

AL SKETCH ..................................... 98














LIST OF TABLES


Page

3.1 Elemental Analysis of Ruthenium Complexes.... 20

4.1 Half-Wave Potentials for the
[Ru(bpy)3-n(R2-bpy)n]2+/+ Couples (v) ........ 28

4.2 Half-Wave Potentials for the
[Ru(bpy)3-n(R2-bpy)n]3+/2+ Couples (v) ....... 30

5.1 Half-Wave Potentials for the
[(R2-bpy) 2Ru(L-L)Ru(R2'-bpy)2n+
III-III/III-II Couples (v) .................... 38

5.2 Half-Wave Potentials for the
[(R2-bpy)2Ru(L-L)Ru(R2'-bpy)2]n+ III-II/II-II
Couples (v) .................................. 39

7.1 Intervalence Transfer Data and Hush Param-
eters for the Mixed-Valence Dimqrs
[(R2-bpy) 2Ru(BiBzIm)Ru(R2-bpy)] 3+............ 63

7.2 PKS Parameters for [(R2-bpy)Ru(BiBzIm)Ru(R2-
bpy) 2] 3+..................................... 80













LIST OF FIGURES


Page

2.1 Diagram of the Electrochemical Cell ............ 7

4.1 Cyclic Voltammogram of [Ru(ome2-bpy)3] (PF6)2 in
0.1 M TBAH/CH3CN (scan rate = 200 mV/s)........ 26

5.1 Cyclic Voltammograms of
[(R2-bpy) 2Ru(BiBzIm)Ru(R2-bpy)2 (PF6)2 in 0.1 M
TBAH/CH3CN (scan rate = 200 mV/s) ............... 37

6.1 Potential Energy (E) vs. Reaction Coordinate
(q) for a) Symmetric and b) Asymmetric Mixed-
Valence Complexes............................... 45

6.2 Potential Energy Surfaces for Class I through
Class III Mixed-Valence Complexes............... 48

7.1 Near Infrared Spectra of
[(R2-bpy)2Ru(BiBzIm)Ru(R2-bpy)2] in 0.1 M
TBAH/CD3CN (Methyl Series) ...................... 59

7.2 Near Infrared Spectra of 3+
[(R2-bpy) 2Ru(BiBzIm)Ru(R2-bpy)2] in 0.1 M
TBAH/CD3CN (Phenyl Series)...................... 60

7.3 Near Infrared Spectra of
[(R2-bpy) 2Ru(BiBzIm)Ru(R2-bpy)2] in 0.1 M
TBAH/CD3CN (Methoxy Series) ..................... 61

7.4 Matrix Hmn for Totally Symmetric Vibronic Wave-
function (PKS Theory) ........................... 65

7.5 Energy Matrix E+ and Coefficient Matrix r
(PKS Theory) ............................. ...... 66

7.6 Allowed Transitions for Intervalence Transfer
Absorption--Symmetric Case...................... 68

7.7 Schematic for H Matrix in the Asymmetric PKS
Calculation..................................... 69

7.8 Energy and Coefficient Matrix for Asymmetric
PKS Calculation.............. ................... 70
vii







Page


7.9 Experimental and Theoretical (PKS) Intervalence
Transfer Spectra for [(R2-bpy)2Ru(BiBzIm)Ru(R2-
3+
bpy) 2 R=R'=H .............................. 73

7.10 Experimental and Theoretical (PKS) Intervalence
Transfer Spectra for [(R2-bpy) 2Ru(BiBzIm)Ru(R2-
3+
bpy)2] R=R'=me............................. 74

7.11 Experimental and Theoretical (PKS) Intervalence
Transfer Spectra for [(R2-bpy)2Ru(BiBzIm)Ru(R2-
3+
bpy)2] R=R'=ph............................. 75

7.12 Experimental and Theoretical (PKS) Intervalence
Transfer Spectra for [(R2-bpy)2Ru(BiBzIm)Ru(R2-
3+
bpy)2] R=R'=ome............................ 76

7.13 Experimental and Theoretical (PKS) Intervalence
Transfer Spectra for [(R2-bpy) 2Ru(BiBzIm)Ru(R2-
3+
bpy)21 R=H; R'=me.......................... 77

7.14 Experimental and Theoretical (PKS) Intervalence
Transfer Spectra for [(R2-bpy) 2Ru(BiBzIm)Ru(R2-
3+
bpy)2] R=H; R'=ph.......................... 78

7.15 Experimental and Theoretical (PKS) Intervalence
Transfer Spectra for [(R2-bpy) 2Ru(BiBzIm)Ru(R2-
3+
bpy)2] R=H; R'=ome......................... 79

7.16 Potential Surfaces for
[(R2-bpy) 2Ru(BiBzIm)Ru(R2-bpy)2] Potential
Energy vs. Breathing Mode q. R=R'=H........... 81

7.17 Potential Surfaces for
[(R2-bpy) 2Ru(BiBzIm)Ru(R2-bpy)2] Potential
Energy vs. Breathing Mode q. R=R'=me.......... 82

7.18 Potential Surfaces for
[(R2-bpy) 2Ru(BiBzIm)Ru(R2-bpy)2] Potential
Energy vs. Breathing Mode q. R=R'=ph.......... 83

7.19 Potential Surfaces for 3
[(R2-bpy) 2Ru(BiBzIm)Ru(R2-bpy)2] Potential
Energy vs. Breathing Mode q. R=R'=ome......... 84

7.20 Potential Surfaces for
[(R2-bpy) 2Ru(BiBzIm)Ru(R2-bpy)] Potential
Energy vs. Breathing Mode q. R=H; R'=me....... 85


viii







Page


7.21 Potential Surfaces for 3+
[(R2-bpy) 2Ru(BiBzIm)Ru(R2-bpy)2] Potential
Energy vs. Breathing Mode q. R=H; R'=ph........ 86

7.22 Potential Surfaces for 3+
[(R2-bpy) 2Ru(BiBzIm)Ru(R2-bpy) 2] Potential
Energy vs. Brathing Mode q. R=H; R'=ome........ 87

8.1 Near Infrared Spectra of [Ru(es2-bpy) m(bpy) -m+
in 0.1 M TBAH/CH3CN............................. 91













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


ELECTROCHEMICAL AND INTERVALENCE TRANSFER PROPERTIES
OF NEW MONONUCLEAR AND BINUCLEAR RUTHENIUM COMPLEXES

By

Skiles Albert Montague

April 1984


Chairman: Professor Eric V. Dose
Major Department: Chemistry


A new series of mononuclear and binuclear ruthenium com-

plexes were synthesized and their electrochemical and inter-

valence transfer (IT) properties studied. Techniques

employed include cyclic voltammetry, coulometry, and near

infrared spectroscopy.

From cyclic voltammetric measurements the conpropor-

tionation constants, substituent group effects, and relative

potentials of redox sites are determined. Substituent group

effects lend valuable information toward the extent of delo-

calization of electrons between redox sites within a series

of mixed-valence (MV) compounds. Coulometry provides access

to the MV complex through stoichiometric addition or subtrac-

tion of electrons.

Theoretical treatments given by S. B. Piepho,

E. R. Krausz and P. N. Schatz (PKS) and by N. S. Hush allow








for interpretation of experimental IT data. Calculations of

electronic and vibronic coupling parameters, thermal electron

transfer activation energies and rate constants, fundamental

vibrational frequencies, and differences in potential between

redox sites follow from these theories.

Series of binuclear ruthenium complexes of the form

[(R2-bpy) 2Ru(BiBzIm)Ru(R2-bpy)]n+ (n = 2-4), symmetric

(R = R' = H, methyl, methoxy or phenyl) and asymmetric

(R = methyl, methoxy or phenyl; R' = H) have been prepared

and studied. Near infrared spectral properties of the MV

complexes appear to be consistent with the PKS and not the

Hush theory. This is, in fact, reasonable as these complexes

were determined to be fairly delocalized. The PKS theory is

explicitly derived to treat delocalized systems whereas the

Hush theory is strictly valid only in the strongly localized

limit.

Series of mixed-ligand ruthenium complexes,

[Ru(bpy) 3-m(R2-bpy) Mn+ (m = 0-3; n = 1, 2; R = H, methyl,

methoxy, phenyl, or ethyl carboxylate), were prepared and

studied. Electrochemical studies suggest that the unpaired

electron in the singly reduced (monocationic) form is local-

ized on a single ligand at any given time for series with

electron-withdrawing groups (ethyl carboxylate and phenyl).

Such studies suggest the opposite behavior for series with

electron-donating groups (methyl and methoxy). One possible

explanation for this behavior is that the electron-donating

groups lower the small thermal electron transfer barrier via

a build up of electron density in the ligand 7* system.













CHAPTER I

GENERAL INTRODUCTION



Chemists have known for many years of the unusual prop-

erties associated with mixed-valence compounds [1]. It was

not until 1967 that Robin and Day [1], Allen and Hush [2],

and Hush [3] systematically reviewed these properties and

presented the first comprehensive theoretical framework

treating mixed-valence compounds as a unique class of chemi-

cal substances. Since that time the field of mixed-valence

chemistry has experienced rapid growth with the appearance of

several review articles [4-7].

Robin and Day 11] adopted the phrase "mixed-valence" to

describe inorganic compounds which contain a single element

in more than one oxidation state. This mixed-valence state

occurs most frequently in transition metal complexes, as the

central metal ions can usually form stable complexes in more

than one oxidation state. Transfer of electrons between

metal centers is usually facile as bonds are rarely broken or

formed, and in most cases the gross symmetry around the metal

center is maintained. This long range electron-transfer

process gives rise to unusual physicochemical properties and

is the essence of mixed-valence chemistry.







In mixed-valence complexes electron transfer can be

optically induced giving rise to a broad, and occasionally

intense, absorption in the optical spectrum. This process is

termed intervalence transfer (IT). A thermal electron trans-

fer process is also predicted to occur [3,8] but is difficult

and often impossible to study [9]. There are a few reported

cases where thermal electron transfer has been studied

directly [10-12], but these instances are few and studies are

still in the early stages.

Interest in mixed-valence chemistry centers mainly

around the relationship between thermal and optical electron

transfer. In principle one can derive important information

concerning thermal electron transfer from intervalence trans-

fer studies if an accurate theoretical model is applied.

It was proposed by Robin and Day [1] that mixed-valence

complexes be divided into three classes depending on the

degree of electron delocalization between the metal redoxx)

centers. Class I compounds are those in which there is vir-

tually no electron delocalization (i.e., the valences are

strongly trapped). In this case both optical and thermal

electron transfer processes are forbidden. Compounds in this

class do not possess the unique electron transfer properties

associated with mixed-valence compounds. Class II mixed-

valence compounds are those where there is some electron

delocalization, but some degree of valence trapping still

exists. Both optical and thermal electron transfer are pre-

dicted. Strongly delocalized mixed-valence complexes are







grouped in Class III. Distinct valences do not exist, and

the metal centers are assigned an average oxidation state.

An optical absorption is predicted for this class of com-

pounds, but it corresponds to a purely electronic transition

and not to the intervalence transfer process.

Intervalence transfer data obtained to date have been

interpreted almost exclusively in light of the Hush theory

[4]. A major problem with such interpretations is that the

Hush theory is strictly valid only for systems where the

electrons are strongly localized (Class I in the Robin and

Day scheme) [3,7]. Applicability of the Hush theory falls

off as the systems become more delocalized and approach the

Class III description.

In 1978 Piepho et al. [8] presented a dynamic model, re-

ferred to here as the PKS model, for intervalence transfer

which includes explicitly the role of vibronic coupling in

mixed-valence systems. In this model the "trapped valence"

assumption is not made, and the model is proposed to be

applicable to mixed-valence systems of essentially any degree

of delocalization. An important factor to be considered in

applying the PKS theory is the neglect of solvent in its

derivation [13]. As a result strict applicability of the PKS

theory should be confined to more delocalized systems where

solvent contributions to electron transfer energy barriers

are small. The PKS theory as currently applied would give an

incomplete description of intervalence transfer for localized

systems where solvent contributions are important and for

which the Hush theory is applicable.







This work focuses on the preparation and study of

bridged binuclear ruthenium complexes, symmetric and asym-

metric, where electronic coupling is moderate. Small organic

groups, electron-withdrawing and electron-donating, have been

substituted onto terminal bipyridyl ligands during the syn-

thesis process. While these groups do not affect the gross

symmetry of the complex, they do affect the degree of elec-

tronic coupling. In the asymmetric cases the substituent

groups cause differences in potential between the metal

centers. As shown below these complexes allow for a unique

test of the Hush and especially the PKS theories.

Certain mononuclear complexes of ruthenium have been

shown to undergo what is believed to be intra- or interligand

electron transfer [14]. Spectroscopy and electrochemistry

have been used to study a series of mixed-ligand monomers in

an attempt to determine the nature of this process. Assuming

Koopman's theorem electrochemical studies of the monocations

and dications are applicable to transitions involving the

lowest triplet metal-to-ligand charge-transfer excited state

(3CT) of the dications [15-21].













CHAPTER II

PHYSICAL MEASUREMENTS



Materials


Reagent grade acetonitrile (Fisher) was dried by

refluxing over phosphorus pentoxide followed by distillation

on a one meter fractionating column. For a 2000 ml distil-

lation the first 400 ml were discarded and the next 1000 ml

collected. The solvent was degassed by four freeze-pump-thaw

cycles and stored under nitrogen. Tetrabutylammonium hexa-

fluorophosphate (TBAH) (electrometric grade, Southwestern

Analytical Chemicals) was dried under vacuum before use.

Deuterated acetonitrile (Merck) was 99% isotopically pure

and used as purchased.

Potassium hexafluorophosphate (Alfa), ruthenium tri-

chloride (Alfa), 2,2'-bipyridine (Eastman), 4,4'-dimethyl-

2,2'-bipyridine (G. Fredrick Smith), 4,4'-diphenyl-2,2'-

bipyridine (G.F.S), and Sephadex LH-20 (Sigma) were used

without further purification. All other chemicals were pur-

chased as reagent grade and used without further purification

unless otherwise specified. In general solvents were deoxy-

genated before use in reactions by bubbling dry nitrogen

through them for fifteen minutes.







Apparatus and Technique


Electrochemical experiments were carried out employing

a standard three-electrode circuit. A Princeton Applied

Research (PAR) Model 173 Potentiostat/Galvanostat with a

Model 178 Electrometer Probe was used for potential control.

Triangular waveforms for cyclic voltammetry were generated

using a PAR Model 175 Universal Programmer. Coulometric

electrolysis was monitored with a PAR Model 179 Digital

Coulometer. Cyclic voltammograms were recorded on a Houston

Instruments Omnigraphic 2000 Recorder.

All electrochemical experiments were run at ambient

temperature (2520C) and referenced to a saturated potassium

chloride calomel electrode (SCE). Figure 2.1 diagrams the

electrochemical cell. The reference electrode was partially

isolated from the electrochemical solution by a fritted disc.

For cyclic voltammetry a platinum bead working electrode and

a two-inch length of platinum wire (28 guage) auxilliary

electrode were used. All electrodes were positioned into a

one centimeter pathlength quartz spectrometer cuvette by a

custom-fabricated teflon cap. When running coulometry exper-

iments it was found necessary to separate the reference

electrode from the electrochemical cell by a fritted disc. A

platinum coil (12 in of 28 guage wire wound around a 2 mm

diameter) served as the working electrode, and a small mag-

netic stir bar was placed into the cell.

Electrochemical experiments were performed under nitro-

gen. The platinum electrodes were cleaned after each use by












SCE -


teflon cap -


supporting
electrolyte
solution
solution
level
spectrometer
cuvette

fritted disc -
sample
solution


Ir


'-4-


-- :--


Pt coil
working
electrode


au:
--- el


Killiary
ectrode


- Pt bead


Figure 2.1. Diagram of the Electrochemical Cell.


g








immersing them in concentrated nitric acid for at least

5 min followed by rinsing with large volumes of methanol.

The electrochemical cell was assembled complete with weighed

sample (minus the reference electrode) and allowed to dry

under vacuum before introduction into the drybox.

Cyclic voltammograms of supporting electrolyte in

acetonitrile gave no detectable waves, and currents were

less than 1 pA in the range +1.8 V to -2.0 V at a scan rate

of 200 mV/s. Sample concentrations for cyclic voltammetric

experiments were 1.0x103 M in a supporting electrolyte

solution of 0.10 M TBAH in acetonitrile.

Coulometry experiments were run in the above electro-

lyte solution at 2.00x10-4M sample concentrations. In the

dimer studies where it was desired to obtain optical spectra

up to 2600 nm in the near infrared, d3-acetonitrile was used

as the solvent. Electrolysis was determined complete when a

stoichiometric number of coulombs had passed. The elec-

trodes were removed from the spectrometer cuvette and the

cuvette tightly capped. Near infrared spectra were recorded

on a Perkin Elmer 330 UV/VIS/NIR Spectrometer. The inter-

valence transfer band of a sample inside the capped cell had

a typical half-life of about two days.














CHAPTER III

PREPARATIONS



Notes on Preparations


All mononuclear and binuclear complexes of ruthenium

are synthesized in the laboratory. Ligands include

2,2'-bipyridine (bpy), 4,4'-R2-2,2'-bipyridine (R2-bpy)

[R = H, methyl (me), phenyl (ph), methoxy (ome), and ethyl

carboxylate (es)], bibenzimidazole (BiBzImH2), bibenzimida-

zolate (BiBzIm), and bipyrimidine (Bipyrm). The last two

are employed as bridging ligands for the binuclear complexes.

Sephadex column chromatography is used to purify the

chloride salts of the mononuclear and binuclear complexes

prior to formation of the PF6 salts through metathesis.

The number of successive elutions required for a pure

compound depends on the band separation and on the evenness

of the packing. In general compounds are separated by

molecular weight with the higher molecular weight compounds

eluting first. Complexes are usually identifiable on the

column by their colors, luminescence properties, and order

of elution. Nonelectrolytes such as ligands and

[Ru(R2-bpy) 2C12] complexes elute very slowly in pure meth-

anol, and a small amount of hydrochloric acid (6 drops in

30 ml methanol) is added to "rinse" the column of these.








After the addition of 300 ml more methanol, the column is

ready for use.

An Altex 1 m x 2.5 cm I.D. column is used in the prep-

arations. To assure the column is vertical before packing,

a 1.5 m plumb line is used. A slurry of 100 g Sephadex

LH-20 in 500 ml methanol is added and allowed to settle in

the column while the elution tube is open. Once the Sepha-

dex completely settles (about 4 hr), a thin layer of sand

is added to facilitate addition of reaction mixtures with-

out disturbance of the Sephadex.

To perform a separation the sample is dissolved in a

small amount of methanol (1-4 ml) and filtered. The metha-

nol level in the column is allowed to drop to the level of

the sand, and the sample solution is carefully added. As

the solution reaches the level of the sand, methanol is added

and maintained above the sand as the compound elutes through

the column. Ruthenium complexes usually elute in 2-3 hr.



Ligands


4,4'-Bis(ethyl carboxylate)-2,2'-bipyridine

Synthesis of this ligand is adopted from procedures

described by Case [22] and Maerker and Case [23]. To a

solution of potassium permanganate (55.0 g) in water

(950 ml), 4,4'-dimethyl-2,2'-bipyridine (4.00 g) is added

and heated to reflux until the solution becomes colorless

(about 4 hr). After filtering off the precipitated manganese

dioxide, the solution is extracted with three 200 ml portions








of diethyl ether to remove any unreacted 4,4'-dimethyl-2,2'-

bipyridine. Concentrated hydrochloric acid is added to the

aqueous phase until acidic to precipitate an insoluble white

powder which is collected by filtration. Yield for the

crude 2,2'-bipyridine-4,4'-dicarboxylic acid after drying is

5.1 g (39%).

This acid is refluxed with 55 ml concentrated sulfuric

acid in 120 ml absolute ethanol for 10 hr. The solution is

cooled and poured over ice (about 200 g) followed by neutral-

ization with 25% sodium hydroxide. Upon neutralization the

solution turns light pink, and a white bulky precipitate

forms which is collected by filtration, washed with water,

and dried under vacuum. Recrystallizing twice from 95%

ethanol and drying under vacuum yields 2.2 g of long white

fibrous crystals of 4,4'-bis(ethyl carboxylate)-2,2'-bipyri-

dine (37%; mp = 158.5-160.5C, Lit = 159-160.5C [23]).


4,4'-Dimethoxy-2,2'-bipyridine

This synthesis was adopted from the procedures of Jones

et al. [24] and Case [22]. The compound 2,2'-bipyridine

(25.0 g), 30% hydrogen peroxide (25 ml), and glacial acetic

acid (125 ml) are heated on a water bath at 100C for 4 hr.

The solution is cooled, another 25 ml portion of hydrogen

peroxide is added, and the solution is heated at 100C for

another 4 hr. After cooling to 0C the solution is neutral-

ized with cold 25% sodium hydroxide causing a bulky white

precipitate to form. The precipitate is collected by filtra-

tion, washed with small portions of water, and recrystallized







from water. White fibrous crystals are collected and dried

under vacuum to give 21 g of 2,2'-bipyridine-1,1'-dioxide

(70%; mp = 310C dec, Lit = 3100C dec [25]).

This compound in 100 ml concentrated sulfuric and

100 ml 90% nitric acids is heated on a water bath at 100C

for 8 hr. The yellow solution is cooled and poured over ice

(-400 g), followed by neutralization with cold 25% aqueous

sodium hydroxide. Upon neutralization the solution turns

orange and a yellow precipitate forms which is collected by

filtration. The precipitate is washed with water followed

by two 50 ml portions of hot absolute ethanol and dried under

vacuum yielding 9.5 g or crude 2,2'-bipyridine-4,4'-dinitro-

l,l'-dioxide (31%).

This compound is added to a solution of sodium methoxide

prepared by adding 2.85 g metallic sodium to 380 ml methanol.

The suspension is stirred 3.25 hr while maintaining the tem-

perature at 3320 on a water bath. The solution is cooled to

0C, neutralized with concentrated sulfuric acid, filtered,

and the white filtercake discarded. The yellow solution is

evaporated to dryness on a rotary evaporator and extracted

with three 300 ml portions of hot chloroform. The extracts

are combined and refluxed 10 min with activated carbon (5 g),

filtered, and the volume reduced to 500 ml. Hot petroleum

ether (300 ml; 70-110C) is added to produce a fluffy yellow

precipitate. Yield for the crude 4,4'-dimethyl-2,2'-bipyri-

dine-1,1'-dioxide is 5.4 g (67%).

This compound is mixed with 68 ml of dry chloroform and

cooled to -30C. Phosphorus trichloride (10.8 ml) is added,





13

and the suspension is refluxed for 75 min, cooled, and poured

onto crushed ice (-100 g). After phase separation the chlo-

roform phase is extracted with four 50 ml portions of water,

and the aqueous extracts are combined with the aqueous layer

of the reaction mixture. Neutralization with 25% sodium

hydroxide causes a bulky white precipitate to form which,

after cooling, is collected by filtration and washed with

water. Recrystallization from absolute ethanol gives 2.4 g

of white crystals of 4,4'-dimethoxy-2,2'-bipyridine (53%;

mp = 170-172C, Lit = 170-172 [23]).


2,2'-Bibenzimidazole

Preparation of this ligand is taken from Fieselmann et

al. [26] where 0-phenylenediamine (22.5 g) and oxamide (8.8 g)

are refluxed in 20 ml ethylene glycol for 24 hr. The solu-

tion is added to 400 ml of boiling water causing a thick

yellow precipitate to form which is collected by filtration,

washed, and dried under vacuum. This material is recrystal-

lized in 900 ml ethylene glycol with activated carbon. The

compound is dried under vacuum yielding 9.2 g bibenzimidazole

(39%; mp = 395C dec).



Ruthenium Complexes


[Ru(bpy) 3-n)R2-bpy)n] (PF6)2

Several syntheses have appeared in the literature for

the complex ion [Ru(bpy)3]2' [27,281. The latest and most

commonly used preparation by Braddock and Meyer [27] involves







refluxing RuCl3*nH20 with a stoichiometric amount of bpy in

N,N'-dimethylformamide (DMF) for several hours. We have du-

plicated this preparation in our laboratory and have found

[Ru(bpy)3]2+ prepared in this manner to contain a significant

amount of a byproduct we believe is [Ru(bpy)2(CO)Cl]+ [29],

which we could not separate completely from the product using

Sephadex LH-20 in methanol. A procedure has been developed

for preparing [Ru(bpy)3] 2+ free from this impurity using eth-

ylene glycol as the solvent for the reaction. This synthetic

route is useful in preparing several analogs of the above

complex using substituted bipyridine ligands in place of bpy.
2+
When [Ru(bpy) 3] is prepared by refluxing RuC13-nH20

with a stoichiometric amount of bpy in DMF and the residue

from the reaction mixture is eluted through a Sephadex col-

umn using methanol as the eluent, four "bands" appear on the

column. The first to elute is the bright orange luminescent

[Ru(bpy)3]2+ complex. Superimposed on the trailing edge of

this band is a dull brown-orange (nonluminescent) band which

is hard to separate completely from the former. Several elu-

tions through the column taking narrow cuts still leave a

small amount of the impurity and greatly reduced the
2+
[Ru(bpy)3] yield. Other bands on the column include a

small amount of neutral (Ru(bpy)2Cl2] (purple) and unreacted

bpy (otherwise colorless but luminesces blue in the presence

of light).

When RuCl3.nH20 is refluxed with a small stoichiometric

excess of bpy in ethylene glycol, the solution turns bright







orange within minutes. Upon distilling off the solvent under

vacuum at 1000C, the residue is dissolved in a minimum amount

of methanol and eluted through a Sephadex column. Now only

two bands appear on the column--a luminescent orange leading

band corresponding to [Ru(bpy) 3] and a faint bpy band which

elutes very slowly. The preparation gives nearly quantita-

tive yields of the corresponding [Ru(R2-bpy) 3] chloride

salt when bpy is replaced with R2-bpy (where R = me, ph and

ome), with the only other impurity being the excess ligand.

The PF6 salts of these complexes were used for electrochem-

ical and spectroscopic measurements. The metathesis is eas-

ily performed by dissolving the chloride salt in a small

excess of water (for complexes that are relatively insoluble

in water, a small amount of methanol is added). While main-

taining fast stirring rates, 0.1 M KPF6 is added dropwise

through a filter. When precipitation is complete (superna-

tent becomes almost colorless) the product is filtered and

washed with water.

The compounds RuCl *3H20 (260 mg) and bpy (470 mg) are

refluxed with 20 ml ethylene glycol for 30 min. The ethyl-

ene glycol is distilled off under vacuum at 1000C, and the

residue is dissolved in 3 ml methanol. This solution is

eluted through a Sephadex column, and the bright orange band

is collected. Upon removal of the methanol, the solid is

dissolved in 20 ml water. The PF6 salt is prepared as

described above in this chapter, yielding 840 mg [Ru(bpy)3]-

(PF6)2 (98%). Similar procedures are followed for complexes

involving substituted R2-bpy ligands.








The complex [Ru(es2-bpy)3] (PF6)2 is not prepared in

ethylene glycol to prevent transesterification of the es

group. This preparation is adapted from Sprintschnik et

al. [30] in which RuCl3*3H20 (260 mg) and es2-bpy (650 mg)

are suspended in 50 ml absolute ethanol and the mixture

heated in a sealed glass tube at 140C for 4 days. After

adding 2 ml water, the solution is refrigerated for 8 hr.

The mixture is filtered yielding a black filtercake (which

is discarded) and a dark red solution which is evaporated

to dryness under vacuum at 100C. The residue is dissolved

in 4 ml methanol, filtered, and eluted through a Sephadex

column. The PF6 salt is prepared yielding 410 mg

[Ru(es2-bpy)] (PF6)2 (32%).


[Ru(R2-bpy) 2Cl2]

Several methods have been published for the prepara-

tions of [Ru(R2-bpy)2C12] complexes [30-33), many of them

requiring much experimental effort and producing small

yields. Presently the most viable synthetic route toward

the preparations of these complexes [30] involves refluxing

RuCl3*nH20 with a stoichiometric amount of R2-bpy in DMF for

several hours. Yields for these reactions are typically low

with the formation of large amounts of the corresponding

mono- [31] and trissubstituted R2-bpy complexes, as well as

[Ru(R2-bpy) 2(CO)Cl] [29], as byproducts.

A simple technique has been developed in our laboratory

for the preparation of [Ru(R2-bpy)2Cl2] complexes in high

yields by using 4:1 ethylene glycol/ethanol as the reaction







solvent. When [Ru(R2-bpy)Cl2] (R = H, me, ph or ome) is

prepared by refluxing RuCl3 nH20 with a stoichiometric quan-

tity of the R2-bpy ligand in the above solvent for 3 hr, the

product is formed in relatively high yields (typically

70-85%) with only small amounts of the corresponding mono-

and trissubstituted complexes and no [Ru(R2-bpy) 2(CO)Cl] .

The complex RuC13*3H20 (260 mg) and bpy (310 mg) are

refluxed in 50 ml 4:1 ethylene glycol/ethanol for 3 hr. The

solvent is removed under vacuum at 100C and the residue

refluxed in 100 ml 1:1 ethanol/water for one hour and fil-

tered. Lithium chloride (10 g) is added to the filtrate and

the ethanol is distilled off (85-90C). The solution is

sealed and maintained at 0C for 3 hr. Green/black crystals

are collected by filtration-and washed with large volumes of

water. The product is dried under vacuum to yield 409 mg

[Ru(bpy) 2C12 (85%). Similar procedures are followed for

complexes involving substituted R2-bpy ligands.

The complex [Ru(es2-bpy) 2Cl2] is prepared by a modifi-

cation of the method of Sprintschnik et al. [30], using DMF

as the reaction solvent. The RuCl3*3H20 (260 mg) and es2bpy

(600 mg) are refluxed in 60 ml of DMF for 3 hr. The volume

is reduced to 10 ml under vacuum at 1000C. Acetone is added

while hot, and the flask is capped and stored at 0C for

8 hr. Black crystals are collected by filtration, recrys-

tallized from methylene chloride/acetonitrile, and dried

under vacuum, yielding 178 mg of product (23%).







[Ru(bpy) (R2-bpy)2] (PF6)2

The [Ru(me2bpy)2Cl2] complex (100 mg) and bpy (30 mg)

are added to 20 ml of absolute ethanol and refluxed 3 hr.

During this time the solution becomes bright orange. After

removal of the ethanol under vacuum, the residue is purified

using Sephadex chromatography collecting the luminescent

orange band. The PF salt is obtained through metathesis

and, after drying, yields 100 mg of product (68%). This

procedure is used to prepare complexes where R = ph, ome and

es, producing yields between 40-70%.


[Ru(bpy)2(R2-bpy)] (PF6)2

Preparations of complexes in this series follow as

above by replacing [Ru(R2-bpy)2Cl2] and bpy with

[Ru(bpy)2Cl2] and R2-bpy. Yields range from 70-80%.


[Ru(bpy)2(BiBzImH2)]C12

This preparation is adapted from the method of Haga [34].

The [Ru(bpy)2Cl2] complex (484 mg) and BiBzImH2 (350 mg) are

refluxed in 20 ml absolute ethanol during which time the

solution turns bright red-orange. The ethanol is removed

under vacuum, and the residue is purified by Sephadex chro-

matography collecting the luminescent orange band. After

removal of the methanol under vacuum, the solid is collected

and dried, yielding 620 mg of product (86%).


[(R2-bpy) 2Ru(BiBzIm)Ru(bpy)2' (PF6)2

Complexes in this series are prepared by a modification

of the method of Haga [34]. The [Ru(bpy)2(BiBzImH2)]C12








complex (100 mg) is added to [Ru(me2bpy)2Cl2] (100 mg) in

20 ml absolute ethanol. Five drops of triethylamine are

added, and the mixture is refluxed 3 hr during which time

the solution turns bright red. The ethanol is removed under

vacuum and purified by Sephadex chromatography, collecting

the leading red (nonluminescent) band. A luminescent orange

band, superimposed on the trailing edge, makes it difficult

to obtain a pure product and can decrease yields substan-

tially. Yields are typically low for all the dimers ranging

from 20-50%. For the present preparation, after metathesis

to the PF6 salt and drying, the yield is 96 mg (49%). Com-

plexes where R = me, ome and ph are prepared using the same

general procedure. The R = ph complex requires a longer

reflux time (8 hr).


[(R2-bpy) 2Ru(BiBzIm)Ru(R2-bpy)2 (PF6)2

Preparations of complexes in this series are similar to
2+
the above except that the [Ru(R2-bpy)2(BiBzImH 2)] complex

is prepared in situ. The [Ru(R2-bpy)2Cl2] complex (540 mg)

and BiBzImH2 (117 mg) are refluxed in 20 ml absolute ethanol

1 hr. Five drops of triethylamine are added, and reflux is

continued 3 hr longer. Purification procedures are similar

to the above, yielding 314 mg product (43%).


Microanalysis

All elemental analyses were performed at the Department

of Chemistry, University of Florida, and are listed in

Table 3.1.















H H
C N

dP CN C %
















Q)



0
U

5







,--In
-H oH n




O c C



4- O







0 U z







'0
S10 44


r-


















a0
Hp


0 v,
o *q*
In 0
H H




























In In


m







(*. .Cl
e H
























o m
In r-i


t.0 CM


n H

0o 0
H H













m











. .*
Iz Uz
v3 4tr


aa O
* .
H r-H
























n r-

gr qw
. .
*e


, In
H N













H .












%0 CN


'n 'n


H 4
H H
H H
r-I r-l











SLA






( N






(N '0


CN





(N












H
CN

















N
A
4!
04


N
0


0H












I
N




>1



4)
O
CM













CHAPTER IV

ELECTROCHEMISTRY OF THE MONOMERS



Introduction


Tris(2,2'-bipyridyl)ruthenium and its analogues continue

to be of considerable interest as central subjects in the

study of general photosensitization [35] as well as in stud-

ies of singlet oxygen production [36] and of possible photol-

ysis of H20 [37]. While the electronic structure of the

reduced, monocationic forms of these complexes is a factor in

certain luminescence quenching [38] and chemiluminescent [39]

processes, most physical studies of these complexes have

focused upon the reactivity of the dications' lowest triplet

metal-to-ligand charge-transfer excited state (3CT) primarily

responsible for the interesting behavior of the ions. The

answer to one of the earliest such questions remains uncer-

tain: whether the optical electron is delocalized over all

three bidentate aromatic ligands or localized on just one

ligand at a given time. Reports by Hager et al. [15] account

for excited-state properties of [Ru(bpy)3]2+ (bpy = 2,2'bipyr-

idyl) through a model of the 3CT state derived from a metal-

t2g-to-ligand 7* charge-transfer model of D3 symmetry (delo-

calized). However, two recent fluorescence polarization stud-

ies 118,19], and recent resonance Raman [20] and time-resolved








resonance Raman [21] studies indicate a localized 3CT state.

Assuming that Koopman's theorem is valid in the comparison

of the monocation with the excited dication, esr [40] and

electrochemical [41] studies are also consistent with a

localized 3CT state.

Ligand 7* orbitals are the lowest-energy acceptor or-

bitals in both charge-transfer-to-ligand excitations and

complex reductions to the monocation, although some charge-

transfer-to-solvent character of the 3CT state apparently

does exist [39]. The strictly exponential [15] luminescence

decay of mixed-ligand complexes of Ru(II), unlike the multi-

exponential behavior of mixed-ligand complexes of Rh(III)

[42,43], is consistent with either a delocalized electronic

structure or an equilibration (which is faster than lumines-

cence decay rates of about 106 sec-1) of the optical electron

among ligand i* orbitals. The latter is in turn consistent

with the low interligand electron-hopping barriers estimated

from the temperature-dependence of esr broadening [40].

If the T* electron in [Ru(bpy)31 is localized, there

could then be three reduced forms, each corresponding to

occupation of a different ligand 7* orbital by the highest-

energy electron. If the one-electron reduction potential En
+
to a single reduced from M+ (where n = 1, 2 or 3) corre-
n
sponds to occupation of a 7* orbital in ligand n [44], then

at a given applied electrochemical potential E and tempera-

ture T, the ratio of the concentration of each such reduced

form in solution to that of the dicationic form M2+ is








[Mn] e (E-En)F/RT (4.1)
M2+ = e (4.1)
[M ]

Since rapid and reversible electrochemical reduction to

rapidly equilibrating products will result in a summation of

currents from reduction to each form, at any potential E the

apparent equilibrium constant Kapp may be defined as


apapp
K = L e n (4.2)
app n=l

Any such pattern of n* orbital energies will yield but a

single apparent reduction wave centered at a potential which

can in principle be calculated from the relevant E values.
n
For the present case there are two types of calculated poten-

tials--those for reductions of symmetric complexes [RuB3]2+

and those for reductions of mixed-ligand complexes [RuB2B'] 2+

In the first case the equivalence of El, E2 and E3 (all equal

to EB, the one-orbital potential for coordinated ligand B)

leads to a small difference of statistical origin [44]

between EB for the ligand and EB for the complex. Thus the

apparent reduction potential EB3 for such a couple is



3
E3 = E+ -- ln(3) (4.3)


For the mixed-ligand case [RuB2B']2+/+,


EB2B = EB +RT ln (2+ eB-EB')F/RT (44)


Thus experimental reduction potentials for the two limiting








symmetric forms and the assumption of rapid equilibration

between reduced forms lead to prediction of observed poten-

tials for the associated mixed-ligand complexes. These

predicted potentials of the mixed-ligand complexes will

almost always differ significantly from those predicted from

linear free energy dependence following from either a metal-

centered or a delocalized ligand-centered reduction.



Experimental


Cyclic voltammograms were recorded as described in

Chapter II for the series [Ru(bpy) 3-n(R2-bpy)n 2+ where

R = me, ph, ome and es (n = 0-3). Baselines of supporting

electrolyte in CH3CN gave no discernible waves in the range

-1.8 to +2.0 V vs. SCE, and currents did not exceed 1 vA at

scan rates of 200 mV/s.

One reversible oxidation wave corresponding to the

RuII/III couple [45] and three reversible reduction waves

corresponding to three successive ligand-centered reductions

[14] were recorded for each of the above complexes. A cyclic

voltammogram is presented in Figure 4.1 for the R = ome

(n = 1) complex. Other monomer complexes yield cyclic vol-

tammograms similar to this and are not shown. Peak separa-

tions for the above couples vary from 0.070-0.090 V and are

invarient with sweep rates of 100-500 mV/s. This behavior is

due presumedly to uncompensated solution resistance. Several

known reversible couples including [Ru(bpy) 3 3+/2+ have been

reported to yield peak separations of 60-100 mV under



























- .


r 4





I II


04



or



U
0 d











HO
0
m U













U ,-4
-4
0a



>





U *-



a)
,-1
m<

44






































O
0

0
o


o m







II l0

I + -







II II


X

w 0
< w
o
M: -








conditions similar to ours [46], and thus all electrochem-

ical couples in this work are assumed to be reversible

despite small deviations of AE from the theoretical value
pp
of 0.059 V [47].

Listed in Table 4.1 are half-wave potentials corre-

sponding to oxidations of the monomers. Since these oxida-

tions are metal centered, effects of ligand substituent

groups can be treated as perturbations at the metal center,

the effects of which will be additive; i.e., there should be

a linear free energy relationship (LFER) between the half-

wave potentials and the number of substituent groups [45].

Also listed in Table 4.1 are calculated half-wave potentials

for the two mixed ligand species assuming LFER and interpol-

ating between potentials of the corresponding symmetric

species.

Given an accuracy in measurement of E to be 0.005 V,

it is seen that LFER is followed closely for oxidation poten-

tials of the above set of complexes. Contributions per

substituent group to E are listed:


Substituent Group E (ox)

H =0
me -0.027
ph -0.011
ome -0.050
es +0.060


From the above table it can be seen that the me, ph and ome

groups are electron-donating (more facile oxidation), and

that the es group is strongly electron-withdrawing (less

facile oxidation).









Table 4.1.


Half-Wave Potentials for the
[Ru(bpy) 3-n(R2-bpy) n2++ Couples
*3 (R 2-b


n Experimental


R = ph







R = es






R = me


Localized
Model

a
-1.254
-1.239


a
-0.879
-0.861


-1.292
-1.257
-1.235
-1.230


-1.292
-0.960
-0.898
-0.851

-1.292
-1.323
-1.353
-1.408

-1.292
-1.357
-1.400
-1.460


Delocalized
Model

a
-1.271
-1.251


a
-1.145
-0.998


a
-1.339
-1.369
a


a
-1.348
-1.404
a


a Fixed point.


(v).


a
-1.302
-1.320
a


a
-1.302
-1.320
a


R = ome







The mechanisms for these substituent effects are, in the

ph, ome and es cases, assumed to originate via resonance with

the 7 system of the bipyridine ligand [48]. For the me case

it is assumed that induction through the 7 system is impor-

tant. Regardless of the origin, these substituent effects act

in a way to alter the electron density around the metal cen-

ter.

Reductions of the above complexes are ligand centered in

nature. Table 4.2 lists the first reduction half-wave poten-

tials for the above monomer series as well as potentials cal-

culated assuming both the localized and delocalized descrip-

tions. In the delocalized limit it would be expected that

the substituent groups would affect E(RED) values in a lin-

ear (LFER) manner since the effect of each substituent group

would be averaged over the three ligands. In the localized

limit equations 4.3 and 4.4 are used to calculate the E (RED)

values.



Discussion


The agreement between the experimental reduction poten-

tials for the mixed-ligand complexes involving the phenyl and

ethyl carboxylate substituent groups and those calculated

from our application of the ligand-localized model to the

symmetric complex potentials argues in favor of that model's

adoption over the alternate metal-centered and ligand-delocal-

ized models for the monocationic complexes. Although such

agreement in the [Ru(bpy)3 n(es2bpy)n]2+/+ case is not
j~n not









Table 4.2. Half-Wave Potentials o the
[Ru(bpy) 3-n(R2-bpy) ] 2++ Couples (v).


Experimental


Calc LFER


R = ph






R = es


1.310
1.293
1.268
1.244

1.310
1.394
1.517
1.610

1.310
1.258
1.216
1.149

1.310
1.173
1.061
0.949


a Fixed Point.


a
1.288
1.266
a

a
1.310
1-.510
a

a
1.256
1.202
a

a
1.189
1.069
a


R = me


R = ome








strictly observed, the experimental potentials of those

couples clearly resemble those from the localized model more

than those from any delocalized model. Further, potentials

for the +/0 reductions (i.e., -1.493 V, -1.421 V, -1.099 V,

and -1.014 V for n = 0, 1, 2 and 3) and for the 0/- reduc-

tions (-1.736 V, -1.612 V, -1.534 V, and -1.231 V) for the

same series indicate that the rT* electrons localize to the

extent possible in the lowest energy orbitals available.

For the mixed-ligand complexes involving the methyl and

methoxy substituent groups, agreement occurs between the

experimental potentials and those calculated from our appli-

cation of the ligand-delocalized model. Thus it is seen

that electron-withdrawing substituent groups favor the

localized description whereas electron-donating groups favor

the opposite.

One explanation for this apparent discrepancy may be

offered if the monomer monocations are viewed as interligand

mixed-valence species. Taking into consideration the low

interligand electron-hopping barriers, corresponding to

thermal electron transfer, estimated from the temperature

dependence of esr broadening by Motten et al. [40], one can

imagine that electron-donating groups such as me and ome may

lower this thermal barrier through an increase in electron

density in the ligand 7* system. Just the opposite effect

would be expected for electron-withdrawing groups.

Our hypothesis is that the potential of a dication/

monocation couple will rather closely resemble the reduction

potential of the symmetric tris-complex of the more easily








reduced coordinated ligand. The fact that the void in

potential space between the potentials of the two limiting

tris-complexes is not covered at all evenly by potentials

of the intermediate mixed-ligand complexes (as we find is

true for metal-centered 3+/2+ redox) will probably make

reduction potentials more difficult to "tune" than are oxi-

dation potentials. The large magnitude of the energy gaps

of about 3600 cm-1 reported [49,50] to lie between the

dications' 3CT charge-transfer state (t 5 Tr*l) and the low-

est ligand field (t2g e*1) state argues for the equivalence

of orbital ordering between the ground-state monocations and

the excited-state dications. If in addition it is noted that

the d5 electronic structure of the 3CT dication is far more

likely to contribute to structural and electronic distortion

from D3 symmetry than is the monocation's d6 metal electronic

structure, it is clear that a conclusion of ground-state

monocation T* electron localization/delocalization leads to

a similar conclusion in the dication 3CT state. Thus we

have acquired information about the electronic structure of

an excited state from studies on ground states.













CHAPTER V

ELECTROCHEMISTRY OF THE DIMERS



Introduction


In mixed-valence complexes for which there is a large

degree of electronic coupling between the metal centers, it

is often difficult to determine whether the unpaired electron

is localized or delocalized between them. Electrochemical

data are presented that allow for a qualitative determination

of the extent of electron delocalization in moderately

coupled ruthenium mixed-valence dimers. Structural varia-

tions in a series of complexes provide for calculations of

redox potentials, assuming both the localized and the delo-

calized descriptions of the mixed-valence state. Comparisons

of experimental redox potentials with the calculated poten-

tials provide insight into the extent of electron delocaliza-

tion within a given series.

Each series consists of three complexes, two symmetric

and one asymmetric:


1) [(bpy)2Ru(L-L)Ru(bpy)2 ]n+

2) [(R2-bpy)2Ru(L-L)Ru(bpy)2 n+

3) [(R2-bpy)2Ru(L-L)Ru(R2-bpy)2] n+


(L-L is the bridging ligand; BiBzIm or Bipyrm). These







complexes undergo reversible oxidations corresponding to the

III-III/III-II and the III-II/II-II redox couples where III-II

refers to the oxidation states of the metal centers in the

dimer [e.g., RuIII(L-L)RuII]. For a given series the reduc-

tion potentials (corresponding to the above couples) for the

asymmetric complex can be calculated from those of the sym-

metric complexes. Two models are used for these calcula-

tions based on the localized and the delocalized descrip-

tions of the mixed-valence state.

Assuming a localized mixed-valence state and using

arguments similar to those in Chapter IV, reduction poten-

tials for the asymmetric dimers are calculated for the

III-III/III-II couples.


RT RT (ER'R'ERR)F/RT
ERR, = ERR+ ln(2) + F- In(l + e (


and for the III-II/II-II couples


RT RT (E RR-E R' )F/RT
RT RT l + RRe 'R'
ERR = ERR + ln(2) ln 1 + e


where ERR and ER'R, are the apparent (experimental) reduc-

tion potentials for the symmetric complexes and ERR, for the

asymmetric complexes.

Calculations assuming the delocalized description fol-

low from a linear (LFER) interpolation between the experi-

mental reduction potentials for the symmetric complexes,

i.e., the average of the two potentials.







Experimental and Results


Cyclic voltammograms for the R = ome series are presented

in Figure 5.1 and are similar to those for other series (not

shown). Two reversible oxidation waves were recorded for

each complex corresponding to the III-III/III-II and the

III-II/II-II couples; four reversible ligand-centered reduc-

tion waves were recorded for each complex as well. For the

symmetric complexes two of the ligand-centered reductions are

superimposed, yielding two two-electron reduction waves, and

are resolved into four one-electron reduction waves in the

presence of an asymmetric ligand arrangement. All waves are

shifted to more positive potentials in the presence of elec-

tron-donating substituent groups (me, ph and ome). Peak

separations AE for the couples vary from 0.075-0.090 V and

are assumed reversible from criteria presented in Chapter IV.

Listed in Tables 5.1 and 5.2 are half-wave potentials

corresponding to the III-III/III-II and the III-II/II-II

couples along with calculated potentials, assuming the local-

ized and the delocalized descriptions of the mixed-valence

(III-II) state. It is observed that the experimental reduc-

tion potentials, in every case, lie between the two calcu-

lated values and that closest agreement occurs with poten-

tials calculated from the localized description.



























Figure 5.1. Cyclic Voltammograms of
[(R2-bpy) 2Ru (BiBzIm) Ru (R2-bpy) 2] (PF6) 2
in 0.1 M TBAH/CH3CN (scan rate = 200 mV/s).













10 11A


R =R= H


R = H, R' = me


R = R = me


I I I I


1.0


0.0 -1.0


-2.0








Table 5.1. Half-Wave Potentials for the [(R2-bpy)2Ru(L-L)-
Ru(R2'-bpy)2]1n+ III-III/III-II Couples (v).


R R'

H H

H me

me me


H H

H ph

ph ph


H H

H ome

ome ome



H H

H me

me me


Experimental

1.056


1.030

0.950



1.056

1.045

1.026



1.056

1.007

0.815



1.731

1.707

1.635


Localized
Model

a

1.038(8)


1.045(0)


1.038(31)


1.713(6)


Delocalized
Model

a


1.004(14)


1.041(4)


0.935(72)


1.683(24)


a Fixed point.

Values in parentheses are deviations from the experimental in
mV.


(L-L)

BiBzIm


BiBzIm


BiBzIm


Bipyrm








Table 5.2. Half-Wave Potentials for the [(R2-bpy)2Ru(L-L)-
Ru(R2'-bpy)21+ III-II/II-II Couples (V).


Experimental

0.765

0.700

0.668


BiBzIm








BiBzIm


n ome

ome ome


Bipyrm


0.765

0.760

0.757


0.765

0.590

0.538


1.548

1.471

1.441


Localized
Model

a

0.686(14)

a


a

0.760(0)

a



a

0.556(24)

a



a

1.459(12)

a


Delocalized
Model

a

0.717(17)

a


a

0.761(1)

a



a

0.652(62)

a



a

1.495(24)

a


a Fixed point.

Values in parentheses are deviations from the experimental in
mV.


(L-L)

BiBzIm








Discussion


Experimental reduction potentials are not consistent

with either the totally localized or the totally delocalized

descriptions of the mixed-valence state but are consistent

with a combination of the two. It is concluded that both

models are important in describing the nature of these mixed-

valence systems, i.e., a moderate amount of electron delocal-

ization is present but that the valences are trapped to some

degree. Further inspection of the data indicates that the

localized description is preferred in every case.

In comparing bridging ligands (for the methyl series),

it is observed that both bibenzimidazole and bipyrimidine

allow for similar degrees of delocalization. Assuming the

M-M distances are similar for either bridging ligand, the

anionic bibenzimidazole bridge would favor electron delocal-

ization over the neutral bipyrimidine bridge [51]. What must

be considered also is that the electron coupling VAB decreases

with the number of conjugated atoms in the bridge [51]. Thus

a cancellation of effects may allow for similar bridging

effects in both systems.

Very small, but finite, thermal electron transfer bar-

riers would be expected for these mixed-valence complexes [8].

These results are later compared to those from treatments of

the intervalence transfer absorptions of the same using the

Hush and PKS theories.














CHAPTER VI

THEORY OF INTERVALENCE TRANSFER



Energy barriers are generally associated with electron

transfer since otherwise the electron would be effectively

delocalized between metal centers leaving each with a non-

integral formal charge. The magnitude of an electron trans-

fer barrier depends on 1) the relative ground-state poten-

tial energy difference, if any, of the electron between the

two centers; 2) the degree of electronic coupling between the

centers; and 3) changes in configuration (bond lengths and

force constants) with oxidation state. In order to under-

stand rates and mechanisms of electron transfer, one must

understand the origin of these barriers and factors that

influence them.

Studies described in this work focus on binuclear

ruthenium complexes in solution where electrons are trans-

ferred between metal centers in the same complex (the term

"electron transfer" will be used from now on to refer specif-

ically to the process where electrons are transferred between

metal centers). Electron transfer is mediated via a bridge

that bonds the metal centers and is, in this case, termed

"inner-sphere." Electron transfer between non-covalently

bonded species, where only weak forces such as dipole-dipole







or van der Waals forces hold the species in close contact, is

termed "outer-sphere." There is a close relationship between

inner- and outer-sphere electron transfer, and theories men-

tioned here are applicable to either case as they do not

explicitly distinguish between the types of bonding between

metal centers [4 ]. Studies involving outer-sphere systems

are complicated by the appearance of "extra" parameters such

as contact time and internuclear distances which are, in

inner-sphere systems, usually better defined and more readily

available.



Simple Model


A simple model for electron transfer will be described

using binuclear mixed-valence ruthenium complexes as a "model"

system. This model will be used to gain a physical interpre-

tation of optical and thermal electron transfer, and it will

serve as a starting point for the more complex theories of

Hush [6] and of Piepho et al. [8].

For a symmetric binuclear complex the potential energy

difference between the metal centers (Eo in the Hush theory

and W in the PKS theory) is zero. Barriers to electron

transfer are imposed due to the changes in metal-ligand bond

lengths that accompany oxidation state changes at the metal

centers. It is assumed that the gross symmetry around the

metal center is the same for the metal in either oxidation

state so that only the totally symmetric vibrational modes

(breathing modes) contribute to the barrier [8].








The parabolas (harmonic oscillator approximation) in

Figure 6.1 represent (for each configuration, II/III and

III/II, of the electron) the potential surfaces for the

asymmetric combination of metal-ligand breathing modes [8].

It has been shown that contributions to the potential sur-

faces arising from the symmetric combinations of breathing

modes do not enter into calculations of intervalence transfer

properties in cases where the force constants are equal for

the metal in different oxidation states (a fundamental ap-

proximation of the Hush and PKS theories). The curves are

displaced by a distance X (proportional to the average metal-

ligand bond length change with oxidation state) along the

axis q. The PKS parameters X and q are dimensionless.

Electronic coupling between the metal centers causes the

curves to split at the surface crossing region.

Intervalence transfer is shown by the vertical arrow of

energy Eop (Franck-Condon approximation) in Figure 6.1a.

This route is thermally forbidden as the products would be

formed directly in a vibrationally excited state and energy

would not be conserved [4]. The thermal electron transfer

process involves successively exciting vibrational modes

until an amount of energy Ea is absorbed. When the metal-

ligand bond lengths on both metal centers are equal (remem-

bering q corresponds to the asymmetric combination of breath-

ing modes), the electron will be transferred to the other

surface with a probability K (adiabaticity factor) related to

the splitting of VAB. At a given temperature the rate




























Figure 6.1. Potential Energy (E) vs. Reaction
Coordinate (q) for a) Symmetric and
b) Asymmetric Mixed-Valence Complexes.



























1 q I
-)_
2 ~q 2


-2
2 2








constant of thermal electron transfer is


-E /RT
K =

where R is the gas constant, T is the temperature, and v is

the fundamental frequency of the coupling vibrational mode.

In the case that VAB is very small, it is easily shown that


Ea = E op/4


and thus a simple relationship exists between the two elec-

tron transfer processes. For the asymmetric case where

Eo $ 0, the curves are displaced vertically from one another

as shown in Figure 6.1b.



Classification of Mixed-Valence Complexes


Mixed-valence complexes are classified according to the

degree of electron delocalization between the metal centers.

Figures 6.2a-c display potential surfaces for Class I-III

symmetric mixed-valence complexes.

Class I complexes (Figure 6.2c) are those where virtually

no electronic coupling exists between the metal centers. Both

optical and thermal electron transfer are forbidden. The

intensity of the intervalence transfer absorption is dependent

on VAB and is zero for VAB = 0. Thermal excitation of vibra-

tional modes does not give rise to electron transfer because

the curves are not split and there is zero probability for the

electron to cross surfaces (K = 0).






























Figure 6.2. Potential Energy Surfaces for Class I
through Class III Mixed-Valence Complexes.

















a) Class I
















b) Class II


c) Class III


V E
AB 4








Class II complexes (Figure 6.2b) are those where the

surfaces split but a finite barrier to thermal electron

transfer is present. Both optical and thermal electron

transfer can occur. The intensity of the intervalence

absorption and the rate of thermal electron transfer both

increase with increasing VAB.

Class III complexes (Figure 6.2c) are those where elec-

tronic coupling is large enough to completely overcome the

thermal barrier. There is only one minimum in the potential

well, and the electron is effectively delocalized between the

metal centers. The optical absorption now corresponds to an

electronic transition and not to an electron transfer proc-

ess.

For asymmetric complexes the above classification scheme

still applies, but there are a few points worth noting. For

metal centers of different energies, electronic coupling will

generally be smaller than for the asymmetric cases. In addi-

tion the thermal barrier on the low energy side will be low-

ered by an amount E0. Both of these factors favor valence

trapping, and as a result, asymmetric complexes tend to be

valence trapped. Since there is a preferred orientation in

these complexes, the optical transition corresponds to an

electron transfer process even in the delocalized case.



Hush Theory


The Hush theory is applied in a series of four equa-


tions:








Ea = Eop/4


(Ak)2 = 2312 max(cm-1) [symmetric case]


(A7 )2 = 2312(7max Eo/hc) [asymmetric case]



a2 = 4.24x10-4 Emax A
max

Eop, Ea and E have been previously defined. When expressed

in wave numbers E becomes max(hcmax = Eop). The band

half-width A7(cm-") is defined as the value of A; where


(I Vmax/Imaxv) =


The extinction coefficient at the band maximum is given as

emax and the internuclear separation between metal centers as
o
R(A). The degree of valence delocalization is given as a2.

The Hush theory takes into account both the high-

frequency inner-sphere modes and the low-frequency solvent

modes in its treatment of experimental data. Inner-sphere

contributions arise from changes in metal-ligand bond lengths

with the oxidation state of the metal center (as described

above with the simple model). Contributions from the solvent

arise from rearrangements of the dielectric environment sur-

rounding the complex.

Following from Marcus and Sutin 152], the energy of an

intervalence transfer absorption can be divided into contri-

butions from the inner-sphere (Xin) and the outer-sphere

(Xout) rearrangement energies.








Eop = in +out = sym (6.5)


Eop = in + Xout + Eo = asym + Eo (6.6)


X sym(1) + Xsym(2)
asym 2


For an asymmetric complex Xasym can be calculated from Asym

of the two symmetric complexes.

The Hush theory was derived assuming that electronic

coupling is very small compared to E This in principle

limits applicability of the Hush theory to weakly coupled

Class II mixed-valence complexes. Vibrational motion is

treated semi-classically such that transitions are assumed to

occur vertically (Franck-Condon approximation) between the

surfaces of the potential wells (turning points) and that a

continuum of vibrational levels is populated. This is a

good approximation in the high temperature limit where the

fundamental metal-ligand vibrational frequency v_ is of much

lower energy than KT (v_ << KT). From the above description

a gaussian bandshape is expected for intervalence transfer

absorption [6], and a2 is derived accordingly.



PKS Theory


In the Hush theory it was assumed that transitions com-

prising the intervalence transfer absorption occur between

two potential surfaces corresponding to the electron on either

metal center. As electronic coupling becomes important, this

assumption is no longer valid. Electronic coupling mixes the







potential surfaces and the vibrational eigenfunctions contain

contributions from both [7].

Piepho et al. [8] derived expressions for these vibra-

tional-electronic (vibronic wave functions for both symmet-

ric and asymmetric mixed-valence systems. The symmetric

vibronic wave functions are given below.


+= + r x + M r x (6.8)
v + vn n un n "
n=0,2,4,... n=1,3,5,...



V + nI vnn I- (69)
n=1,3,5,... n=0,2,4,...


T are q independent electronic wavefunctions

xn are harmonic oscillator functions in coordinate q

r and s are coefficients of harmonic oscillator
functions

designates the symmetries of the wavefunctions with an
interchange of nuclei

v designates a given vibronic wavefunction


From these wavefunctions two sets of secular equations

are derived.


r (H 6 E) = 0 m=0,l,2,... (6.10)
n=0 vn mn mn v n=0,1,2,...

Hmn = X[(m/2) mn+l + (m+1/2) mn-I + (m+-(-l)m)6mn


s (H 6 E-) = 0 m=0,l,2,... (6.11)
n=0 vn mn mn + v=0,1,2,...


Hmn = X[(m/2) 6mn+l+ (m+l/2) 6 ]n- + m++(-l)mS)6







Solving the secular equations for a given X and e yields

values for the vibronic energy levels from which transitions

can occur. Selection rules allow for t -+ 7 transitions.

For asymmetric mixed-valence systems, the vibronic

wavefunctions are given below.



S= (T+r nx + _r nxn) (6.12)
n=0


where the symmetry in $% upon interchange of the nuclei has

been lost. The secular equations are



Srn(Hmn 6mnE + I r'" = 0 (6.13)
n=0 n=0



r n(Hm 6mnE) + rvnHmn = 0
n=0 n=0


m = 0,1,2,...
v = 0,1,2,...


where Hmn = (m++E)6mn, Hmn = (m+-c)6mn, and

IHn = X[(m/2)6m,n+l + (m+l/2) m,n-1] + W6m,n. Solving the
secular equations for a given X, c and W yields values for

the vibronic energy levels from which transitions can occur.

The selection rules vanish with the asymmetry, and transition

may occur between any two energy levels.

Once the energy levels are determined, the intensities

of the transitions (dipole strengths) are calculated.


-v(N.-N) (
A~v>^) ^ ^ (e^/^)(6.14)








where


NV e-E\,/KT (6.15)
N Z e(-E ,/KT)
V'

for the symmetric case


6 = Erv,nsvn (6.16)


and the asymmetric case


6 = Er r' + r.' r (6.17)
v'v vI'n vn v'n vn


These calculations yield the stick spectrum for the interva-

lence absorption. The intervalence transfer band contour is

generated by converting each of the sticks into a gaussian

curve and summing the intensities.

The thermal rate constants are calculated:


S-E /KT -E /KT
2v- I (AE 2(e V + e I
P = (6.18)
C e-E+/KT -E-/KT
I (e V + e )
v=0


and the potential surfaces (classical) may be generated


W,2 = e22 + 1q2 (6.19)


for a given X, e and v_.

The PKS theory neglects contributions from the solvent

(X ) in treating experimental intervalence transfer data.
out








Although this approximation may be valid in moderately cou-

pled systems where solvent effects are small [13], the same

cannot be justified for weakly coupled systems. This limits

applicability of the PKS theory to the former. The harmonic

oscillator approximation and the consideration of only

totally symmetric vibrational modes in the derivation of the

PKS theory are good approximations for systems where the bond

length changes are small and gross symmetries are maintained

around the metal centers.

Thus it seems that the PKS theory would give a good

description for delocalized systems where the coordination

environment remains relatively constant. However, care must

be taken in applying such a simple model to systems where the

coupling energy approaches in magnitude the energies Eop and

Ea. Electronic coupling can no longer be described accurately

by a simple parameter c and factors such as the nature of the

bridge and molecular orbitals must be taken into account [53].



Discussion


The Hush theory has been applied to numerous mixed-

valence systems localized and delocalized. It has been shown

to give a good interpretation of intervalence transfer in

localized complexes as demonstrated by comparison of rate

constant data derived from the intervalence transfer absorp-

tion with rate constant data measured or estimated by other

means 19,10,54-56]. Powers and Meyer [57] have shown that

solvent contributions can be determined by separating the








intervalence transfer energy into inner-sphere (A. in) and

outer-sphere (Xout) components using a dielectric continuum

model to describe the latter [13]. They have shown solvent

contributions to be small or zero for delocalized systems and

to be sizeable for localized systems. In some cases, however,

where solvent contributions were determined to be very small,

E values (from Xin of similar complexes) were estimated to

be much smaller than the experimental values. Thus caution

should be taken when separating E into inner-sphere and

outer-sphere contributions as this is not always a good

approximation.

The PKS theory has not been explored to the extent of

the Hush theory, although Tanner and Ludi [58] have applied

the PKS theory to several systems localized and delocalized.

The intensities of the delocalized systems were always much

larger than expected when normalized to the localized systems.

When the intensities of the localized systems were normalized

to the delocalized systems, the calculated intensities were

much smaller than the experimental, and the bands were highly

asymmetrical. However, they did get expected trends when NH3

terminal ligands were replaced with bpy ligands. Although

the PKS theory may not give a good description for highly de-

localized systems, it does provide a means of correlating IT

properties with structure.














CHAPTER VII

INTERVALENCE TRANSFER OF DIMERS



Introduction


This chapter describes in detail the gathering and

treatment of experimental intervalence transfer data for

three series of ruthenium mixed-valence dimers. The experi-

mental data are interpreted using both the Hush and PKS

theories, and the results of these treatments are evaluated.



Experimental


Intervalence transfer spectra were obtained as described

in Chapter II for the following mixed-valence dimers:


1) [(bpy) 2Ru(BiBzIm)Ru(bpy) 2] 3+

2) [(R2-bpy)2Ru(BiBzIm)Ru(bpy) 2]3+

3) [(R2-bpy)2Ru(BiBzIm)Ru(R2-bpy) 2 3+

R = me, ph and ome


Bibenzimidazole bridged dimers were oxidized to the III/II

mixed-valence state via one-electron electrolysis of the

II/II complex. Bipyrimidine bridged dimers were unstable to

oxidation and the mixed-valence species could not be studied

optically. Electrolysis was performed by maintaining solution








potentials 150 mV higher than E for a given couple. Oxida-

tion was determined complete when a stoichiometric number of

electrons had passed through the electrochemical solution.

Final solution potentials ranged randomly from 50-100 mV

higher than the corresponding E values. Solutions of the

II-II species were red-orange and turned yellow upon one-

electron oxidations and blue upon two-electron oxidations.

To determine the actual concentrations of the mixed-

valence species in solution after electrolysis is necessary

to evaluate conproportionation constants Kc [59] for the

reactions


III-III + II-II -- 2(III-II)


Kc = [III-II]2/[III-III] [II-II] exp[38.9(E1-E2)]


where E1 and E2 are the half-wave potentials for the

III-III/III-II and the III-II/II-II couples, respectively.

Potential differences between successive oxidations are in

all cases greater than 250 mV, giving rise to very large Kc

values. For this reason it is not necessary to correct the

sample concentrations for the above equilibrium.

Intervalence transfer spectra for the bibenzimidazole

bridged complexes are presented in Figures 7.1, 7.2 and 7.3.

Haga [34] has previously observed the infrared spectrum for

the unsubstituted dimer and assigned the absorption at

1950 nm to the intervalence transfer transition.

From the spectra it is observed that substituent effects

are relatively small for the symmetric complexes, affecting
















rH

0



+







NC




H
N





CN












E-1
ra
a)









4-1

HFU



Z E-


o o 0 0
o o o o )0
o 0 o o


!t-
4v m*H
1-1 h

a4






60








H






>1-








CN
-(-

















r-4 O
S0II
' 0 t 0?
04 r.

a)





I
I U I 1-1










o 0 s 0
11 H
\-n



"I





61










S/ /











Im
S I I
I





>'I -(






0 1
/ N
/




0 to
S / >-

E/ x




0 0
40 (






e4
ZE


CO)







0 I I 0

O C -
II
\ y \ 1z41n








the intensities and band maximums only slightly. This is

not so, however, for the asymmetric complexes where substit-

uent groups are observed to have pronounced effects (for

R = ome and me) on both the intensities and the band maxi-

mums. The magnitudes of the substituent effects increase in

the order R = ph, me and ome. This same ordering is

observed with the oxidation half-wave potentials (Chap-

ters IV and V).

The II-II complexes give no absorptions in the region of

the intervalence transfer absorptions, and the III-III com-

plexes give only weak absorptions in this region which are

presumed to originate from the presence of small concentra-

tions of the III-II mixed-valence species.



Hush Treatment


Data from the intervalence transfer spectra (max,

and A) are recorded in Table 7.1 along with calculated

Hush parameters. Values of E0 for the asymmetric complexes

are calculated from equations (6.5), (6.6) and (6.7). From

equation (6.3) AU3 is calculated for comparison with the

experimental value. The valence delocalization parameter U2

is calculated from equation (6.4), assuming an internuclear

separation (R) of 5.455 A [60] [estimated from crystal

structure data of biimidazole bridged rhodium(I) dimer].

A criterion for application of the Hush theory is that

the calculated half-width of the intervalence transfer band

be smaller than the experimental value [4]. This puts a







63





io o
0 o 0 -
C o o 0 o 0 i-I LA N

0















e +
L 0 r-





enH U 0 0 0 0 0 0 0





S4 <

E-I 0 12

ox W



CO (N
H (
S0 0 0 0 0 0 0

n4 qw fq C ( N m 04
S0 w

H 4



CD CD 0 0 0 0 0 0 0

iX LA "W -W I LA LA %0








m) a w
>43 J I o o o o o a,
^4->~ ~ ~ l. g ^' i o m n '
(I)~~~ M4 0- *q o M Oi o








lower limit on the experimental half-width as band broaden-

ing (due to solvent effects [55]) causes the experimental

value to be larger than predicted [4]. From Table 7.1 it is

observed that only the last complex listed meets this crite-

rion. This is reasonable because asymmetry leads to valence

trapping, and this complex has the largest E It is con-

cluded that all but perhaps one of the above complexes are

too delocalized for the Hush treatment to apply.



PKS Treatment


The PKS calculations were carried out in collaboration

with Cliff Stodden of the Quantum Theory Project, University

of Florida. The QTP VAX computer system was used to gener-

ate theoretical spectra.

Intervalence transfer spectra were entered into the

computer in digital form. By varying the PKS parameters X,

, W and '_, the theoretical spectra could be manipulated

to give a best fit of the experimental spectra. Initial

(starting) parameters were calculated [4].


W = E0 (cm-1)/._
= V 125_
max assuming a delocalized system



9_ = 500 cm-"


By choosing and A values, the matrix Hmn correspond-

ing to the totally symmetric vibronic wave functions is

generated using equation (6.10) (Figure 7.4).


























0 0 0 <
lZ




0 -<
-l %


0 0


,x o O o *


0 0 0


M0 0M r
Co oC c a


M ( n




S r-4
0 ,- 0


O


0


0 r-4


0 0 0


***


** *



















"r

H p


0


c N
H1 M
S-i


r-l i r-4
0 ,-. N.




0 0 0
0 r-l


+ >

X *

43
< Oi
-rl




>i E-
t>

( M


+
o o o 0 *



+
o o o M o ***


+ 4
0 0



+ r-I




+0
M O O


0 0 *.*


0 0 *


0 0 *


+r>


IT

S-I ***

qRT







s-i *
.4.


- **



r-*







S-i *








Diagonalization of this matrix yields the energy matrix E+

and coefficient matrix r n (Figure 7.5). Using equation

(6.11) the matrix H corresponding to the asymmetric

vibronic wavefunction is diagonalized forming the energy

matrix E and coefficient matrix s
v )n
The r and s values are the coefficients for the
vn vn
vibronic wavefunctions given by equations (6.8) and (6.9)

with eigenvalues E and E respectively. Figure 7.6 dia-

grams the energy levels and transitions following the .

selection rule.

The relative populations of energy levels are calculated

using the Boltzman distribution given in equation (6.14), and

the intensities are calculated from equations (6.14) and

(6.16). This gives the stick spectrum for the IT transition.

Each transition of energy D has an intensity I associated

with it and is converted to a gaussian curve with a half-

width (A) given in units of v_. The sum of these gaussian

curves comprises the IT transition.

For asymmetric species generation of the theoretical

spectra is complicated by the introduction of the asymmetry

term W. From equations (6.13) H mn, H and H values are

calculated for a given X, e and W. These form a matrix H,

diagrammed in Figure 7.7. This matrix is twice the size as

that given for the symmetric case for a given number of

energy levels. Diagonalization of this matrix gives the

energy matrix E and the coefficient matrix containing r n

and r' (Figure 7.8).
vn





68



---- -------------- E
I T 3


L I


-


+
-E
2





--- E3

E_


tunneling
transitions


IT
transitions


Figure 7.6. Allowed Transitions for Intervalence Transfer
Absorption--Symmetric Case.


















Hm
Mn


Hmn"


Hmn


Hmn


Figure 7.7. Schematic for H Matrix in the Asymmetric PKS
Calculation.


0 0 0 0 0




























N CN N
0 -H CM
H H H





H 5 H




CO H
C0 r- CM
4 p $4


I *
* *
* *
1 *


I '

-r-o C4
I S

I H H- H
I $-4

-0 -H -e'a




I 0
D- -r C4
I >-


II



44 P

a4-1
u r


m
o o o 0


CN





0 0
O N O



0
W 0 0


S *


O *


O


* **


** *


** *


***









The coefficients r and r' represent the vibronic
uvn vn
wave-functions given by equation (6.12) with eigenvalues E .

In the asymmetric case the T selection rule no longer

holds and transitions are allowed to occur between all

levels. Relative populations, intensities, and intervalence

transfer band contours are calculated in a similar manner as

for the symmetric case.

In simulating the intervalence transfer spectra, the

parameter ._ was first determined. The effect of this param-

eter was to "rock" the intervalence transfer band. Increase-

ing 5_ caused the band to tail off in the low energy region

and to sharpen in the high energy region. A value of

360 (cm-1) for V_ was determined to be consistent with the

experimental data. Once v_ had been determined the param-

eters X and 6 were varied to get the best fit. The effect of

increasing X was to shift the band to higher energy and to

broaden it by lowering the intensity. The effect of increas-

ing e was to shift the spectra to higher energy and to narrow

it by increasing the intensity. The simulated spectra were

very sensitive to the parameters X and and not so sensi-

tive to v_. For the asymmetric species the parameter W (E0

in the Hush theory) had to be included. Since W was hard to

determine by trial and error, electrochemical data from

Chapter V were used to estimate these parameters. Since

redox potentials give a measure of the potential of an elec-

tron at a given site, it was assumed that W could be estim-

ated from redox potentials involving the mixed-valence state.









The potential difference between the sites (W) was cal-

culated for the asymmetric complexes as the difference

between the first oxidation potentials for the corresponding

symmetric complexes. Similar values were obtained from the

second oxidation potentials, and the average values were

taken as W.

Experimental and PKS "best fit" intervalence transfer

spectra are presented in Figures 7.9-7.15. The PKS generated

spectra fit reasonably well with the experimental spectra

and the "best fit" parameters are listed in Table 7.2. For

the asymmetric species it was found that W values calculated

from electrochemical data generated the best overall spectra.

This reinforces the viability of the PKS theory for this

series of compounds.

The PKS parameters A, e and W were used to generate

"classical" potential surfaces from which the intervalence

transfer transitions occur and are presented in Figures 7.16-

7.22. Thermal electron transfer rate constants were calcu-

lated using equation (6.18) and are presented in Table 7.2.

The small thermal electron transfer barriers are consistent

with the high thermal rate constants and indicate a fairly

high degree of valence delocalization. More important is

the fact that finite barriers do exist for the thermal elec-

tron transfer process.

Thus it seems that the PKS theory gives a good descrip-

tion of these systems which are moderately delocalized. As

mentioned in Chapter VI, applicability of the PKS theory

falls off as the systems become strongly delocalized.






















R = R' = H


4000


3000



2000

e (M-1)

1000


X (nm/100)


Figure 7.9. Experimental and Theoretical (PKS) Intervalence
Transfer Spectra for [ (R2-bpy) 2Ru(BiBzIm)Ru(R2-
bpy) 2 R=R'=H.




















R = R' = me


12 14 16 18 20 22


4000



3000

(M-1)

2000



1000


X (nm/100)





Figure 7.10. Experimental and Theoretical (PKS) Interva-
lence Transfer Spectra for 3+
[(R2-bpy) 2Ru(BiBzIm)Ru(R2-bpy) 2 R=R'=me.




















R = R' = ph


12 14 16 18 20 22


4000



3000

E (M-1)

2000



1000


X (nm/100)




Figure 7.11. Experimental and Theoretical (PKS) Intervalence
Transfer Spectra for
[(R2-bpy)2Ru(BiBzIm)Ru(R2-bpy)2] 3+. R=R'=ph.




















R = R' = ome


12 14 16 18 20 22


4000



3000

E (M-1)

2000



1000


X (nm/100)



Figure 7.12. Experimental and Theoretical (PKS) Intervalence
Transfer Spectra for
[ (R2-bpy) 2Ru(BiBzIm)Ru(R2-bpy) 23+. R=R'=ome.




















R = H; R' = me


12 14 16 18 20 22


4000



3000

E (M-)

2000



1000


X (nm/100)




Figure 7.13. Experimental and Theoretical (PKS) Intervalence
Transfer Spectra for
[(R2-bpy)2Ru(BiBzIm)Ru(R2-bpy) 23+. R=H; R'=me.



















R = H; R' = ph


12 14 16 18 20 22


4000



3000

E (M-1)

2000



1000


X (nm/100)




Figure 7.14. Experimental and Theoretical (PKS) Intervalence
Transfer Spectra for
[(R2-bpy) 2Ru(BiBzIm)Ru(R2-bpy) 2]3+. R=H; R'=ph.




















R=H; R'=ome


12 14 16 18 20 22


4000



3000

E (M-)

2000



1000


A (nm/100)



Figure 7.15. Experimental and Theoretical (PKS) Intervalence
Transfer Spectra for
[(R2-bpy) 2Ru(BiBzIm)Ru(R2-bpy) 23+. R=H;
R'=ome.






80

Table 7.2. PKS Parameters for [(R2-bpy)Ru(BiBzIm)Ru(R'-
bpy) 2 ]3+.


KxlO-12
R R' A W (S-1)

H H 3.01 -6.46 6.9

me me 2.95 -6.22 7.2

ph ph 2.87 -6.12 8.4

ome ome 2.91 -5.99 7.2

H me 2.46 -5.97 2.25 -

H ph 2.95 -6.30 0.42

H ome 2.25 -1.69 5.25





81











R = R' = H


Figure 7.16. Potential Surfaces for
[(R -bpy) Ru(BiBzIm)Ru(R2-bpy) 23+ Potential
Energy vs. Breathing Mode q. R=R'=H.

















R = R' = me


36



28

E (5_)

20



12



4



-4


Figure 7.17. Potential Surfaces for 3+
[(R2-bpy)2Ru(BiBzIm)Ru(R2-bpy)2] Potential
Energy vs. Breathing Mode q. R=R'=me.






83











R = R' = ph


Figure 7.18. Potential Surfaces for
[(R2-bpy)2Ru(BiBzIm)Ru(R2-bpy)2]3+. Potential
Energy vs. Breathing Mode q. R=R'=ph.


36



28

E (7_

20



12



4



-4






84











R = R' = ome


Figure 7.19. Potential Surfaces for
[ (R2-bpy) 2Ru(BiBzIm)Ru(R2-bpy)2 3+. Potential
Energy vs. Breathing Mode q. R=R'=ome


36



28



20

E (_)

12



4



-4






85










R = H; R' = me


Figure 7.20. Potential Surfaces for
I(R2-bpy) 2Ru(BiBzIm)Ru (R-bpy) 23+. Potential
Energy vs. Breathing Mode q. R=H; R'=me.


E ("

















R = H; R' = ph


36



28



20
E (-_)

12



4



-4


Figure 7.21. Potential Surfaces for
[(2-bpy) 2Ru(BiBzIm)Ru(R2-bpy) 23+. Potential
Energy vs. Breathing Mode q. R=H; R'=ph.






87











R = H; R' = ome


Figure 7.22. Potential Surfaces for 3+
[(R2-bpy) 2Ru(BiBzIm)Ru(R2-bpy)2] Potential
Energy vs. Breathing Mode q. R=H; R'=ome.


36



28



20

E (-_)

12



4


-4






88

Therefore it is likely that the complexes studied here repre-

sent the delocalized limit for applicability of the PKS

theory.














CHAPTER VIII

NEAR INFRARED STUDIES OF MONOMER MONOCATIONS



Introduction


Through temperature dependent ESR studies, Motten et

al. [40] have observed small electron-hopping barriers be-

tween the bipyridine ligands in the excited [Ru(bpy)3 2+

complex. Assuming Koopman's theorem to compare the mono-

cation with the excited dication, these studies predict an

electron transfer absorption in the near infrared region.

Elliott [14] has observed near infrared absorption for

the reduced forms of the [Ru(es2-bpy)3] ion. These absorp-

tions are similar in nature (broad and occurring in the near

infrared spectrum) to the intervalence transfer transitions

of the mixed-valence dimers. Since reductions of these mon-

omeric species are ligand-centered, it was proposed that

these transitions originate from intra- or inter-ligand

electron hopping [14]. If the latter mechanism is accurate,

these absorptions will be closely related to the electro-

chemical studies of Chapter V. Near infrared studies were

performed on a series of mixed-ligand monocations,

[Ru(es2-bpy) n(bpy)3-n] to further explore this phenomenon.




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81,9(56,7< 2) )/25,'$


ELECTROCHEMICAL AND INTERVALENCE TRANSFER PROPERTIES
OF NEW MONONUCLEAR AND BINUCLEAR RUTHENIUM COMPLEXES
BY
SKILES ALBERT MONTAGUE
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1984

to my family

ACKNOWLEDGMENTS
I would like to thank those who made my stay in
Gainesville some of the best years of my life.
in

TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS iii
LIST OF TABLES vi
LIST OF FIGURES vii
ABSTRACT X
CHAPTER
I GENERAL INFORMATION 1
II PHYSICAL MEASUREMENTS 5
Materials 5
Apparatus and Technique 6
III PREPARATIONS 9
Notes on Preparations 9
Ligands 10
Ruthenium Complexes 13
IV ELECTROCHEMISTRY OF THE MONOMERS 21
Introduction 21
Experimental 24
Discussion 29
V ELECTROCHEMISTRY OF THE DIMERS 33
Introduction 33
Experimental and Results 35
Discussion 40
VI THEORY OF INTERVALENCE TRANSFER 41
Simple Model 4 2
Classification of Mixed-Valence Complexes 46
Hush Theory 4 9
PKS Theory 51
Discussion 55
VII INTERVALENCE TRANSFER OF DIMERS 57
Introduction 57
Experimental 57
iv

CHAPTER
Page
VII Hush Treatment 62
PKS Treatment 64
VIII NEAR INFRARED STUDIES OF MONOMER MONOCATIONS.. 89
Introduction 8 9
Experimental 90
Discussion 90
IX SUMMARY 9 2
REFERENCES 94
BIOGRAPHICAL SKETCH
98

LIST OF TABLES
Page
3.1 Elemental Analysis of Ruthenium Complexes.... 20
4.1 Half-Wave Potentials for the
[Ru(bpy)3_n(R2~bpy)n]2 + /+ Couples (v) 28
4.2 Half-Wave Potentials for the
[Ru(bpy)3_n(R2~bpy)n]3+/2+ Couples (v) 30
5.1 Half-Wave Potentials for the
[(R2~bpy)2Ru(L-L)Ru(R2'-bpy)9n+
III-III/III-II Couples (v) 38
5.2 Half-Wave Potentials for the
[(R2-bpy)2Ru(L-L)Ru(R2’-bpy)2]n+ III-II/II-II
Couples (v) 39
7.1 Intervalence Transfer Data and Hush Param¬
eters for the Mixed-Valence Dimers
[ (R2~bpy) 2Ru (BiBzIm) Ru (R2-bpy) ] 3+ 63
7.2 PKS Parameters for [(R^-bpy)Ru(BiBzIm)Ru(Ri-
bPy)2]3+ : :.. 80
vi

LIST OF FIGURES
Page
2.1 Diagram of the Electrochemical Cell 7
4.1 Cyclic Voltammogram of [Ru (on^-bpy) (PFg^ in
0.1 M TBAH/CH3CN (scan rate = 200 mV/s) 26
5.1 Cyclic Voltammograms of
[(R2~bpy)2^u(BiBzIm)Ru(R^-bpy)(PFg)2 in 0.1 M
TBAH/CH3CN (scan rate = 200 mV/s) 37
6.1 Potential Energy (E) vs. Reaction Coordinate
(q) for a) Symmetric and b) Asymmetric Mixed-
Valence Complexes 45
6.2 Potential Energy Surfaces for Class I through
Class III Mixed-Valence Complexes 4 8
7.1 Near Infrared Spectra of 3
[(R2~bpy)2^u(BiBzIm)Ru(R^-bpy)in 0.1 M
TBAH/CD3CN (Methyl Series) 59
7.2 Near Infrared Spectra of _
[(R2~bpy)2^u(BiBzIm)Ru(R^-bpy)2 1 in 0.1 M
TBAH/CD3CN (Phenyl Series) 60
7.3 Near Infrared Spectra of -
[(R2~bpy)2Ru(BiBzIm)Ru(R^-bpy)21 ^ in 0.1 M
TBAH/CD3CN (Methoxy Series) 61
7.4 Matrix Hmn for Totally Symmetric Vibronic Wave-
function (PKS Theory) 65
7.5 Energy Matrix E+ and Coefficient Matrix r
(PKS Theory)...V Y1?. . . . 66
7.6 Allowed Transitions for Intervalence Transfer
Absorption--Symmetric Case 68
7.7 Schematic for H Matrix in the Asymmetric PKS
Calculation 69
7.8 Energy and Coefficient Matrix for Asymmetric
PKS Calculation 70
vii

Page
7.9 Experimental and Theoretical (PKS) Intervalence
Transfer Spectra for [(R^-bpy)2Ru(BiBzIm)Ru(R^-
7.10 Experimental and Theoretical (PKS) Intervalence
Transfer Spectra for [(R^-bpy)_Ru(BiBzIm)Ru(R'~
3+ z z z
bpy)2] • R=R'=me
7.11 Experimental and Theoretical (PKS) Intervalence
Transfer Spectra for [(R~-bpy)^Ru(BiBzIm)Ru(Rl-
3+ z z z
bpy)2] • R=R'=ph
7.12 Experimental and Theoretical (PKS) Intervalence
Transfer Spectra for [ (R2~bpy) 2Ru (BiBzIm) Ru (R^,-
bpy)2]3+- R=R'=ome
7.13 Experimental and Theoretical (PKS) Intervalence
Transfer Spectra for [(R9-bpy)9Ru(BiBzIm)Ru(Rl-
3+ z z z
bpy)2) • R=H; R'=me
7.14 Experimental and Theoretical (PKS) Intervalence
Transfer Spectra for [ (R2“bpy) 2Ru (BiBzIm) Ru (R^,-
bpy)3+* R=H? R'=ph
7.15 Experimental and Theoretical (PKS) Intervalence
Transfer Spectra for [(R_-bpy)_Ru(BiBzIm)Ru(Rl-
3+ z z z
bpy)2] • R=H; R'=ome
7.16 Potential Surfaces for 3
[(R2-bpy)2Ru(BiBzIm)Ru(R^-bpy)21J • Potential
Energy vs. Breathing Mode q. R=R'=H
7.17 Potential Surfaces for 3
[(R2-bpy)2Ru(BiBzIm)Ru(R^-bpy)2J • Potential
Energy vs. Breathing Mode q. R=R'=me
7.18 Potential Surfaces for 3
[(R2-bpy)2Ru(BiBzIm)Ru(R^-bpy)2]^ • Potential
Energy vs. Breathing Mode q. R=R'=ph
7.19 Potential Surfaces for ~
[(R2-bpy)2Ru(BiBzIm)Ru(R^-bpy)21^ • Potential
Energy vs. Breathing Mode q. R=R'=ome
7.20 Potential Surfaces for 3+
[(R2~bpy)2ru(BiBzIm)Ru(R2~bpy)2] • Potential
Energy vs. Breathing Mode q. R=H; R'=me
viii
73
74
75
76
77
78
79
81
82
83
84
85

Page
7.21 Potential Surfaces for
[ (F^-bpy) (BiBzIm) Ru (R^-bpy) 21 J • Potential
Energy vs. Breathing Mode q. R=H; R'=ph 86
7.22 Potential Surfaces for
[(R2_bpy)(BiBzIm)Ru(R^-bpy)2]J • Potential
Energy vs. Brathing Mode q. R=H; R' =ome 87
8.1 Near Infrared Spectra of [Ru(es~-bpy) (bpy) ]+
in 0.1 M TBAH/CH3CN 7 â„¢ 7.... 91
IX

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
ELECTROCHEMICAL AND INTERVALENCE TRANSFER PROPERTIES
OF NEW MONONUCLEAR AND BINUCLEAR RUTHENIUM COMPLEXES
By
Skiles Albert Montague
April 1984
Chairman: Professor Eric V. Dose
Major Department: Chemistry
A new series of mononuclear and binuclear ruthenium com¬
plexes were synthesized and their electrochemical and inter¬
valence transfer (IT) properties studied. Techniques
employed include cyclic voltammetry, coulometry, and near
infrared spectroscopy.
From cyclic voltammetric measurements the conpropor-
tionation constants, substituent group effects, and relative
potentials of redox sites are determined. Substituent group
effects lend valuable information toward the extent of delo¬
calization of electrons between redox sites within a series
of mixed-valence (MV) compounds. Coulometry provides access
to the MV complex through stoichiometric addition or subtrac¬
tion of electrons.
Theoretical treatments given by S. B. Piepho,
E. R. Krausz and P. N. Schatz (PKS) and by N. S. Hush allow
x

for interpretation of experimental IT data. Calculations of
electronic and vibronic coupling parameters, thermal electron
transfer activation energies and rate constants, fundamental
vibrational frequencies, and differences in potential between
redox sites follow from these theories.
Series of binuclear ruthenium complexes of the form
[ (í*2 -bp y) (BiBzIm) Ru (R^-bpy) ] n+ (n = 2-4), symmetric
(R = R' = H, methyl, methoxy or phenyl) and asymmetric
(R = methyl, methoxy or phenyl; R' = H) have been prepared
and studied. Near infrared spectral properties of the MV
complexes appear to be consistent with the PKS and not the
Hush theory. This is, in fact, reasonable as these complexes
were determined to be fairly delocalized. The PKS theory is
explicitly derived to treat delocalized systems whereas the
Hush theory is strictly valid only in the strongly localized
limit.
Series of mixed-ligand ruthenium complexes,
[Ru(bpy)3_m(R2~bpy)m]n+ (m = 0-3; n = 1, 2; R = H, methyl,
methoxy, phenyl, or ethyl carboxylate), were parepared and
studied. Electrochemical studies suggest that the unpaired
electron in the singly reduced (monocationic) form is local¬
ized on a single ligand at any given time for series with
electron-withdrawing groups (ethyl carboxylate and phenyl).
Such studies suggest the opposite behavior for series with
electron-donating groups (methyl and methoxy). One possible
explanation for this behavior is that the electron-donating
groups lower the small thermal electron transfer barrier via
a build up of electron density in the ligand tt* system.

CHAPTER I
GENERAL INTRODUCTION
Chemists have known for many years of the unusual prop¬
erties associated with mixed-valence compounds [1]. It was
not until 1967 that Robin and Day [1], Allen and Hush [2],
and Hush [3] systematically reviewed these properties and
presented the first comprehensive theoretical framework
treating mixed-valence compounds as a unique class of chemi¬
cal substances. Since that time the field of mixed-valence
chemistry has experienced rapid growth with the appearance of
several review articles [4-7].
Robin and Day [1] adopted the phrase "mixed-valence" to
describe inorganic compounds which contain a single element
in more than one oxidation state. This mixed-valence state
occurs most frequently in transition metal complexes, as the
central metal ions can usually form stable complexes in more
than one oxidation state. Transfer of electrons between
metal centers is usually facile as bonds are rarely broken or
formed, and in most cases the gross symmetry around the metal
center is maintained. This long range electron-transfer
process gives rise to unusual physicochemical properties and
is the essence of mixed-valence chemistry.
1

2
In mixed-valence complexes electron transfer can be
optically induced giving rise to a broad, and occasionally
intense, absorption in the optical spectrum. This process is
termed intervalence transfer (IT). A thermal electron trans¬
fer process is also predicted to occur [3,8] but is difficult
and often impossible to study [9]. There are a few reported
cases where thermal electron transfer has been studied
directly [10-12], but these instances are few and studies are
still in the early stages.
Interest in mixed-valence chemistry centers mainly
around the relationship between thermal and optical electron
transfer. In principle one can derive important information
concerning thermal electron transfer from intervalence trans¬
fer studies if an accurate theoretical model is applied.
It was proposed by Robin and Day [1] that mixed-valence
complexes be divided into three classes depending on the
degree of electron delocalization between the metal (redox)
centers. Class I compounds are those in which there is vir¬
tually no electron delocalization (i.e., the valences are
strongly trapped). In this case both optical and thermal
electron transfer processes are forbidden. Compounds in this
class do not possess the unique electron transfer properties
associated with mixed-valence compounds. Class II mixed-
valence compounds are those where there is some electron
delocalization, but some degree of valence trapping still
exists. Both optical and thermal electron transfer are pre¬
dicted. Strongly delocalized mixed-valence complexes are

3
grouped in Class III. Distinct valences do not exist, and
the metal centers are assigned an average oxidation state.
An optical absorption is predicted for this class of com¬
pounds, but it corresponds to a purely electronic transition
and not to the intervalence transfer process.
Intervalence transfer data obtained to date have been
interpreted almost exclusively in light of the Hush theory
[4]. A major problem with such interpretations is that the
Hush theory is strictly valid only for systems where the
electrons are strongly localized (Class I in the Robin and
Day scheme) [3,7]. Applicability of the Hush theory falls
off as the systems become more delocalized and approach the
Class III description.
In 1978 Piepho et al. [8] presented a dynamic model, re¬
ferred to here as the PKS model, for intervalence transfer
which includes explicitly the role of vibronic coupling in
mixed-valence systems. In this model the "trapped valence"
assumption is not made, and the model is proposed to be
applicable to mixed-valence systems of essentially any degree
of delocalization. An important factor to be considered in
applying the PKS theory is the neglect of solvent in its
derivation [13]. As a result strict applicability of the PKS
theory should be confined to more delocalized systems where
solvent contributions to electron transfer energy barriers
are small. The PKS theory as currently applied would give an
incomplete description of intervalence transfer for localized
systems where solvent contributions are important and for
which the Hush theory is applicable.

4
This work focuses on the preparation and study of
bridged binuclear ruthenium complexes, symmetric and asym¬
metric, where electronic coupling is moderate. Small organic
groups, electron-withdrawing and electron-donating, have been
substituted onto terminal bipyridyl ligands during the syn¬
thesis proces. While these groups do not affect the gross
symmetry of the complex, they do affect the degree of elec¬
tronic coupling. In the asymmetric cases the substituent
groups cause differences in potential between the metal
centers. As shown below these complexes allow for a unique
test of the Hush and especially the PKS theories.
Certain mononuclear complexes of ruthenium have been
shown to undergo what is believed to be intra- or interligand
electron transfer [14]. Spectroscopy and electrochemistry
have been used to study a series of mixed-ligand monomers in
an attempt to determine the nature of this process. Assuming
Koopman's theorem electrochemical studies of the monocations
and dications are applicable to transitions involving the
lowest triplet metal-to-ligand charge-transfer excited state
(3CT) of the dications [15-21].

CHAPTER II
PHYSICAL MEASUREMENTS
Materials
Reagent grade acetonitrile (Fisher) was dried by
refluxing over phosphorus pentoxide followed by distillation
on a one meter fractionating column. For a 2000 ml distil¬
lation the first 400 ml were discarded and the next 1000 ml
collected. The solvent was degassed by four freeze-pump-thaw
cycles and stored under nitrogen. Tetrabutylammonium hexa-
fluorophosphate (TBAH) (electrometric grade, Southwestern
Analytical Chemicals) was dried under vacuum before use.
Deuterated acetonitrile (Merck) was 99% isotopically pure
and used as purchased.
Potassium hexafluorophosphate (Alfa), ruthenium tri¬
chloride (Alfa), 2,2'-bipyridine (Eastman), 4,4'-dimethyl-
2, 2'-bipyridine (G. Fredrick Smith), 4,4'-diphenyl-2,2'-
bipyridine (G.F.S), and Sephadex LH-20 (Sigma) were used
without further purification. All other chemicals were pur¬
chased as reagent grade and used without further purification
unless otherwise specified. In general solvents were deoxy-
genated before use in reactions by bubbling dry nitrogen
through them for fifteen minutes.
5

6
Apparatus and Technique
Electrochemical experiments were carried out employing
a standard three-electrode circuit. A Princeton Applied
Research (PAR) Model 173 Potentiostat/Galvanostat with a
Model 178 Electrometer Probe was used for potential control.
Triangular waveforms for cyclic voltammetry were generated
using a PAR Model 175 Universal Programmer. Coulometric
electrolysis was monitored with a PAR Model 179 Digital
Coulometer. Cyclic voltammograms were recorded on a Houston
Instruments Omnigraphic 2000 Recorder.
All electrochemical experiments were run at ambient
temperature (25±2°C) and referenced to a saturated potassium
chloride calomel electrode (SCE). Figure 2.1 diagrams the
electrochemical cell. The reference electrode was partially
isolated from the electrochemical solution by a fritted disc.
For cyclic voltammetry a platinum bead working electrode and
a two-inch length of platinum wire (28 guage) auxilliary
electrode were used. All electrodes were positioned into a
one centimeter pathlength quartz spectrometer cuvette by a
custom-fabricated teflon cap. When running coulometry exper¬
iments it was found necessary to separate the reference
electrode from the electrochemical cell by a fritted disc. A
platinum coil (12 in of 28 guage wire wound around a 2 mm
diameter) served as the working electrode, and a small mag¬
netic stir bar was placed into the cell.
Electrochemical experiments were performed under nitro¬
gen. The platinum electrodes were cleaned after each use by

7
Figure 2.1. Diagram of the Electrochemical Cell.

8
immersing them in concentrated nitric acid for at least
5 min followed by rinsing with large volumes of methanol.
The electrochemical cell was assembled complete with weighed
sample (minus the reference electrode) and allowed to dry
under vacuum before introduction into the drybox.
Cyclic voltammograms of supporting electrolyte in
acetonitrile gave no detectable waves, and currents were
less than 1 yA in the range +1.8 V to -2.0 V at a scan rate
of 200 mV/s. Sample concentrations for cyclic voltammetric
experiments were 1.0x10 ^ M in a supporting electrolyte
solution of 0.10 M TBAH in acetonitrile.
Coulometry experiments were run in the above electro-
-4
lyte solution at 2.00xio M sample concentrations. In the
dimer studies where it was desired to obtain optical spectra
up to 2600 nm in the near infrared, d^-acetonitrile was used
as the solvent. Electrolysis was determined complete when a
stoichiometric number of coulombs had passed. The elec¬
trodes were removed from the spectrometer cuvette and the
cuvette tightly capped. Near infrared spectra were recorded
on a Perkin Elmer 330 UV/VIS/NIR Spectrometer. The inter¬
valence transfer band of a sample inside the capped cell had
a typical half-life of about two days.

CHAPTER III
PREPARATIONS
Notes on Preparations
All mononuclear and binuclear complexes of ruthenium
are synthesized in the laboratory. Ligands include
2,2'-bipyridine (bpy) , 4,4 '-R2~2,2'-bipyridine (R2~bpy)
[R = H, methyl (me), phenyl (ph), methoxy (ome), and ethyl
carboxylate (es) ] , bibenzimidazole (BiBzImH2) , bibenzimida-
zolate (BiBzIm), and bipyrimidine (Bipyrm). The last two
are employed as bridging ligands for the binuclear complexes.
Sephadex column chromatography is used to purify the
chloride salts of the mononuclear and binuclear complexes
prior to formation of the PF^.- salts through metathesis.
The number of successive elutions required for a pure
compound depends on the band separation and on the evenness
of the packing. In general compounds are separated by
molecular weight with the higher molecular weight compounds
eluting first. Complexes are usually identifiable on the
column by their colors, luminescence properties, and order
of elution. Nonelectrolytes such as ligands and
[Ru(R2~bpy)2C12] complexes elute very slowly in pure meth¬
anol, and a small amount of hydrochloric acid (6 drops in
30 ml methanol) is added to "rinse" the column of these.
9

10
After the addition of 300 ml more methanol, the column is
ready for use.
An Altex 1 m x 2.5 cm I.D. column is used in the prep¬
arations. To assure the column is vertical before packing,
a 1.5 m plumb line is used. A slurry of 100 g Sephadex
LH-20 in 500 ml methanol is added and allowed to settle in
the column while the elution tube is open. Once the Sepha¬
dex completely settles (about 4 hr), a thin layer of sand
is added to facilitate addition of reaction mixtures with¬
out disturbance of the Sephadex.
To perform a separation the sample is dissolved in a
small amount of methanol (1-4 ml) and filtered. The metha¬
nol level in the column is allowed to drop to the level of
the sand, and the sample solution is carefully added. As
the solution reaches the level of the sand, methanol is added
and maintained above the sand as the compound elutes through
the column. Ruthenium complexes usually elute in 2-3 hr.
Ligands
4,4'-Bis(ethyl carboxylate)-2,2'-bipyridine
Synthesis of this ligand is adopted from procedures
described by Case [22] and Maerker and Case [23]. To a
solution of potassium permanganate (55.0 g) in water
(950 ml), 4,4'-dimethyl-2,2'-bipyridine (4.00 g) is added
and heated to reflux until the solution becomes colorless
(about 4 hr). After filtering off the precipitated manganese
dioxide, the solution is extracted with three 200 ml portions

11
of diethyl ether to remove any unreacted 4,4'-dimethyl-2,2'-
bipyridine. Concentrated hydrochloric acid is added to the
aqueous phase until acidic to precipitate an insoluble white
powder which is collected by filtration. Yield for the
crude 2,21-bipyridine-4,4'-dicarboxylic acid after drying is
5.1 g (39%) .
This acid is refluxed with 55 ml concentrated sulfuric
acid in 120 ml absolute ethanol for 10 hr. The solution is
cooled and poured over ice (about 200 g) followed by neutral¬
ization with 25% sodium hydroxide. Upon neutralization the
solution turns light pink, and a white bulky precipitate
forms which is collected by filtration, washed with water,
and dried under vacuum. Recrystallizing twice from 95%
ethanol and drying under vacuum yields 2.2 g of long white
fibrous crystals of 4,4'-bis(ethyl carboxylate)-2,2'-bipyri¬
dine (37%; mp = 158.5-160.5°C, Lit = 159-160.5°C [23]).
4,4'-Dimethoxy-2,2'-bipyridine
This synthesis was adopted from the procedures of Jones
et al. [24] and Case [22]. The compound 2,21-bipyridine
(25.0 g), 30% hydrogen peroxide (25 ml), and glacial acetic
acid (125 ml) are heated on a water bath at 100°C for 4 hr.
The solution is cooled, another 25 ml portion of hydrogen
peroxide is added, and the solution is heated at 100°C for
another 4 hr. After cooling to 0°C the solution is neutral¬
ized with cold 25% sodium hydroxide causing a bulky white
precipitate to form. The precipitate is collected by filtra¬
tion, washed with small portions of water, and recrystallized

12
from water. White fibrous crystals are collected and dried
under vacuum to give 21 g of 2,2'-bipyridine-1,1'-dioxide
(70%; mp = 310°C dec, Lit = 310°C dec [25]).
This compound in 100 ml concentrated sulfuric and
100 ml 90% nitric acids is heated on a water bath at 100°C
for 8 hr. The yellow solution is cooled and poured over ice
(-400 g), followed by neutralization with cold 25% aqueous
sodium hydroxide. Upon neutralization the solution turns
orange and a yellow precipitate forms which is collected by
filtration. The precipitate is washed with water followed
by two 50 ml portions of hot absolute ethanol and dried under
vacuum yielding 9.5 g or crude 2,2'-bipyridine-4,4'-dinitro-
l,l'-dioxide (31%).
This compound is added to a solution of sodium methoxide
prepared by adding 2.85 g metallic sodium to 380 ml methanol.
The suspension is stirred 3.25 hr while maintaining the tem¬
perature at 33+2° on a water bath. The solution is cooled to
0°C, neutralized with concentrated sulfuric acid, filtered,
and the white filtercake discarded. The yellow solution is
evaporated to dryness on a rotary evaporator and extracted
with three 300 ml portions of hot chloroform. The extracts
are combined and refluxed 10 min with activated carbon (5 g),
filtered, and the volume reduced to 500 ml. Hot petroleum
ether (300 ml; 70-110°C) is added to produce a fluffy yellow
precipitate. Yield for the crude 4,4'-dimethyl-2,2'-bipyri¬
dine-1 , 1 ' -dioxide is 5.4 g (67%).
This compound is mixed with 68 ml of dry chloroform and
cooled to -3°C. Phosphorus trichloride (10.8 ml) is added,

13
and the suspension is refluxed for 75 min, cooled, and poured
onto crushed ice (~100 g). After phase separation the chlo¬
roform phase is extracted with four 50 ml portions of water,
and the aqueous extracts are combined with the aqueous layer
of the reaction mixture. Neutralization with 25% sodium
hydroxide causes a bulky white precipitate to form which,
after cooling, is collected by filtration and washed with
water. Recrystallization from absolute ethanol gives 2.4 g
of white crystals of 4,4'-dimethoxy-2,2'-bipyridine (53%;
mp = 170-172°C, Lit = 170-172° [23]).
2,2' -Bibenzimidazole
Preparation of this ligand is taken from Fieselmann et
al. [26] where O-phenylenediamine (22.5 g) and oxamide (8.8 g)
are refluxed in 20 ml ethylene glycol for 24 hr. The solu¬
tion is added to 400 ml of boiling water causing a thick
yellow precipitate to form which is collected by filtration,
washed, and dried under vacuum. This material is recrystal¬
lized in 900 ml ethylene glycol with activated carbon. The
compound is dried under vacuum yielding 9.2 g bibenzimidazole
(39%; mp = 395°C dec).
Ruthenium Complexes
[Ru(bpy)3_n)R2-bpy)n](pF6>2
Several syntheses have appeared in the literature for
°+
the complex ion [Ru(bpy)3]“ [27,28]. The latest and most
commonly used preparation by Braddock and Meyer [27] involves

14
refluxing RuCl^'nH^O with a stoichiometric amount of bpy in
N,N'-dimethylformamide (DMF) for several hours. VJe have du¬
plicated this preparation in our laboratory and have found
2+
[Ru(bpy)3] prepared in this manner to contain a significant
amount of a byproduct we believe is [Ru(bpy)2(CO)Cl]+ [29],
which we could not separate completely from the product using
Sephadex LH-20 in methanol. A procedure has been developed
2+
for preparing [Ruibpy)^] free from this impurity using eth¬
ylene glycol as the solvent for the reaction. This synthetic
route is useful in preparing several analogs of the above
complex using substituted bipyridine ligands in place of bpy.
2 +
When [Ruibpy)^] is prepared by refluxing RuCl^'ni^O
with a stoichiometric amount of bpy in DMF and the residue
from the reaction mixture is eluted through a Sephadex col¬
umn using methanol as the eluent, four "bands" appear on the
column. The first to elute is the bright orange luminescent
2 +
[Ruibpy)^] complex. Superimposed on the trailing edge of
this band is a dull brown-orange (nonluminescent) band which
is hard to separate completely from the former. Several elu¬
tions through the column taking narrow cuts still leave a
small amount of the impurity and greatly reduced the
2+
[Ruibpy)^] yield. Other bands on the column include a
small amount of neutral [Ru(bpy)2C121 (purple) and unreacted
bpy (otherwise colorless but luminesces blue in the presence
of light).
When RuCl^’nl^O is refluxed with a small stoichiometric
excess of bpy in ethylene glycol, the solution turns bright

15
orange within minutes. Upon distilling off the solvent under
vacuum at 100°C, the residue is dissolved in a minimum amount
of methanol and eluted through a Sephadex column. Now only
two bands appear on the column—a luminescent orange leading
band corresponding to [Ruíbpy)^"1"1" and a faint bpy band which
elutes very slowly. The preparation gives nearly quantita¬
tive yields of the corresponding [Ru(I^-bpy)++ chloride
salt when bpy is replaced with R2~bpy (where R = me, ph and
ome), with the only other impurity being the excess ligand.
The PFg salts of these complexes were used for electrochem¬
ical and spectroscopic measurements. The metathesis is eas¬
ily performed by dissolving the chloride salt in a small
excess of water (for complexes that are relatively insoluble
in water, a small amount of methanol is added). While main¬
taining fast stirring rates, 0.1 M KPFg is added dropwise
through a filter. When precipitation is complete (superna-
tent becomes almost colorless) the product is filtered and
washed with water.
The compounds RuCl^'SH^O (260 mg) and bpy (470 mg) are
refluxed with 20 ml ethylene glycol for 30 min. The ethyl¬
ene glycol is distilled off under vacuum at 100°C, and the
residue is dissolved in 3 ml methanol. This solution is
eluted through a Sephadex column, and the bright orange band
is collected. Upon removal of the methanol, the solid is
dissolved in 20 ml water. The PF^ salt is prepared as
described above in this chapter, yielding 840 mg [Ruibpy)^]-
(PF6)2 (98%). Similar procedures are followed for complexes
involving substituted R2-bpy ligands.

16
The complex [Ru(es2~bpy)3](PFg)2 is not prepared in
ethylene glycol to prevent transesterification of the es
group. This preparation is adapted from Sprintschnik et
al. [30] in which RuC13*3H20 (260 mg) and es2~bpy (650 mg)
are suspended in 50 ml absolute ethanol and the mixture
heated in a sealed glass tube at 140°C for 4 days. After
adding 2 ml water, the solution is refrigerated for 8 hr.
The mixture is filtered yielding a black filtercake (which
is discarded) and a dark red solution which is evaporated
to dryness under vacuum at 100°C. The residue is dissolved
in 4 ml methanol, filtered, and eluted through a Sephadex
column. The PFg salt is prepared yielding 410 mg
[Ru(es2~bpy)](PFg)2 (32%).
[Ru(R2-bpy)2c12^
Several methods have been published for the prepara¬
tions of [Ru(R2~bpy)2C12] complexes [30-33], many of them
requiring much experimental effort and producing small
yields. Presently the most viable synthetic route toward
the preparations of these complexes [30] involves refluxing
RuCl3*nH20 with a stoichiometric amount of R2~bpy in DMF for
several hours. Yields for these reactions are typically low
with the formation of large amounts of the corresponding
mono- [31] and trissubstituted R2~bpy complexes, as well as
[Ru(R2~bpy)2(CO)Cl]+ [29], as byproducts.
A simple technique has been developed in our laboratory
for the preparation of [Ru(R2~bpy)2C12] complexes in high
yields by using 4:1 ethylene glycol/ethanol as the reaction

17
solvent. When [Ru (í^-bpy) Cl2] (R = H, me, ph or ome) is
prepared by refluxing RuCI^tiH^O with a stoichiometric quan¬
tity of the R2~bpy ligand in the above solvent for 3 hr, the
product is formed in relatively high yields (typically
70-85%) with only small amounts of the corresponding mono-
and trissubstituted complexes and no [Ru(R^-bpy)2(CO)Cl]+.
The complex RuC12*3H20 (260 mg) and bpy (310 mg) are
refluxed in 50 ml 4:1 ethylene glycol/ethanol for 3 hr. The
solvent is removed under vacuum at 100°C and the residue
refluxed in 100 ml 1:1 ethanol/water for one hour and fil¬
tered. Lithium chloride (10 g) is added to the filtrate and
the ethanol is distilled off (85-90°C). The solution is
sealed and maintained at 0°C for 3 hr. Green/black crystals
are collected by filtration and washed with large volumes of
water. The product is dried under vacuum to yield 409 mg
[Ru(bpy)2C12] (85%). Similar procedures are followed for
complexes involving substituted R2~bpy ligands.
The complex [Ru(es2~bpy)2C12] is prepared by a modifi¬
cation of the method of Sprintschnik et al. [30], using DMF
as the reaction solvent. The RuCl2*3H20 (260 mg) and es2bpy
(600 mg) are refluxed in 60 ml of DMF for 3 hr. The volume
is reduced to 10 ml under vacuum at 100°C. Acetone is added
while hot, and the flask is capped and stored at 0°C for
8 hr. Black crystals are collected by filtration, recrys¬
tallized from methylene chloride/acetonitrile, and dried
under vacuum, yielding 178 mg of product (23%).

18
[Ru(bpy) (R2-bpy)2] (PFg)2
The [Ru(me2bpy)2C12] complex (100 mg) and bpy (30 mg)
are added to 20 ml of absolute ethanol and refluxed 3 hr.
During this time the solution becomes bright orange. After
removal of the ethanol under vacuum, the residue is purified
using Sephadex chromatography collecting the luminescent
orange band. The PFg salt is obtained through metathesis
and, after drying, yields 100 mg of product (68%) . This
procedure is used to prepare complexes where R = ph, ome and
es, producing yields between 40-70%.
[Ru(bpy)2(R2~bpy)] (PF6)2
Preparations of complexes in this series follow as
above by replacing [Ru(R2~bpy)2C12] and bpy with
[Ru(bpy)2C12] and R2~bpy. Yields range from 70-80%.
[Ru(bpy)2(BiBzImH2)]Cl2
This preparation is adapted from the method of Haga [34].
The [Ru(bpy)2C12] complex (484 mg) and BiBzImH2 (350 mg) are
refluxed in 20 ml absolute ethanol during which time the
solution turns bright red-orange. The ethanol is removed
under vacuum, and the residue is purified by Sephadex chro¬
matography collecting the luminescent orange band. After
removal of the methanol under vacuum, the solid is collected
and dried, yielding 620 mg of product (86%).
[(R2~bpy)2Ru(BiBzIm)Ru(bpy)2](PFg)2
Complexes in this series are prepared by a modification
of the method of Haga [34], The [Ru(bpy)2(BiBzImH2)]Cl2

19
complex (100 mg) is added to [Ru(me2bpy)2C12] (100 mg) in
20 ml absolute ethanol. Five drops of triethylamine are
added, and the mixture is refluxed 3 hr during which time
the solution turns bright red. The ethanol is removed under
vacuum and purified by Sephadex chromatography, collecting
the leading red (nonluminescent) band. A luminescent orange
band, superimposed on the trailing edge, makes it difficult
to obtain a pure product and can decrease yields substan¬
tially. Yields are typically low for all the dimers ranging
from 20-50%. For the present preparation, after metathesis
to the PFg salt and drying, the yield is 96 mg (49%) . Com¬
plexes where R = me, ome and ph are prepared using the same
general procedure. The R = ph complex requires a longer
reflux time (8 hr).
[(R2~bpy)2Ru(BiBzIm)Ru(R2~bpy)2](PFg)2
Preparations of complexes in this series are similar to
2+
the above except that the [Ru(R2~bpy)2(BiBzImH2)] complex
is prepared in situ. The [Ru(R2~bpy)2C12] complex (540 mg)
and BiBzImH2 (117 mg) are refluxed in 20 ml absolute ethanol
1 hr. Five drops of triethylamine are added, and reflux is
continued 3 hr longer. Purification procedures are similar
to the above, yielding 314 mg product (43%).
Microanalysis
All elemental analyses were performed at the Department
of Chemistry, University of Florida, and are listed in
Table 3.1.

Table 3.1. Elemental Analysis of Ruthenium Complexes.
Complex
%C
%H
%N
[(bpy)2Ru(BiBzIm)Ru(bpy)2](PFg)7
caled
48.08
2.99
12.46
found
47.55
2.71
12.21
[(me2-bpy)2Ru(BiBzIm)Ru(me2~bpy)2](PFg)2
50.96
4.86
11.50
50.39
3.86
11.04
[(ph2~bpy)2Ru(BiBzIm)Ru(ph2~bpy)2](PFg)2
62.58
3.71
8.59
62.19
3.66
8.31
[(ome2-bpy)2Ru(BiBzIm)Ru(ome2~bpy)2] (PFg)2
46.85
3.55
10.58
46.08
3.50
10.15
[(bpy)2Ru(BiBzIm)Ru(me2~bpy)](PFg)2
49.58
3.44
11.96
48.72
3.39
11.36
[(bpy)2Ru(BiBzIm)Ru(ph2~bpy)](PFg)2
56.66
3.41
10.17
56.22
3.34
9.75
[(bpy)2Ru(BiBzIm)Ru(ome2bpy)](PFg)2
47.42
3.29
11.44
46.79
2.95
11.01

CHAPTER IV
ELECTROCHEMISTRY OF THE MONOMERS
Introduction
Tris(2,2'-bipyridyl)ruthenium and its analogues continue
to be of considerable interest as central subjects in the
study of general photosensitization [35] as well as in stud¬
ies of singlet oxygen production [36] and of possible photol¬
ysis of H20 [37]. While the electronic structure of the
reduced, monocationic forms of these complexes is a factor in
certain luminescence quenching [38] and chemiluminescent [39]
processes, most physical studies of these complexes have
focused upon the reactivity of the dications' lowest triplet
metal-to-ligand charge-transfer excited state (3CT) primarily
responsible for the interesting behavior of the ions. The
answer to one of the earliest such questions remains uncer¬
tain: whether the optical electron is delocalized over all
three bidentate aromatic ligands or localized on just one
ligand at a given time. Reports by Hager et al. [15] account
• 0_1_
for excited-state properties of [Ru(bpy)^] (bpy = 2,2'bipyr¬
idyl) through a model of the 3CT state derived from a metal-
t2g-to-ligand tt* charge-transfer model of symmetry (delo¬
calized) . However, two recent fluorescence polarization stud¬
ies [18,19], and recent resonance Raman [20] and time-resolved
21

22
resonance Raman [21] studies indicate a localized 3CT state.
Assuming that Koopman's theorem is valid in the comparison
of the monocation with the excited dication, esr [40] and
electrochemical [41] studies are also consistent with a
localized 3CT state.
Ligand t:* orbitals are the lowest-energy acceptor or¬
bitals in both charge-transfer-to-ligand excitations and
complex reductions to the monocation, although some charge-
transfer-to-solvent character of the 3CT state apparently
does exist [39]. The strictly exponential [15] luminescence
decay of mixed-ligand complexes of Ru(II), unlike the multi¬
exponential behavior of mixed-ligand complexes of Rh(III)
[42,43], is consistent with either a delocalized electronic
structure or an equilibration (which is faster than lumines¬
cence decay rates of about 106 sec-1) of the optical electron
among ligand tt* orbitals. The latter is in turn consistent
with the low interligand electron-hopping barriers estimated
from the temperature-dependence of esr broadening [40].
If the tt* electron in [Ruibpy)^"1” is localized, there
could then be three reduced forms, each corresponding to
occupation of a different ligand tt* orbital by the highest-
energy electron. If the one-electron reduction potential En
to a single reduced from M+ (where n = 1, 2 or 3) corre¬
sponds to occupation of a tt* orbital in ligand n [44] , then
at a given applied electrochemical potential E and tempera¬
ture T, the ratio of the concentration of each such reduced
form in solution to that of the dicationic form M2+ is

23
[M ]
n
e (E-En)F/RT
(4.1)
Since rapid and reversible electrochemical reduction to
rapidly equilibrating products will result in a summation of
currents from reduction to each form, at any potential E the
= l e(E"En)F/RT
n=l
(4.2)
K
Any such pattern of tt* orbital energies will yield but a
single apparent reduction wave centered at a potential which
can in principle be calculated from the relevant E^ values.
For the present case there are two types of calculated poten-
2 +
tials--those for reductions of symmetric complexes [RuB^]
2+
and those for reductions of mixed-ligand complexes [RuB2B']
In the first case the equivalence of E^, E2 and E^ (all equal
to Eg, the one-orbital potential for coordinated ligand B)
leads to a small difference of statistical origin [44]
between ED for the ligand and ED for the complex. Thus the
•D .D ^
apparent reduction potential ED for such a couple is
B3
E
B
3
(4.3)
. 2 + / +
For the mixed-ligand case [RuB2B']
E
(4.4)
Thus experimental reduction potentials for the two limiting

24
symmetric forms and the assumption of rapid equilibration
between reduced forms lead to prediction of observed poten¬
tials for the associated mixed-ligand complexes. These
predicted potentials of the mixed-ligand complexes will
almost always differ significantly from those predicted from
linear free energy dependence following from either a metal-
centered or a delocalized ligand-centered reduction.
Experimental
Cyclic voltammograms were recorded as described in
2+
Chapter II for the series [Ru(bpy)^_n(R2~bpy)where
R = me, ph, ome and es (n = 0-3). Baselines of supporting
electrolyte in CH^CN gave no discernible waves in the range
-1.8 to +2.0 V vs. SCE, and currents did not exceed ±1 yA at
scan rates of 200 mV/s.
One reversible oxidation wave corresponding to the
RuII/III couple [45] and three reversible reduction waves
corresponding to three successive ligand-centered reductions
[14] were recorded for each of the above complexes. A cyclic
voltammogram is presented in Figure 4.1 for the R = ome
(n = 1) complex. Other monomer complexes yield cyclic vol¬
tammograms similar to this and are not shown. Peak separa¬
tions for the above couples vary from 0.070-0.090 V and are
invarient with sweep rates of 100-500 mV/s. This behavior is
due presumedly to uncompensated solution resistance. Several
3+/2+
known reversible couples including [Rutbpy)^] have been
reported to yield peak separations of 60-100 mV under

Figure 4.1. Cyclic Voltammogram of [Ru (on^-bpy) 3 ] (PF^ )
in 0.1 M TBAH/CH3CN (scan rate = 200 mV/s).

0.070-0.090 V
AE
PP
E, (ox)
»*5
Ep(c) - Ep(a) =
E (a) + E (c)/2
E (a)
tv)
cn
-2.0
1.0
0.0
-1.0
Volts vs. SCE

27
conditions similar to ours [46] , and thus all electrochem¬
ical couples in this work are assumed to be reversible
despite small deviations of AE from the theoretical value
PP
of 0.059 V [47].
Listed in Table 4.1 are half-wave potentials corre¬
sponding to oxidations of the monomers. Since these oxida¬
tions are metal centered, effects of ligand substituent
groups can be treated as perturbations at the metal center,
the effects of which will be additive; i.e., there should be
a linear free energy relationship (LFER) between the half¬
wave potentials and the number of substituent groups [45].
Also listed in Table 4.1 are calculated half-wave potentials
for the two mixed ligand species assuming LFER and interpol¬
ating between potentials of the corresponding symmetric
species.
Given an accuracy in measurement of E, to be ±0.005 V,
it is seen that LFER is followed closely for oxidation poten¬
tials of the above set of complexes. Contributions per
substituent group to E^ are listed:
Substituent Group Ej (ox)
*5
H E0
me -0.027
ph -0.011
ome -0.050
es +0.060
From the above table it can be seen that the me, ph and ome
groups are electron-donating (more facile oxidation), and
that the es group is strongly electron-withdrawing (less
facile oxidation).

28
Table 4.1. Half-Wave Potentials for the
[Ru(bpy)3_n(R2~bpy)n]2+/+ Couples (v).
Localized Delocalized
n
Experimental
Model
Model
R = ph
0
-1.292
a
a
1
-1.257
-1.254
-1.271
2
-1.235
-1.239
-1.251
3
-1.230
a
a
R = es
0
-1.292
a
a
1
-0.960
-0.879
-1.145
2
-0.898
-0.861
-0.998
3
-0.851
a
a
R = me
0
-1.292
a
a
1
-1.323
-1.302
-1.339
2
-1.353
-1.320
-1.369
3
-1.408
a
a
R = ome
0
-1.292
a
a
1
-1.357
-1.302
-1.348
2
-1.400
-1.320
-1.404
3
-1.460
a
a
a Fixed point.

29
The mechanisms for these substituent effects are, in the
ph, ome and es cases, assumed to originate via resonance with
the tt system of the bipyridine ligand [48] . For the me case
it is assumed that induction through the tt system is impor¬
tant. Regardless of the origin, these substituent effects act
in a way to alter the electron density around the metal cen¬
ter .
Reductions of the above complexes are ligand centered in
nature. Table 4.2 lists the first reduction half-wave poten¬
tials for the above monomer series as well as potentials cal¬
culated assuming both the localized and delocalized descrip¬
tions. In the delocalized limit it would be expected that
the substituent groups would affect E^, (RED) values in a lin¬
ear (LFER) manner since the effect of each substituent group
would be averaged over the three ligands. In the localized
limit equations 4.3 and 4.4 are used to calculate the E^(RED)
values.
Discussion
The agreement between the experimental reduction poten¬
tials for the mixed-ligand complexes involving the phenyl and
ethyl carboxylate substituent groups and those calculated
from our application of the ligand-localized model to the
symmetric complex potentials argues in favor of that model's
adoption over the alternate metal-centered and ligand-delocal¬
ized models for the monocationic complexes. Although such
agreement in the [Ru(bpy)^_n(es^bpy) ]2+//+
case is not

30
Table 4.2. Half-Wave Potentials for the
[Ru(bpy)3_n(R2~bpy)n]3+/2+ Couples (v).
n
Experimental
Calc LFER
R = ph
0
1.310
a
1
1.293
1.288
2
1.268
1.266
3
1.244
a
R = es
0
1.310
a
1
1.394
1.310
2
1.517
I-. 510
3
1.610
a
R = me
0
1.310
a
1
1.258
1.256
2
1.216
1.202
3
1.149
a
R = ome
0
1.310
a
1
1.173
1.189
2
1.061
1.069
3
0.949
a
a Fixed Point.

31
strictly observed, the experimental potentials of those
couples clearly resemble those from the localized model more
than those from any delocalized model. Further, potentials
for the +/0 reductions (i.e., -1.493 V, -1.421 V, -1.099 V,
and -1.014 V for n = 0, 1, 2 and 3) and for the 0/- reduc¬
tions (-1.736 V, -1.612 V, -1.534 V, and -1.231 V) for the
same series indicate that the tt* electrons localize to the
extent possible in the lowest energy orbitals available.
For the mixed-ligand complexes involving the methyl and
methoxy substituent groups, agreement occurs between the
experimental potentials and those calculated from our appli¬
cation of the ligand-delocalized model. Thus it is seen
that electron-withdrawing substituent groups favor the
localized description whereas electron-donating groups favor
the opposite.
One explanation for this apparent discrepancy may be
offered if the monomer monocations are viewed as interligand
mixed-valence species. Taking into consideration the low
interligand electron-hopping barriers, corresponding to
thermal electron transfer, estimated from the temperature
dependence of esr broadening by Motten et al. [40], one can
imagine that electron-donating groups such as me and ome may
lower this thermal barrier through an increase in electron
density in the ligand tt* system. Just the opposite effect
would be expected for electron-withdrawing groups.
Our hypothesis is that the potential of a dication/
monocation couple will rather closely resemble the reduction
potential of the symmetric tris-complex of the more easily

32
reduced coordinated ligand. The fact that the void in
potential space between the potentials of the two limiting
tris-complexes is not covered at all evenly by potentials
of the intermediate mixed-ligand complexes (as we find is
true for metal-centered 3+/2+ redox) will probably make
reduction potentials more difficult to "tune" than are oxi¬
dation potentials. The large magnitude of the energy gaps
of about 3600 cm-1 reported [49,50] to lie between the
dications
est ligand field (t
of orbital ordering between the ground-state monocations and
the excited-state dications. If in addition it is noted that
5 ,
the d electronic structure of the CT dication is far more
likely to contribute to structural and electronic distortion
r
from symmetry than is the monocation's d metal electronic
structure, it is clear that a conclusion of ground-state
monocation it* electron localization/delocalization leads to
a similar conclusion in the dication 3CT state. Thus we
have acquired information about the electronic structure of
an excited state from studies on ground states.

CHAPTER V
ELECTROCHEMISTRY OF THE DIMERS
Introduction
In mixed-valence complexes for which there is a large
degree of electronic coupling between the metal centers, it
is often difficult to determine whether the unpaired electron
is localized or delocalized between them. Electrochemical
data are presented that allow for a qualitative determination
of the extent of electron delocalization in moderately
coupled ruthenium mixed-valence dimers. Structural varia¬
tions in a series of complexes provide for calculations of
redox potentials, assuming both the localized and the delo¬
calized descriptions of the mixed-valence state. Comparisons
of experimental redox potentials with the calculated poten¬
tials provide insight into the extent of electron delocaliza¬
tion within a given series.
Each series consists of three complexes, two symmetric
and one asymmetric:
1) [(bpy)2Ru(L-L)Ru(bpy)2]n+
2) [(R2-bpy)2Ru(L-L)Ru(bpy) ]n+
3) [(R2~bpy)2Ru(L-L)Ru(R2~bpy)2]n+
(L-L is the bridging ligand; BiBzIm or Bipyrm). These
33

34
complexes undergo reversible oxidations corresponding to the
III-III/III-II and the III-II/II-II redox couples where III-II
refers to the oxidation states of the metal centers in the
dimer [e.g., RuIII(L-L)RuII]. For a given series the reduc¬
tion potentials (corresponding to the above couples) for the
asymmetric complex can be calculated from those of the sym¬
metric complexes. Two models are used for these calcula¬
tions based on the localized and the delocalized descrip¬
tions of the mixed-valence state.
Assuming a localized mixed-valence state and using
arguments similar to those in Chapter IV, reduction poten¬
tials for the asymmetric dimers are calculated for the
III-III/III-II couples.
JRR 1
+
RT . , 0.
— ln<2)
+
f m
1 + e
,ER'R'-ERR»F/RT-
and for the III-II/II-II couples
JRR 1
err + F ln(2>
RT .
- — inf!
+
(err-er-r')f/rt^
e J
where E and E_.,Dl are the apparent (experimental) reduc-
KK K K
tion potentials for the symmetric complexes and EDD, for the
KK
asymmetric complexes.
Calculations assuming the delocalized description fol¬
low from a linear (LFER) interpolation between the experi¬
mental reduction potentials for the symmetric complexes,
i.e., the average of the two potentials.

35
Experimental and Results
Cyclic voltammograms for the R = ome series are presented
in Figure 5.1 and are similar to those for other series (not
shown). Two reversible oxidation waves were recorded for
each complex corresponding to the III-III/III-II and the
III-II/II-II couples; four reversible ligand-centered reduc¬
tion waves were recorded for each complex as well. For the
symmetric complexes two of the ligand-centered reductions are
superimposed, yielding two two-electron reduction waves, and
are resolved into four one-electron reduction waves in the
presence of an asymmetric ligand arrangement. All waves are
shifted to more positive potentials in the presence of elec¬
tron-donating substituent groups (me, ph and ome), Peak
separations AE for the couples vary from 0.075-0.090 V and
PP
are assumed reversible from criteria presented in Chapter IV.
Listed in Tables 5.1 and 5.2 are half-wave potentials
corresponding to the III-III/III-II and the III-II/II-II
couples along with calculated potentials, assuming the local¬
ized and the delocalized descriptions of the mixed-valence
(III-II) state. It is observed that the experimental reduc¬
tion potentials, in every case, lie between the two calcu¬
lated values and that closest agreement occurs with poten¬
tials calculated from the localized description.

Figure 5.1. Cyclic Voltammograms of
[(R2~bpy)2Ru(BiBzIm)Ru(R^-bpy)2](PF^)2
in 0.1 M TBAH/CH3CN (scan rate = 200 mV/s).

37
1
1.0
0.0
-1.0
L
-2.0

38
Table 5.1. Half-Wave Potentials for the [(R2~bpy)2Ru(L-L)-
Ru(R2'-bpy)2]n+ III-III/III-II Couples (v).
Localized
Delocalized
(L-L)
R
R'
Experimental
Model
Model
BiBzIm
H
H
1.056
a
a
H
me
1.030
1.038 (8)
1.004(14)
me
me
0.950
a
a
BiBzIm
H
H
1.056
a
a
H
ph
1.045
1.045(0)
1.041(4)
ph
ph
1.026
a
a
BiBzIm
H
H
1.056
a
a
H
ome
1.007
1.038(31)
0.935 (72)
ome
ome
0.815
a
a
Bipyrm
H
H
1.731
a
a
H
me
1.707
1.713(6)
1.683(24)
me
me
1.635
a
a
a Fixed point.
Values in parentheses are deviations from the experimental in
mV.

39
Table 5.2. Half-Wave Potentials for the [(R_-bpy)„Ru(L-L)-
, - i ¿mí*
Ru(R2*-bpy)2] III-II/II-II Couples (V).
(L-L)
R
¿.
R'
Experimental
Localized
Model
Delocalized
Model
BiBzIm
H
H
0.765
a
a
H
me
0.700
0.686 (14)
0.717(17)
me
me
0.668
a
a
BiBzIm
H
H
0.765
a
a
H
ph
0.760
0.760 (0)
0.761(1)
ph
ph
0.757
a
a
BiBzIm
H
H
0.765
a
a
H
ome
0.590
0.556 (24)
0.652 (62)
ome
ome
0.538
a
a
Bipyrm
H
H
1.548
a
a
H
me
1.471
1.459 (12)
1.495(24)
me
me
1.441
a
a
a Fixed point.
Values in parentheses are deviations from the experimental in
mV.

40
Discussion
Experimental reduction potentials are not consistent
with either the totally localized or the totally delocalized
descriptions of the mixed-valence state but are consistent
with a combination of the two. It is concluded that both
models are important in describing the nature of these mixed-
valence systems, i.e., a moderate amount of electron delocal¬
ization is present but that the valences are trapped to some
degree. Further inspection of the data indicates that the
localized description is preferred in every case.
In comparing bridging ligands (for the methyl series),
it is observed that both bibenzimidazole and bipyrimidine
allow for similar degrees of delocalization. Assuming the
M-M distances are similar for either bridging ligand, the
anionic bibenzimidazole bridge would favor electron delocal¬
ization over the neutral bipyrimidine bridge [51]. What must
be considered also is that the electron coupling decreases
with the number of conjugated atoms in the bridge [51], Thus
a cancellation of effects may allow for similar bridging
effects in both systems.
Very small, but finite, thermal electron transfer bar¬
riers would be expected for these mixed-valence complexes [8].
These results are later compared to those from treatments of
the intervalence transfer absorptions of the same using the
Hush and PKS theories.

CHAPTER VI
THEORY OF INTERVALENCE TRANSFER
Energy barriers are generally associated with electron
transfer since otherwise the electron would be effectively
delocalized between metal centers leaving each with a non¬
integral formal charge. The magnitude of an electron trans¬
fer barrier depends on 1) the relative ground-state poten¬
tial energy difference, if any, of the electron between the
two centers; 2) the degree of electronic coupling between the
centers; and 3) changes in configuration (bond lengths and
force constants) with oxidation state. In order to under¬
stand rates and mechanisms of electron transfer, one must
understand the origin of these barriers and factors that
influence them.
Studies described in this work focus on binuclear
ruthenium complexes in solution where electrons are trans¬
ferred between metal centers in the same complex (the term
"electron transfer" will be used from now on to refer specif¬
ically to the process where electrons are transferred between
metal centers). Electron transfer is mediated via a bridge
that bonds the metal centers and is, in this case, termed
"inner-sphere." Electron transfer between non-covalently
bonded species, where only weak forces such as dipole-dipole
41

42
or van der Waals forces hold the species in close contact, is
termed "outer-sphere." There is a close relationship between
inner- and outer-sphere electron transfer, and theories men¬
tioned here are applicable to either case as they do not
explicitly distinguish between the types of bonding between
metal centers [ 4 ]. Studies involving outer-sphere systems
are complicated by the appearance of "extra" parameters such
as contact time and internuclear distances which are, in
inner-sphere systems, usually better defined and more readily
available.
Simple Model
A simple model for electron transfer will be described
using binuclear mixed-valence ruthenium complexes as a "model"
system. This model will be used to gain a physical interpre¬
tation of optical and thermal electron transfer, and it will
serve as a starting point for the more complex theories of
Hush [6] and of Piepho et al. [8].
For a symmetric binuclear complex the potential energy
difference between the metal centers (EQ in the Hush theory
and W in the PKS theory) is zero. Barriers to electron
transfer are imposed due to the changes in metal-ligand bond
lengths that accompany oxidation state changes at the metal
centers. It is assumed that the gross symmetry around the
metal center is the same for the metal in either oxidation
state so that only the totally symmetric vibrational modes
(breathing modes) contribute to the barrier [8].

43
The parabolas (harmonic oscillator approximation) in
Figure 6.1 represent (for each configuration, II/III and
III/II, of the electron) the potential surfaces for the
asymmetric combination of metal-ligand breathing modes [8].
It has been shown that contributions to the potential sur¬
faces arising from the symmetric combinations of breathing
modes do not enter into calculations of intervalence transfer
properties in cases where the force constants are equal for
the metal in different oxidation states (a fundamental ap¬
proximation of the Hush and PKS theories). The curves are
displaced by a distance A (proportional to the average metal-
ligand bond length change with oxidation state) along the
axis q. The PKS parameters A and q are dimensionless.
Electronic coupling between the metal centers causes the
curves to split at the surface crossing region.
Intervalence transfer is shown by the vertical arrow of
energy E (Franck-Condon approximation) in Figure 6.1a.
This route is thermally forbidden as the products would be
formed directly in a vibrationally excited state and energy
would not be conserved [4]. The thermal electron transfer
process involves successively exciting vibrational modes
until an amount of energy Ea is absorbed. When the metal-
ligand bond lengths on both metal centers are equal (remem¬
bering q corresponds to the asymmetric combination of breath¬
ing modes), the electron will be transferred to the other
surface with a probability < (adiabaticity factor) related to
the splitting of V .
At a given temperature the rate

Figure 6.1. Potential Energy (E) vs. Reaction
Coordinate (q) for a) Symmetric and
b) Asymmetric Mixed-Valence Complexes.

45
2 9 2
-X
2
X
2

46
constant of thermal electron transfer is
K
-E_/RT
Kve a
where R is the gas constant, T is the temperature, and v is
the fundamental frequency of the coupling vibrational mode.
In the case that is very small, it is easily shown that
Ea " Eop/4
and thus a simple relationship exists between the two elec¬
tron transfer processes. For the asymmetric case where
Eq f 0, the curves are displaced vertically from one another
as shown in Figure 6.1b.
Classification of Mixed-Valence Complexes
Mixed-valence complexes are classified according to the
degree of electron delocalization between the metal centers.
Figures 6.2a-c display potential surfaces for Class I-III
symmetric mixed-valence complexes.
Class I complexes (Figure 6.2c) are those where virtually
no electronic coupling exists between the metal centers. Both
optical and thermal electron transfer are forbidden. The
intensity of the intervalence transfer absorption is dependent
on VAB and is zero for VAB = 0. Thermal excitation of vibra¬
tional modes does not give rise to electron transfer because
the curves are not split and there is zero probability for the
electron to cross surfaces (k = 0).

Figure 6.2. Potential Energy Surfaces for Class I
through Class III Mixed-Valence Complexes.

8
= 0 /
a) Class I
Eop/
T < —
AB 4/
* b) Class II
- E°p
AB 4 /
* c) Class III

49
Class II complexes (Figure 6.2b) are those where the
surfaces split but a finite barrier to thermal electron
transfer is present. Both optical and thermal electron
transfer can occur. The intensity of the intervalence
absorption and the rate of thermal electron transfer both
increase with increasing V„_.
Class III complexes (Figure 6.2c) are those where elec¬
tronic coupling is large enough to completely overcome the
thermal barrier. There is only one minimum in the potential
well, and the electron is effectively delocalized between the
metal centers. The optical absorption now corresponds to an
electronic transition and not to an electron transfer proc¬
ess.
For asymmetric complexes the above classification scheme
still applies, but there are a few points worth noting. For
metal centers of different energies, electronic coupling will
generally be smaller than for the asymmetric cases. In addi¬
tion the thermal barrier on the low energy side will be low¬
ered by an amount E . Both of these factors favor valence
trapping, and as a result, asymmetric complexes tend to be
valence trapped. Since there is a preferred orientation in
these complexes, the optical transition corresponds to an
electron transfer process even in the delocalized case.
Hush Theory
The Hush theory is applied in a series of four equa¬
tions :

50
Ea =
Eop/^
(Av^)2
= 2312 "max*â„¢"1)
[symmetric
case]
= 2312 (W - Eo/hc)
[asymmetric
case]
e Av.
a2 = 4.24xl0~4 —h.
v R2
max
EQp, Ea and EQ have been previously defined. When expressed
in wave numbers EQp becomes vmax (hc~max = Eop) . The band
half-width Av^(cm-1) is defined as the value of Av where
^Ivvmax//Imaxv' = %
The extinction coefficient at the band maximum is given as
e and the internuclear separation between metal centers as
max
° o
R(A) . The degree of valence delocalization is given as a .
The Hush theory takes into account both the high-
frequency inner-sphere modes and the low-frequency solvent
modes in its treatment of experimental data. Inner-sphere
contributions arise from changes in metal-ligand bond lengths
with the oxidation state of the metal center (as described
above with the simple model). Contributions from the solvent
arise from rearrangements of the dielectric environment sur¬
rounding the complex.
Following from Marcus and Sutin [52], the energy of an
intervalence transfer absorption can be divided into contri¬
butions from the inner-sphere (A^ ) and the outer-sphere
(Aout) rearrangement energies.

51
E
op
^in + ^out ^sym
(6.5)
Eop -
^in + ^out + Eo = ^asym + Eo
(6.6)
^sym(l) + ^sym(2)
(6.7)
Aasym
2
For an asymmetric complex XaSym can be calculated from Xg
of the two symmetric complexes.
The Hush theory was derived assuming that electronic
coupling is very small compared to E0p* This in principle
limits applicability of the Hush theory to weakly coupled
Class II mixed-valence complexes. Vibrational motion is
treated semi-classically such that transitions are assumed to
occur vertically (Franck-Condon approximation) between the
surfaces of the potential wells (turning points) and that a
continuum of vibrational levels is populated. This is a
good approximation in the high temperature limit where the
fundamental metal-ligand vibrational frequency v_ is of much
lower energy than KT (v_ << KT). From the above description
a gaussian bandshape is expected for intervalence transfer
absorption [6], and a2 is derived accordingly.
PKS Theory
In the Hush theory it was assumed that transitions com¬
prising the intervalence transfer absorption occur between
two potential surfaces corresponding to the electron on either
metal center. As electronic coupling becomes important, this
assumption is no longer valid. Electronic coupling mixes the

52
potential surfaces and the vibrational eigenfunctions contain
contributions from both [7].
Piepho et al. [8] derived expressions for these vibra¬
tional-electronic (vibronic wave functions for both symmet¬
ric and asymmetric mixed-valence systems. The symmetric
vibronic wave functions are given below.
v
- t I
n=0,2,4,..
r x + ¥
vn n
n=l,3,5,..
r x (6.8)
vn n
= Y,
n=l,3,5,..
s x + y
vn n
l
n=0,2,4,.
svnxn (6-9)
t+ are q independent electronic wavefunctions
x are harmonic oscillator functions in coordinate q
n ^
r and s , are coefficients of harmonic oscillator
vn vn
functions
± designates the symmetries of the wavefunctions with an
interchange of nuclei
v designates a given vibronic wavefunction
are
H
mn
H
mn
From these wavefunctions two sets of secular equations
derived.
00
y r (H - 6 E ) = 0
Ln vn mn mn v
n=0
m=0,1,2,...
n=0,1,2,...
(6.10)
= X [ (m/2) 26 , -i + (m+1/2) ^6 . ] + (m+h~ (-1) me) 8 „
m,n+l m,n-i m,n
Y s (H - ó E )
vn mn mn v
n=0
= X[(m/2) 26 .. +
m, n+l
q m=0,1,2,... (6.11)
v=0,1,2,...
(m+1/2)^6 n ,] + m+h+(-1)me)6 n
m,n-i m, n

53
Solving the secular equations for a given X and e yields
values for the vibronic energy levels from which transitions
can occur. Selection rules allow for I -*â–  + transitions.
For asymmetric mixed-valence systems, the vibronic
wavefunctions are given below.
$v = I ^+rvnxn + 'i'-r;nXn) (6-L
n=0
where the symmetry in $v upon interchange of the nuclei has
been lost. The secular equations are
1 rvn(Hmn “ ^mnEv) + I rvnHmn ®
n=0 n=0
I rvn (Hmn
n=0
+
oo
l
n=0
r,._H"
vn mn
0
m = 0,1,2,...
v = 0,1,2,...
where Hmn = (m+*s+e) ¿>mn, H,^ = and
Him - X[(m/2)!56m,n+l + + W6m,n' Solvin9 the
secular equations for a given A, e and W yields values for
the vibronic energy levels from which transitions can occur.
The selection rules vanish with the asymmetry, and transition
may occur between any two energy levels.
Once the energy levels are determined, the intensities
of the transitions (dipole strengths) are calculated.
(Nv.-Nv)
A(v’+v)
N
62,v(e2R2/4)
(6.14)

54
where
N
v'
-E ,/KT
e v'
(6.15)
N
Z e(-E ,/KT)
v' v
for the symmetric case
6
(6.16)
v' v
and the asymmetric case
6
v' v
. r ' + r ' , r
v'n vn v'n vn
(6.17)
These calculations yield the stick spectrum for the interva¬
lence absorption. The intervalence transfer band contour is
generated by converting each of the sticks into a gaussian
curve and summing the intensities.
The thermal rate constants are calculated:
-E+/KT -E~/KT
v . v
oo
l (AEV)2 (e
v=0
)
+ e
(6.18)
P
v=0
and the potential surfaces (classical) may be generated
(6.19)
W
1,2
for a given X, e and v_.
The PKS theory neglects contributions from the solvent
(X ) in treating experimental intervalence transfer data.

55
Although this approximation may be valid in moderately cou¬
pled systems where solvent effects are small [13], the same
cannot be justified for weakly coupled systems. This limits
applicability of the PKS theory to the former. The harmonic
oscillator approximation and the consideration of only
totally symmetric vibrational modes in the derivation of the
PKS theory are good approximations for systems where the bond
length changes are small and gross symmetries are maintained
around the metal centers.
Thus it seems that the PKS theory would give a good
description for delocalized systems where the coordination
environment remains relatively constant. However, care must
be taken in applying such a simple model to systems where the
coupling energy approaches in magnitude the energies EQp and
Ea. Electronic coupling can no longer be described accurately
by a simple parameter e and factors such as the nature of the
bridge and molecular orbitals must be taken into account [53] .
Discussion
The Hush theory has been applied to numerous mixed-
valence systems localized and delocalized. It has been shown
to give a good interpretation of intervalence transfer in
localized complexes as demonstrated by comparison of rate
constant data derived from the intervalence transfer absorp¬
tion with rate constant data measured or estimated by other
means [9,10,54-56]. Powers and Meyer [57] have shown that
solvent contributions can be determined by separating the

56
intervalence transfer energy into inner-sphere (A^n) and
outer-sphere (^out) components using a dielectric continuum
model to describe the latter [13]. They have shown solvent
contributions to be small or zero for delocalized systems and
to be sizeable for localized systems. In some cases, however,
where solvent contributions were determined to be very small,
E values (from of similar complexes) were estimated to
be much smaller than the experimental values. Thus caution
should be taken when separating EQp into inner-sphere and
outer-sphere contributions as this is not always a good
approximation.
The PKS theory has not been explored to the extent of
the Hush theory, although Tanner and Ludi [58] have applied
the PKS theory to several systems localized and delocalized.
The intensities of the delocalized systems were always much
larger than expected when normalized to the localized systems.
When the intensities of the localized systems were normalized
to the delocalized systems, the calculated intensities were
much smaller than the experimental, and the bands were highly
asymmetrical. However, they did get expected trends when NH^
terminal ligands were replaced with bpy ligands. Although
the PKS theory may not give a good description for highly de¬
localized systems, it does provide a means of correlating IT
properties with structure.

CHAPTER VII
INTERVALENCE TRANSFER OF DIMERS
Introduction
This chapter describes in detail the gathering and
treatment of experimental intervalence transfer data for
three series of ruthenium mixed-valence dimers. The experi¬
mental data are interpreted using both the Hush and PKS
theories, and the results of these treatments are evaluated.
Experimental
Intervalence transfer spectra were obtained as described
in Chapter II for the following mixed-valence dimers:
1) [(bpy)2Ru(BiBzIm)Ru(bpy)2]
2) [(R2~bpy)2Ru(BiBzIm)Ru(bpy)2]3+
3) [(R2~bpy)2Ru(BiBzIm)Ru(R2~bpy)2]
R = me, ph and ome
Bibenzimidazole bridged dimers were oxidized to the III/II
mixed-valence state via one-electron electrolysis of the
II/II complex. Bipyrimidine bridged dimers were unstable to
oxidation and the mixed-valence species could not be studied
optically. Electrolysis was performed by maintaining solution
57

58
potentials 150 mV higher than E, for a given couple. Oxida-
^S
tion was determined complete when a stoichiometric number of
electrons had passed through the electrochemical solution.
Final solution potentials ranged randomly from 50-100 mV
higher than the corresponding E^ values. Solutions of the
II-II species were red-orange and turned yellow upon one-
electron oxidations and blue upon two-electron oxidations.
To determine the actual concentrations of the mixed-
valence species in solution after electrolysis is necessary
to evaluate conproportionation constants Kc [59] for the
reactions
III-III + II-II 2(III-II)
Kc = [III-II]2/[III-III][II-II] S exp[38.9(E1-E2)]
where E^ and E^ are the half-wave potentials for the
III-III/III-II and the III-II/II-II couples, respectively.
Potential differences between successive oxidations are in
all cases greater than 250 mV, giving rise to very large Kc
values. For this reason it is not necessary to correct the
sample concentrations for the above equilibrium.
Intervalence transfer spectra for the bibenzimidazole
bridged complexes are presented in Figures 7.1, 7.2 and 7.3.
Haga [34] has previously observed the infrared spectrum for
the unsubstituted dimer and assigned the absorption at
1950 nm to the intervalence transfer transition.
From the spectra it is observed that substituent effects
are relatively small for the symmetric complexes, affecting

e (M
Figure 7.1. Near Infrared Spectra of [(R -bpy)„Ru(BiBzIm)Ru(R'-bpy)9]3+ in 0.1 M
TBAH/CD3CN (Methyl Series). ¿ ¿

3+
Figure 7.2. Near Infrared Spectra of [(R„-bpy)~Ru(BiBzIm)Ru(R'-bpy)„]
TBAH/CD3CN (Phenyl Series). ¿ ¿ ¿
in 0.1 M

3+
Figure 7.3. Near Infrared Spectra of [(R^-bpy)_Ru(BiBzIm)Ru(R'-bpy)«]
TBAH/CD3CN (Methoxy Series). ¿ ¿ ¿
in 0.1 M

62
the intensities and band máximums only slightly. This is
not so, however, for the asymmetric complexes where substit¬
uent groups are observed to have pronounced effects (for
R = one and me) on both the intensities and the band máxi¬
mums. The magnitudes of the substituent effects increase in
the order R = ph, me and ome. This same ordering is
observed with the oxidation half-wave potentials (Chap¬
ters IV and V).
The II-II complexes give no absorptions in the region of
the intervalence transfer absorptions, and the III-III com¬
plexes give only weak absorptions in this region which are
presumed to originate from the presence of small concentra¬
tions of the III-II mixed-valence species.
Hush Treatment
Data from the intervalence transfer spectra (v , e
c max
and Av, ) are recorded in Table 7.1 along with calculated
Hush parameters. Values of Eq for the asymmetric complexes
are calculated from equations (6.5), (6.6) and (6.7). From
equation (6.3) Av, is calculated for comparison with the
experimental value. The valence delocalization parameter a2
is calculated from equation (6.4), assuming an internuclear
O
separation (R) of 5.455 A [60] [estimated from crystal
structure data of biimidazole bridged rhodium(I) dimer].
A criterion for application of the Hush theory is that
the calculated half-width of the intervalence transfer band
be smaller than the experimental value [4]. This puts a

Table 7.1.
Intervalence Transfer Data and Hush Parameters
for the Mixed-Valence Dimers
[(R2~bpy)2Ru(BiBzIm)Ru(R^-bpy)]^+.
R
R'
vmax (cm'1)
e (m-1)
Av^ (expt)
Av^ (calc)
i
g
o
EQ (cm-
H
H
5130
4440
2370
3440
5130
0
me
me
4950
4850
2770
3380
4950
0
ph
ph
4870
4360
2120
3350
4870
0
ome
ome
4830
4950
2260
3340
4830
0
H
me
5650
2830
3210
3410
5040
610
H
ph
5050
3540
2240
3400
5000
50
H
ome
6750
2350
3860 .
3390
4980
1770

64
lower limit on the experimental half-width as band broaden¬
ing (due to solvent effects [55]) causes the experimental
value to be larger than predicted [4], From Table 7.1 it is
observed that only the last complex listed meets this crite¬
rion. This is reasonable because asymmetry leads to valence
trapping, and this complex has the largest Eg. It is con¬
cluded that all but perhaps one of the above complexes are
too delocalized for the Hush treatment to apply.
PKS Treatment
The PKS calculations were carried out in collaboration
with Cliff Stodden of the Quantum Theory Project, University
of Florida. The QTP VAX computer system was used to gener¬
ate theoretical spectra.
Intervalence transfer spectra were entered into the
computer in digital form. By varying the PKS parameters X,
e, W and v_, the theoretical spectra could be manipulated
to give a best fit of the experimental spectra. Initial
(starting) parameters were calculated [4].
W
£
X
V,
Eg (cm-1)/v _
v /2v_
max
£^
- assuming a delocalized system
500 cm
-1
By choosing £ and X values, the matrix correspond¬
ing to the totally symmetric vibronic wave functions is
generated using equation (6.10) (Figure 7.4).

X
o
o
H01
0
0
0
• • •
h+e
Aa
0
0
0
Hio
H11
H12
0
0
• • •
/JA
l-e
2 t
A
0
0
0
H21
H22
H2 3
0
• • •
0
/Fa
/I A
2
0
• •
0
0
H32
H33
H34
• • •
0
0
/|A
2_e
2
/F A
• •
0
0
0
•
•
H43
H44
•
•
•
• • •
0
0
0
/Fa
f+e
• •
Figure 7.4. Matrix H for Totally Symmetric Vibronic Wavefunction (PKS Theory)

ES
0
0
0
0
* • •
roo
i—i
o
5-1
CN
O
S-)
r03
r04
• • •
0
Ei
0
0
0
. . .
rio
ril
ri2
r13
r14
• • •
0
0
E2
0
0
• * •
r =
vn
r20
r21
r22
r23
r24
• • •
0
0
0
E+
E3
0
• • •
r 30
r31
r 32
r3 3
r34
• • •
0
0
0
0
E+
• • •
r40
r41
r42
r4 3
r44
• • •
•
•
•
•
•
*
•
•
•
•
•
•
•
•
•
•
•
•
•

CTi
Figure 7.5.
Energy Matrix E+ and Coefficient Matrix rvn
(PKS Theory).

67
Diagonalization of this matrix yields the energy matrix E*
and coefficient matrix r^n (Figure 7.5). Using equation
(6.11) the matrix Hmn corresponding to the asymmetric
vibronic wavefunction is diagonalized forming the energy
matrix E and coefficient matrix s
v vn
The r and s values are the coefficients for the
vn vn
vibronic wavefunctions given by equations (6.8) and (6.9)
with eigenvalues E+ and Ey/ respectively. Figure 7.6 dia¬
grams the energy levels and transitions following the ± -> +
selection rule.
The relative populations of energy levels are calculated
using the Boltzman distribution given in equation (6.14), and
the intensities are calculated from equations (6.14) and
(6.16). This gives the stick spectrum for the IT transition.
Each transition of energy v has an intensity I associated
with it and is converted to a gaussian curve with a half¬
width (A) given in units of v_. The sum of these gaussian
curves comprises the IT transition.
For asymmetric species generation of the theoretical
spectra is complicated by the introduction of the asymmetry
term W. From equations (6.13) H , H ' and H " values are
^ mn mn mn
calculated for a given X, e and W. These form a matrix H,
diagrammed in Figure 7.7. This matrix is twice the size as
that given for the symmetric case for a given number of
energy levels. Diagonalization of this matrix gives the
energy matrix E^ and the coefficient matrix containing r^n
and r' (Figure 7.8).

68
tunneling
transitions
IT
transitions
Figure 7.6. Allowed Transitions for Intervalence Transfer
Absorption—Symmetric Case.

69
H
Figure 7.
•
•
•
II
Hmn
Hmn
•
•
•
•
Hmn"
•
•
•
Hmn’
•
•
•
•
Schematic for H Matrix in the Asymmetric PKS
Calculation.

Eo
0
0
0
• • •
o
o
U
roi
r02
• • •
0
E1
0
0
• • •
rio
rll
r12
• • •
0
0
E2
0
• • •
r20
r21
r22
• • •
0
0
0
E3
• • •
•
•
•
•
•
•
•
•
•
•
9
•
Coeff =
r1
00
r'
01
r'
02
• • •
matrix
r'
10
rll
r 1
12
• • •
r1
20
r'
21
r'
22
• • •
Figure 7.8. Energy and Coefficient Matrix for Asymmetric PKS Calculation

71
The coefficients r and r' represent the vibronic
vn vn
wave-functions given by equation (6.12) with eigenvalues E .
In the asymmetric case the - -*â–  + selection rule no longer
holds and transitions are allowed to occur between all
levels. Relative populations, intensities, and intervalence
transfer band contours are calculated in a similar manner as
for the symmetric case.
In simulating the intervalence transfer spectra, the
parameter v_ was first determined. The effect of this param¬
eter was to "rock" the intervalence transfer band. Increase-
ing v_ caused the band to tail off in the low energy region
and to sharpen in the high energy region. A value of
360 (cm-1) for was determined to be consistent with the
experimental data. Once v_ had been determined the param¬
eters X and e were varied to get the best fit. The effect of
increasing X was to shift the band to higher energy and to
broaden it by lowering the intensity. The effect of increas¬
ing e was to shift the spectra to higher energy and to narrow
it by increasing the intensity. The simulated spectra were
very sensitive to the parameters X and e and not so sensi¬
tive to v_. For the asymmetric species the parameter W (Eg
in the Hush theory) had to be included. Since W was hard to
determine by trial and error, electrochemical data from
Chapter V were used to estimate these parameters. Since
redox potentials give a measure of the potential of an elec¬
tron at a given site, it was assumed that W could be estim¬
ated from redox potentials involving the mixed-valence state.

72
The potential difference between the sites (W) was cal¬
culated for the asymmetric complexes as the difference
between the first oxidation potentials for the corresponding
symmetric complexes. Similar values were obtained from the
second oxidation potentials, and the average values were
taken as W.
Experimental and PKS "best fit" intervalence transfer
spectra are presented in Figures 7.9-7.15. The PKS generated
spectra fit reasonably well with the experimental spectra
and the "best fit" parameters are listed in Table 7.2. For
the asymmetric species it was found that W values calculated
from electrochemical data generated the best overall spectra.
This reinforces the viability of the PKS theory for this
series of compounds.
The PKS parameters X, e and W were used to generate
"classical" potential surfaces from which the intervalence
transfer transitions occur and are presented in Figures 7.16-
7.22. Thermal electron transfer rate constants were calcu¬
lated using equation (6.18) and are presented in Table 7.2.
The small thermal electron transfer barriers are consistent
with the high thermal rate constants and indicate a fairly
high degree of valence delocalization. More important is
the fact that finite barriers do exist for the thermal elec¬
tron transfer process.
Thus it seems that the PKS theory gives a good descrip¬
tion of these systems which are moderately delocalized. As
mentioned in Chapter VI, applicability of the PKS theory
falls off as the systems become strongly delocalized.

73
R = R' = H
4000
3000
2000
£ (M-1)
1000
Figure 7.9. Experimental and Theoretical (PKS) Intervalence
Transfer Spectra for [(R--bpy)_Ru(BiBzIm)Ru(R'-
bpy)2]3+- R=R'=H. 2 ¿

4000
3000
e (M-1)
2000
1000
Figure 7.10. Experimental and Theoretical (PKS) Interva¬
lence Transfer Spectra for
[(R2-bpy)2Ru(BiBzIm)Ru(R2-bpy)2]
R=R'=me.

75
R = R' = ph
4000
3000
£ (M-1)
2000
1000
Figure 7.11. Experimental and Theoretical (PKS) Intervalence
Transfer Spectra for
[(R2“bpy)2RU(BiBzIm)Ru(R^-bpy)2j + . R=R'=ph.

76
R = R' = ome
4000
3000
e (M- 1)
2000
1000
Figure 7.12. Experimental and Theoretical (PKS) Intervalence
Transfer Spectra for
[(R2-bpy)2Ru(BiBzIm)Ru(R^-bpy)2]3+. R=R'=ome.

77
R = H; R' = me
Figure 7.13. Experimental and Theoretical (PKS) Intervalence
Transfer Spectra for
[(R2~bpy)2Ru(BiBzIm)Ru(R2-bpy)2]3+.
R=H; R'=me.

78
R = H; R' = ph
4000
3000
e (M-1)
2000
1000
Figure 7.14. Experimental and Theoretical (PKS) Intervalence
Transfer Spectra for
[(R2~bpy) 2RU (BiBzIm) Ru (R^-bpy) 2] J + . R=H; R'=ph.

79
R=H; R'=ome
4000
3000
e (M_1)
2000
1000
Figure 7.15. Experimental and Theoretical (PKS) Intervalence
Transfer Spectra for
[(R2~bpy)2Ru(BiBzIm)Ru(R^-bpy) ]3+. R=H;
R'=ome.
X (nm/100)

80
Table 7.2. PKS Parameters for [(R0-bpy)Ru(BiBzIm)Ru(R'-
bpy)„]3+. 2 2
R
R'
X
H
H
3.01
me
me
2.95
ph
ph
2.87
ome
ome
2.91
H
me
2.46
H
ph
2.95
H
ome
2.25
KxlO-12
e
W
(s"1
-6.46
-
6.9
-6.22
-
7.2
-6.12
-
8.4
-5.99
-
7.2
-5.97
2.25
-
-6.30
0.42
-
-1.69
5.25
—

81
R = R' = H
q
Figure 7.16. Potential Surfaces for
[ (R2-bpy) 2Ru (BiBzIm) Ru (RJj-bpy) 21 3 + .
Energy vs. Breathing Mode q. R=R'=
Potential

82
R = R' = me
q
Figure 7.17. Potential Surfaces for 2+
[(R2-bpy)2Ru(BiBzIm)Ru(R^-bpy)2] • Potential
Energy vs. Breathing Mode q. R=R'=me.

83
R = R' = ph
Figure 7.18. Potential Surfaces for
[(R2-bpy)2Ru(BiBzIm)Ru(R¿-bpy)2]3+. Potential
Energy vs. Breathing Mode q. R=R'=ph.

84
R = R' = ome
Figure 7.19. Potential Surfaces for
[(R2~bpy)(BiBzIm)Ru(R^-bpy)2 J +* Potential
Energy vs. Breathing Mode q. R=R'=ome

85
R = H; R' = me
Figure 7.20. Potential Surfaces for
I(R2~bpy)2Ru(BiBzIm)Ru(R2-bpy)213+• Potential
Energy vs. Breathing Mode q. R=H; R'=me.

86
R = H; R' = ph
q
Figure 7.21. Potential Surfaces for
[(E^-bpy) (BiBzIm) Ru (R^-bpy) 2 ] J • Potential
Energy vs. Breathing Mode q. R=H; R'=ph.

87
R = H; R' = ome
q
Figure 7.22. Potential Surfaces for
[(R2~bpy)(BiBzIm)Ru(R^-bpy)2]
Energy vs. Breathing Mode q. R=H;
Potential
'=ome.

88
Therefore it is likely that the complexes studied here repre¬
sent the delocalized limit for applicability of the PKS
theory.

CHAPTER VIII
NEAR INFRARED STUDIES OF MONOMER MONOCATIONS
Introduction
Through temperature dependent ESR studies, Motten et
al. [40] have observed small electron-hopping barriers be-
2+
tween the bipyridine ligands in the excited [Rulbpy)^]
complex. Assuming Koopman’s theorem to compare the mono¬
cation with the excited dication, these studies predict an
electron transfer absorption in the near infrared region.
Elliott [14] has observed near infrared absorption for
2 +
the reduced forms of the [Ru(es2~bpy)^] ion. These absorp¬
tions are similar in nature (broad and occurring in the near
infrared spectrum) to the intervalence transfer transitions
of the mixed-valence dimers. Since reductions of these mon¬
omeric species are ligand-centered, it was proposed that
these transitions originate from intra- or inter-ligand
electron hopping [14]. If the latter mechanism is accurate,
these absorptions will be closely related to the electro¬
chemical studies of Chapter V. Near infrared studies were
performed on a series of mixed-ligand monocations,
[Ru(es2-bpy)n(bpy)3_n]+ to further explore this phenomenon.
89

90
Experimental
Near infrared spectra were obtained as described in
Chapter II for the following complexes.
1) [Ru(bpy)2(es-bpy)]+
2) [Ru(bpy) (es2~bpy)2] +
3) [Ru(e s 2 ~bpy)3 3 +
All other monomer species were unstable upon reduction and
could not be studied optically. Electrolysis was performed
by maintaining solution potentials 150 mV higher than E^ for
the redox couple until a stoichiometric number of coulombs
had passed through the electrochemical solution. Solutions
of the reduced species were a dull red-orange color. Near
infrared spectra for the monocations are shown in Figure 8.1
Due to the relative instability of these complexes, it was
impossible to obtain accurate extinction coefficients.
Discussion
Due to the lack of reliable spectra through a series,
no conclusions can be drawn toward the nature of the infra¬
red absorptions demonstrated by the mixed-ligand monocations
What is significant is the fact that the mixed-ligand com¬
plexes do demonstrate absorptions in this region, and with
more complete study the nature of these absorptions may be
elucidated. Temperature dependent EPR studies of the
excited mixed-ligand monomers may also prove fruitful.

91
Figure 8.1
Near Infrared Spectra of [Ru(es2-bpy) (bpy)3_m]+
in 0.1 M TBAH/CH3CN.

CHAPTER IX
SUMMARY
In mixed-valence complexes where strong electronic cou¬
pling exists between metal centers, it is often difficult to
determine whether the unpaired electron is localized or
delocalized. The Creutz-Taube ion [61] is an example of
such a complex. Numerous studies have been performed on
this complex and indicate both the localized [62-67] and
delocalized [7-9,68] descriptions. The PKS model was used
to fit the intervalence transfer spectrum of this complex but
was unable to account for the broad tail in the high energy
region [7]. From these studies, however, it was determined
that the Creutz-Taube ion is strongly delocalized.
Although the PKS theory may not give an accurate
description of electron transfer in strongly delocalized
systems, we have demonstrated that it can give a fair
description for moderately delocalized systems where some
degree of valence trapping still exists. Electrochemical
techniques developed here for estimation of degree of valence
trapping yield results consistent with the PKS theory. These
electrochemical techniques need to be explored further with
systems of varying degrees of delocalization. Reinforced
with PKS calculations studies of this nature may provide a

93
powerful probe for exploring electron transfer in moderately
coupled systems.
These studies have demonstrated that the PKS theory can
be applied successively to asymmetric mixed-valence complexes
where asymmetry is introduced by substitution onto the termi¬
nal ligands. The substituent groups do not change the coor¬
dination around the metal centers but do perturb the potential
energy. This allows for straight forward interpretation and
comparison of experimental data.
Near infrared absorptions, similar in nature to those
observed in binuclear mixed-valence complexes, have been
observed in the reduced forms of mononuclear complexes [14].
Temperature dependent ESR studies [40] may provide valuable
information toward the origin of these absorptions.

REFERENCES
1. M. B. Robin and P. Day, Adv. Inorg. Radiochem. , 1_0, 247
(1967) .
2. G. C. Allen and N. S. Hush, Prog. Inorg. Chem. , 8^, 357
(1967).
3.
N. S. Hush, Prog. Inorg. Chem., 8,
391 (1967).
4.
C. Creutz, Prog. Inorg. Chem., 30,
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BIOGRAPHICAL SKETCH
Skiles Albert Montague was born August 18, 1956, in
Merced, California. After traveling to and fro for several
years, he ended up at Potomac State College in Keyser,
West Virginia, where he studied during his first two years
of college. From there he transferred to The Pennsylvania
State University where he received his B.S. in chemistry in
1978. Distraught by the cold and in pursuit of his Ph.D.,
he transferred to the chemistry department at the University
of Florida. He is presently attending medical school at the
University of Miami—Class of 1987.

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.
/JL—
Eric V. Dose, Chairman
Assistant 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.
Jw 0< ÚbA
Samuel 0. Colgate
Associate 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.
R. Carl Stoufer //
Associate 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.
Assistant 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.
David A. Drake
Professor of Mathematics
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 Council, and was accepted
as partial fulfillment of the requirements for the degree of
Doctor of Philosophy.
April 1984
Dean for Graduate Studies and
Research

UNIVERSITY OF FLORIDA
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