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Spectroscopic investigations of metal clusters and metal carbonyls in rare gas matrices

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Title:
Spectroscopic investigations of metal clusters and metal carbonyls in rare gas matrices
Creator:
Bach, Stephan Bruno Heinrich, 1959-
Publication Date:
Language:
English
Physical Description:
xiv, 187 leaves : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Argon ( jstor )
Atoms ( jstor )
Electron paramagnetic resonance ( jstor )
Electrons ( jstor )
Line spectra ( jstor )
Magnetic fields ( jstor )
Molecules ( jstor )
Neon ( jstor )
Orbitals ( jstor )
Perpendicular lines ( jstor )
Electron paramagnetic resonance ( lcsh )
Fourier transform infrared spectroscopy ( lcsh )
Matrix isolation spectroscopy ( lcsh )
Metal carbonyls ( lcsh )
Metal crystals ( lcsh )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1987.
Bibliography:
Includes bibliographical references (leaves 178-186).
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Stephan Bruno Heinrich Bach.

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University of Florida
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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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021938232 ( ALEPH )
AFB9323 ( NOTIS )
18287365 ( OCLC )

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SPECTROSCOPIC INVESTIGATIONS OF
METAL CLUSTERS AND METAL CARBONYLS
IN RARE GAS MATRICES














By

STEPHAN BRUNO HEINRICH BACH


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


1987



































TO MY PARENTS










ACKNOWLEDGEMENTS

The author wishes to extend his deepest thanks and

appreciation to Professor William Weltner, Jr., whose

patience, understanding, encouragement, and professional

guidance have made all of this possible. Thanks are also due

to Professor Bruce Ault for the initial opportunity do matrix

work and the encouragement to continue on to do graduate work

in the field. Thanks need also be given to Professor

Weltner's research group, specifically to Dr. Richard Van

Zee, whose help and guidance were invaluable in completing

this work.

The author also wishes to acknowledge the assistance of

the electronics, machine, and glass shops within the

Department of Chemistry. They kept the equipment

functioning, and fabricated new pieces of apparatus when

necessary making it possible to perform the desired

experiments. Thanks are also due to Larry Chamusco for many

enlightening conversations regarding the present work and

also for his help in preparing this work for publication.

Thanks are also due to Ngal Wong for his assistance in

preparing the final version of this publication.

The author also wishes to acknowledge the support of

the National Science Foundation (NSF) for this work as well

as Division of Sponsored Research for support in completing

the work for this project.


iii













TABLE OF CONTENTS
page

ACKNOWLEDGEMENTS ...................................... ii

LIST OF TABLES .......... ......... ..................... vii

LIST OF FIGURES ........................................ ix

ABSTRACT .................................................. xiii

CHAPTERS

I INTODUCTION .................................. 1

Matrix Isolation ........................ 1
Theory of Cluster Formation ........... 19
ESR Theory .............................. 30
The Hyperfine Splitting Effect ..... 34
Doublet Sigma Molecules ............ 40
The spin Hamiltonian ............ 40
The g tensor ...................... 42
The A tensor ...................... 46
Randomly oriented molecules ...... 49
Molecular parameters and
the observed spectrum .......... 51
Spin densities .................. 56
Quartet Sigma Molecules (S=3/2) .... 58
The spin Hamiltonian ............ 59
Sextet Sigma Molecules ............ 66
The spin Hamiltonian .............. 66
Infrared Spectroscopy ................ 67
Theory ................................ 70
Fourier Transform IR Spectroscopy .. 76

II METAL CARBONYLS ............................... 79

ESR of VCO, Molecules ................. 79
Introduction ..................... 79
Experimental ......................... 80
ESR Spectra ....................... 81
V CO .. .. .. .. .. 8 1
51VCO(A) and 5VCO(a) in argon ... 81
51V13CO(A) and 51V13CO(a) in argon 82
51VCO(A) in neon ................ 82
51VCO(a) in krypton .............. 88
51V(12CO)2 and V(13CO)2 in neon 89
51V(12C0)3 and 51V(13CO)3 in neon 89















Analysis ......
VCO, (A) and
V(CO)2 ......
V(CO)3 ......
Discussion ....
VCO .........
V(CO)2 ......
V(CO)3 ......
Conclusion ....
Infrared Spectrosc
Transition Metal
Introduction
Experimental
Spectra .......
Discussion ....
Conclusion ....


(


...........
a ) .. .











py of First
Carbonyls.........
...........
...........
...........
...........
............
py of First
Carbonyls .
...........
...........
...........
...........
...........


III ESR STUDY OF A SILVER SEPTAMER .............


Introduction ..........................
Experimental ..........................
ESR Spectra ...........................
Analysis and Discussion ...............


IV ESR OF METAL SILICIDES .....................


ESR of AgSi and MnSi ......
Introduction ...........
Experimental ...........
ESR Spectra ............
AgSi .................
MnSi .................
Analysis and Discussion
A gS i ...... .. ..... ....
MnSi .................
ESR of Hydrogen-Containing
Silicon Clusters ........
Introduction ...........
Experimental ...........
ESR Spectra ............
HScSiHn ..............
H2ScSIHn .............
Analysis and Discussion
HScSiHn ..............
H2ScSiHn .............


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....
....






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....
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...
....
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....
....


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Row

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96
96
98
98
100
100
106
107
108


109
109
109
110
115
119


121


121
122
123
129


137


137
137
137
138
138
139
139
139
145


148
148
149
150
150
156
157
157
166


...
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um-

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page

V CONCLUSION.... ............................... 172

REFERENCES ........................................... 178

BIOGRAPHICAL SKETCH .................................. 187










LIST OF TABLES


Table Page

II-1. Observed and calculated line positions (in G)
for VCO (X6E) in conformation (A) in argon at
4 K. v = 9.5596 GHz ............................. 83

11-2. Observed and calculated line positions (in G)
for VCO (X6O) in conformation (a) in argon at
4 K. v = 9.5596 GHz ............................. 84

11-3. Observed line positions (in G) for VCO (X6O)
in conformation (A) in neon at 4 K.
v = 9.5560 GHz................................... 90

11-4. Observed and calculated line positions (in G)
for V(CO)2 (X4 g) isolated in neon at 4 K.
v = 9 .5560 GHz ................................. 91

11-5. Calculated and observed line positions and
magnetic parameters of the V(CO)3 molecule
in neon matrix at 4 K. v = 9.55498 GHz........... 92

II-6. Carbonyl Stretching Frequencies for the First
Row Transition Metal Carbonyls................... 112

III-1. Calculated and observed ESR lines of 109Ag7 in
solid neon at 4 K (v = 9.5338 GHz)
See Figure III-3 ................................. 125

III-2. Magnetic parameters and s-electron spin
densities for 109Ag7 cluster in its A2
ground state.(a) ............................. 131

III-3. Comparison of the magnetic parameters of
107Ag7 (this work) with those of Howard,
et al s 107Ag5 cluster ......................... 135

III-4. Spin densities (s-electron) compared for the
2A2 ground states of the Na7, K7, and Ag7....... 136

IV-1. Observed and Calculated Line Positions (in Gauss)
for AgSi in argon at 14 K. (v = 9.380 GHz)...... 140

IV-2. Observed and Calculated Line Positions (in Gauss)
for MnSi in argon at 14 K. (v = 9.380 GHz)...... 141

IV-3. Hyperfine parameters and calculated spin densities
for MnSI in argon at 14 K. (v = 9.380 GHz)...... 147


vii








page


IV-4. Observed and calculated line positions (in Gauss)
for HScSiHn in argon at 14 K. (v = 9.380 GHz)... 151

IV-5. Hyperfine parameters and calculated spin densities
for HScSiHn in argon at 14 K. (v = 9.380 GHz)... 152

IV-6. Observed and Calculated Line Positions (in
Gauss) for H2ScSiHn, the (A) site, in argon
at 14 K. (v = 9.380 GHz) ........................ 158

IV-7. Hyperfine parameters and calculated spin
densities for H2ScSiHn, site (A), in argon
at 14 K. (v = 9.380 GHz)......................... 159

IV-8. Observed and Calculated Line Positions (in
Gauss) for H2ScSIHn, the (a) site, in argon
at 14 K. (v = 9.380 GHz) ........................ 160

IV-9. Hyperfine parameters and calculated spin
densities for H2ScSiH,, site (a), in argon
at 14 K. (v = 9.380 GHz)......................... 161


viii











LIST OF FIGURES


Figure Page

I-1. The furnace flange with copper electrodes and
a tantalum cell attached......................... 10

1-2. The EPR cavity and deposition surface within
the vacuum vessel. The apparatus is capable
of cooling the rod to 4 K, because of the
liquid helium transfer device (Heli-Tran)
on the top ........................................ 11

I-3. The ESR cavity and deposition surface within
the vacuum vessel. The apparatus is capable of
cooling to 12 K because of the closed cycle
helium refrigeration device (Displex) on the
t o p . . .. 1 2

1-4. The vacuum vessel, deposition surface, Displex,
and furnace assembly for infrared experiments... 13

I-5. Zeeman energy levels of an electron interacting
with a spin 1/2 nucleus ......................... 52

1-6. (a) Absorption and (b) first derivative line-
shapes of randomly oriented molecules with
axial symmetry and gj (c) first derivative lineshape of randomly
oriented, axially symmetric molecules
g- with a spin 1/2 nucleus (A
1-7. Energy levels for a 4E molecule in a magnetic
field; field perpendicular to molecular axis.... 63

1-8. Energy levels for a 4E molecule in a magnetic
field; field parallel to molecular axis......... 64

1-9. Resonant fields of a 4E molecule as a function
of the zero field splitting...................... 65

1-10. Energy levels for a 6E molecule in a magnetic
field for 9 = 0, 30, 600, and 90 ............ 68

1-11. Resonant fields of a 6E molecule as a function
of the zero field splitting...................... 69








page


II-1. ESR spectrum of an unannealed matrix at 4 K
containing 51VCO(A), with hfs of about 100 G,
and 51VCO(a), with hfs of about 60 G. For the
conformation (A) two perpendicular lines and
an off principle axis line are shown.
v = 9.5585 GHz.................................. 85

11-2. ESR spectrum of an annealed argon matrix at 4 K
containing only 51VCO in conformation (a). Two
perpendicular lines and off principal axis
line are shown. v = 9.5585 GHz.................. 86

11-3. ESR spectrum of the perpendicular xy1 line of
51V13CO in conformation (a) in an argon matrix
at 4 K. v = 9.5531 GHz ......................... 87

11-4. ESR lines in a neon matrix at 4 K attributed to
51VCO in conformation (A). v = 9.5560 GHz...... 93

11-5. ESR lines in a neon matrix at 4 K attributed to
51V(CO)2. v = 9.5560 GHz ....................... 94

11-6. (Top) ESR spectrum near g=2 in a neon matrix
at 4 K attributed to an axial 51V(CO)3 molecule.
v = 9.5584 GHz.
(Bottom) Simulated spectrum using g, A(51V)
parameters and linewidths given in the text.... 95

11-7. Molecular orbital scheme for the 6z VCO
molecule (modeled after Fig. 5-43 in DeKock
and Gray (84 )) .................................. 101

11-8. Infrared spectrum of CrCO using both 12CO and
13CO in argon. The top trace has a 1:200 CO/Ar
concentration and the bottom has a 1:1:200
12C0/13CO/Ar concentration ..................... 113

11-9. Infrared spectrum of Mn and CO codeposited into
an argon matrix. The bottom trace is after
annealing the matrix to about 30 K and cooling
back down to 14 K............................... 114

II-10. Plot of the CO stretching frequencies in the
first row transition metal monocarbonyl
molecules MCO (circled points are tentative).
Also shown is the variation of the energy of
promotion corresponding to 4s23dn-2 to 4sl3dn-,
where n is the number of valence electrons(91). 117








page


III-1. The pentagonal bipyramid structure ascribed to
Ag7 in its 2A2 ground state. It has D5h symmetry
with two equivalent atoms along the axis and
five equivalent atoms in the horizontal plane.. 126

III-2. The ESR spectrum of 109Ag in solid neon matrix
at 4 K (v = 9.5338 GHz). The top trace is the
overall spectrum, and the bottom traces are
expansions of the three regions of interest
after annealing. Notice the large intensity
of the silver atom lines at 3000 G before
annealing ...... ................................ 127

III-3. The ESR spectrum of 109Ag7 in a solid neon
matrix at 4 K (v = 9.5338 GHz). The fields
indicated are the positions of the four
hyperfine lines corresponding to
IJ,Mj> = 11,1>, 11,0>, 10,0>, and 11,1>
(see Table III-1). The spacing within each of
the four 6-line patterns is uniformly 8.7 G.
The few extra lines in the background of the
lines centered at 3006 G are due to residual
109Ag atom signals.............................. 128

IV-1. The ESR spectrum of AgSI is an argon matrix at
12 K. The line positions of the impurities (CH3
and SlH3) are noted. v = 9.380 GHz ............. 142

IV-2. The ESR spectrum of MnSI in an argon matrix at
12 K. v = 9.380 GHz ............................ 143

IV-3. The ESR spectrum of Sc codeposited with Sl into
an argon matrix at 12 K. The eight sets of
doublets are shown for HScSiHn. v = 9.380 GHz.. 153

IV-4. The mi= -1/2 and -3/2 transitions for HScSiHn
at 12 K. Two different rod orientations are shown.
The top is with the rod parallel to the field and
the bottom trace is for the rod perpendicular to
the field. v = 9.380 GHz ....................... 154

IV-5. The ESR spectrum in the g=2 region after
annealing a matrix containing both Si and Sc
(v = 9.380 GHz). The doublets due to HScSiHn have
disappeared. The only remaining lines are due to
impurities and H2ScSiHn (noted) ................ 155








page


IV-6. The ESR spectrum (mi=7/2 and 5/2) for H2ScSiHn
in argon at 12 K after annealing to about 30 K.
The top trace is for the rod perpendicular to
the field and the bottom trace is for the rod
parallel to the field. v = 9.380 GHz ........... 162

IV-7. Same as Figure IV-6 except the mi=3/2 and -3/2
transitions are shown........................... 163

IV-8. Same as Figure IV-6 except the m=l1/2 transition
is shown........................................ 164

IV-9. Same as Figure IV-6 except the mi=-5/2 and -7/2
transitions are shown .......................... 165


xil















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



SPECTROSCOPIC INVESTIGATIONS OF METAL CLUSTERS AND
METAL CARBONYLS IN RARE GAS MATRICES

By

STEPHAN BRUNO HEINRICH BACH

December, 1987

Chairman: Professor William Weltner, Jr.
Major Department: Chemistry

Three vanadium carbonyls were formed by codeposition of

vanadium vapor and small amounts of 12CO and 13CO in neon,

argon, and krypton. Two of the species were high spin (S>1)

molecules. For VCO (S=5/2) two conformations of almost equal

stability were trapped in various matrices. The dicarbonyl

was also observed and found to have an S=3/2 ground state and

a zero field splitting parameter DI = 0.30 cm-1. Also

observed only in a neon matrix was V(CO)3. The ground state
2 2 depending on
for this axial molecule is either A or 2A depending on

whether it has planar D3h or pyramidal C3V symmetry.

Other first row transition metal carbonyls were studied

using Fourier transform infrared spectroscopy. When chromium

and CO were codeposited into an argon matrix, a molecule was

formed with CO for which a stretching frequency at 1977 cm-1

xiii








was observed. An attempt is made to relate the bonding of

first row transition metal monocarbonyl molecules to the

observed infrared CO stretching frequencies of these

molecules.

A cluster of seven silver atoms was produced when the

109 isotope of silver was vaporized and deposited into a neon

matrix and analyzed using electron spin resonance

spectroscopy. The product signals were strongest after the

matrix had been annealed. From the observed hyperfine

splitting it was determined that the cluster has a
2 "
pentagonal bipyramidal (D5h symmetry) structure with a A2

ground state. Its properties are shown to be similar to

those found by other workers for the Group IA alkali metal

septamers.

Pure metal clusters were isolated when silicon was

codeposited with silver and manganese. Silver silicide was

isolated in an argon matrix and found to have a doublet

ground state. Manganese silicide was observed in both argon

and neon matrices and found to have an S=3/2 ground state.

Hyperfine parameters have been determined for both species.

Silicon-containing scandium hydrides have also been observed

in argon matrices upon codeposition of silicon and scandium

vapor. The two species identified contained one and two

hydrogens attached to the scandium. Both molecules were

found to have doublet ground states. Hyperfine parameters

were determined for both species.


xiv












CHAPTER I
INTRODUCTION


Matrix Isolation

Matrix isolated metal clusters and metal carbonyls can

be studied in a variety of ways and are thought to aid in the

understanding of metal catalysts. The methods of studying

these compounds are as diverse as the compounds themselves,

varying from optical methods such as infrared. Raman,

uv-visible, to electron spin resonance and magnetic circular

dichroism spectroscopies which probe the cluster for its

magnetic and electronic properties. Using these varied

techniques, it is possible to determine the electronic

structure of the metal clusters. This information can then

be tied together with theoretical calculations to elucidate

the properties of the metal cluster.

Before the advent of matrix isolation, the study of

metal clusters was carried out either in the gas phase or in

solutions. Matrix isolation was developed in the mid-1950's

by George Pimentel and coworkers (1). The technique was

developed as a means of studying highly unstable reaction

intermediates which would, under standard conditions, be too

short lived to be observed. It has since been applied to a

wide variety of systems which have one thing in common: The

species of interest are too unstable to be studied under

normal laboratory conditions.








2

Several things are required in order to do matrix

isolation. First, the experiments require a high vacuum

environment. This means a pressure below 1x10-6 torr must be

maintained in order to minimize the amount of atmospheric

impurities that will be trapped within the matrix. This type

of a vacuum is usually achieved using an oil diffusion and a

mechanical pump with a liquid nitrogen cold trap.

Matrix isolation experiments are usually carried out

between 4 and 15 K. This temperature range can be achieved

by one of two methods depending upon the desired minimum

temperature. Using commercially available closed cycle

helium refrigerators is one way to cool the deposition

surface to the desired temperature. The only drawback of

this system is that the minimum temperature the refrigerator

can achieve lies at about 12 K (Recent advances have produced

a closed cycle system which is capable of 4 K, but their cost

is prohibitive). An alternative to this method is to simply

use liquid helium to cool the deposition surface. This can

be done by using either a dewar or a commercially available

transfer device such as the Air Products Hell-tran. These

devices can achieve a low temperature in the neighborhood of

4 K.

The final consideration in setting up this type of

experiment is the substrate on which to deposit the matrix.

Types of material for this surface range from CsI (or other

suitable alkali halide salts), to sapphire, or to polished








3

metal surfaces. Factors to be considered when choosing the

substrate depend on the type of experiment being done, but

all such solids must have high thermal conductivity. Also,

optical properties must be considered when doing absorption

or emission studies, whereas magnetic susceptibilities are of

concern in ESR and MCD. Obviously, the purity of the solid

substrate is important since even small amounts of some

impurities can cause strong absorptions or magnetic

perturbations.

The term "matrix isolation" comes about because the

molecules of interest are trapped in a matrix of inert

material, usually a noble gas such as neon, argon, krypton,

or nitrogen. The trapping site is usually a substitutional

site or an imperfection in the crystalline structure of the

solid gas, and the trapped species, seeing only inert nearest

neighbors, are isolated and can not react further.

Trapping the metal atom in the matrix is fairly

straightforward once the method of atomizing the metal has

been determined. But, a problem arises in producing metal

dl, tri, and higher-order species. It is unusual to simply

deposit a matrix and get a species other than a monomer or a

dimer. In order to get these higher order species of

interest several techniques can be used.

The most common technique used is to simply anneal the

matrix. Annealing involves depositing the matrix, and then

warming it. The amount that the matrix is warmed depends on








4

two things, the matrix gas being used and the trapped

species. A matrix can usually be annealed up to a

temperature equal to approximately one third that of its

melting point without solid state diffusion occurring. The

problem that occasionally arises is that once the temperature

of the matrix has begun to rise, it is possible for some

reactions to occur due to diffusion of smaller atoms or

molecules that are trapped. This might induce an exothermic

reaction, causing the matrix to heat more rapidly than

intended, exceeding the capability of the cooling system to

dissipate the heat produced. The pressure then rises and

rapid evaporation of the matrix occurs (2).

Photoaggregation is another method employed to produce

metal clusters after the matrix has been deposited. This

method usually involves photo-excitation of the metal which

causes local warming of the matrix as the metal atom

dissipates the excess energy. This partial warming loosens

the matrix around the metal atom allowing it to diffuse and

possibly interact with other metal atoms in the vicinity.

This method has been used to successfully produce silver

clusters by Ozin and coworkers (3).

Using different matrix gases can also give differing

results as to the size of the metal molecules formed. These

differences arise for several reasons. The most obvious is

that the different solid "gases" will have different sized

substitutional and interstitial spaces. Another consideration










is the rate at which the matrix freezes. This will depend

not only on the capacity of the cooling system to dissipate

the excess energy, but also on the freezing point of the gas.

It is important to remember that the amount of energy that

the cooling system can dissipate depends on the temperature

to which it must cool the deposition surface. The Displex or

Helium dewar can dissipate substantially more energy at a

higher temperature, such as that necessary to freeze krypton

(melting point 140 K) rather than neon, which freezes at

about 20 K. This difference in freezing rates will allow a

varying amount of time for the atoms to move around on the

surface of the matrix which is in a semi-liquid state. The

longer the atoms can move on the surface of the matrix, the

greater the chance for the aggregation and formation of small

metal molecules (2). The kinetics of cluster formation will

be discussed later in greater detail.

In the last 30 years a wide variety of methods has been

applied to the study of molecules and atoms which have been

trapped in matrices. One technique used to obtain data is

resonance Raman spectroscopy. In this case a polished

aluminum surface is used as the deposition surface for the

matrix. The metal is vaporized by electrically heating a

metal ribbon filament and codepositing the vapor with the

matrix gas. The aluminum deposition surface is contained in

a pyrex or quartz bell to facilitate viewing and irradiating

the matrix with an argon laser (4).










In this type of an experiment one can limit the amount

of metal entering the matrix to half of the aluminum surface,

leaving the other half virtually free of metal atoms. It is

then possible to probe various parts of the matrix to

determine the distribution of metal in the matrix (Moskovits

purposely screened part of the metal stream so as to achieve

a concentration gradient within the matrix) (4). From

resonance Raman experiments it is possible to determine the

vibrational frequency (at the equilibrium internuclear

separation (we)), and the first order anharmonicity constant

(oexe). Typical molecules which have been investigated using

this technique are Fe2, NiFe, V2, Ti2, Ni3, Sc2, Sc3, and

Mn2. Another common way of determining the presence of metal

in the matrix is the color of the matrix. Most matrices

containing metal atoms or molecules will have a

characteristic color (4).

Magnetic circular dichroism (MCD) spectroscopy is

another technique which has been used to study matrix

isolated metal clusters. MCD is the differential absorbance

of left and right circularly polarized light by a sample

subjected to a magnetic field parallel to the direction of

propagation of the incident radiation. A one inch diameter

CaF2 deposition window is used, and the magnet (.55T) is

rolled up around the vacuum shroud surrounding the deposition

surface. Before an MCD spectrum is taken, a double beam

absorption spectrum is usually taken, the reference beam








7

being routed around the vacuum shroud through the use of

mirrors, in order to maximize the signal to noise ratio of

the MCD spectrum. The optimum absorbance value has been

found to be 0.87, and deposition times are controlled

accordingly (5). The information gained from this type of

experiment is very useful in assigning the electronic ground

state of the species under study. The MCD technique also has

the advantage of being able to assign spin-forbidden

electronic transitions. Properties of excited electronic

states have also been investigated utilizing MCD (5).

Optical absorption spectroscopy has also been done on

matrix isolated samples; for example, PtO and Pt2 have been

studied in argon and krypton. Atomic platinum lines were

also observed. A KBr cold surface was used as a deposition

surface. A hollow cathode arrangement was used to vaporize

platinum wire, which was being used as the anode. This was

then put into a stainless steel vacuum vessel equipped with

an optical pathway. Deposition times were varied from a few

minutes for Pt up to two hours to make PtO and Pt2. The

absorption spectrum was then taken (6).

The present work has utilized two types of analysis,

namely electron spin resonance spectroscopy and Fourier

transform infrared spectroscopy. When doing ESR, two types

of deposition surfaces are usually used, either a copper or a

single-crystal sapphire rod. Both are magnetically inert,

and they, like other deposition surfaces, have good thermal








8

transport properties. In order to do ESR the sample has to

be placed into a homogeneous magnetic field. This is usually

accomplished by mounting the vacuum shroud surrounding the

deposition surface on rails. The matrix can then be

deposited outside of the confines of the magnet's pole

faces (7,8).

In order to perform a typical matrix isolation

experiment using electron spin resonance to analyze the

matrix, several pieces of specialized equipment are

necessary. Measurements on the matrix take place between the

pole faces of an electromagnet. This inherently restricts

the size of the vacuum chamber and deposition surface. The

set-up used is typically in two parts. One half contains the

metal deposition set-up or "furnace" (Figure I-1). The

second part contains the deposition surface and the ESR

cavity (Figures I-2 and 1-3). Figure I-2 shows the system

configured with the Hell-Tran liquid helium transfer device

from Air Products, and Figure I-3 has the set-up configured

with the Air Products Displex closed cycle helium

refrigeration system. The two halves are separated by a set

of gate valves so that they can be disconnected from each

other without compromising the high vacuum conditions

maintained in each. Once separated the rod is lowered into

the ESR cavity with the aid of pneumatic pistons. After the

rod is in the cavity, the half containing the ESR cavity and










the rod is rolled into the magnet so that the ESR cavity and

rod are located between the pole faces of the magnet.

Infrared work can also be done in a fashion similar to

that used for ESR. The primary difference is that the

deposition surface is usually CsI or quartz because of their

optical properties (No significant absorptions between 4000

and 200 wavenumbers). For this type of work the vacuum

shroud containing the deposition window usually sits in the

sample compartment of the infrared spectrometer aligned so

that the sample beam passes through the deposition window.

The apparatus for doing infrared experiments has some

similarities to that used for the ESR experiments. There is

a furnace and a dewar, and gate valves separating the two

(Figure 1-4). But a much smaller vacuum shroud can be used

because only a deposition window is contained inside of it.

It is important that the infrared beam passes into the vacuum

vessel, through the deposition surface (in most cases), and

back out again so that the beam can reach the detector, which

means that the matrix, as well as the windows through which

the infrared beam must pass, needs to be able to transmit

radiation in the infrared region. The deposition window

usually remains in the infrared instrument for the entire

experiment, which then enables one to follow the deposition

of the matrix.

Several options are available to vaporize the metal

sample. The usual method is resistive heating. The metal is































































Figure I-1. The furnace flange with copper electrodes
and a tantalum cell attached.






































































Figure I-2. The EPR cavity and deposition surface
within the vacuum vessel. The apparatus is capable of
cooling the rod to 4 K, because of the liquid helium
transfer device (Heli-Tran) on the top.


I































































Figure 1-3. The ESR cavity and deposition surface
within the vacuum vessel. The apparatus is capable of
cooling to 12 K because of the closed cycle helium
refrigeration device (Displex) on the top.

















ELECTRICAL


He GAS
C-


THERMOCOUPLE
and
HEATING WIRES

EXPANDER
Ist STAGE
2nd STAGE




COPPER COLD TIP
TARGET WINDOW

RADIATION SHIELD

MATRIX GAS INLET

GATE VALVES


ROTATABLE
JOINT




FURNACE
ASSEMBLY


VACUUM
PUMPS


Figure 1-4. The vacuum vessel, deposition surface,
Displex, and furnace assembly for infrared experiments.










placed into a cell made of a high melting metal with good

electrical properties. (Mixed metal species may sometimes

arise in high temperature work because a significant portion

of the cell may also vaporize with the sample.) Heating in

this fashion, it is possible to achieve temperatures in

excess of 2000 C. An alternative method is to put the

sample cell into an inductive heating coil; in this manner,

comparable temperatures can usually be attained. The

temperature of the furnace is estimated by using an optical

pyrometer; more accurate measurements require an estimate of

the emissivity of the hot surface.

The determination of what has been trapped can

sometimes be simple or, at other times, rather complex. In

the case of Sc2 it was rather straightforward. The ESR

spectrum was measured by Knight and co-workers (9). Since

the Sc nucleus has a spin of 7/2 (1=7/2), the hyperfine

structure observed identified the trapped species. A

resonance Raman experiment determined the vibrational

frequency of the ground state molecule to be 238.9 cm-1 (10).

From this information it was then possible to determine

whether a chemical bond exists between the trapped species.

In the case of discandium, a single bond and not van der

Waals forces binds the two atoms (11).

A more controversial diatomic molecule, dichromium, is

not quite as straightforward; it has a singlet ground state

and is therefore not observable using ESR. Theoretical











studies of Cr2 indicate a variety of bonding configurations.

A resonance Raman study has examined both di and tri chromium

(10). For the dichromium species it was first necessary to

decide which of the spectral features belonged to dichromium

and which belonged to trichromium. This was done in two

ways. The change in relative intensities of the bands was

observed as the concentration was varied (the assumption

being that a more concentrated matrix would favor a larger

cluster), and a high resolution scan of one of the observed

lines was fit with the calculated isotopic fine-structure

spectrum, assuming the carrier of the line to be Cr2. The

vibrational frequency could then be determined from the

spectra, and from this a force constant indicating the

strength of bonding. The results from the experiment

indicate that multiple bonding does exist (k=2.80 mdyne/A).

(Dicopper with a single bond has a k=1.3 mdyne/A.) The

extent of the multiple bonding can not be determined from

these results (11).

Divanadium has also been investigated using the

resonance Raman technique to yield an equilibrium vibrational

constant of 537.5 cm-1 (4), but mass spectrometric data were

needed to complete the picture. It was determined that the

dissociation energy for divanadium is about 1.85 eV (11).

From spectroscopy done in a two-photon-lonization mass

selective experiment, on a supersonically expanded metal
0
beam, a value of 1.76 A for the equilibrium distance was










measured (12). The short bond distance coupled with a high

vibrational frequency shows that the molecule is strongly

bonded by 3d electrons (11).

Higher order metal clusters such as Mn5 have also been

trapped, and ESR spectra measured in matrices. In this case

several equally spaced (300 G) lines were observed in the

spectrum. From the number of these fine-structure lines it

was determined that the molecule has 25 unpaired electrons

(Hyperfine splitting were not resolved.). On this basis it

is possible to postulate the cluster size. Smaller clusters

are improbable on the basis of S=25/2. It is also important

to remember that the larger clusters are unlikely to form in

the matrix initially. The structure of Mn5 is thought to be

pentagonal with single bonds between each of the manganese

atoms and with each of the atoms having five unpaired

electrons. The ESR spectrum indicates that all of the

manganese atoms in the molecule are equivalent; a pentagonal

structure fulfills this requirement (13).

A similar problem arises in the case of doing a high

concentration scandium experiment. In this case it is

thought that a molecule with 13 Sc atoms is made. The ESR

spectrum contains over 60 lines in the g=2 region of the

spectrum, which usually indicates one unpaired electron in

the molecule. Because the intensity of the lines drops off

at the fringes of the hyperfine structure, it is difficult to

ascertain exactly how many lines exist. With the observed










lines there are at least nine Sc atoms in the molecule. The

Sc13 molecule seems likely because of theoretical

calculations done on transition metal clusters with 13 atoms.

A single Self-Consistent Field Xa-Scattered wave calculation

has been done for Sc13 giving a single unpaired electron, in

agreement with the ESR results (14).

Matrix isolation is more of a technique than a method

of analysis. It can be used in conjunction with various

analytical tools which then can be used to determine the

composition and structure of the trapped compound. It is

important to use some forethought in choosing the method of

analyzing the trapped molecule because the method chosen will

determine what information can be obtained from the

experiment. Data from various methods will tend to

complement each other. For example, if the molecule of

interest does not contain an unpaired electron, then it would

not be worthwhile to do ESR since this method requires the

presence of at least one unpaired electron in order to

produce a spectrum. Analyzing the molecule for its

vibrational structure by using resonance Raman or infrared

spectroscopy will only give the molecule's vibrational modes.

From these modes it may or may not be possible to determine

the molecule's structure, depending on the complexity of the

molecule and the degeneracy of the modes. Another problem,

when dealing with clusters, is that it is sometimes difficult

to determine the size of the cluster from the observed








18

spectra. Also, once the molecule is trapped, its trapping

environment may not be uniform throughout the matrix. This

will cause splitting in the observed lines of the spectrum

due to different trapping sites. The trapping site may also

cause a lowering of the observed point group of the molecule,

which will cause lines to split because they are no longer

degenerate. Matrix isolation is a useful tool which aids in

determining the structure of unstable species, but it is best

used in conjunction with other techniques if accurate

structures are to be determined.

As can be seen from what other workers have done,

matrix isolation can be used to trap very reactive and also

very interesting species. We set out to use this technique

to further elucidate the properties of transition metals and

transition metal carbonyls. Following this line of interest

has lead us to study various first row transition-metal

carbonyls using both ESR and FTIR. We continued our work

with transition metals by investigating the group IB metals

and attempted to produce larger clusters. We finally turned

our attention to the first row transition-metal silicides.

Our hope in these endeavors was to produce various metal

containing species in order to determine structure and to

obtain possible enlightenment as to the reaction processes

occurring to form them.

Producing these metal species as well as analyzing the

resultant spectra tends to be a rather complicated process.










A review of the kinetics of cluster formation is very helpful

in pointing out and understanding some of the processes

involved in producing these exotic species. The analysis of

the ESR spectra can sometimes be rather simple when one is

dealing with only a few lines. But when the trapped species

produces many lines, the analysis rapidly becomes complicated

and a review of relevant theory becomes mandatory. A brief

review of infrared spectroscopy will also be presented.



Theory of Cluster Formation

In recent years the area of metal cluster chemistry

has become rather active. The main reason behind this is the

hope that the metal cluster will be useful in the

investigation of the chemistry that occurs at metal surfaces.

This interest has lead to two major thrusts, one involving

the reproducible production of these clusters and the other

concerning itself with the mechanisms involved in the

evolution of the clusters. Both of these areas are now being

actively pursued by various workers (15-19).

Experimentally, the production of these clusters and

their identification have proven extremely challenging.

Three primary methods of vaporizing the metal exist, laser

vaporization, resistively heating of a cell containing the

metal of interest, or heating a wire made of the appropriate

metal. Of these the most successful has been the use of

lasers. A major problem in determining the kinetics involved








20

in cluster formation is the reproducibility of the

distribution of cluster sizes from experiment to experiment.

Several groups have had some success at this and even have

begun to react these metal clusters with various types of

reactants (20,21).

In developing a general mean-field kinetic model of

cluster formation one must look first at the aggregation

process in the thermal vaporization source. Second, a method

needs to be found to calculate probabilities for cluster

formation taking into account atom-atom collisions to form

dimers as well as collisions between clusters. This would

have to include not only aggregation but also cluster

fragmentation from collisions, structural stabilities of

certain clusters, how energy is dissipated upon collision,

and possible transition states of the clusters. It should

also be able to explain the cluster distribution found in

mass spectra of these systems.

The metal clusters are produced by laser vaporization

in a supersonic nozzle source and then allowed to enter a

fast-flow reactor, before being mass analyzed. The source of

the metal of interest is a rod about 0.63 cm in diameter.

The rod is placed in the high pressure side of a pulsed

supersonic nozzle, operating with a ten atmosphere back

pressure. The frequency doubled output of a Q-switched

Nd:YAG laser (30 to 40 mJ/pulse, 6 ns pulse duration) is

focused to a spot approximately 0.1 cm in diameter on the








21

target rod, and fired at the time of maximum density in the

helium carrier gas pulse. The target rod is continually

rotated and translated, thus preventing the formation of deep

pits, which would otherwise result in erratic fluctuations in

the sizes of the metal clusters. The helium-metal vapor

mixture then flows at near sonic velocity through a

cluster-formation and thermalizatlon channel, 0.2 cm in

diameter and 1.8 cm in length, before expanding into a 1 cm

diameter, 10 cm long reaction tube. Effectively, all cluster

formation in such a nozzle source is accomplished in the

thermalization channel since expansion into the 1 cm diameter

reaction tube produces a 25 fold decrease in density of both

the metal vapor and the helium buffer gas (20).

The reaction tube has four needles which can be used to

inject various reactants into the flowing mixture of carrier

gas and metal. Following the reaction tube, the reaction gas

mixture is allowed to expand freely into a large vacuum

chamber. A molecular beam is extracted from the resulting

supersonic free jet by a conical skimmer and collimated by

passage through a second skimmer. The resulting well-

collimated, collisionless beam is passed, without

obstruction, through the ionization region of a time-of-

flight mass spectrometer (TOFMS). Detection of the metal

clusters and their reaction products is accomplished by

direct one photon ionization in the extraction region of the

TOFMS (20).








22

With the advent of this type of a device, it is now

possible to produce metal clusters under relatively

controlled conditions with a fairly reproducible distribution

of cluster sizes. The reproducibility of cluster size

distribution between experiments has made it possible to

compare the results to kinetic studies dealing with the

formation of metal clusters. The kinetic analysis of the

clusters has been able to explain why some cluster sizes are

favored, to suggest the relative importance of kinetic and

thermodynamic effects, and to shed some light on the possible

influence of ionization of the clusters.

The kinetic theory applicable is that of aggregation

and nucleation. The mean-field rate equations governing the

aggregation of particles developed by Smoluchowski (22) are



i-1 x i = N
(I-1) Xi j~1Kjii Xj X i_ 1 Xj X I = 1,...,N




In equation I-1, Xi denotes the concentration of clusters of

size i. The aggregation kernel, Kij, determines the

time-dependent aggregation probability. The first term on

the right hand side of the equation describes the increase in

concentration of clusters size I due to the fusion of two

clusters size j and i-j. The second term describes the

reduction of clusters size i due to the formation of larger

clusters. The equation must be generalized in order that the











neutral-positive, neutral-negative, and positive-negative

cluster fusions are included because the vaporization process

will produce some ions. But, since the electrons and the

ions are attracted by long range Coulomb forces, the

recombination processes are very fast, leading to a

population of neutral atoms that is much larger than the

population of ions. Therefore, the probability for

positive-negative cluster fusion is much smaller than that of

neutral-positive and neutral-negative cluster fusion and can

be neglected (15).

The terms due to the formation of positive clusters are

.0 0+ 0 +
(1-2) Xi = Xi Kij Xi Xj


and

.+ 1i-1 0+ 0 + N 0+ 0 +
(1-3) Xi j 1 Kji X Xi-j Kji X Xi i = 1,.....N



where Xi is defined by the right hand side of equation I-1
.0 .+
and Xi and Xi denote the concentration of the neutral and

positively charged clusters, respectively. The kernels Kij
0+
and Kij describe the neutral-neutral and neutral-positive

aggregation probabilities. Analogous terms are introduced

due to the presence of the negatively charged clusters (15).

During cluster growth, there is also the possibility of

charge transfer between the charged and the neutral clusters

without the accompanying cluster fusion. The probability of

electron transfer between the negatively charged and the








24

neutral clusters is much greater than the probability of

electron transfer between the neutral and the positively

charged species since electron affinities are much smaller

than the ionization potentials for small and medium sized

clusters. Therefore, only the electron transfer terms from

the negatively charged to the neutral clusters are included



.0 .0 0 T 0 -
(I-4) X i J= Tij Xi Xj + j Tji Xj Xi

and
S- 0 0-
(1-5) Xi = Xi + = Ti X X Tji Xj X
J=J ij i j ji

where Tij is the nonsymmetric charge transfer kernel. The

coupled rate equations I-(2 through 5) can then be solved

simultaneously for the concentrations of the neutral and the

charged clusters (15).

Classically, the aggregation probability for clusters I

and j with diffusion coefficients Di and Dj is proportional

to DijRij, where Dij = Di + Dj is the joint coefficient for

the two clusters, and Rij is the catching radius within which

the clusters will stick with unit probability. In a reactive

aggregation, one has to consider the reaction probability

within the interaction radius. The expression for reactive

aggregation becomes


Kiu = 4nDijRij[Pij/(Pij+PD)]


(1-6)








25

where P.j is the reaction probability per unit time and PD is

the probability of the reactants to diffuse away. One has PD

= 1/tij, where rij is the average time in which the clusters

remain within the reaction distance Rij. From the diffusion

equation,



(1-7) D = (kBT)3/2/(apmO.5
He

one can easily show that 1/rij= 6Dij/(Rj)2 leading to



(1-8) Kij = 4DIRijRj[Pij/(Pij+(6Dij/Rij2))]



The limiting forms of equation I-8 are of particular

interest. If PIj>PD, Kij z 4xDijRj and the distribution of

cluster sizes is governed by the classical aggregation

kinetics. No reaction-induced magic numbers will arise in

this case. The true solution to equation I-1 can be

approximated in this case by the ones corresponding to the

exactly solvable simple kernels. Since the variation of the

kernels with cluster size is not very strong in the classical

limit, a constant kernel solution may be used where Kij = 2C

and xl(t=O) = x0 may be used for qualitative purposes.



(I-9) Xi(t) = X0(CXot)i-1/(l+CXOt)1+1



A more accurate solution can be obtained provided one

includes the variation of the diffusion coefficients and the








26

catching radii with cluster size. Since cluster reactivity

varies with its structure, the uniqueness of the structure

explains the reproducibility of the reactivity data for small

transition metal clusters (15).

The application of classical kinetics is best

exemplified by transition metal clusters. The mass

distribution spectra of these clusters are essentially

featureless. This is what is predicted by classical

kinetics. However, although the distribution of transition

metal clusters is classical, the small and medium size

clusters will probably have unique or nearly unique shapes.

This will result in a certain amount of nonclassical behavior

which will cause certain cluster sizes to be favored (15).

In the other limit of equation I-8, where PD =

6Dij/(Rij)2 > Pij, the growth of clusters is reaction

limited. In this case, one can neglect Pij in the

denominator. Since the diffusion constants cancel, the

equation becomes



(I-10) Ku = 4x/[6(Rij)3Pij].



Thus the aggregation probability in the reaction limited

regime is dependent only on the reaction probability and does

not depend on the value of the diffusion coefficient.

Therefore, the aggregating clusters will undergo several

collisions before fusion. Significant variations in cluster








27

size are likely to occur since the reaction probabilities

depend on structure, symmetry, and the stability of the

reacting clusters. This is the reason why magic numbers are

observed. The reproducibility of the measured magic numbers

under a wide variety of experimental conditions is due to the

independence of the rate of fusion on the diffusion

coefficient (15).

The knowledge of reaction probabilities for each pair

of reacting clusters, including their charge dependence, is

required to calculate the cluster distribution in the

reaction limited regime. Since this is computationally

prohibitive, one is forced to make several approximations in

order to make the calculation feasible. The final expression

for the aggregation kernel becomes




(I3 e-(AGI+AGJ)/KBTav
(1-11) Kj = GRije v




after using the Polanyl-Bronsted relationship to estimate the

relative differences between transition state energies.

Also, since the reactants are probably going to undergo

considerable structural rearrangement after initial

attachment, scaled derivatives are used to describe the

energy gained upon addition of a single atom. Gibbs free

energies can be used to account for the possible temperature










dependent structures which can arise due to the dependence of

cluster entropy with structure (15).

The charge transfer kernel is approximated by




3 e-(Ai+Aj)/KBTav
(I-12) Tij= oR1e


Since the electronic wave function of a negatively charged

cluster has a relatively large radius, the Polanyi-Bronsted

proportionality factor, C, in the charge transfer kernel is

significantly larger than the corresponding factor in the

aggregation kernel (15).

The final two equations require electronic structure

calculations for only the end products (those observed in a

mass spectrum). The average temperature, Tay, is not known

at the outset, but the analysis of experimental spectra

provides an upper bound. The spectra of positively charged

clusters are thus determined by two adjustable parameters,

where as those of negatively charged clusters require an

additional parameter (C) (15).

Ziff and co-workers (16) have studied the validity of

using the Smoluchowski equation for cluster-cluster

aggregation kinetics. They investigated the validity of the

mean-field assumption by looking at the concentrations of the

cluster species and also by investigating the asymptotic

behavior of the equations. They found the mean-field

Smoluchowski equation to be appropriate in describing the








29

aggregation of particles which form fractal clusters. The

only problem was in determining the fractal properties of the

kernel. Even though these properties are difficult to

determine, once they are known the entire description of the

kinetics follows Smoluchowski, as presented by Bernholc and

Phillips (15).

The kinetic theory for clustering as presented by

Bernholc and Phillips (15) has been able to model the cluster

distributions found for carbon by Smalley and co-workers

(23). Bernholc and Phillips used the calculated formation

energies with a semiempirical estimate of the entropy

difference between chains and rings as input for the kinetic

energy calculations. They found that the cluster

distributions were in good agreement with the experimental

work of Smalley. This includes the data for both the

positive and negative ions produced directly in the source.

The magic numbers in the range of n equal 10 to 25 were well

reproduced. They also found that electron transfer effects

have a strong effect on the measured distributions of small

and medium clusters of the negative ions. For the positive

ions produced from photolonization of neutral clusters, the

calculated cluster distributions show that photofragmentation

and/or photothreshold and photolonization cross section

dependence on cluster size have a major effect on the

measured spectra up to about n equals 25. This was not found

to be true for larger clusters.








30

Even though these are just beginnings in the

understanding of what is involved in cluster formation, it

is essential to realize that the clusters which are seen by

experimentalists are the products of a complicated set of

circumstances which may possibly be at the control of the

experimentalist. With this type of background it may be

possible in the future to produce a desired cluster size by

finely tuning the experimental conditions. To be able to do

this, it will be necessary to understand what the critical

factors are in the formation of clusters. Is it the overall

flux of metal in the carrier gas? Can the amount of

ionization be controlled in order to produce the desired

cluster sizes? Or will the inherent stabilities of certain

clusters override these factors and limit the variation of

cluster size which can be easily produced? These are

questions which will only be answered through a close

synergic relationship between experiment and theory.



ESR Theory



Electron Spin Resonance (ESR) spectroscopy is concerned

with the analysis of paramagnetic substances containing

permanent magnetic moments of atomic or nuclear magnitude.

The theory of ESR spectroscopy has been dealt with by many

authors, and if desired a more in depth treatment can be

found there (24-29). In the absence of an external field










such dipoles are randomly oriented, but application of a

field results in a redistribution over the various

orientations in such a way that the substance acquires a net

magnetic moment. If an electron or nucleus possesses a

resultant angular momentum or spin, a permanent magnetic

dipole results and the two are related by



(1-13) _= TP_



where g is the magnetic dipole moment vector, pis the

angular momentum (an integral or half-integral multiple of

h/2x = f, where h is Planck's constant), and T is the

magnetogyric ratio. The motion of these vectors in a

magnetic field H consists of uniform precession about H at

the Larmor precession frequency



(1-14) w= -rH.



The component of u along H remains fixed in magnitude, so the

energy of the dipole in the field (the Zeeman energy)



(1-15) W= -f*H



is a constant of the motion.

The relationship between the angular momentum and the








32

magnetic moment is expressed by the magnetogyric ratio in

equation 1-13 and is defined by



(I-16) r = -g[e/(2mc)]



where e and m are the electronic charge and mass,

respectively, and c is the speed of light. The g factor is

equal to one for orbital angular momentum and is equal to

2.0023 (ge) for spin angular momentum. Defining the Bohr

magneton as 3=ef/2mc and combining the g factor with equation

1-13 we have (along the field direction)



(1-17) PS = -germs-



Only 2p+l orientations are allowed along the magnetic field

and are given by mSh where mS is the magnetic quantum number

taking the values



(1-18) mS = s, s-1,..., -8



because the angle of the vector g_is space quantized with

respect to the applied field H. This accounts for the

appearance in Eq. (1-17) of the mS factor for spin angular

momentum.

In the case of an atom in a 2S1/2 state where only spin








33

angular momentum arises, the 2S+1 energy levels separate in a

magnetic field. Each level will have an energy of



(1-19) EM= gem"SH




which will be separated by geSH. The g factor is an

experimental value and mS an "effective" spin quantum number

because the angular momentum does not usually enter into the

experiment as purely spin, i.e. some orbital angular momentum

usually enters into the observed transitions. For orbitally

degenerate states described by strong coupling scheme

(Russell-Saunders), J=L+S, L+S-1, ..., IL-S) and



(1-20) Ej = gjpmjH

where

(1-21) gj = 1 + [S(S+1)+ J(J+1)- L(L+1)]/[2J(J+1)]



is the Lande splitting factor. This reduces to the free

electron value for L=O.

The simplest case of a free spin where mj = mS = +1/2

will give two energy levels. The equation for the resonance

condition follows:


(1-22) hv = geAHo








34

where HO is the static external field and v is the frequency

of the oscillating magnetic field associated with the

microwave radiation. In this research a frequency of about

9.3 GHz (X-band) was employed. The transitions observed can

be induced by application of magnetic dipole radiation

obtained from a second magnetic field at right angles to the

fixed field which has the correct frequency to cause the spin

to flip.



The Hyperfine Splitting Effect

As described above, an ESR spectrum would consist of

only one line. This would allow one to determine only a

value for the g factor for the species. Fortunately, this is

not the only interaction which can be observed via ESR

spectroscopy. These other interactions tend to greatly

increase the observed number of lines. One of the most

important of these interactions is the nuclear hyperfine

interaction. ESR experiments are usually designed so that at

least one nucleus in the species under investigation has a

non-zero magnetic moment. The magnetic moment of the odd

electron can interact with this nuclear moment and split the

single ESR line into hyperfine structure.

In the simplest case of a nucleus having a spin 1=1/2

interacting with a single electron, the magnetic field sensed

by the electron is the sum of the applied fields (external

and local). A local field would be one caused by the moment










of the magnetic nucleus. This local field is controlled by

the nuclear spin state (I=1/2, in this case). Because there

are two nuclear levels (21+1), the electron will find itself

in one of two local fields due to the nucleus. This allows

two values of the external field to satisfy the resonance

condition, which is



(1-23) Hr = (H' + (A/2)) = (H' AMI)



where A/2 is the value of the local magnetic field (A being

the hyperfine coupling constant), and H' is the resonant

field for A=O.

A good example of an ESR spectrum is that of the

hydrogen atom with the Zeeman energy levels shown in Figure

I-5. Hydrogen has one unpaired electron for which a

transition at about ge should be observed. Because of the

spin angular momentum of the electron interacting with the

spin angular momentum of the nucleus (1=1/2), two lines are

observed. The lines are split around the "g" value for a

free electron which is ge = 2.0023 and occurs at about 3,400

Gauss in an X-Band experiment. The magnitude of the

splitting hyperfinee interaction) of the two lines about the

free electron position at ge is due to the interaction of the

free electron with the nuclear moment of the hydrogen atom.

The spin angular momentum of the unpaired electron can also

be split by several nuclei that have spins, as is the case








36

with CH3. The carbon nuclei (99%) are 12C which has zero

spin (1=0). The hyperfine interaction in this case arises

from the three equivalent hydrogen nuclei (each with 1=1/2)

which gives an overall 1=3/2, and four lines are observed

(30,31).

Several interactions are involved when a paramagnetic

species with a non-zero nuclear spin interacts with a

magnetic field. The obvious one is the direct interaction of

the magnetic moment with the external field. The precession

of the nuclear magnetic moment in the external field results

in a similar term. The equation



(1-24) gi1l= --/9N



relates the nuclear magnetic moment Iy to the nuclear g

factor (gy). In the equation the nuclear magneton, ON, is

defined as ei/2Mc where M is the proton mass and is about

1/2000th of the Bohr magneton.

The Hamiltonian can be written as



(1-25) {H) = gjeH__*{J} + hA{Ij*{Jj gPNHL*{ji



where { } indicates that the term is an operator. Small

effects such as the nuclear electric quadrupole interaction,

as well as the interaction of the nuclear moment with the








37

external magnetic field (Nuclear Zeeman term), which is the

last term in equation 1-25, are small and will be neglected.

The Zeeman effect in weak fields is characterized by an

external field splitting which is small compared to the

natural hyperfine splitting (hA{IJ)*({ > gSH*()J) in equation

1-25. The orbital electrons and the nuclear magnet remain

strongly coupled. The total angular momentum F = I+J orients

itself with the external field and can take the values I+J,

I+J-1,..., I-Jj. The component of F_along the field

direction, mF, has 2F+1 allowed values. In a weak field the

individual hyperfine levels can split into 2F+1 equidistant

levels which gives a total of (2J+1)(2I+1) Zeeman levels.

(Not all levels are degenerate even at zero field.)

The splitting becomes large compared to the natural

hyperfine splitting in the strong field (Paschen-Back)

region. Decoupling of I and J occurs because of strong

interaction with the external field. Therefore F is no

longer a good quantum number. Since J and I have components

along the field direction, the Zeeman level of the multiple

characterized by a fixed mj is split into as many Zeeman

hyperfine lines as there are possible values of mi (21+1).

The total energy states are still given by (2J+1)(2I+1) since

there are still (2J+1) levels for a given J. The levels in

this case form a completely symmetric pattern around the

energy center of gravity of the hyperfine multiple.








38

Intermediate fields are somewhat more difficult to

treat. The transition between the two limiting cases takes

place in such a way that the magnetic quantum number, m, is

preserved (In a strong field m = mi + mj, in a weak field m =

mF). The Zeeman splitting is of the order of the zero field

hyperfine splitting in this region.

With so many possible levels, the observed ESR spectrum

needs to be explained in terms of selection rules. The

transition between Zeeman levels involves changes in magnetic

moments so it is necessary to consider magnetic dipole

transitions and the selection rules pertaining to them. A

single line is observed for the mS = 1/2 <-> -1/2 transition

in the pure spin system (I=0). A change in spin angular

momentum of +f is necessary. This corresponds to selection

rule of Amj = +1. A photon has an intrinsic angular momentum

equal to f. Conservation of angular momentum therefore

dictates that only one spin can flip (electronic or nuclear)

upon absorption of a photon. The transitions usually

observed with fields and frequencies employed in the standard

ESR experiment are limited to the selection rules Amj = +1,

and AmI = 0 (The opposite of NMR work).

These interactions can be categorized as isotropic and

anisotropic, and are related to the kind interactions of the

electron with the nucleus, and can be deduced from the ESR

spectrum. The isotropic interaction is the energy of the

nuclear moment in the magnetic field produced at the nucleus








39

by electric currents associated with the spinning electron.

This interaction only occurs with s electrons because they

have a finite electron density at the nucleus. The isotropic

hyperfine coupling term is given by



(1-26) as = (86/3)geSgNON1((0O)2



where the final term represents the electron density at the

nucleus. There is no classical analog to this term. The as

value, also known as the Fermi contact term, is proportional

to the magnetic field, and can be of the order of 105 gauss.

It is obvious then very large hyperfine splitting can arise

from unpaired s electrons interacting with the nucleus.

Classical dipolar interactions between two magnetic

moments are the basis for describing the anisotropic

interaction. This interaction can be described by



(1-27) E = (pe*jU)/r3 -[3 (je*r) ("*rj_)]/r5



where r_ is the radius vector from the moment ge to an, and r

is the distance between them. Substituting the operators,

-g{S_) and gNN{I), for .e and Aj respectively, gives the

quantum mechanical version of equation 1-27 as



(I-28) Hdip = -gSgNPN[{I~*({L)-{S})/r3

-3(({I)*r ({SJ*r)/r5].












Then a dipolar term arises



(1-29) a = gepgIPN[(3cos20-1)/r3]



where 0 is the angle between the line connecting the two

dipoles and the direction of the magnetic field. The angular

term found in Eq. (1-29) needs to be averaged over the

electron probability distribution function because the

electron is not localized. The average of cos20 over all 0

vanishes for an s orbital because of the spherical symmetry

of the orbital.



Doublet Sigma Molecules

The spin Hamiltonian

The full spin Hamiltonian involves all the interactions

of the unpaired spin within the molecule, not just the ones

directly affected by the magnetic field. The full

Hamiltonian contains the terms below,

(1-30) H = HF + HZe + HLS + Hhf + HZn



the magnitude of the terms on the right side of Eq. (1-30)

tend to decrease going from left ot right. The first term in

equation 1-30 is the total kinetic energy of the electrons.

The "Ze" and "Zn" terms describe the electronic and nuclear

Zeeman interactions, respectively. The energy, HLS, is due








41

to the spin-orbit coupling interaction. The term, Hhf,

accounts for the hyperfine interaction due to the electronic

angular momentum and magnetic moment interacting with a

nearby nuclear magnetic moment. These terms have been

adequately described in detail by several authors (24-27).

This full Hamiltonian is rather complicated and difficult

to use in calculations, and the higher order terms which

could be observed in crystals have not been included. Using

a spin Hamiltonian in a simplified manner, it is possible to

interpret experimental ESR data. This was first done by

Abragam and Pryce (32). The ESR data are usually of the

lowest-lying spin resonance levels which are commonly

separated by a few cm-1. All other states lie considerably

higher in energy and are generally not observed. The

behavior of this smaller group of levels in the spin system

can be described by a simplified Hamiltonian. The splitting

are the same as if one ignored the orbital angular momentum

and replaced its effect by an anisotropic coupling between

the spin and the external magnetic field.

Since (S_ cannot represent a true spin, it represents an

"effective" spin. This is related to the anisotropy found in

the g factor which does not necessarily equal ge. By

convention, the "effective" g factor is defined so that the

observed number of levels equals 2S+1, just like the real

spin multiple. Therefore all the magnetic properties of a

system can be related to this effective spin by the spin










Hamiltonian. This is possible because the spin Hamiltonian

combines all of the terms in the full Hamltonian that are

effected by spin. Nuclear spins can be treated in a similar

fashion, so that the spin Hamiltonian which corresponds to

Eq. (1-30) can be written as



(1-31) HSpin = AHO*g*{S. + (I)*A*{S)



where g and A are tensor quantities and the nuclear Zeeman

term has been neglected.



The g tensor

The anisotropy of the g-tensor arises from the orbital

angular momentum of the electron through spin-orbit coupling.

The anisotropy occurs even in the sigma states which

nominally have zero orbital angular momentum. Apparently the

pure spin ground state interacts with low-lying excited

states which add a small amount of orbital angular momentum

to the ground state. This small amount is enough to change

the values of the g tensor. The interaction is generally

inversely proportional to the energy separation between the

states. This spin-orbit interaction is given by



(1-32) {H)LS = = A(L}x{S}x + {L}y(S)y + (L)z{S)z)



This term is added to the Zeeman term in the spin Hamiltonian












(1-33) {H)= BH*({L)+g({S)) + (L)*{S).



For an orbitally nondegenerate ground state represented by

IG,Ms>, the first order energy is given by the diagonal

matrix element



(1-34) WG =

+

where the first term is the spin-only electronic Zeeman

effect. The term, , vanishes since the ground

state is orbitally non-degenerate. The second order

correction to each element in the Hamiltonian is given by



(1-35) (H) MSM = [(l
+ geH*SnM )/n W(0)



where the prime designates summation over all states except

the ground state. The matrix elements of ge.HJSj will vanish

because = 0.

Expanding this, it is possible to factor out a quantity



(0) (0)
(1-36) A= (-E )/(Wn WG)
nn G








44

which is a second rank tensor. The ijth element of this

tensor is given by



(0) (0)
(1-37) Aij = (-E )/(Wn W )




where Li and Lj are orbital angular momentum operators

appropriate to the x, y, or z directions. Substituting this

tensor into HMSM yields



(1-38) HMS,MS =
+ 22{S)*{A}*{S})M'>
S


The first operator does not need to be considered any further

since it represents a constant contribution to the

paramagnetism. The second and third terms constitute a

Hamiltonian which operates only on spin variables. The spin

Hamiltonian results when the operator ge${H)*{S} is combined

with the last two terms of Eq. (1-38). The spin Hamiltonian

takes the form of



(I-39) HSpin = {(H}*(ge{l + 2A{A})*{S} + A2{S}*{A)*{S}

= P{H}*{g}*{S} + (S)*(D}*{S}

where

(1-40) {g)= g ({1) + 2A{A}

and










(1-41) (D} = 2(A}.



The final term in equation 1-39 Is effective only in systems

with S>l. The first term is then the spin Hamiltonian for a

2E molecule. The anisotropy of the g-tensor arises from the

spin-orbit interaction due to the orbital angular momentum of

the electron which is evident from the derivation.

The g-tensor would be isotropic and equal to 2.0023 if

the angular momentum of the system is due solely to spin

angular momentum. Deviation (anisotropy) from this value

results from the mixing in of orbital angular momentum from

excited states which is expressed through the {A} tensor.

If a molecule has axes of symmetry, they need to

coincide with the principal axes of the g tensor. Three

cases of interest can be outlined. The simplest case is one

in which g is equal to gg. This is a spin only system for

which g is isotropic. For a system containing an n-fold axis

of symmetry (n>3) there are two equivalent axes. The axis

designated z is the unique axis and the g value for the field

(H) perpendicular to z is g- and gl is the value for g when H

is parallel to z. The spin Hamiltonian therefore becomes



(1-42) HSpin = $(giHx{S)} + g-Hy)yS} + gHz{S}z).



The third case deals with the situation where the molecule


L








46

contains no equivalent axes (orthorhombic symmetry), where

gxx' gyy, and gzz are not equal and



(1-43) {H)Spin = (gxxHS)x + gyyHy(S)y + gzHz(S)}).



The A tensor

The hyperfine tensor takes into account three types of

interactions. The first term involves the interaction

between the magnetic field produced by the orbital momentum

and the nuclear moment, L*I which is usually small. More

important terms involve the interactions due to the amount of

s character of the wavefunction (the Fermi contact term) and

to the non-s character of the wavefunction also need to be

accounted for.

The isotropic interaction due to the s character is

called Aiso. Fermi (33) has shown that for systems with one

electron the isotropic interaction energy is approximately

given by



(1-44) Wiso = -(8x/3)|T(0)2 PeANPN



where W(0) represents the wave function evaluated at the

nucleus.

The interaction arising from the dipole-dipole

interaction of the nucleus and electron (non-s character) is

called Adip. The dipolar interaction gives rise to the








47

anisotropic component of hyperfine coupling in the rigid

matrix environment. The expression for the dipolar

interaction energy between an electron and nucleus separated

by a distance r is



(1-45) Wdipolar = (e*N)/r3 [3(Pe*r)(PN*r)]/r5



The term, Hhf, can now be written as



(1-46) Hhf = Hiso + Hdip

= [Aiso + Hdip]l*S



where Aiso has been given in Eq. (1-26) and Adip can be

expressed by equation 1-29. The brackets indicate the

average of the expressed operator over the wave function W.

In tensor notation the term become



(1-47) Hhf = I*A*S



where A_ = Asol + T. Here 1 is the unit tensor and T is the

tensor representing the dipolar interaction. The components

of the A tensor becomes


Aj = Aisol + Tij.


(1-48)








48

For a completely isotropic system the components of the A

tensor (Ax, Ayy, Agz) will equal Aiso. A system with axial

symmetry is treated in a manner similar to that of the g

tensor where Axx and Ayy are equal to A-. The term, Al, is

given by



(1-49) A = Also + Txx



and Azz is equal to Ag which is given by



(1-50) A, = Azz + Tzz



And finally for a system which exhibits a completely

anisotropic A tensor Ax, A yy Azz are not equal to each

other.

In matrix isolation experiments only the absolute values

of the hyperfine parameters can be determined. In most

matrix isolation experiments, it is found that for the most

part, the signs of A_ and A, are positive. There are two

general exceptions to this. First, this may not generally be

true for very small hyperfine interactions, such as the

hyperfine interaction in CN where the splitting due to 14N is

only 5 to 10 gauss. Second, if gI is negative, the A values

will usually be negative, also (34).










Randomly oriented molecules

There is a very distinct difference between samples

held in a single crystal and those trapped in matrices. In

the case of a single crystal, the sample can be aligned to

the external field and spectra recorded at various angles of

the molecular axes to the field. Matrix isolated samples are

usually randomly oriented within the field and the observed

spectra will contain contributions from molecules at various

angles. This was first considered by Bleaney (35,36), and

later by others (37-43)

In the orthorhombic case the spin Hamiltonian can be

solved (assuming the g tensor to be diagonal), and the energy

levels can be given by



(1-51) E = OSHH(g12sin20cos2 + g22sinsin20

+ g32cos20)0.5

= OgHSHH
where S1 is the component of the spin vector S along H, gH is

the g value in the direction of H, 8 is the angle between the

molecular z axis and the field direction, and 0 is the angle

from the x axis to the projection of the field vector in the

xy plane. Returning to axial symmetry

(1-52) gH = (g2sin2 + g 2cos20)0.5


and the energy of the levels is given by








50

(1-53) E = PSHH(gL2sin20 + g12cos20).



It is obvious that the splitting between the energy levels

are angularly dependent. This makes the transitions between

the energy levels also angularly dependent.

The absorption intensity as a function of angle is

proportional to the number of molecules lying between 0 and

O+dO, assuming the transition probability is independent of

orientation. Since g is a function of 0 for a fixed

frequency v, the resonant magnetic field is



(1-54) H = (hv/A)(g 2cos29 + g 2sin2)-0*.5



and from this



(1-55) sin20 = (g0HO/H)2 gs2)/(ge2 g12)



where go equals (g, + 2g.)/3 and Ho equals hv/go0. From the

above equations we have



(1-56) H = hv/gl = go0H/g, at 0 = 00

and

(1-57) H = hu/g#3 = g0gH/g. at 0 = 90.



The absorption intensity varies from 0* to 900 and when

plotted against magnetic field, takes the appearance of








51

Figure I-6a, for g >g_. In a typical ESR experiment one

usually measures the first derivative of the absorption

signal. This spectrum appears in part b of Figure 1-6. The

perpendicular component is generally easily determined from

such a powder pattern. It is usually the strongest signal

observed. The parallel component is typically much weaker

and usually more difficult to detect. The values of g. and

g- can be determined as indicated assuming that the g tensor

is not very anisotropic.

Hyperfine interaction with spin containing nuclei can

split the pattern shown in Figure I-6b into (21+1) such

patterns. A simple case would be that of a molecule

containing an 1=1/2 nucleus. This is presented in Figure

I-6c. One important point is that the orientation of the

mi=l/2 pattern is opposite to that of the mi=-1/2 pattern.

This is because g, is approximately equal to g-, and Aj
Another common situation is that of the hyperfine splitting

for both parallel and perpendicular orientations are almost

equal and gi is shifted up-field from g,. In this case the

spectrum would contain two features like Figure I-6b

separated by the hyperfine splitting, A.



Molecular parameters and the observed spectrum

With all of this theory, the question now becomes what

can be learned from an ESR spectrum? To answer this, let us

begin with the solution of the spin Hamiltonian in axial









hvz=g/3Ho9,500 MHz

g =2.0023






H-A


Ho


MI Ms
1/2
1/2





-1/2





-1/2 1/2
1/2/2
1/2


H


Figure Figure 1-5. Zeeman energy levels of an electron
interacting with a spin 1/2 nucleus.














(a)



T I


I


(c)


Figure I-6. (a) Absorption and (b) first derivative
lineshapes of randomly oriented molecules with axial
symmetry and gS randomly oriented, axially symmetric molecules g . including hyperfine interaction with a spin 1/2 nucleus
(Az


( b)








54

symmetry including second order perturbations. This will

then show what molecular parameters can be uncovered from an

ESR spectrum.

Several authors (24,26,27,38) have given detailed

discussions of the spin Hamiltonian



(1-58) H})Spin = gjHz{S)z + g(3(Hx{S)x + Hy{S}y)

+ AI(I)z{S)z + Az({I)x{S}x + {I)y{S)y).



Considering the Zeeman term first, a transformation of axes

is performed to generate a new coordinate system x', y', and

z', with z' parallel to the field. If the direction of H is

taken as the polar axis and 0 is the angle between z and H,

then y can be arbitrarily chosen to be perpendicular to H and

hence y=y'. Therefore only x and z need to be transformed.

The Hamiltonian is transformed to



(I-59) {H} = gAH{S}z, + K{I}z,(S)z, + (AtA./K)(I)x,{S}x,

+ [(A 2-A1 2)/K](glg_/g2)sin0cosO{I}x,{S)I ,

+ A. I} )y,{S})y


n n
where 12 = AglcosO/Kg, 1x = AlgLsinx/Kg, and K22 =

A 2g2cos 2 + A.22g 2sin2e. Dropping the primes and using

ladder operators {S)+ = {S)x + i{S}y and {S)- = {S)x i{S)y,

this can be rewritten in the final form










(1-60) HSpin = g"H{S}z + K(S)zI)z

+ [((A 2 Al2)/K)((gig-)/g2)

cos9sine(({S)+ + {S)-)/2){})z]

+ [((AIAA )/4K) + AI/4]((S)+{I)+ + {S)-{I)-

+ [((A[A-)/4K) + A./4]({S)+(I)- + {S)- I)+).



This Hamiltonian can be solved for the energies at any angle

by letting the Hamiltonian matrix operate on the spin kets

IMS, MI>. The solution of the spin Hamiltonian is difficult

to solve at all angles except at 0=00 and 90'. Elimination

of some of the off-diagonal elements results in some

simplification and is usually adequate. The solution is then

correct to second order, and can be used when g#H >> A, and

A-, as is typically the case. The general second-order

solution is given by Rollman and Chan (44) and by Bleaney

(36). The energy levels are given by



(I-61) AE(M,m) = g3H + Km + (A.2/8G)[(A 2 + K2)/K2]

S[I(I+1) m2] + (A H2)(AI/K)(2M 1)



where K is AI and A- at 0=00 and 90, respectively, and

G=gSH/2. Also, M is the electron spin quantum number of the

lower level in the transition, and m is the nuclear spin

quantum number. The first two terms on the right result from

the diagonal matrix elements and yield equidistant hyperfine

lines. The last two terms cause spacing of the hyperfine








56

lines at higher field to increase, which is referred to as a

second-order effect. This solution is routinely applied

because the hyperfine energy is usually small and not

comparable to the Zeeman energy.

As described above, the hyperfine coupling constant

consists of both an isotropic and anisotropic part. The

isotropic part (Aiso) can be written as



(1-62) Aiso = (A, + 2AL)/3 = (8x/3)ge sgNN I(0)12



The isotropic hyperfine parameter can be used to determine

the amount of unpaired s spin density. The dipolar component

can be written as



(1-63) Adip = (A + AL)/3 = ge2gNN<(3cos20 1)/2r3>



These then relate the fundamental quantities W((0) 2 and

<(3cos20-1)/(2r3)> to the observed ESR spectrum. Approximate

spin densities in the molecule can also be obtained from Ais

and Adip.

Spin densities

The electron spin density, px at a nucleus X is the

unpaired electron probability density at the nucleus. In the

case of a single unpaired electron it is the fraction of that

electron/cm3 at a particular nucleus. The spin density of

the unpaired electron is generally split among s, p and d








57

orbitals. The spin density at nucleus X for an s electron is

given by psXlXsX(0)l2 and for electrons in a pa orbital the

spin density is given by Ppox.

Similar expressions can be given for px and da, etc.

orbitals. The terms psX and ppaX represent the contributions

of the s and pa orbitals to the spin density at nucleus X.

The isotropic and anisotropic hyperfine parameters can be

written as



X
(1-64) Aiso (molecule) = (8x/3)ge egiPNPsXIXsX(0)I



X
(1-65) Adip (molecule) = ge egIONPpoX

.


Since the equations above are characteristic of atom X, it is

possible to rewrite them for Aiso and Adip as given below



X X
(I-66) Also (molecule) = PsXAlso (atom)



X X
(1-67) Adip (molecule) = PpoXAdip (atom).


From Eqs. (1-66,67) one can easily obtain an expression

relating the unpaired spin density to the isotropic and

anisotropic hyperfine parameters,












X X
(1-68) PsX = Aiso (molecule)/Aiso (atom)

X X
(1-69) P2poX = Adip (molecule)/Adip (atom).



The hyperfine parameters for the molecule are obtained from

the ESR spectra. The hyperfine parameters for the atoms can

be obtained from tables (see Weltner (24), Appendix B) and

multiplied by the appropriate correction factors. The

correct value of Adip is calculated by taking the free atom

value of P = gepgNAN and multiplying it by an angular factor

a/2 = <(3cos2a-l)/2>. The factor equals 2/5 for a p

electron, 2/7 for a d electron and 4/15 for an f electron.

The value for Aiso (atom) can be found in Table B1 (column 5)

of Weltner (24) and the uncorrected value for Adip (atom) can

be found in column 7 of the same Table.



Quartet Sigma Molecules (S=3/2)

These high spin molecules (S>1) often contain transition

metals. The metal atom will generally have a large zero

field splitting (D) value due to its large spin-orbit

coupling constant ((})). If there are only a few ligands

attached to the metal atom, the unpaired electrons will be

confined to a small volume which will cause a sizable

spin-spin interaction. A large D value will cause many

predicted lines to be unobservable.










The spin Hamiltonian

A 4E molecule will exhibit a fine structure spectrum. A

theorem due to Kramer states that in the absence of an

external magnetic field the electronic states of any molecule

with an odd number of electrons will be at least doubly

degenerate. In the case of a quartet molecule the zero

field splitting produces two Kramer's doublets, or degenerate

pairs of states, with MS values of +1/2 and +3/2.

The spin Hamiltonian for a quartet sigma molecule with

axial symmetry can be written as



(1-70) (H}spin = gS Hz{S}z + g.Hx{S)x + D(({S}))2-5/4).



This equation does not take into account hyperfine structure.

A 4X4 spin matrix can be calculated which upon

diagonalization yields four eigenvalues



(1-71) W(+3/2) = D + (3/2)gSH

(1-72) W(+1/2) = D + (1/2)g,3H



and at zero field the +3/2 level and the +1/2 level are

separated by 2D. With H parallel to the molecular axis, the

energy levels will vary linearly with the magnetic field.

For the applied field perpendicular to the principal axis

(Haz) with Hx = H and Hz = 0, the eigenvalues are more

difficult to calculate because the off-diagonal terms are no








60

longer zero. The eigenvalue matrix can be expanded to yield

a quartic equation



(1-73) E4 1/2(1 + 15x2)E2 + 3x2E

+ (1/16)(1 + 6x2 + 81x4) = 0,



where E = W/2D and x = g-H/(2(3) O5D). Singer (45) has

developed a more general form of the equation which can be

applied to any angle. The eigenvalues for Hz can be

expressed as



(1-74) W(+3/2) = D + (3/8D)(g-SH)2 +

(1-75) W(+1/2) = -D + g- H (3/8D)(gj H )2 + ...



when H/D or x is small. By expanding E it can then be given

as E = a + bx + cx2 +... with the levels indexed by the low

field quantum numbers.

When D > gPH*({S all the matrix elements of the type

<+3/2|(H)Spinl1/2> = <+1/2{H})Spinl+3/2> vanish. This

approach yields the eigenvalues below,



(1-76) W(+3/2) = D + (3/2)gS3Hcose

(1-77) W(+1/2) = -D + (1/2)OzH(g12cos20 + 4gL2sin28)0.5



remembering that Hz = HcosO and Hx = Hsin6 and that the angle

between the molecular axis and the applied field is 9. This








61

is used to introduce the "effective" or apparent g value.

The effective g value generally indicates where the

transition occurs and is defined by assuming that the

resonance is occurring within the doublet, that is between MS

= +1/2 levels with g = ge. The g values of the observable

transitions 1+3/2> <-> 1-3/2> and 1+1/2> <-> |-1/2> become



(I-78) MS = +3/2 g = 3g, = 6.0 g = 0.0

(1-79) MS = +1/2 g- = go = 2.0 f. = 2gi = 4.0



for a large zero field splitting. The underlines indicate

the effective g value. The derivative signal for the +3/2

transition is usually undetectable because of the low

population of that level. There is not a significant

population of the +3/2 level unless D is very small. Also,

the absorption pattern corresponding to the g values for this

transition would be very broad. Finally, assuming that H/D

is large implies that the transition is forbidden. The

transitions usually observed for this spin state are those

between the +1/2 levels (the lower Kramer's doublet).

Kasal (46) and Brom et al. (47) have analyzed 4E molecules

and found the following spin Hamiltonian,

(I-80) (H}Spin = g$3Hz{S}z + g-p(Hx{S}x + Hy{S)y)

+ AI(I)z(S)z + A.({I}x(S}x + (I)y{S}y)

+ D[(S}z)2 (1/3)S(S+1)]










and rewrote it as an effective spin Hamiltonian



(I-81) (H)Spin = giHz({S}) + 2gpB(Hx(S)x + Hy{S}y)

+ A ({I)z(S)z + 2AL((I}x S})x + (I})y S)y)



for the +1/2 transition. The D term vanishes and S is taken

to be 1/2. The effective spin Hamiltonian can be rearranged

to be diagonal. The Zeeman terms become



(1-82) {H}spin = gOH{S}z + A(I)}{S)z

+ ((4(A12) (Ap)2)/A)

(2glg./g2)sin0cose{I)z{S}z

+ (1/2)A.[(AI + A)/A]( I})+(S}- + {I)-(S}+)

+ (1/2)A.[(Al + A)/A]((I)+(S)+ + (I)-(S}-)



where g2 = (g)2cos2O + 4(g )2sin20, and A2 = ((A )2

*(g1)2/g2) cos20 + (16(A.)2(g._)2/g2)sin2 This equation can

be solved analytically at 0 = 0 and by a continued fraction

method at 0 = 90". A computer program is usually used to

match the observed lines with those calculated by the

iterative procedure in order to come up with the values for g

and A.

The observed transitions and therefore the energy levels

are typically very dependent on 0 and D. Figures I-7 and I-8

indicate the levels as a function of field for the

perpendicular and parallel orientations, respectively. Two
































































Figure 1-7. Energy levels for a 4Z molecule in a
magnetic field; field perpendicular to molecular axis.






















980
0.0-
LP ,3.220
0. I1

LI 0.2-

0.3 -

04 ----------------------
0 I 2 3 4 5 6 7 8 9 10

H (Kilogauss)



Figure 1-8. Energy levels for a 4E molecule in a
magnetic field; field parallel to molecular axis.












1.0-

0.9 -

0.8-

0.7-

0.6-


0.5

0.4


0.2

0.1


234


6 7


8 9 10


H (Kilogauss)


Figure I-9. Resonant fields of a 4' molecule as a
function of the zero field splitting.


E
U








66

transitions are indicated between the same two levels at 690

and 1840 G. The reason for this can be seen in Figure 1-9.

The xy2 line is shown as an arc which reaches a maximum at

about 1000 G.



Sextet Sigma Molecules

The molecules considered here will have S=5/2, axial

symmetry (at least a three-fold symmetry axis), and a large

D. Ions such as Fe3 and Mn2+ fall in this category in some

coordination complexes.



The spin Hamiltonian

The spin Hamiltonian for a 6E molecule with axial

symmetry can be given as



(1-83) (H)Spin = geiHz(S)z + g--SHx{(S)xsin

+ D(((S})2 35/12)



including all angles. For 0 = 00 all of the off diagonal

elements are zero and the eigenvalues of the 6X6 matrix are

given below;



(1-84) E(+5/2) = (10/3)D + (5/2)g,~H

(1-85) E(+3/2) = -(2/3)D + (3/2)glOH

(I-86) E(+1/2) = -(8/3)D + (1/2)glpH.








67

Three levels appear at zero field which are separated by 2D

and 4D. Applying the magnetic field will split these into

three Kramers' doublets, which diverge linearly with field at

high fields and with slopes proportional to Ms.

A mixing of states occurs in the perpendicular case and

no simple solution is possible. A direct solution is

possible using a computer. This type of a solution has been

done by Aasa (48), Sweeney and coworkers (49), and by Dowsing

and Gibson (50). The eigenvalues of the 6X6 matrix

calculated by computer are shown in Figure I-10. The

diagonalization of the secular determinant was done at many

fields and at four angles. It is evident that the resonant

field for some transitions is very dependent on the angle.

The plot of zero field splitting versus the resonant field is

given in Figure I-11. It was prepared by solution of the

Hamiltonian matrix at many fields and D values for 0 equal to

0 and 90". For the situation were D >> hv the xy, line at

g=6 and the z3 line at g=2 will be most easily observed. As

can be seen in Figure I-10, these correspond to +1/2

transitions.



Infrared Spectroscopy



Sir William Herschel discovered infrared radiation in

1800, but it was not until the turn of the century that

infrared absorption investigations of molecules began (51).











1.6 d 0" -
300 -.... .. 6
60o --
1.4 90 -
1.2

1.0 .------ =-

0.8

0.6 -


0.2
0.0

-0.2
-0. 2 .. .. .... ... ... ..
----- ---






-0.6
>-O8





1.0 = ge -----
D = 1.32cm'''
-1.2 = 9.4 GHz
0 2 4 6 8 10 12 14 16 18 20
FIELD (kG)

Figure 1-10. Energy levels for a 6Z molecule in a
magnetic field for = 0, 30, 60, and 90.




















,0.5-
'E
%0.4-
Q-


I 2 3 4 5 6 7 8 9 10
H (Kilogauss)


Figure 1-11. Resonant fields of a 6E molecule as a
function of the zero field splitting.








70

The typical IR source is a Nernst glower which is heated by

passing electricity through it. The radiation, which is

emitted over a continuous range by the source, is dispersedby

using a prism, such as KBr, which is transparent over the

range of interest. Various types of detectors ranging from

thermocouples to photodetectors are used to analyze the light

which has passed through the sample.

When dealing with infrared spectroscopy, one usually

deals with three specific regions of the spectrum. The

region from 800 to 2500 nm is the near infrared region and

adjoins the visible region of the spectrum. The infrared

region is found between 2500 to 50,000 nm. And the far

infrared region borders the microwave region of the spectrum

and starts at 50,000 nm and extends to about 1,000,000 nm.

The far infrared region is used to analyze vibrational

transitions of molecules containing metal-metal bonds, as

well as the pure rotational transitions of light molecules.

Most spectrometers are used in the mid-infrared region.

This is where most molecular rotational and vibrational

transitions occur (51).



Theory

Since infrared spectra are due to the vibration and

rotations of molecules, a brief review of the theory may be

useful. When a particle is held by springs between two fixed

points and moved in the direction of one of the fixed points,










it is constrained to move linearly. A restoring force

develops as the particle is moved farther from its

equilibrium position. The springs want to return to their

equilibrium position. Hooke's law states that the restoring

force is proportional to the displacement.



(I-87) f = kx



where k is a constant of proportionality and called the force

constant. The displacement is given by x, and the restoring

force is f. The force constant is used as a measure of the

stiffness of the springs. When the particle is released

after the displacement, it undergoes vibrational motion. The

frequency of oscillation can be written as



(1-88) v = (1/2x)(k/m)0.5

where m is the mass of the particle. The frequency can also

be expressed in wavenumbers (cm-1) by dividing the right side

of the equation with the speed of light. Because we are

dealing with small particles (atoms in this case), it is

necessary to enter into a quantum mechanical description of

the oscillation. The allowed energy values are given by


Ev = (v + (1/2))hy,


(I-89)








72

where v is found in Eq.(I-88) and v is the vibrational

quantum number. The equation above tells us that the energy

of the harmonic oscillator can have values only of positive

half-integral multiples of hy. The energy levels are evenly

spaced, and the lowest possible energy is (1/2)hv even at

absolute zero (52).

If one analyzes the vibrational behavior of a simple

molecular system, such as a diatomic molecule, the system's

oscillatory motion will be nearly harmonic and the frequency

of the motion can be described by



(1-90) v(cm-1) = (1/2xc)(k/g)0.5



where p is the reduced mass of the particles and is defined

as



(1-91) p = (ml"2)/(m1 + m2)

Since the motion of the atoms is not completely harmonic, we

must look at the energy levels of an anharmonic oscillator.

This is given by



(1-92) Ev = (v + (1/2))hv (v + (1/2))2huvx

+ (v + (1/2))3hvye .



where the constants Xe, Ye, ... are anharmonicity constants.










These are small and typically positive and usually of the

magnitude IXel > |Yel > Izel >... (53).

Anharmonicity in a molecule allows transitions to be

observed which are called overtones. These are transitions

between v=0 and v=2 or v=3 which are designated the first and

second overtones, respectively. The first overtone is

usually found at a frequency which is a little less than

twice the fundamental frequency. Combination bands can also

arise. These are caused by the sum or difference of two or

more fundamentals.

The force constant for a molecule is related to the bond

strength between the atoms. The force constant for a

molecule containing a multiple bond is expected to be larger

than the force constant of a single bond. A large force

constant is also usually indicative of a strong bond. For

diatomic molecules there is a good correlation between (k)0.5

and u(cm-1). This relationship unfortunately does not hold

for polyatomic molecules. In this case force constants must

be calculated by a normal coordinate analysis of the

molecule. Several authors have presented detailed

descriptions of this method (51-54).

The vibrations of a molecule depend on the motions of

all of the atoms in the molecule. To describe the location

of the atoms relative to each other one looks at the degrees

of freedom of the molecule. In a molecule with N atoms, 3N

coordinates are required to describe the location of all of











the atoms (3 coordinates for each atom). The position of the

entire molecule in space (its center of gravity) is

determined by 3 coordinates. Three more degrees of freedom

are needed to define the orientation of the molecule. Two

angles are needed to locate the principal axis and 1 to

define the rotational position about this axis. For a linear

molecule the rotation about the molecular axis is not an

observable process. The number of vibrations of a polyatomic

molecule is given then by



(1-93) number of vibrations = 3N 6



for a nonlinear molecule and



(1-94) number of vibrations = 3N 5



for a linear molecule.

What is observed in an infrared spectrum is usually a

series of absorptions. These correspond to various

stretching and bending frequencies of the sample molecule. In

order for an infrared transition to be observed, there needs

to be a change in the dipole moment of the molecule when it

undergoes a stretching or bending motion. The strongest

bands are those corresponding to the selection rule


(1-95) Avk = +1


1


and Avi =













where j does not equal k and k equals 1, ..., 3N-6.

The most intense absorptions are those from the ground

vibrational level since that is typically the most populated

level. These type of transitions are called fundamental

frequencies. These frequencies differ from the equilibrium

vibrational frequencies, Vl,e, v2,e ..... .The fundamental

frequencies are the ones generally used in force constant

calculations because the available information is typically

not sufficient to allow the calculation of anharmonicity

constants. The fundamental frequencies of the molecule need

not be the most intense absorptions. This can happen if the

change in dipole moment, (6d/6Qk), is small or zero (51).

The phase or environment that the molecule is in will

affect the appearance of the IR spectrum. With gas phase

samples it is often possible to resolve the rotational fine

structure of the compound using high resolution instruments.

On the other hand, when dealing with a matrix isolated

sample, there usually is not much, if any, rotational fine

structure even under high resolution. This is because the

molecule is rigidly held (small molecules such as HC1 exhibit

a rotational spectrum due to a hindered rotation within the

matrix site) within the lattice of the matrix, and is not

able to rotate freely as it is able to do in the gas phase.

The elimination of the rotational fine structure simplifies

the spectrum and enables the analysis of more complicated








76

vibrational spectra which arise when studying larger

molecules.



Fourier Transform IR Spectroscopy

The basic components of an FTIR instrument are an

infrared source, a moving mirror, a stationary mirror, and a

beamsplitter. The source in a typical FTIR spectrometer is a

glower which is heated to about 1100 *C by passing an

electrical current through it. The beam from the glower is

directed to a Michelson interferometer where the intensity of

each wavelength component is converted into an ac modulated

audio frequency waveform. Assuming that the source is truly

monochromatic, a single frequency, A/c, hits the

beamsplitter, where half is transmitted to the moving mirror

and half to the fixed mirror. The two components of the

light will return in phase only when the two mirrors are

equidistant from the beamsplitter. In this case constructive

interference occurs and they reinforce each other.

Destructive interference occurs when the moving mirror has

moved a distance of A/4 from the zero position. This means

that the radiation which goes to the moving mirror will have

to travel A/2 further than the radiation that went to the

fixed mirror, and the two will be 180* out of phase. As the

components go in and out of phase, the sample and the

detector will experience light and dark fields as a function










of the mirror traveling +x or -x from its zero position. The

intensity at the detector can be expressed as


(I-96)


I(x) = B(v)cos(2nxv),


where I(x) is the intensity, B(v) is the amplitude of

frequency v, and x is the mirror distance from the zero

position. For a broadband source the signal at the detector

will be the summation of Eq.(I-96) over all frequencies, and

the output, as a function of mirror movement x, is called an

interferogram (53).

The interferogram can then be converted into the

typical intensity versus frequency spectrum by performing a

Fourier transformation. The signal is transformed from a

time domain signal, which arises from the motion of the

mirror, to a frequency domain signal which is observed in the

typical IR spectrum. This can be done mathematically by

using

(1-97) C(y) = fI(x)cos(2xxv)dx,



where C(v) is the intensity as a function of frequency.

There are several advantages in using an FTIR

instrument. The detector in a Fourier transform instrument

gets the full intensity of the source without an entrance

slit. This yields a 100 fold improvement over the typical

prism and grating instrument. The signal to noise ratio is








78

theoretically improved by a factor of M1/2, where M is the

number of resolution elements. This has been termed

Fellgett's advantage since it results mathematically from one

of his derivations. A direct result of Fellgett's advantage

is that a dispersive instrument requires 3000 seconds to

collect a spectrum, whereas an interferometer needs only

about 60 seconds to collect an IR spectrum with the same

signal to noise ratio. (M equals about 3000 and the

observation time is about 1 sec/element) (53).

A complete IR investigation, when possible, can enable

one to determine the structure of the molecule of interest.

The IR spectrum allows one to determine force constants of

the various bonds and from that information the bond

strengths can be determined. The bending frequencies even

enable one to determine the bond angle between the atoms

involved in the bending motion. The shift in both stretching

frequencies and bending frequencies caused by the

substitution of isotopes into a molecule is very useful

towards this purpose since the amount of the shift is

dependent on the change in mass when the isotope is

substituted into the molecule.












CHAPTER II
METAL CARBONYLS


ESR of VCOn Molecules

Introduction

Transition-metal carbonyl molecules continue to be of

great interest, partially because of their relevance to

catalysis. The simplest molecules, those containing only one

metal atom, have been studied spectroscopically, and electron

spin resonance (ESR) has been applied successfully in some

cases, specifically to V(CO)4, V(CO)5 (55), V(CO)6 (56-59),

Mn(CO)5 (60), Co(CO)3. Co(CO)4 (61.62), CuCO, Cu(CO)3

(63,64), and AgCO, Ag(CO)3 (65,66). (Ionic carbonyls have

also been observed via ESR (67.68) but will not be explicitly

discussed here.) Theoretical discussions of the geometries,

ground states, and bonding in these types of molecules have

been given by several authors beginning perhaps with Kettle

(69) and then by DeKock (70), Burdett (71,72), Elian and

Hoffmann (73), and Hanlan, Huber, and Ozin (74). Although a

number of ab initio calculations have been made on such

carbonyls, the vanadium molecules considered here apparently

have not been treated in detail.

The background for the present investigation was

provided by the matrix work of Hanlan, Huber, and Ozin (74)

who observed the infrared spectra of V(CO)n where n equals 1








80

to 5, in the solid rare gases. Most notably, those authors

concluded, from experiment and theory, that [1] VCO is

nonlinear, [2] V(CO)2 exists in linear, cis, and trans forms

in all three matrices, argon, krypton, and xenon, [3] V(CO)3

is probably of D3h trigonal planar geometry. It should be

emphasized that the supporting theory usually assumed

low-spin ground states.

Morton and Preston have prepared V(CO)4 and V(CO)5 in

krypton matrices by irradiation of trapped V(CO)6. From ESR

they assign V(CO)4 as a high-spin 6A1 in tetrahedral (Td)

symmetry and V(CO)5 as 2B2 with distorted trigonal bipyramid

(C2v) symmetry. The V(CO)6 molecule is a well known stable

free radical which has been rather thoroughly researched by

infrared (75), MCD (76), ultraviolet (77), electron and X-ray

diffraction (78), and ESR. It is presumably a Jahn-Teller

distorted octahedral (2T2g) molecule at low temperatures

leading to a 2B2g ground state.

Our ESR findings are only for V(CO)n, where n equals 1

to 3, and are not always in agreement with conclusions from

optical work and semiempirical theory. The most explicit

departure is in finding that VCO and V(CO)2 are high-spin

molecules.

Experimental

The vanadium carbonyls synthesized in this work were

made in situ by co-condensing neon (Airco, 99.996% pure),

argon (Airco, 99.999% pure), or krypton (Airco, 99.995% pure)








81

doped with 0.1-5 mol% 12CO (Airco, 99.3% pure) or 13C0

(Merck, 99.8% pure) with vanadium metal [99% pure, 99.8%

51V(I=7/2)] onto a flat sapphire rod maintained at 4-6 K but

capable of being annealed to higher temperatures.

The furnace, Hell-Tran, and IBM/Bruker X-band ESR

spectrometer have been previously described (79). Vanadium

was vaporized from a tungsten cell at 1975 *C, as measured

with an optical pyrometer (uncorrected for emissivity).



ESR Spectra

VCO

Two ESR spectra of the VCO molecule were observed in

matrices prepared by condensing vanadium into CO/argon

mixtures at 4 K. We designate these two forms of VCO below

as (A) and (a). This symbolism is derived from one of their

distinguishing features: one has a considerably larger 51V

hyperfine splitting (hfs) than the other. Only the (a) form

survived after annealing the argon matrices and only it

appeared in a krypton matrix. Only (A) was observed in solid

neon.



51VCO(A) and 51VCO(a) in argon

Upon depositing vanadium metal into an argon matrix

doped with 1.0 mol% 12CO, we obtained the 4 K ESR spectrum

shown in Figure II-1. The two sets of eight strong, sharp

lines centered near 1200 G could be attributed to separate








82

species since upon annealing one set [designated by (A)]

disappeared. The hyperfine splitting (hfs) in the

perpendicular xy1 and xy3 lines of the (A) species due to

51V(I=7/2) is approximately 100G, whereas that in the (a)

species is about 60 G. The line centered at about 8100 G has

been observed with that intensity only once, but its

appearance, and disappearance upon annealing, correlates best

with the (A) molecule. Its complex hfs is indicative of an

off-principal axis line where forbidden AmI not equal to zero

transitions can also occur. The observed lines of both (a)

and (A) are listed in Tables II-1 and 11-2.

Annealing to 16 K and quenching to 4 K converted the

VCO (A) species into (a) which has the spectrum in argon in

Figure 11-2. Again the xy1 and xy3 lines have the same hfs,

now about 60 G, and an "extra" line appears but centered at

about 6700 G.



51V13CO (A) and 51V13CO (a) in argon

These same spectra can be observed when 13CO replaces

12CO and the effect upon the xy1 line, which is the same

effect for (A) and (a), is shown in Figure 11-3. Each line

is split into a doublet separated by about 6 G, indicating

most importantly that there is only one CO in each species.

51VCO (A) in neon

In neon only one VCO molecule appears to be trapped,

the one designated as (A) in argon with the hfs of about













Table II-1. Observed and calculated line positions
(in G) for VCO (X6W) in conformation (A)
in argon at 4 K. (v = 9.5596 GHz)

MI(51V)a xy1 xy3 Extra lines
0 = 100
Obs. Calc. Obs. Calc. Obs. Calc.

7/2 797 789 5065 5082 7906 7897
5/2 882 877 5154 5170 8015 8012
3/2 974 971 5254 5262 8119 8124
1/2 1072 1072 5364 5360 8252 8234
-1/2 1174 1176 5473 5463 8346 8344
-3/2 1282 1285 5584 5573 8467 8453
-5/2 1396 1400 5692 5689 -- 8562
-7/2 1511 1519 5819 5814 -- 8671
AMI=l+ transitions
Derived Parameters Obs. Calc.

g| 2.002(37) 7944 7938
g- 1.989(5) 7976 7970
IAi(51V)I 247(28)MHz 8054 8052
IA(51V)I 288(6) MHz 8083 8083
|DI 0.603(2)cm-1 8161 8164
Aiso(51V)a 274(13)MHz 8192 8194
Adip(55V)a -14(11)MHz 8252 8274
AL(13C)O 17(3) MHz 8304 8304
8380 8384
8423 8413
-- 8493
8514 8521
-- 8603
-- 8630


a Assuming A, and A- are positive

() Error of the reported value













Table II-2. Observed and calculated line positions
(in G) for VCO (X6W ) in conformation (a)
in argon at 4 K. (v = 9.5596 GHz)

MI(51V)a xy1 xy3 Extra lines
0 = 12*
Obs. Calc. Obs. Calc. Obs. Calc.


7/2 940 940 4460 4461 6449 6448
5/2 1000 999 4520 4520 6530 6526
3/2 1061 1060 4581 4580 6603 6603
1/2 1124 1124 4645 4644 6684 6680
-1/2 1191 1190 4710 4709 6756 6755
-3/2 1258 1257 4777 4777 6828 6831
-5/2 1326 1327 4847 4847 6906 6907
-7/2 1396 1398 4918 4921 -- 6983


AMI=l transitions


Dervived


gl
g-
IA (51V)
fA (51V)

|D I

Also(51V)a
Adip(51V)a
IAL(13C) I


Paramenters


2.002(10)
1.998(3)
165(14)MHz
183(1) MHz
0.452(2)cm-1
177(5) MHz
-6(5) MHz
17(3) MHz


Obs.
6476
6502
6563
6590
6637
6665
6711


6782
6804
6857
6887
6934


a Assuming A, and A-. are positive.

() Error in the indicated value


Calc.
6479
6496
6556
6573
6633
6650
6709
6726
6785
6802
6861
6877
6937
6953










6I VCO(A)/ARGON


I I I I 1 I I 1 I


I I I I I I


VCO(a)


I I I I I II .I


7.7 79 8.1 8.3 8.5





I I I I I I I I
5.0 5.2 5.4 5.6 5.8


1 1, I 1, IX Y,


I I I I I I I I


_I H(KG)

Figure II-1. ESR spectrum of an unannealed matrix at
4 K containing 51VCO(A). with hfs of about 100 G, and
51VCO(a), with hfs of about 60 G. For the conformation
(A) two perpendicular lines and an off principle axis
line are shown. v = 9.5585 GHz.


VCO(A)

I


e==1i


I I I I I I I


I































































Figure 11-2. ESR spectrum of an annealed argon matrix
at 4 K containing only 51VCO in conformation (a). Two
perpendicular lines and off principal axis line are
shown. v = 9.5585 GHz.




Full Text

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


SPECTROSCOPIC INVESTIGATIONS OF
METAL CLUSTERS AND METAL CARBONYLS
IN RARE GAS MATRICES
By
STEPHAN BRUNO HEINRICH jJIACH
A DISSERTATION PRESENTED TO
OF THE UNIVERSITY
IN
PARTIAL
THE
THE GRADUATE SCHOOL
OF FLORIDA
FULFILLMENT OF THE REQUIREMENTS FOR
DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1987

TO MY PARENTS

ACKNOWLEDGEMENTS
The author wishes to extend his deepest thanks and
appreciation to Professor William Weltner, Jr., whose
patience, understanding, encouragement, and professional
guidance have made all of this possible. Thanks are also due
to Professor Bruce Ault for the initial opportunity do matrix
work and the encouragement to continue on to do graduate work
in the field. Thanks need also be given to Professor
Weltner's research group, specifically to Dr. Richard Van
Zee, whose help and guidance were invaluable in completing
this work .
The author also wishes to acknowledge the assistance of
the electronics, machine, and glass shops within the
Department of Chemistry. They kept the equipment
functioning, and fabricated new pieces of apparatus when
necessary making it possible to perform the desired
experiments. Thanks are also due to Larry Chamusco for many
enlightening conversations regarding the present work and
also for his help in preparing this work for publication.
Thanks are also due to Ngai Wong for his assistance in
preparing the final version of this publication.
The author also wishes to acknowledge the support of
the National Science Foundation (NSF) for this work as well
as Division of Sponsored Research for support in completing
the work for this project.

TABLE OF CONTENTS
page
ACKNOWLEDGEMENTS iii
LIST OF TABLES vii
LIST OF FIGURES ix
ABSTRACT xiii
CHAPTERS
I INTODUCTI ON 1
Matrix Isolation 1
Theory of Cluster Formation 19
ESR Theory 30
The Hyperfine Splitting Effect 34
Doublet Sigma Molecules 40
The spin Hamiltonian 40
The g tensor 42
The A tensor 46
Randomly oriented molecules 49
Molecular parameters and
the observed spectrum 51
Spin densities 56
Quartet Sigma Molecules (S=3/2) .... 58
The spin Hamiltonian 59
Sextet Sigma Molecules 66
The spin Hamiltonian 66
Infrared Spectroscopy 67
Theory 70
Fourier Transform IR Spectroscopy .. 76
II METAL CARBONYLS 79
ESR of VCOn Molecules 79
Introduction 79
Experimental 80
ESR Spectra 81
VCO 81
51VC0(A) and 51VC0(a) in argon ... 81
51v13Co(a) and 51V*3CO(a) in argon 82
51VCO(A) in neon 82
51VC0(a) in krypton 88
51V(12CO)2 and SlV(13C0)2 in neon 89
51V(12C0)3 and 51V(13CO)3 in neon 89

page
Analysis 96
VCO, (A) and (a) 96
V(CO)2 98
V(C0)3 98
Discussion 100
VCO 100
V(CO)2 106
V(C0)3 107
Conclus ion 108
Infrared Spectroscopy of First Row
Transition Metal Carbonyls 109
Introduction 109
Experimental 109
Spectra 110
Discussion 115
Conclusion 119
III E SR STUDY OF A SILVER SEPTAMER 121
Introduction 121
Experimental 122
ESR Spectra 123
Analysis and Discussion 129
IV ESR OF METAL SILICIDES 137
ESR of AgSi and MnSi 137
Introduction 137
Experimental 137
ESR Spectra 138
AgSi 138
MnSi 139
Analysis and Discussion 139
AgSi 139
MnSi 145
ESR of Hydrogen-Conta ining Scandium-
Silicon Clusters 148
Introduction 148
Experimental 149
ESR Spectra 150
HScSiHn 150
H2ScSiHn 156
Analysis and Discussion 157
HScSiHn 157
H2ScSiHn 166
v

page
V CONCLUSION 172
REFERENCES 178
BIOGRAPHICAL SKETCH 187
vi

LIST OF TABLES
Table Page
11 — 1. Observed and calculated line positions (In G)
for VCO (X6£) in conformation (A) in argon at
4 K . v = 9.5596 GHz 83
I I - 2 . Observed and calculated line positions (in G)
for VCO (X6£) in conformation (a) in argon at
4 K. v = 9.5596 GHz 84
II - 3. Observed line positions (in G) for VCO (X6£)
in conformation (A) in neon at 4 K.
v = 9.5560 GHz 90
11 -4 . Observed and calculated line positions (in G)
for V(C0)2 (X4£ ) isolated in neon at 4 K.
v = 9.5560 GHz.7 91
11 - 5 . Calculated and observed line positions and
magnetic parameters of the V(CO)3 molecule
in neon matrix at 4 K. v = 9.55498 GHz 92
11 - 6 . Carbonyl Stretching Frequencies for the First
Row Transition Metal Carbonyls 112
II I — 1 . Calculated and observed ESR lines of 109Ag7 in
solid neon at 4 K {v = 9.5338 GHz)
See Figure 11 I -3 125
III -2 . Magnetic parameters and s-electron snin
densities for *09Ag7 cluster in its ^A2
ground state, (a) 131
II I — 3. Comparison of the magnetic parameters of
107Agrj (this work) with those of Howard,
et al.'s 107Ag5 cluster 135
III — 4. Spin densities (s-electron) compared for the
^A2 ground states of the Na7, K7> and Ag7 136
IV-1 . Observed and Calculated Line Positions (in Gauss)
for AgSi in argon at 14 K. (v = 9.380 GHz) 140
IV-2 . Observed and Calculated Line Positions (in Gauss)
for MnSi in argon at 14 K. (v = 9.380 GHz) 141
IV-3. Hyperfine parameters and calculated spin densities
for MnSi in argon at 14 K. (y = 9.380 GHz) 147
vi i

page
IV-4. Observed and calculated line positions (in Gauss)
for HScSiHn in argon at 14 K. (u = 9.380 GHz)... 151
IV-5. Hyperfine parameters and calculated spin densities
for HScSiHn in argon at 14 K. {v = 9.380 GHz)... 152
IV-6. Observed and Calculated Line Positions (in
Gauss) for H2ScSiHn, the (A) site, in argon
at 14 K . ( v = 9.380 GHz ) 158
IV-7. Hyperfine parameters and calculated spin
densities for H2ScSiH , site (A), in argon
at 14 K. ( v = 9.380 GHz ) 159
IV-8 . Observed and Calculated Line Positions (in
Gauss) for H2ScSiHn> the (a) site, in argon
at 14 K. (v = 9.380 GHz) 160
IV- 9 . Hyperfine parameters and calculated spin
densities for H2ScSiHn, site (a), in argon
at 14 K. (v = 9.380 GHz ) 161
vi i i

LIST OF FIGURES
Figure
Page
1-1. The furnace flange with copper electrodes and
a tantalum cell attached 10
1-2. The EPR cavity and deposition surface within
the vacuum vessel. The apparatus is capable
of cooling the rod to 4 K, because of the
liquid helium transfer device (Heli-Tran)
on the top 11
1-3. The ESR cavity and deposition surface within
the vacuum vessel. The apparatus is capable of
cooling to 12 K because of the closed cycle
helium refrigeration device (Displex) on the
top 12
1-4. The vacuum vessel, deposition surface, Displex,
and furnace assembly for infrared experiments... 13
1-5. Zeeman energy levels of an electron interacting
with a spin 1/2 nucleus 52
1-6. (a) Absorption and (b) first derivative line-
shapes of randomly oriented molecules with
axial symmetry and gj_ (c) first derivative lineshape of randomly
oriented, axially symmetric molecules
g-i- with a spin 1/2 nucleus (A_l 1-7. Energy levels for a 4£ molecule in a magnetic
field; field perpendicular to molecular axis.... 63
1-8. Energy levels for a 4£ molecule in a magnetic
field; field parallel to molecular axis 64
1-9. Resonant fields of a 4£ molecule as a function
of the zero field splitting 65
I-10. Energy levels for a £ molecule in a magnetic
field for 0 = 0°, 30°, 60°, and 90° 68
I — 11 . Resonant fields of a £ molecule as a function
of the zero field splitting 69
ix

page
11 — 1 . ESR spectrum of an unannealed matrix at 4 K
containing 51VCO(A), with hfs of about 100 G,
and 51VC0(a), with hfs of about 60 G. For the
conformation (A) two perpendicular lines and
an off principle axis line are shown.
v = 9.5585 GHz 85
I I - 2 . ESR spectrum of an annealed argon matrix at 4 K
containing only 51VC0 in conformation (a). Two
perpendicular lines and off principal axis
line are shown, v = 9.5585 GHz 86
II-3. ESR spectrum of the perpendicular xy^ line of
51y13co in conformation (a) in an argon matrix
at 4 K. v = 9.5531 GHz 87
II — 4 . ESR lines in a neon matrix at 4 K attributed to
51VC0 in conformation (A), v = 9.5560 GHz 93
11 -5 . ESR lines in a neon matrix at 4 K attributed to
51V(C0)2. v = 9.5560 GHz 94
11 — 6 . (Top) ESR spectrum near g = 2 in a neon matrix
at 4 K attributed to an axial 31V(C0)3 molecule.
v = 9.5584 GHz.
(Bottom) Simulated spectrum using g, A(51V)
parameters and linewidths given in the text.... 95
11-7. Molecular orbital scheme for the 6£ VC0
molecule (modeled after Fig. 5-43 in DeKock
and Gray (84)) 101
11 - 8. Infrared spectrum of CrCO using both 12C0 and
13C0 in argon. The top trace has a 1:200 CO/Ar
concentration and the bottom has a 1:1:200
12CO/13C0/Ar concentration 113
11 — 9. Infrared spectrum of Mn and CO codeposited into
an argon matrix. The bottom trace is after
annealing the matrix to about 30 K and cooling
back down to 14 K 114
11 -10. Plot of the CO stretching frequencies in the
first row transition metal monocarbonyl
molecules MC0 (circled points are tentative).
Also shown is the variation of the energy of
promotion corresponding to 4s23dn_2 to As^d11-1,
where n is the number of valence e1ectrons(91 ) . 117
x

page
111 -1 .
The pentagonal bipyramid structure ascribed to
Ag7 in its 2A2 ground state. It has D5fl symmetry
with two equivalent atoms along the axis and
five equivalent atoms in the horizontal plane.. 126
III-2. The ESR spectrum of 109Ag in solid neon matrix
at 4 K (v = 9.5338 GHz). The top trace is the
overall spectrum, and the bottom traces are
expansions of the three regions of interest
after annealing. Notice the large intensity
of the silver atom lines at 3000 G before
annealing 127
I I I -3 . The ESR spectrum of 109Agy in a solid neon
matrix at 4 K (v = 9.5338 GHz). The fields
indicated are the positions of the four
hyperfine lines corresponding to
| J , Mj > = |1,1>, |1,0>, | 0,0 > , and J1 , 1 >
(see Table III-l). The spacing within each of
the four 6-line patterns is uniformly 8.7 G.
The few extra lines in the background of the
lines centered at 3006 G are due to residual
109Ag atom signals 128
IV-1. The ESR spectrum of AgSi is an argon matrix at
12 K. The line positions of the impurities (CHg
and S i H 3) are noted, v = 9.380 GHz 142
IV-2. The ESR spectrum of MnSi in an argon matrix at
1 2 K . v = 9.380 GHz 143
IV-3. The ESR spectrum of Sc codeposited with Si into
an argon matrix at 12 K. The eight sets of
doublets are shown for HScSiHn. v = 9.380 GHz.. 153
IV-4. The mj= -1/2 and -3/2 transitions for HScSiHn
at 12 K. Two different rod orientations are shown.
The top is with the rod parallel to the field and
the bottom trace is for the rod perpendicular to
the field, v = 9.380 GHz 154
IV-5. The ESR spectrum in the g=2 region after
annealing a matrix containing both Si and Sc
(u = 9.380 GHz). The doublets due to HScSiHn have
disappeared. The only remaining lines are due to
impurities and H2ScSiHn (noted) 155
xi

page
IV-6. The ESR spectrum (mj=7/2 and 5/2) for H2ScSiHn
in argon at 12 K after annealing to about 30 K
The top trace is for the rod perpendicular to
the field and the bottom trace is for the rod
parallel to the field, v = 9.380 GHz 162
IV-7. Same as Figure IV-6 except the mj=3/2 and -3/2
transitions are shown 163
IV-8. Same as Figure IV-6 except the mj = l/2 transition
is shown 164
IV-9. Same as Figure IV-6 except the mj = -5/2 and -7/2
transitions are shown 165
xi i

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
SPECTROSCOPIC INVESTIGATIONS OF METAL CLUSTERS AND
METAL CARBONYLS IN RARE GAS MATRICES
By
STEPHAN BRUNO HEINRICH BACH
December, 1987
Chairman: Professor William Weltner, Jr.
Major Department: Chemistry
Three vanadium carbonyls were formed by codeposition of
vanadium vapor and small amounts of x CO and AOC0 in neon,
argon, and krypton. Two of the species were high spin (S>1)
molecules. For VCO (S=5/2) two conformations of almost equal
stability were trapped in various matrices. The dicarbonyl
was also observed and found to have an S=3/2 ground state and
a zero field splitting parameter |D| = 0.30 cm’ , Also
observed only in a neon matrix was V(C0)g. The ground state
2 1 2
for this axial molecule is either Aj or A^ depending on
whether it has planar D3fl or pyramidal C 3 V symmetry.
Other first row transition metal carbonyls were studied
using Fourier transform infrared spectroscopy. When chromium
and CO were codeposited into an argon matrix, a molecule was
formed with CO for which a stretching frequency at 1977 cm’-*
x i i i

was observed. An attempt is made to relate the bonding of
first row transition metal monocarbonyl molecules to the
observed infrared CO stretching frequencies of these
molecules.
A cluster of seven silver atoms was produced when the
109 isotope of silver was vaporized and deposited into a neon
matrix and analyzed using electron spin resonance
spectroscopy. The product signals were strongest after the
matrix had been annealed. From the observed hyperfine
splittings it was determined that the cluster has a
pentagonal bipyramidal (05^ symmetry) structure with a A2
ground state. Its properties are shown to be similar to
those found by other workers for the Group IA alkali metal
septamers .
Pure metal clusters were isolated when silicon was
codeposited with silver and manganese. Silver silicide was
isolated in an argon matrix and found to have a doublet
ground state. Manganese silicide was observed in both argon
and neon matrices and found to have an S=3/2 ground state.
Hyperfine parameters have been determined for both species.
Si 1 i con-conta ining scandium hydrides have also been observed
in argon matrices upon codeposition of silicon and scandium
vapor. The two species identified contained one and two
hydrogens attached to the scandium. Both molecules were
found to have doublet ground states. Hyperfine parameters
were determined for both species.
x i v

CHAPTER I
INTRODUCTION
Matrix Isolation
Matrix isolated metal clusters and metal carbonyls can
be studied in a variety of ways and are thought to aid in the
understanding of metal catalysts. The methods of studying
these compounds are as diverse as the compounds themselves,
varying from optical methods such as infrared. Raman,
uv-visible. to electron spin resonance and magnetic circular
dichroism spectroscopies which probe the cluster for its
magnetic and electronic properties. Using these varied
techniques, it is possible to determine the electronic
structure of the metal clusters. This information can then
be tied together with theoretical calculations to elucidate
the properties of the metal cluster.
Before the advent of matrix isolation, the study of
metal clusters was carried out either in the gas phase or in
solutions. Matrix isolation was developed in the mid-1950's
by George Pimentel and coworkers (1). The technique was
developed as a means of studying highly unstable reaction
intermediates which would, under standard conditions, be too
short lived to be observed. It has since been applied to a
wide variety of systems which have one thing in common: The
species of interest are too unstable to be studied under
normal laboratory conditions.
1

2
Several things are required in order to do matrix
isolation. First, the experiments require a high vacuum
— fi
environment. This means a pressure below 1x10 torr must be
maintained in order to minimize the amount of atmospheric
impurities that will be trapped within the matrix. This type
of a vacuum is usually achieved using an oil diffusion and a
mechanical pump with a liquid nitrogen cold trap.
Matrix isolation experiments are usually carried out
between 4 and 15 K. This temperature range can be achieved
by one of two methods depending upon the desired minimum
temperature. Using commercially available closed cycle
helium refrigerators is one way to cool the deposition
surface to the desired temperature. The only drawback of
this system is that the minimum temperature the refrigerator
can achieve lies at about 12 K (Recent advances have produced
a closed cycle system which is capable of 4 K, but their cost
is prohibitive). An alternative to this method is to simply
use liquid helium to cool the deposition surface. This can
be done by using either a dewar or a commercially available
transfer device such as the Air Products Heli-tran. These
devices can achieve a low temperature in the neighborhood of
4 K .
The final consideration in setting up this type of
experiment is the substrate on which to deposit the matrix.
Types of material for this surface range from Csl (or other
suitable alkali halide salts), to sapphire, or to polished

3
metal surfaces. Factors to be considered when choosing the
substrate depend on the type of experiment being done, but
all such solids must have high thermal conductivity. Also,
optical properties must be considered when doing absorption
or emission studies, whereas magnetic susceptibilities are of
concern in ESR and MCD. Obviously, the purity of the solid
substrate is important since even small amounts of some
impurities can cause strong absorptions or magnetic
perturbations.
The term "matrix isolation" comes about because the
molecules of interest are trapped in a matrix of inert
material, usually a noble gas such as neon, argon, krypton,
or nitrogen. The trapping site is usually a substitutional
site or an imperfection in the crystalline structure of the
solid gas, and the trapped species, seeing only inert nearest
neighbors, are isolated and can not react further.
Trapping the metal atom in the matrix is fairly
straightforward once the method of atomizing the metal has
been determined. But, a problem arises in producing metal
di, tri, and higher-order species. It is unusual to simply
deposit a matrix and get a species other than a monomer or a
dimer. In order to get these higher order species of
interest several techniques can be used.
The most common technique used is to simply anneal the
matrix. Annealing involves depositing the matrix, and then
warming it. The amount that the matrix is warmed depends on

4
two things, the matrix gas being used and the trapped
species. A matrix can usually be annealed up to a
temperature equal to approximately one third that of its
melting point without solid state diffusion occurring. The
problem that occasionally arises is that once the temperature
of the matrix has begun to rise, it is possible for some
reactions to occur due to diffusion of smaller atoms or
molecules that are trapped. This might induce an exothermic
reaction, causing the matrix to heat more rapidly than
intended, exceeding the capability of the cooling system to
dissipate the heat produced. The pressure then rises and
rapid evaporation of the matrix occurs (2).
Photoaggregation is another method employed to produce
metal clusters after the matrix has been deposited. This
method usually involves photo-excitation of the metal which
causes local warming of the matrix as the metal atom
dissipates the excess energy. This partial warming loosens
the matrix around the metal atom allowing it to diffuse and
possibly interact with other metal atoms in the vicinity.
This method has been used to successfully produce silver
clusters by Ozin and coworkers (3).
Using different matrix gases can also give differing
results as to the size of the metal molecules formed. These
differences arise for several reasons. The most obvious is
that the different solid "gases" will have different sized
substitutional and interstitial spaces. Another consideration

5
is the rate at which the matrix freezes. This will depend
not only on the capacity of the cooling system to dissipate
the excess energy, but also on the freezing point of the gas.
It is important to remember that the amount of energy that
the cooling system can dissipate depends on the temperature
to which it must cool the deposition surface. The Displex or
Helium dewar can dissipate substantially more energy at a
higher temperature, such as that necessary to freeze krypton
(melting point 140 K) rather than neon, which freezes at
about 20 K. This difference in freezing rates will allow a
varying amount of time for the atoms to move around on the
surface of the matrix which is in a semi-liquid state. The
longer the atoms can move on the surface of the matrix, the
greater the chance for the aggregation and formation of small
metal molecules (2). The kinetics of cluster formation will
be discussed later in greater detail.
In the last 30 years a wide variety of methods has been
applied to the study of molecules and atoms which have been
trapped in matrices. One technique used to obtain data is
resonance Raman spectroscopy. In this case a polished
aluminum surface is used as the deposition surface for the
matrix. The metal is vaporized by electrically heating a
metal ribbon filament and codepositing the vapor with the
matrix gas. The aluminum deposition surface is contained in
a pyrex or quartz bell to facilitate viewing and irradiating
the matrix with an argon laser (4).

6
In this type of an experiment one can limit the amount
of metal entering the matrix to half of the aluminum surface,
leaving the other half virtually free of metal atoms. It is
then possible to probe various parts of the matrix to
determine the distribution of metal in the matrix (Moskovits
purposely screened part of the metal stream so as to achieve
a concentration gradient within the matrix) (4). From
resonance Raman experiments it is possible to determine the
vibrational frequency (at the equilibrium internuclear
separation (we)), and the first order anharmonicity constant
(c«exe). Typical molecules which have been investigated using
this technique are Fe2, NiFe, V2 , Ti2, Nig, Sc2, Sc3, and
Mn2. Another common way of determining the presence of metal
in the matrix is the color of the matrix. Most matrices
containing metal atoms or molecules will have a
characteristic color (4).
Magnetic circular dichroism (MCD) spectroscopy is
another technique which has been used to study matrix
isolated metal clusters. MCD is the differential absorbance
of left and right circularly polarized light by a sample
subjected to a magnetic field parallel to the direction of
propagation of the incident radiation. A one inch diameter
CaF2 deposition window is used, and the magnet (.55T) is
rolled up around the vacuum shroud surrounding the deposition
surface. Before an MCD spectrum is taken, a double beam
absorption spectrum is usually taken, the reference beam

7
being routed around the vacuum shroud through the use of
mirrors, in order to maximize the signal to noise ratio of
the MCD spectrum. The optimum absorbance value has been
found to be 0.87, and deposition times are controlled
accordingly (5). The information gained from this type of
experiment is very useful in assigning the electronic ground
state of the species under study. The MCD technique also has
the advantage of being able to assign spin-forbidden
electronic transitions. Properties of excited electonic
states have also been investigated utilizing MCD (5).
Optical absorption spectroscopy has also been done on
matrix isolated samples; for example, PtO and Pt¿ have been
studied in argon and krypton. Atomic platinum lines were
also observed. A KBr cold surface was used as a deposition
surface. A hollow cathode arrangement was used to vaporize
platinum wire, which was being used as the anode. This was
then put into a stainless steel vacuum vessel equipped with
an optical pathway. Deposition times were varied from a few
minutes for Pt up to two hours to make PtO and Pt2- The
absorption spectrum was then taken (6).
The present work has utilized two types of analysis,
namely electron spin resonance spectroscopy and Fourier
transform infrared spectroscopy. When doing ESR, two types
of deposition surfaces are usually used, either a copper or a
single-crysta 1 sapphire rod. Both are magnetically inert,
and they, like other deposition surfaces, have good thermal

8
transport properties. In order to do ESR the sample has to
be placed into a homogeneous magnetic field. This is usually
accomplished by mounting the vacuum shroud surrounding the
deposition surface on rails. The matrix can then be
deposited outside of the confines of the magnet's pole
faces (7,8).
In order to perform a typical matrix isolation
experiment using electron spin resonance to analyze the
matrix, several pieces of specialized equipment are
necessary. Measurements on the matrix take place between the
pole faces of an electromagnet. This inherently restricts
the size of the vacuum chamber and deposition surface. The
set-up used is typically in two parts. One half contains the
metal deposition set-up or "furnace" (Figure 1-1). The
second part contains the deposition surface and the ESR
cavity (Figures 1-2 and 1-3). Figure 1-2 shows the system
configured with the Heli-Tran liquid helium transfer device
from Air Products, and Figure 1-3 has the set-up configured
with the Air Products Displex closed cycle helium
refrigeration system. The two halves are separated by a set
of gate valves so that they can be disconnected from each
other without compromising the high vacuum conditions
maintained in each. Once separated the rod is lowered into
the ESR cavity with the aid of pneumatic pistons. After the
rod is in the cavity, the half containing the ESR cavity and

9
the rod is rolled into the magnet so that the ESR cavity and
rod are located between the pole faces of the magnet.
Infrared work can also be done in a fashion similar to
that used for ESR. The primary difference is that the
deposition surface is usually Csl or quartz because of their
optical properties (No significant absorptions between 4000
and 200 wavenumbers). For this type of work the vacuum
shroud containing the deposition window usually sits in the
sample compartment of the infrared spectrometer aligned so
that the sample beam passes through the deposition window.
The apparatus for doing infrared experiments has some
similarities to that used for the ESR experiments. There is
a furnace and a dewar, and gate valves separating the two
(Figure 1-4). But a much smaller vacuum shroud can be used
because only a deposition window is contained inside of it.
It is important that the infrared beam passes into the vacuum
vessel, through the deposition surface (in most cases), and
back out again so that the beam can reach the detector, which
means that the matrix, as well as the windows through which
the infrared beam must pass, needs to be able to transmit
radiation in the infrared region. The deposition window
usually remains in the infrared instrument for the entire
experiment, which then enables one to follow the deposition
of the matrix.
Several options are available to vaporize the metal
sample. The usual method is resistive heating. The metal is

Figure 1-1. The furnace flange with copper electrodes
and a tantalum cell attached.

Liquid Helium Flow
Figure 1-2. The EPR cavity and deposition surface
within the vacuum vessel. The apparatus is capable of
cooling the rod to 4 K, because of the liquid helium
transfer device (Heli-Tran) on the top.

12
Electrical'
high
a
He Gas
low <—
Thermocouple
and
Heater feedthrough
Thrust Bearing-H
Expander:
first Stage —
second Stage —
Pneumatic Piston-
Radiation Shield-
an
Rod —
Window -
Cavity Cover—J.
EPR Cavity
\
1
r “ -i
\
Window-
Figure 1-3. The ESR cavity and deposition surface
within the vacuum vessel. The apparatus Is capable of
cooling to 12 K because of the closed cycle helium
refrigeration device (Displex) on the top.

13
Figure 1-4. The vacuum vessel, depositio
Displex, and furnace assembly for infrared
surface ,
experiments.

14
placed into a cell made of a high melting metal with good
electrical properties. (Mixed metal species may sometimes
arise in high temperature work because a significant portion
of the cell may also vaporize with the sample.) Heating in
this fashion, it is possible to achieve temperatures in
excess of 2000 °C. An alternative method is to put the
sample cell into an inductive heating coil; in this manner,
comparable temperatures can usually be attained. The
temperature of the furnace is estimated by using an optical
pyrometer; more accurate measurements require an estimate of
the emissivity of the hot surface.
The determination of what has been trapped can
sometimes be simple or, at other times, rather complex. In
the case of Sc2 it was rather straightforward. The ESR
spectrum was measured by Knight and co -workers (9). Since
the Sc nucleus has a spin of 7/2 (1=7/2), the hyperfine
structure observed identified the trapped species. A
resonance Raman experiment determined the vibrational
frequency of the ground state molecule to be 238.9 cm-1 (10).
From this information it was then possible to determine
whether a chemical bond exists between the trapped species.
In the case of discandium, a single bond and not van der
Waals forces binds the two atoms (11).
A more controversial diatomic molecule, dichromium, is
not quite as straightforward; it has a singlet ground state
and is therfore not observable using ESR. Theoretical

15
studies of Cr2 Indicate a variety of bonding configurations.
A resonance Raman study has examined both di and tri chromium
(10). For the dichromlum species it was first necessary to
decide which of the spectral features belonged to dichromium
and which belonged to trichromium. This was done in two
ways. The change in relative intensities of the bands was
observed as the concentration was varied (the assumption
being that a more concentrated matrix would favor a larger
cluster), and a high resolution scan of one of the observed
lines was fit with the calculated isotopic fine-structure
spectrum, assuming the carrier of the line to be Cr2> The
vibrational frequency could then be determined from the
spectra, and from this a force constant indicating the
strength of bonding. The results from the experiment
indicate that multiple bonding does exist (k=2.80 mdyne/A).
o
(Dicopper with a single bond has a k=1.3 mdyne/A.) The
extent of the multiple bonding can not be determined from
these results (11).
Divanadium has also been investigated using the
resonance Raman technique to yield an equilibrium vibrational
constant of 537.5 cm”1 (4), but mass spectrornetric data were
needed to complete the picture. It was determined that the
dissociation energy for divanadium is about 1.85 eV (11).
From spectroscopy done in a two-photon-ion ization mass
selective experiment, on a supersonically expanded metal
O
beam, a value of 1.76 A for the equilibrium distance was

16
measured (12). The short bond distance coupled with a high
vibrational frequency shows that the molecule is strongly
bonded by 3d electrons (11).
Higher order metal clusters such as Mn5 have also been
trapped, and ESR spectra measured in matrices. In this case
several equally spaced (300 G) lines were observed in the
spectrum. From the number of these fine-structure lines it
was determined that the molecule has 25 unpaired electrons
(Hyperfine splittings were not resolved.). On this basis it
is possible to postulate the cluster size. Smaller clusters
are improbable on the basis of S=25/2. It is also important
to remember that the larger clusters are unlikely to form in
the matrix initially. The structure of Mn5 is thought to be
pentagonal with single bonds between each of the manganese
atoms and with each of the atoms having five unpaired
electrons. The ESR spectrum indicates that all of the
manganese atoms in the molecule are equivalent; a pentagonal
structure fulfills this requirement (13).
A similar problem arises in the case of doing a high
concentration scandium experiment. In this case it is
thought that a molecule with 13 Sc atoms is made. The ESR
spectrum contains over 60 lines in the g=2 region of the
spectrum, which usually indicates one unpaired electron in
the molecule. Because the intensity of the lines drops off
at the fringes of the hyperfine structure, it is difficult to
ascertain exactly how many lines exist. With the observed

lines there are at least nine Sc atoms in the molecule. The
Sc13 molecule seems likely because of theoretical
calculations done on transition metal clusters with 13 atoms.
A single Self-Consistent Field Xa-Scattered wave calculation
has been done for Sc13 giving a single unpaired electron, in
agreement with the ESR results (14).
Matrix isolation is more of a technique than a method
of analysis. It can be used in conjunction with various
analytical tools which then can be used to determine the
composition and structure of the trapped compound. It is
important to use some forethought in choosing the method of
analyzing the trapped molecule because the method chosen will
determine what information can be obtained from the
experiment. Data from various methods will tend to
complement each other. For example, if the molecule of
interest does not contain an unpaired electron, then it would
not be worthwhile to do ESR since this method requires the
presence of at least one unpaired electron in order to
produce a spectrum. Analyzing the molecule for its
vibrational structure by using resonance Raman or infrared
spectroscopy will only give the molecule's vibrational modes.
From these modes it may or may not be possible to determine
the molecule's structure, depending on the complexity of the
molecule and the degeneracy of the modes. Another problem,
when dealing with clusters, is that it is sometimes difficult
to determine the size of the cluster from the observed

1 8
spectra. Also, once the molecule Is trapped, Its trapping
environment may not be uniform throughout the matrix. This
will cause splittings in the observed lines of the spectrum
due to different trapping sites. The trapping site may also
cause a lowering of the observed point group of the molecule,
which will cause lines to split because they are no longer
degenerate. Matrix isolation is a useful tool which aids in
determining the structure of unstable species, but it is best
used in conjunction with other techniques if accurate
structures are to be determined.
As can be seen from what other workers have done,
matrix isolation can be used to trap very reactive and also
very interesting species. We set out to use this technique
to further elucidate the properties of transition metals and
transition metal carbonyls. Following this line of interest
has lead us to study various first row transition-metal
carbonyls using both ESR and FTIR. We continued our work
with transition metals by investigating the group IB metals
and attempted to produce larger clusters. We finally turned
our attention to the first row transition-metal silicides.
Our hope in these endeavors was to produce various metal
containing species in order to determine structure and to
obtain possible enlightenment as to the reaction processes
occurring to form them.
Producing these metal species as well as analyzing the
resultant spectra tends to be a rather complicated process.

19
A review of the kinetics of cluster formation is very helpful
in pointing out and understanding some of the processes
involved in producing these exotic species. The analysis of
the ESR spectra can sometimes be rather simple when one is
dealing with only a few lines. But when the trapped species
produces many lines, the analysis rapidly becomes complicated
and a review of relevant theory becomes mandatory. A brief
review of infrared spectroscopy will also be presented.
Theory of Cluster Formation
In recent years the area of metal cluster chemistry
has become rather active. The main reason behind this is the
hope that the metal cluster will be useful in the
investigation of the chemistry that occurs at metal surfaces.
This interest has lead to two major thrusts, one involving
the reproducible production of these clusters and the other
concerning itself with the mechanisms involved in the
evolution of the clusters. Both of these areas are now being
actively pursued by various workers (15-19).
Experimentally, the production of these clusters and
their identification have proven extremely challenging.
Three primary methods of vaporizing the metal exist, laser
vaporization, resistively heating of a cell containing the
metal of interest, or heating a wire made of the appropriate
metal. Of these the most successful has been the use of
lasers. A major problem in determining the kinetics involved

20
in cluster formation is the reproducibility of the
distribution of cluster sizes from experiment to experiment.
Several groups have had some success at this and even have
begun to react these metal clusters with various types of
reactants (20,21).
In developing a general mean-field kinetic model of
cluster formation one must look first at the aggregation
process in the thermal vaporization source. Second, a method
needs to be found to calculate probabilities for cluster
formation taking into account atom-atom collisions to form
dimers as well as collisions between clusters. This would
have to include not only aggregation but also cluster
fragmentation from collisions, structural stabilities of
certain clusters, how energy is dissipated upon collision,
and possible transition states of the clusters. It should
also be able to explain the cluster distribution found in
mass spectra of these systems.
The metal clusters are produced by laser vaporization
in a supersonic nozzle source and then allowed to enter a
fast-flow reactor, before being mass analyzed. The source of
the metal of interest is a rod about 0.63 cm in diameter.
The rod is placed in the high pressure side of a pulsed
supersonic nozzle, operating with a ten atmosphere back
pressure. The frequency doubled output of a Q-switched
Nd:YAG laser (30 to 40 mJ/pulse, 6 ns pulse duration) is
focused to a spot approximately 0.1 cm in diameter on the

21
target rod, and fired at the time of maximum density in the
helium carrier gas pulse. The target rod is continually
rotated and translated, thus preventing the formation of deep
pits, which would otherwise result in erratic fluctuations in
the sizes of the metal clusters. The helium-metal vapor
mixture then flows at near sonic velocity through a
c1 uster-formation and therma1 ization channel, 0.2 cm in
diameter and 1.8 cm in length, before expanding into a 1 cm
diameter, 10 cm long reaction tube. Effectively, all cluster
formation in such a nozzle source is accomplished in the
therma1 ization channel since expansion into the 1 cm diameter
reaction tube produces a 25 fold decrease in density of both
the metal vapor and the helium buffer gas (20).
The reaction tube has four needles which can be used to
inject various reactants into the flowing mixture of carrier
gas and metal. Following the reaction tube, the reaction gas
mixture is allowed to expand freely into a large vacuum
chamber. A molecular beam is extracted from the resulting
supersonic free jet by a conical skimmer and collimated by
passage through a second skimmer. The resulting well-
collimated, co 11 ision 1ess beam is passed, without
obstruction, through the ionization region of a time-of-
flight mass spectrometer (TOFMS). Detection of the metal
clusters and their reaction products is accomplished by
direct one photon ionization in the extraction region of the
TOFMS (20).

22
With the advent of this type of a device, it is now
possible to produce metal clusters under relatively
controlled conditions with a fairly reproducible distribution
of cluster sizes. The reproducibility of cluster size
distribution between experiments has made it possible to
compare the results to kinetic studies dealing with the
formation of metal clusters. The kinetic analysis of the
clusters has been able to explain why some cluster sizes are
favored, to suggest the relative importance of kinetic and
thermodynamic effects, and to shed some light on the possible
influence of ionization of the clusters.
The kinetic theory applicable is that of aggregation
and nucleation. The mean-field rate equations governing the
aggregation of particles developed by Smoluchowski (22) are
(I-l) *j - jljKji-l Xj *1-1 -jÍjZKjj Xj Xj i - 1 N
In equation I-l, X.¡ denotes the concentration of clusters of
size i. The aggregation kernel, Kjj, determines the
time-dependent aggregation probability. The first term on
the right hand side of the equation describes the increase in
concentration of clusters size i due to the fusion of two
clusters size j and i-j. The second term describes the
reduction of clusters size i due to the formation of larger
clusters. The equation must be generalized in order that the

23
neutra 1 -positi ve. neutral-negative, and pos i ti ve-negative
cluster fusions are included because the vaporization process
will produce some ions. But, since the electrons and the
ions are attracted by long range Coulomb forces, the
recombination processes are very fast, leading to a
population of neutral atoms that is much larger than the
population of ions. Therefore, the probability for
positi ve-negative cluster fusion is much smaller than that of
neutral-positive and neutra 1-negative cluster fusion and can
be neglected (15) .
The terms due to the formation of positive clusters are
( 1-2 )
.0 . N 0+ 0 +
xi - xi - jl/ij xi xj
and
(1-3)
.+ i — 1 0+ 0 + N 0+ 0 +
*1 -,5, Kji-l Xi Xi-j -jii KJi xj xi 1 ■ 1 »
where X^ is defined by the right hand side of equation 1-1
.0 . +
and X| and X^ denote the concentration of the neutral and
positively charged clusters, respectively. The kernels
0 +
and K^j describe the neutral-neutral and neutral-positive
aggregation probabilities. Analogous terms are introduced
due to the presence of the negatively charged clusters (15).
During cluster growth, there is also the possibility of
charge transfer between the charged and the neutral clusters
without the accompanying cluster fusion. The probability of
electron transfer between the negatively charged and the

24
neutral clusters is much greater than the probability of
electron transfer between the neutral and the positively
charged species since electron affinities are much smaller
than the ionization potentials for small and medium sized
clusters. Therefore, only the electron transfer terms from
the negatively charged to the neutral clusters are included
.0.0 N 0 - N 0-
d-4) Xi - Xj - JjTjj Xi Xj * JjTjj Xj Xj
and
(I-S) X¡ - Xj . jIjTjj X? xj - jliT}l X° Xj
where T^j is the nonsymmetric charge transfer kernel. The
coupled rate equations I -(2 through 5) can then be solved
simultaneously for the concentrations of the neutral and the
charged clusters (15).
Classically, the aggregation probability for clusters i
and j with diffusion coefficients and Dj is proportional
to where D^j = Dj + Dj is the joint coefficient for
the two clusters, and Rjj is the catching radius within which
the clusters will stick with unit probability. In a reactive
aggregation, one has to consider the reaction probability
within the interaction radius. The expression for reactive
aggregation becomes
( 1-6 )
Kij = 4^DijRij[Pij/(Pij+PD) ]

25
where P^j is the reaction probability per unit time and PD is
the probability of the reactants to diffuse away. One has PD
= 1/rij, where r ±j is the average time in which the clusters
remain within the reaction distance Rjj- From the diffusion
equation,
(1-7) D = (kRT)3/2/(apm°‘5)
D He
one can easily show that l/r.jj = eD^j/ÍRjj)2 leading to
(1-8) Kij = 4KDljRij[Plj/(PiJ+(6Dlj/Rij2))]
The limiting forms of equation 1-8 are of particular
interest. If P ^ j > P D , K j j = 4xDjjRjj and the distribution of
cluster sizes is governed by the classical aggregation
kinetics. No reaction-induced magic numbers will arise in
this case. The true solution to equation 1-1 can be
approximated in this case by the ones corresponding to the
exactly solvable simple kernels. Since the variation of the
kernels with cluster size is not very strong in the classical
limit, a constant kernel solution may be used where = 2C
and Xj(t=0) = Xq may be used for qualitative purposes.
(1-9) XA(t) = X0(CX0t)1_1/(l+CX0t)i+1
A more accurate solution can be obtained provided one
includes the variation of the diffusion coefficients and the

26
catching radii with cluster size. Since cluster reactivity
varies with its structure, the uniqueness of the structure
explains the reproducibility of the reactivity data for small
transition metal clusters (15).
The application of classical kinetics is best
exemplified by transition metal clusters. The mass
distribution spectra of these clusters are essentially
featureless. This is what is predicted by classical
kinetics. However, although the distribution of transition
metal clusters is classical, the small and medium size
clusters will probably have unique or nearly unique shapes.
This will result in a certain amount of nonclassical behavior
which will cause certain cluster sizes to be favored (15).
In the other limit of equation 1-8, where PD =
o
6Dj j/(R1:). )*• > Pjj. the growth of clusters is reaction
limited. In this case, one can neglect Pjj in the
denominator. Since the diffusion constants cancel, the
equation becomes
( I-10 ) Kij = 4^/[6(R1J)3PiJ] .
Thus the aggregation probability in the reaction limited
regime is dependent only on the reaction probability and does
not depend on the value of the diffusion coefficient.
Therefore, the aggregating clusters will undergo several
collisions before fusion. Significant variations in cluster

27
size are likely to occur since the reaction probabilities
depend on structure, symmetry, and the stability of the
reacting clusters. This is the reason why magic numbers are
observed. The reproducibility of the measured magic numbers
under a wide variety of experimental conditions is due to the
independence of the rate of fusion on the diffusion
coefficient (15).
The knowledge of reaction probabilities for each pair
of reacting clusters, including their charge dependence, is
required to calculate the cluster distribution in the
reaction limited regime. Since this is computationally
prohibitive, one is forced to make several approximations in
order to make the calculation feasible. The final expression
for the aggregation kernel becomes
(I-ll) - oRJje rUG;*AG;>/KBTav
after using the Polanyi-Bronsted relationship to estimate the
relative differences between transition state energies.
Also, since the reactants are probably going to undergo
considerable structural rearrangement after initial
attachment, scaled derivatives are used to describe the
energy gained upon addition of a single atom. Gibbs free
energies can be used to account for the possible temperature

28
dependent structures which can arise due to the dependence of
cluster entropy with structure (15).
The charge transfer kernel is approximated by
(1-12) T!j = oRjje~^ Since the electronic wave function of a negatively charged
cluster has a relatively large radius, the Pol anyi-Bronsted
proportionality factor, £, in the charge transfer kernel is
significantly larger than the corresponding factor in the
aggregation kernel (15).
The final two equations require electronic structure
calculations for only the end products (those observed in a
mass spectrum). The average temperature, Tgv, is not known
at the outset, but the analysis of experimental spectra
provides an upper bound. The spectra of positively charged
clusters are thus determined by two adjustable parameters,
where as those of negatively charged clusters require an
additional parameter (£) (15).
Ziff and co-workers (16) have studied the validity of
using the Smoluchowski equation for c1 uster-c1 us ter
aggregation kinetics. They investigated the validity of the
mean-field assumption by looking at the concentrations of the
cluster species and also by investigating the asymptotic
behavior of the equations. They found the mean-field
Smoluchowski equation to be appropriate in describing the

29
aggregation of particles which form fractal clusters. The
only problem was in determining the fractal properties of the
kernel. Even though these properties are difficult to
determine, once they are known the entire description of the
kinetics follows Smo1uchowski, as presented by Bernholc and
Phillips (15).
The kinetic theory for clustering as presented by
Bernholc and Phillips (15) has been able to model the cluster
distributions found for carbon by Smalley and co-workers
(23). Bernholc and Phillips used the calculated formation
energies with a semiempirica1 estimate of the entropy
difference between chains and rings as input for the kinetic
energy calculations. They found that the cluster
distributions were in good agreement with the experimental
work of Smalley. This includes the data for both the
positive and negative ions produced directly in the source.
The magic numbers in the range of n equal 10 to 25 were well
reproduced. They also found that electron transfer effects
have a strong effect on the measured distributions of small
and medium clusters of the negative ions. For the positive
ions produced from photoion ization of neutral clusters, the
calculated cluster distributions show that photofragmentation
and/or photothreshold and photoion ization cross section
dependence on cluster size have a major effect on the
measured spectra up to about n equals 25. This was not found
to be true for larger clusters.

30
Even though these are just beginnings in the
understanding of what is involved in cluster formation, it
is essential to realize that the clusters which are seen by
experimentalists are the products of a complicated set of
circumstances which may possibly be at the control of the
experimentalist. With this type of background it may be
possible in the future to produce a desired cluster size by
finely tuning the experimental conditions. To be able to do
this, it will be necessary to understand what the critical
factors are in the formation of clusters. Is it the overall
flux of metal in the carrier gas? Can the amount of
ionization be controlled in order to produce the desired
cluster sizes? Or will the inherent stabilities of certain
clusters override these factors and limit the variation of
cluster size which can be easily produced? These are
questions which will only be answered through a close
synergic relationship between experiment and theory.
ESR Theory
Electron Spin Resonance (ESR) spectroscopy is concerned
with the analysis of paramagnetic substances containing
permanent magnetic moments of atomic or nuclear magnitude.
The theory of ESR spectroscopy has been dealt with by many
authors, and if desired a more in depth treatment can be
found there (24-29). In the absence of an external field

31
such dipoles are randomly oriented, but application of a
field results in a redistribution over the various
orientations in such a way that the substance acquires a net
magnetic moment. If an electron or nucleus possesses a
resultant angular momentum or spin, a permanent magnetic
dipole results and the two are related by
(1-13)
¡L = T£_
where ¡t_ i s the magnetic dipole moment vector, ja_ i s the
angular momentum (an integral or ha 1f-integra 1 multiple of
h/2n = ft, where h is Planck's constant), and j is the
magnetogyric ratio. The motion of these vectors in a
magnetic field H consists of uniform precession about H at
the Larmor precession frequency
(1-14)
w_= -r]L
The component of u_ along H_ remains fixed in magnitude, so the
energy of the dipole in the field (the Zeeman energy)
(1-15)
W=
is a constant of the motion.
The relationship between the angular momentum and the

32
magnetic moment is expressed by the magnetogyric ratio in
equation 1-13 and is defined by
( 1-16) r = -g[e/(2mc)]
where e and m are the electronic charge and mass,
respectively, and c is the speed of light. The g factor is
equal to one for orbital angular momentum and is equal to
2.0023 (ge) for spin angular momentum. Defining the Bohr
magneton as /9 = eh/2mc and combining the g factor with equation
1-13 we have (along the field direction)
(1-17) fi s = -ge/3ms.
Only 2p+l orientations are allowed along the magnetic field
and are given by msh where mg is the magnetic quantum number
taking the values
(1-18) ms = s, s -1 -s
because the angle of the vector ¡i_ i s space quantized with
respect to the applied field H_. This accounts for the
appearance in Eq. (1-17) of the mg factor for spin angular
momentum.
O
In the case of an atom in a S1//2 state where only spin

33
angular momentum arises, the 2S+1 energy levels separate in a
magnetic field. Each level will have an energy of
(I-19> ems= ge^msH
which will be separated by ge|9H. The g factor is an
experimental value and mg an "effective" spin quantum number
because the angular momentum does not usually enter into the
experiment as purely spin, i.e. some orbital angular momentum
usually enters into the observed transitions. For orbitally
degenerate states described by strong coupling scheme
(Russe11-Saunders), J = L + S, L + S-l, .... | L — S J and
(1-20) Ej = gj|3m jH
where
(1-21) gj = 1 + [S(S + 1)+ J(J + l ) - L(L + 1 ) ]/[2J(J + l ) ]
is the Lande splitting factor. This reduces to the free
electron value for L=0.
The simplest case of a free spin where mj = mg = +1/2
will give two energy levels. The equation for the resonance
condition follows:
hy = ge£H0
(1-22)

34
where Hq is the static external field and v is the frequency
of the oscillating magnetic field associated with the
microwave radiation. In this research a frequency of about
9.3 GHz (X-band) was employed. The transitions observed can
be induced by application of magnetic dipole radiation
obtained from a second magnetic field at right angles to the
fixed field which has the correct frequency to cause the spin
to flip.
The Hyperfine Splitting Effect
As described above, an ESR spectrum would consist of
only one line. This would allow one to determine only a
value for the g factor for the species. Fortunately, this is
not the only interaction which can be observed via ESR
spectroscopy. These other interactions tend to greatly
increase the observed number of lines. One of the most
important of these interactions is the nuclear hyperfine
interaction. ESR experiments are usually designed so that at
least one nucleus in the species under investigation has a
non-zero magnetic moment. The magnetic moment of the odd
electron can interact with this nuclear moment and split the
single ESR line into hyperfine structure.
In the simplest case of a nucleus having a spin 1=1/2
interacting with a single electron, the magnetic field sensed
by the electron is the sum of the applied fields (external
and local). A local field would be one caused by the moment

35
of the magnetic nucleus. This local field is controlled by
the nuclear spin state (1=1/2, in this case). Because there
are two nuclear levels (21+1), the electron will find itself
in one of two local fields due to the nucleus. This allows
two values of the external field to satisfy the resonance
condition, which is
(1-23) Hr = (H* + (A/2)) = (H’ - AM j)
where A/2 is the value of the local magnetic field (A being
the hyperfine coupling constant), and H' is the resonant
field for A=0.
A good example of an ESR spectrum is that of the
hydrogen atom with the Zeeman energy levels shown in Figure
1-5. Hydrogen has one unpaired electron for which a
transition at about ge should be observed. Because of the
spin angular momentum of the electron interacting with the
spin angular momentum of the nucleus (1=1/2), two lines are
observed. The lines are split around the "g" value for a
free electron which is ge = 2.0023 and occurs at about 3,400
Gauss in an X-Band experiment. The magnitude of the
splitting (hyperfine interaction) of the two lines about the
free electron position at ge is due to the interaction of the
free electron with the nuclear moment of the hydrogen atom.
The spin angular momentum of the unpaired electron can also
be split by several nuclei that have spins, as is the case

36
with CHg. The carbon nuclei (99%) are 12C which has zero
spin (1=0). The hyperfine interaction in this case arises
from the three equivalent hydrogen nuclei (each with 1=1/2)
which gives an overall 1=3/2, and four lines are observed
(30,31).
Several interactions are involved when a paramagnetic
species with a non-zero nuclear spin interacts with a
magnetic field. The obvious one is the direct interaction of
the magnetic moment with the external field. The precession
of the nuclear magnetic moment in the external field results
in a similar term. The equation
(1-24) gjl_ = ¿4/%
relates the nuclear magnetic moment ¿u j to the nuclear g
factor (gj). In the equation the nuclear magneton, (3N, is
defined as efi/2Mc where M is the proton mass and is about
l/2000th of the Bohr magneton.
The Hamiltonian can be written as
(1-25) (H) = gj|3eÍL*{l} + hA{JJ*{Jj " gi0NiL*UJ
where { } indicates that the term is an operator. Small
effects such as the nuclear electric quadrupole interaction,
as well as the interaction of the nuclear moment with the

37
external magnetic field (Nuclear Zeeman term), which is the
last term in equation 1-25, are small and will be neglected.
The Zeeman effect in weak fields is characterized by an
external field splitting which is small compared to the
natural hyperfine splitting (hA(X)*{Jj > gjSH^ÍJj) in equation
1-25. The orbital electrons and the nuclear magnet remain
strongly coupled. The total angular momentum F = I_^J_ orients
itself with the external field and can take the values I+J,
I+J-l | I — J | . The component of F_along the field
direction, mp, has 2F+1 allowed values. In a weak field the
individual hyperfine levels can split into 2F+1 equidistant
levels which gives a total of (2J+1)(2I+1) Zeeman levels.
(Not all levels are degenerate even at zero field.)
The splitting becomes large compared to the natural
hyperfine splitting in the strong field (Paschen-Back)
region. Decoupling of I_and J_ occurs because of strong
interaction with the external field. Therefore F is no
longer a good quantum number. Since J_and I_have components
along the field direction, the Zeeman level of the multiplet
characterized by a fixed nij is split into as many Zeeman
hyperfine lines as there are possible values of mj (21+1).
The total energy states are still given by (2J+1)(2I+1) since
there are still (2J+1) levels for a given J. The levels in
this case form a completely symmetric pattern around the
energy center of gravity of the hyperfine multiplet.

38
Intermediate fields are somewhat more difficult to
treat. The transition between the two limiting cases takes
place in such a way that the magnetic quantum number, m, is
preserved (In a strong field m = mj + mj, in a weak field m =
mp). The Zeeman splitting is of the order of the zero field
hyperfine splitting in this region.
With so many possible levels, the observed ESR spectrum
needs to be explained in terms of selection rules. The
transition between Zeeman levels involves changes in magnetic
moments so it is necessary to consider magnetic dipole
transitions and the selection rules pertaining to them. A
single line is observed for the mg = 1/2 <-> -1/2 transition
in the pure spin system (1=0). A change in spin angular
momentum of +h is necessary. This corresponds to selection
rule of Antj = +1. A photon has an intrinsic angular momentum
equal to fi. Conservation of angular momentum therefore
dictates that only one spin can flip (electronic or nuclear)
upon absorption of a photon. The transitions usually
observed with fields and frequencies employed in the standard
ESR experiment are limited to the selection rules Amj = +1,
and Airtj = 0 (The opposite of NMR work).
These interactions can be categorized as isotropic and
anisotropic, and are related to the kind interactions of the
electron with the nucleus, and can be deduced from the ESR
spectrum. The isotropic interaction is the energy of the
nuclear moment in the magnetic field produced at the nucleus

39
by electric currents associated with the spinning electron.
This interaction only occurs with s electrons because they
have a finite electron density at the nucleus. The isotropic
hyperfine coupling term is given by
(1-26) as = (87r/3)ge/9gN0N|f(O) | 2
where the final term represents the electron density at the
nucleus. There is no classical analog to this term. The ag
value, also known as the Fermi contact term, is proportional
to the magnetic field, and can be of the order of 103 gauss.
It is obvious then very large hyperfine splittings can arise
from unpaired s electrons interacting with the nucleus.
Classical dipolar interactions between two magnetic
moments are the basis for describing the anisotropic
interaction. This interaction can be described by
(1-27) E = (iLe*14j)/r3 - [3(^*rJ (¿4,*rJ ]/r5
where r_is the radius vector from the moment ^ to , and r
is the distance between them. Substituting the operators,
-g/3{Sj and gN/9N{_L), for He and respectively, gives the
quantum mechanical version of equation 1-27 as
( 1 -28 ) Hdip = -gi3gN|SN[{JL>*({L}-{Sj)/r3
- 3 ( {I_) * rj ( { S_) * rj / r 5 ] .

40
Then a dipolar term arises
(1-29) a = ge^gj(3N [ ( 3cos20-1 )/r3 )
where 0 is the angle between the line connecting the two
dipoles and the direction of the magnetic field. The angular
term found in Eq. (1-29) needs to be averaged over the
electron probability distribution function because the
electron is not localized. The average of cos20 over all 6
vanishes for an s orbital because of the spherical symmetry
of the orbital.
Doublet Sigma Molecules
The spin Hamiltonian
The full spin Hamiltonian involves all the interactions
of the unpaired spin within the molecule, not just the ones
directly affected by the magnetic field. The full
Hamiltonian contains the terms below,
(1-30) H = Hp + HZe + Hls + Hhf + HZn
the magnitude of the terms on the right side of Eq. (1-30)
tend to decrease going from left ot right. The first term in
equation 1-30 is the total kinetic energy of the electrons.
The "Ze" and "Zn” terms describe the electronic and nuclear
Zeeman interactions, respectively. The energy, H^g, is due

41
to the spin- orbit coupling interaction. The term, Hhf>
accounts for the hyperfine interaction due to the electronic
angular momentum and magnetic moment interacting with a
nearby nuclear magnetic moment. These terms have been
adequately described in detail by several authors (24-27).
This full Hamiltonian is rather complicated and difficult
to use in calculations, and the higher order terms which
could be observed in crystals have not been included. Using
a spin Hamiltonian in a simplified manner, it is possible to
interpret experimental ESR data. This was first done by
Abragam and Pryce (32). The ESR data are usually of the
lowest-lying spin resonance levels which are commonly
separated by a few cm-1. All other states lie considerably
higher in energy and are generally not observed. The
behavior of this smaller group of levels in the spin system
can be described by a simplified Hamiltonian. The splittings
are the same as if one ignored the orbital angular momentum
and replaced its effect by an anisotropic coupling between
the spin and the external magnetic field.
Since {^J cannot represent a true spin, it represents an
"effective" spin. This is related to the anisotropy found in
the g factor which does not necessarily equal ge. By
convention, the "effective" g factor is defined so that the
observed number of levels equals 2S+1, just like the real
spin multiplet. Therefore all the magnetic properties of a
system can be related to this effective spin by the spin

42
Hamiltonian. This is possible because the spin Hamiltonian
combines all of the terms in the full Hamiltonian that are
effected by spin. Nuclear spins can be treated in a similar
fashion, so that the spin Hamiltonian which corresponds to
Eq. (1-30) can be written as
(1-31) HSpin = |9H0*g*{S} + {J_} * A* { S_)
where g and A are tensor quantities and the nuclear Zeeman
term has been neglected.
The g tensor
The anisotropy of the g-tensor arises from the orbital
angular momentum of the electron through spin- orbit coupling.
The anisotropy occurs even in the sigma states which
nominally have zero orbital angular momentum. Apparently the
pure spin ground state interacts with low-lying excited
states which add a small amount of orbital angular momentum
to the ground state. This small amount is enough to change
the values of the g tensor. The interaction is generally
inversely proportional to the energy separation between the
states. This spin-orbit interaction is given by
(1-32) (H)ls = ¿{LJMSJ = /U(L}X{S}X + (L)y(S}y + {L}Z(S)Z)
This term is added to the Zeeman term in the spin Hamiltonian

43
(1-33)
( H } = /3H_* ( (U +ge { SJ ) +
For an
orbitally nondegenerate ground state represented by
| G,Mg>,
the first order energy is given by the diagonal
matrix
element
(1-34 )
WG =
+
where the first term is the spin-only electronic Zeeman
effect. The term, , vanishes since the ground
state is orbitally non-degenerate. The second order
correction to each element in the Hamiltonian is given by
(1-35)
M-Mc = -E* [( | o o n
o (0) (0)
+ ge|9JL*{Sj | n , Ms . > 2 I )/(Wn - WG )]
where the prime designates summation over all states except
the ground state. The matrix elements of ggiSHjJL) will vanish
because = 0.
Expanding this, it is possible to factor out a quantity
(1-36)
. (0 ) (0 )
A_= (-Z )/(Wn - W¿ ’)

44
which is a second rank tensor. The ijth element of this
tensor is given by
(1-37)
Aij
(0) ..(0)
l )/(Wn - WQ )
where Lj and Lj are orbital angular momentum operators
appropriate to the x, y, or z directions. Substituting this
tensor into Hu yields
Ms , Mg
(1-38) H„ M' = + ¿2{S)*{A}*{S) I M ' >
s
The first operator does not need to be considered any further
since it represents a constant contribution to the
paramagnetism. The second and third terms constitute a
Hamiltonian which operates only on spin variables. The spin
Hamiltonian results when the operator gei3{H)*{S} is combined
with the last two terms of Eq. (1-38). The spin Hamiltonian
takes the form of
(1-39) HSpln = ,9{H}*(ge{l} + 2¿{A))*{S) + /l 2 { S } * { A ) * { S )
= 0 where
(1-40) {g}= ge{1} + 2^{A >
and

45
( 1-41 ) {D} = /Í2{A} .
The final term in equation 1-39 is effective only in systems
with S>1. The first term is then the spin Hamiltonian for a
2£ molecule. The anisotropy of the g-tensor arises from the
spin-orbit interaction due to the orbital angular momentum of
the electron which is evident from the derivation.
The g-tensor would be isotropic and equal to 2.0023 if
the angular momentum of the system is due solely to spin
angular momentum. Deviation (anisotropy) from this value
results from the mixing in of orbital angular momentum from
excited states which is expressed through the {A} tensor.
If a molecule has axes of symmetry, they need to
coincide with the principal axes of the g tensor. Three
cases of interest can be outlined. The simplest case is one
in which g is equal to gg. This is a spin only system for
which g is isotropic. For a system containing an n-fold axis
of symmetry (n>3) there are two equivalent axes. The axis
designated z is the unique axis and the g value for the field
(H) perpendicular to z is go. and gj is the value for g when H
is parallel to z. The spin Hamiltonian therefore becomes
(J-42) HSpin = 0(g-Hx{S>x + g^Hy{S}y + g|H z{S}z) .
The third case deals with the situation where the molecule

46
contains no equivalent axes (orthorhombic symmetry), where
gxx ’ gyy ’ and gzz are not e(lual and
(1-43) ^^Spin = ^gxxHx^S^x + gyyHy^^y + gzz**z^^z^ '
The A tensor
The hyperfine tensor takes into account three types of
interactions. The first term involves the interaction
between the magnetic field produced by the orbital momentum
and the nuclear moment, L*I which is usually small. More
important terms involve the interactions due to the amount of
s character of the wavefunction (the Fermi contact term) and
to the non-s character of the wavefunction also need to be
accounted for.
The isotropic interaction due to the s character is
called AlsQ. Fermi (33) has shown that for systems with one
electron the isotropic interaction energy is approximately
given by
(1-44) WisQ = -(8k/3) |Â¥(0) | 2A*eKNPN
where V(0) represents the wave function evaluated at the
nucleus.
The interaction arising from the dipo1e-dipo1e
interaction of the nucleus and electron (non-s character) is
called Adip. The dipolar interaction gives rise to the

47
anisotropic component of hyperfine coupling in the rigid
matrix environment. The expression for the dipolar
interaction energy between an electron and nucleus separated
by a distance r is
(1-45)
^dipolar = <^e*^N)/r3 " C 3 ( ne * r ) ( * r ) ] / r 5 .
The term,
can now be written as
(1-46)
Hhf = His o + Hdip
fAiso + Hdip^i^—
where Ajso has been given in Eq . (1-26) and Adlp can be
expressed by equation 1-29. The brackets indicate the
average of the expressed operator over the wave function W
In tensor
notation the term become
(1-47)
Hhf = 1_*A_*S_
where A_ = Aisol_+ T_. Here 1_ i s the unit tensor and T_ i s the
tensor representing the dipolar interaction. The components
of the A tensor becomes
Aij ‘ Aiso^-+ Tij-
(1-48)

48
For a completely isotropic system the components of the A
tensor (Axx, Ayy, Azz) will equal Aiso. A system with axial
symmetry is treated in a manner similar to that of the g
tensor where Axx and Ayy are equal to A_i_. The term, A_l, is
given by
(1-49) Aj_ â–  Also * Txx ,
and Azz is equal to A| which is given by
(1-5°) A, = Azz + Tzz .
And finally for a system which exhibits a completely
anisotropic A tensor Axx, Ayy, Azz are not equal to each
other.
In matrix isolation experiments only the absolute values
of the hyperfine parameters can be determined. In most
matrix isolation experiments, it is found that for the most
part, the signs of Aj_ and Aj are positive. There are two
general exceptions to this. First, this may not generally be
true for very small hyperfine interactions, such as the
hyperfine interaction in CN where the splitting due to 14N is
only 5 to 10 gauss. Second, if fz j is negative, the A values
will usually be negative, also (34).

49
Randomly oriented molecules
There is a very distinct difference between samples
held in a single crystal and those trapped in matrices. In
the case of a single crystal, the sample can be aligned to
the external field and spectra recorded at various angles of
the molecular axes to the field. Matrix isolated samples are
usually randomly oriented within the field and the observed
spectra will contain contributions from molecules at various
angles. This was first considered by Bleaney (35,36), and
later by others (37-43)
In the orthorhombic case the spin Hamiltonian can be
solved (assuming the g tensor to be diagonal), and the energy
levels can be given by
(1-51) E = |9S^H ( gj 2 s i n2 fleos 20 + g22sin20sin20
+ g32cos20 ) ®
= 0gH^HH
where is the component of the spin vector S along H, gH is
the g value in the direction of H, fl is the angle between the
molecular z axis and the field direction, and

from the x axis to the projection of the field vector in the
xy plane. Returning to axial symmetry
(1-52) gH = (g_i_2sin20 + g | 2cos20 ) 0'5
and the energy of the levels is given by

50
(1-53) E = 0S^H ( g_L2s in20 + g|2cos20).
It is obvious that the splittings between the energy levels
are angularly dependent. This makes the transitions between
the energy levels also angularly dependent.
The absorption intensity as a function of angle is
proportional to the number of molecules lying between 9 and
9+d0, assuming the transition probability is independent of
orientation. Since g is a function of 0 for a fixed
frequency v, the resonant magnetic field is
(1-54) H = (hui/i3)(g|2cos20 + go.2 s i n2 9 ) ~0 • 5
and from this
(1-55) sin20 = (g0H0/H)2 - g j 2 ) / ( g_«_2 - g¡2)
where gQ equals (g j + 2g_j_)/3 and HQ equals hv/g0/3. From the
above equations we have
(1-56) H = hiv/g h 0 = g0H0/g|, at 9 = 0 °
and
(1-57) H = hy/gjjS = g0H0/g^ at 0 = 90°.
The absorption intensity varies from 0° to 90° and when
plotted against magnetic field, takes the appearance of

51
Figure I-6a, for g|>g_i_. In a typical ESR experiment one
usually measures the first derivative of the absorption
signal. This spectrum appears in part b of Figure 1-6. The
perpendicular component is generally easily determined from
such a powder pattern. It is usually the strongest signal
observed. The parallel component is typically much weaker
and usually more difficult to detect. The values of gj and
g_L can be determined as indicated assuming that the g tensor
is not very anisotropic.
Hyperfine interaction with spin containing nuclei can
split the pattern shown in Figure I-6b into (21+1) such
patterns. A simple case would be that of a molecule
containing an 1=1/2 nucleus. This is presented in Figure
I-6c. One important point is that the orientation of the
mj=l/2 pattern is opposite to that of the mj=-l/2 pattern.
This is because g j is approximately equal to go., and Aj_ Another common situation is that of the hyperfine splitting
for both parallel and perpendicular orientations are almost
equal and g_u is shifted up-field from g j . In this case the
spectrum would contain two features like Figure I-6b
separated by the hyperfine splitting, A.
Molecular parameters and the observed spectrum
With all of this theory, the question now becomes what
can be learned from an ESR spectrum? To answer this, let us
begin with the solution of the spin Hamiltonian in axial

52
hi/=g/3H0T9,500 MHZ
g = 2.0023
Figure Figure 1-5. Zeeman energy levels of an electron
interacting with a spin 1/2 nucleus.

53
I
%
Figure 1-6. (a) Absorption and (b) first derivative
lineshapes of randomly oriented molecules with axial
symmetry and gj_ randomly oriented, axially symmetric molecules g_L. including hyperfine interaction with a spin 1/2 nucleus
( Aj_< A n ) •

54
symmetry including second order perturbations. This will
then show what molecular parameters can be uncovered from an
ESR spectrum.
Several authors (24,26,27,38) have given detailed
discussions of the spin Hamiltonian
(I-58> Spin = gfleHzz + g-l3(Hx{S}x + Hy{S}y)
+ A|{I}Z{S}Z + A_i_ ({I}X(S}X + {I}y{S}y).
Considering the Zeeman term first, a transformation of axes
is performed to generate a new coordinate system x', y', and
z', with z' parallel to the field. If the direction of H is
taken as the polar axis and 0 is the angle between z and H,
then y can be arbitrarily chosen to be perpendicular to H and
hence y=y'. Therefore only x and z need to be transformed.
The Hamiltonian is transformed to
(1-59) (H) = g£H{S}zi + K{I}zi(S}z, + (A,A^/K){I}x,{S}x,
+ [ ( A_l2-A |j 2 ) /K ] ( g | gj_/g2 )sin0cos0(I}x,{S}x,
+ A^.{l}y , (S}y,
n n
where lz = A j g j co s 9/Kg , lx = A_Lg_i_s i n0/Kg , and K^g^ =
2 2 2 2 2 2
Aj g| cos 0 + A_l go. sin 0 . Dropping the primes and using
ladder operators (S}+ = (S)x + i{S)y and (S}_ = (S)x - i(S}y,
this can be rewritten in the final form

55
(1-60) HSpln = g|9H{S}z + K{S}Z{I}Z
+ [((A_l2 - A | 2 )/K ) ( ( g| g_L.)/g2 )
• cos0sin0( ( (S}+ + {SD/2){I}Z]
+ [ ( ( A | A j.) / 4 K ) + A_i_/4]({S) + {I}+ + {STUD
+ [ ( (A | Aj_) / 4 K ) + Ajl/4] ({S} + {I)_ + {S}"{I}+).
This Hamiltonian can be solved for the energies at any angle
by letting the Hamiltonian matrix operate on the spin kets
|Mg, Mj>. The solution of the spin Hamiltonian is difficult
to solve at all angles except at 0=0° and 90°. Elimination
of some of the off-diagonal elements results in some
simplification and is usually adequate. The solution is then
correct to second order, and can be used when g|SH >> A p and
Aj_, as is typically the case. The general second-order
solution is given by Rollman and Chan (44) and by Bleaney
(36). The energy levels are given by
(1-61) AE (M , m ) = g|9H + Km + ( A_l2/8G ) [ (A j 2 + K2)/K2]
• [1(1 + 1) - m2] + ( A_i_2 ) ( A | / K ) ( 2M - 1)
where K is A j and A_l at 6 = 0° and 90°, respectively, and
G=g$H/2. Also, M is the electron spin quantum number of the
lower level in the transition, and m is the nuclear spin
quantum number. The first two terms on the right result from
the diagonal matrix elements and yield equidistant hyperfine
lines. The last two terms cause spacing of the hyperfine

56
lines at higher field to increase, which is referred to as a
second-order effect. This solution is routinely applied
because the hyperfine energy is usually small and not
comparable to the Zeeman energy.
As described above, the hyperfine coupling constant
consists of both an isotropic and anisotropic part. The
isotropic part (Ajgo) can be written as
(1-62) Aiso = (A, + 2 Aj_) / 3 = ( Qn / 3 ) ge 0 gN0N | V ( 0 ) | 2 .
The isotropic hyperfine parameter can be used to determine
the amount of unpaired s spin density. The dipolar component
can be written as
(1-63) Adip = (A|| + AJ-)/3 = ge3gN)9N< (3cos20 - l)/2r3>
These then relate the fundamental quantities |Â¥(0) | 2 and
O O
<(3cos‘9'l)/(2r0)> to the observed ESR spectrum. Approximate
spin densities in the molecule can also be obtained from Ajso
and Adip.
Spin densities
The electron spin density, px at a nucleus X is the
unpaired electron probability density at the nucleus. In the
case of a single unpaired electron it is the fraction of that
O
electron/cm° at a particular nucleus. The spin density of
the unpaired electron is generally split among s, p and d

57
orbitals. The spin density at nucleus X for an s electron is
o
given by /°sX!XsX(0)| and f°r electrons in a pa orbital the
spin density is given by PpCTX .
Similar expressions can be given for px and da, etc.
orbitals. The terms psX and ppaX represent the contributions
of the s and pa orbitals to the spin density at nucleus X.
The isotropic and anisotropic hyperfine parameters can be
written as
X 9
( I -64) Aiso (molecule) = (8n/3)ge0egjPNPsX|XgX(0 ) | 2
X
(Í-65) Adip (molecule) = gePeS1fiNPpaX
.
Since the equations above are characteristic of atom X, it is
possible to rewrite them for Aiso and Adlp as given below
X X
(1-66) Aiso (molecule) = PsXAiso (atom)
X X
(1-67) Adip (molecule) = PpaXAdip (atom).
From Eqs . ( 1-66,67 ) one can easily obtain an expression
relating the unpaired spin density to the isotropic and
anisotropic hyperfine parameters,

58
(1-68) psX = Also (molecule)/Aiso (atom)
X X
(1-69) p2pax = Adip (molecule)/Adip (atom).
The hyperfine parameters for the molecule are obtained from
the ESR spectra. The hyperfine parameters for the atoms can
be obtained from tables (see Weltner (24), Appendix B) and
multiplied by the appropriate correction factors. The
correct value of A d ^ p is calculated by taking the free atom
value of P = ge(SegN(3N and multiplying it by an angular factor
a/2 = <(3cos^a-1)/2>. The factor equals 2/5 for a p
electron, 2/7 for a d electron and 4/15 for an f electron.
The value for Algo (atom) can be found in Table B1 (column 5)
of Weltner (24) and the uncorrected value for A d ^ p (atom) can
be found in column 7 of the same Table.
Quartet Sigma Mo 1e cu les (S = 3/2)
These high spin molecules (S>1 ) often contain transition
metals. The metal atom will generally have a large zero
field splitting (D) value due to its large spin-orbit
coupling constant ({£})• If there are only a few ligands
attached to the metal atom, the unpaired electrons will be
confined to a small volume which will cause a sizable
spin-spin interaction. A large D value will cause many
predicted lines to be unobservable.

59
The spin Hamiltonian
A molecule will exhibit a fine structure spectrum. A
theorem due to Kramer states that in the absence of an
external magnetic field the electronic states of any molecule
with an odd number of electrons will be at least doubly
degenerate. In the case of a quartet molecule the zero
field splitting produces two Kramer's doublets, or degenerate
pairs of states, with Mg values of +1/2 and +3/2.
The spin Hamiltonian for a quartet sigma molecule with
axial symmetry can be written as
(1-70) This equation does not take into account hyperfine structure.
A 4X4 spin matrix can be calculated which upon
diagonalization yields four eigenvalues
(1-71) W ( + 3 / 2 ) = D + ( 3 / 2 ) g i |SH
(1-72) W ( + 1 / 2 ) = D + ( 1 / 2 ) g | (3H
and at zero field the +3/2 level and the +1/2 level are
separated by 2D. With H parallel to the molecular axis, the
energy levels will vary linearly with the magnetic field.
For the applied field perpendicular to the principal axis
(Hj_z ) with Hx = H and Hz = 0, the eigenvalues are more
difficult to calculate because the off-diagonal terms are no

60
longer zero. The eigenvalue matrix can be expanded to yield
a quartic equation
(1-73) E4 - 1/2(1 + 15x2)E2 + 3x2 E
+ (1/16) (1 + 6x2 + 81 x4 ) = 0 ,
where E = W/2D and x = gj_/3H/( 2 ( 3 ) 0*5D ) . Singer (45) has
developed a more general form of the equation which can be
applied to any angle.
The eigenvalues for H_l.z can be
expressed as
(1-74) W ( + 3 / 2 ) = D + (3/8D) (gj_|9H)2 + ...
(1-75) W ( + 1 / 2 ) = -D + gjL/SH - ( 3 /8D ) ( g_i_/3 H ) 2 +
when H/D or x is small
By expanding E it can then be given
as E = a + bx + cx + .
.. , with the levels indexed by the low
field quantum numbers.
When D > gjSiM'ÍSj all the matrix elements of the type
<13/2|(H)Spln|1l/2> • <*l/2|{H)Spln| +3/2> vanish. This
approach yields the eigenvalues below,
(1-76) W(+3/2) = D + (3/2)g||j3Hcos0
(1-77) W(+l/2) = -D + ( 1/2 )/9zH(gj 2cos2fl + 4 g^2 s i n2 9 ) 0 • 5 ,
remembering that Hz = Hcos8 and Hx = Hsinfl and that the angle
between the molecular axis and the applied field is 9. This

61
is used to introduce the "effective" or apparent g value.
The effective g value generally indicates where the
transition occurs and is defined by assuming that the
resonance is occurring within the doublet, that is between Ms
= +1/2 levels with g = g0 . The g values of the observable
transitions
| + 3 / 2 > <
-> 1
-3/2>
and |
+ 1 / 2 > <->
|-1/2> become
(1-78)
MS
= +3/2
= 3g|
o
CO
11
Kj- -
0.0
(1-79)
MS
= +1/2
£-1
= 2.0
Sj- “
2g_u - 4.0
for a large zero field splitting. The underlines indicate
the effective g value. The derivative signal for the +3/2
transition is usually undetectable because of the low
population of that level. There is not a significant
population of the +3/2 level unless D is very small. Also,
the absorption pattern corresponding to the g values for this
transition would be very broad. Finally, assuming that H/D
is large implies that the transition is forbidden. The
transitions usually observed for this spin state are those
between the +1/2 levels (the lower Kramer's doublet).
Kasai (46) and Brom et al. (47) have analyzed 4£ molecules
and found the following spin Hamiltonian,
* 1 ~80 > Spin = ^Hzz + g^(Hx(S}x + Hy { S } y )
+ As(I}z{S}z + A_l ({I )X(S}X + { I }y{S}y)
+ D[({S}z)2 - (1/3)S(S+1)]

62
and rewrote it as an effective spin Hamiltonian
(1-81) {H}Spin = gj/3Hz{S)z + 2g^(Hx(S)x + Hy{S}y)
+ A|{I}Z{S}Z + 2 A_l ( (I >X{S)X + (I }y(S}y)
for the +1/2 transition. The D term vanishes and S is taken
to be 1/2. The effective spin Hamiltonian can be rearranged
to be diagonal. The Zeeman terms become
(1-82) (H}Spin = g(SH{S}z + A(I)Z{S)Z
+ ((4(A^2) - (A|)2)/A)
4 ( 2g| g_i_/g2 ) sin0cosfl{ I }z (S }z
+ ( 1 / 2 ) Aj_ [ (A | + A)/A] ( { I > + { S } - + (I}~{S}+)
+ ( 1 / 2 ) A_l [ (A || + A)/A] ( { I } + {S}+ + ~{S>“)
where g2 = (gj)2cos20 + 4 ( g_j_) 2s i n2 9 , and A2 = ( (A ^ ) 2
*(g|)2/g2) c o s 2 0 + (16(Aa.)2(gj_)2/g2)sin28. This equation can
be solved analytically at 9 = 0° and by a continued fraction
method at 6 = 90°. A computer program is usually used to
match the observed lines with those calculated by the
iterative procedure in order to come up with the values for g
and A .
The observed transitions and therefore the energy levels
are typically very dependent on 9 and D. Figures 1-7 and 1-8
indicate the levels as a function of field for the
perpendicular and parallel orientations, respectively. Two

63
Figure 1-7. Energy levels for a 4£ molecule in a
magnetic field; field perpendicular to molecular axis

64
Figure 1-8. Energy levels for a 4£ molecule in a
magnetic field; field parallel to molecular axis.

65
Figure 1-9. Resonant fields of a 4£ molecule as a
function of the zero field splitting.

66
transitions are indicated between the same two levels at 690
and 1840 G. The reason for this can be seen in Figure 1-9.
The xy2 line is shown as an arc which reaches a maximum at
about 1000 G.
Sextet Sigma Molecules
The molecules considered here will have S=5/2, axial
symmetry (at least a three-fold symmetry axis), and a large
D. Ions such as Fe3+ and Mn2+ fall in this category in some
coordination complexes.
The spin Hamiltonian
The spin Hamiltonian for a £ molecule with axial
symmetry can be given as
(1-83) {H}Spln = g|0Hz + D(((S)z)2 - 35/12)
including all angles. For 0 = 0° all of the off diagonal
elements are zero and the eigenvalues of the 6X6 matrix are
given below;
(1-84) E ( + 5 / 2 ) = ( 1 0 / 3 ) D + (5/2)gj(5H
(1-85) E ( + 3 / 2 ) = - ( 2 / 3 ) D + (3/2)g|/3H
(1-86) E ( + 1 / 2 ) = - ( 8 / 3 ) D + (l/2)gj|3Ji.

67
Three levels appear at zero field which are separated by 2D
and 4D. Applying the magnetic field will split these into
three Kramers' doublets, which diverge linearly with field at
high fields and with slopes proportional to Mg .
A mixing of states occurs in the perpendicular case and
no simple solution is possible. A direct solution is
possible using a computer. This type of a solution has been
done by Aasa (48), Sweeney and coworkers (49), and by Dowsing
and Gibson (50). The eigenvalues of the 6X6 matrix
calculated by computer are shown in Figure 1-10. The
diagona1 ization of the secular determinant was done at many
fields and at four angles. It is evident that the resonant
field for some transitions is very dependent on the angle.
The plot of zero field splitting versus the resonant field is
given in Figure I — 11 . It was prepared by solution of the
Hamiltonian matrix at many fields and D values for 9 equal to
0° and 90°. For the situation were D >> hv the xy1 line at
g = 6 and the z3 line at g = 2 will be most easily observed. As
can be seen in Figure 1-10, these correspond to +1/2
transitions.
Infrared Spectroscopy
Sir William Herschel discovered infrared radiation in
1800, but it was not until the turn of the century that
infrared absorption investigations of molecules began (51).

68
Figure 1-10. Energy levels for a e£ molecule in a
magnetic field for 9 = 0°, 30°, 60°, and 90°.

69
H (Kilogauss)
Figure I — 11. Resonant fields of a molecule as a
function of the zero field splitting.

70
The typical IR source is a Nernst glower which is heated by
passing electricity through it. The radiation, which is
emitted over a continuous range by the source, is dispersedby
using a prism, such as KBr, which is transparent over the
range of interest. Various types of detectors ranging from
thermocouples to photodetectors are used to analyze the light
which has passed through the sample.
When dealing with infrared spectroscopy, one usually
deals with three specific regions of the spectrum. The
region from 800 to 2500 nm is the near infrared region and
adjoins the visible region of the spectrum. The infrared
region is found between 2500 to 50,000 nm. And the far
infrared region borders the microwave region of the spectrum
and starts at 50,000 nm and extends to about 1,000,000 nm.
The far infrared region is used to analyze vibrational
transitions of molecules containing metal-metal bonds, as
well as the pure rotational transitions of light molecules.
Most spectrometers are used in the mid-infrared region.
This is where most molecular rotational and vibrational
transitions occur (51).
Theory
Since infrared spectra are due to the vibration and
rotations of molecules, a brief review of the theory may be
useful. When a particle is held by springs between two fixed
points and moved in the direction of one of the fixed points,

71
it is constrained to move linearly. A restoring force
develops as the particle is moved farther from its
equilibrium position. The springs want to return to their
equilibrium position. Hooke's law states that the restoring
force is proportional to the displacement.
( 1-87 ) f = kx
where k is a constant of proportionality and called the force
constant. The displacement is given by x, and the restoring
force is f. The force constant is used as a measure of the
stiffness of the springs. When the particle is released
after the displacement, it undergoes vibrational motion. The
frequency of oscillation can be written as
( 1-88 ) v = (\/2n)(k/m)0'5
where m is the mass of the particle. The frequency can also
be expressed in wavenumbers (cm-1) by dividing the right side
of the equation with the speed of light. Because we are
dealing with small particles (atoms in this case), it is
necessary to enter into a quantum mechanical description of
the oscillation. The allowed energy values are given by
(1-89)
(v + (1/2))hv,

72
where v is found in Eq.(I-88) and v is the vibrational
quantum number. The equation above tells us that the energy
of the harmonic oscillator can have values only of positive
ha 1f-integra1 multiples of hv. The energy levels are evenly
spaced, and the lowest possible energy is (l/2)hv even at
absolute zero (52).
If one analyzes the vibrational behavior of a simple
molecular system, such as a diatomic molecule, the system's
oscillatory motion will be nearly harmonic and the frequency
of the motion can be described by
(1-90) y(cm-1) = (1 /2nc ) (k/fi) 0 â–  5
where fi is the reduced mass of the particles and is defined
as
(1-91) n = (mjmgJ/fmj + m2).
Since the motion of the atoms is not completely harmonic, we
must look at the energy levels of an anharmonic oscillator.
This is given by
(1-92) Ev = (v + (l/2))hv - (v + (1/2))2hyxe
+ (v + (1/2))3hvye
where the constants xg, y
are anharmonicity constants.

73
These are small and typically positive and usually of the
magnitude | xg | > |ye| > |ze) >... (53).
Anharmonicity in a molecule allows transitions to be
observed which are called overtones. These are transitions
between v=0 and v=2 or v=3 which are designated the first and
second overtones, respectively. The first overtone is
usually found at a frequency which is a little less than
twice the fundamental frequency. Combination bands can also
arise. These are caused by the sum or difference of two or
more fundamentals.
The force constant for a molecule is related to the bond
strength between the atoms. The force constant for a
molecule containing a multiple bond is expected to be larger
than the force constant of a single bond. A large force
constant is also usually indicative of a strong bond. For
diatomic molecules there is a good correlation between (k)®’®
and v(cm-1)- This relationship unfortunately does not hold
for polyatomic molecules. In this case force constants must
be calculated by a normal coordinate analysis of the
molecule. Several authors have presented detailed
descriptions of this method (51-54).
The vibrations of a molecule depend on the motions of
all of the atoms in the molecule. To describe the location
of the atoms relative to each other one looks at the degrees
of freedom of the molecule. In a molecule with N atoms, 3N
coordinates are required to describe the location of all of

74
the atoms (3 coordinates for each atom). The position of the
entire molecule in space (its center of gravity) is
determined by 3 coordinates. Three more degrees of freedom
are needed to define the orientation of the molecule. Two
angles are needed to locate the principal axis and 1 to
define the rotational position about this axis. For a linear
molecule the rotation about the molecular axis is not an
observable process. The number of vibrations of a polyatomic
molecule is given then by
(1-93) number of vibrations = 3N - 6
for a nonlinear molecule and
(1-94) number of vibrations = 3N - 5
for a linear molecule.
What is observed in an infrared spectrum is usually a
series of absorptions. These correspond to various
stretching and bending frequencies of the sample molecule. In
order for an infrared transition to be observed, there needs
to be a change in the dipole moment of the molecule when it
undergoes a stretching or bending motion. The strongest
bands are those corresponding to the selection rule
Avr = ¿1
Av
j
(1-95)
and
0

75
where j does not equal k and k equals 1, .... 3N-6.
The most intense absorptions are those from the ground
vibrational level since that is typically the most populated
level. These type of transitions are called fundamental
frequencies. These frequencies differ from the equilibrium
vibrational frequencies, vi e. v2 e The fundamental
frequencies are the ones generally used in force constant
calculations because the available information is typically
not sufficient to allow the calculation of anharmonicity
constants. The fundamental frequencies of the molecule need
not be the most intense absorptions. This can happen if the
change in dipole moment, (Ód/áQ^). is small or zero (51).
The phase or environment that the molecule Is in will
affect the appearance of the IR spectrum. With gas phase
samples it is often possible to resolve the rotational fine
structure of the compound using high resolution instruments.
On the other hand, when dealing with a matrix isolated
sample, there usually is not much, if any, rotational fine
structure even under high resolution. This is because the
molecule is rigidly held (small molecules such as HC1 exhibit
a rotational spectrum due to a hindered rotation within the
matrix site) within the lattice of the matrix, and is not
able to rotate freely as It Is able to do in the gas phase.
The elimination of the rotational fine structure simplifies
the spectrum and enables the analysis of more complicated

76
vibrational spectra which arise when studying larger
molecules.
Fourier Transform IR Spectroscopy
The basic components of an FTIR instrument are an
infrared source, a moving mirror, a stationary mirror, and a
beamsplitter. The source in a typical FTIR spectrometer is a
glower which is heated to about 1100 °C by passing an
electrical current through it. The beam from the glower is
directed to a Michelson interferometer where the intensity of
each wavelength component is converted into an ac modulated
audio frequency waveform. Assuming that the source is truly
monochromatic, a single frequency, A/c, hits the
beamsplitter, where half is transmitted to the moving mirror
and half to the fixed mirror. The two components of the
light will return in phase only when the two mirrors are
equidistant from the beamsplitter. In this case constructive
interference occurs and they reinforce each other.
Destructive interference occurs when the moving mirror has
moved a distance of A/4 from the zero position. This means
that the radiation which goes to the moving mirror will have
to travel A/2 further than the radiation that went to the
fixed mirror, and the two will be 180° out of phase. As the
components go in and out of phase, the sample and the
detector will experience light and dark fields as a function

77
of the mirror traveling +x or -x from its zero position. The
intensity at the detector can be expressed as
(1-96) I(x) = B(y)cos(2ixy),
where I(x) is the intensity, B(u) is the amplitude of
frequency v, and x is the mirror distance from the zero
position. For a broadband source the signal at the detector
will be the summation of Eq.(I-96) over all frequencies, and
the output, as a function of mirror movement x, is called an
interferogram (53).
The interferogram can then be converted into the
typical intensity versus frequency spectrum by performing a
Fourier transformation. The signal is transformed from a
time domain signal, which arises from the motion of the
mirror, to a frequency domain signal which is observed in the
typical IR spectrum. This can be done mathematically by
using
(1-97) C(v) = /I(x)cos(2ftxy)dx,
where C(i>) is the intensity as a function of frequency.
There are several advantages in using an FT IR
instrument. The detector in a Fourier transform instrument
gets the full intensity of the source without an entrance
slit. This yields a 100 fold improvement over the typical
prism and grating instrument. The signal to noise ratio is

78
theoretically improved by a factor of M1^2, where M is the
number of resolution elements. This has been termed
Fellgett's advantage since it results mathematically from one
of his derivations. A direct result of Fellgett's advantage
is that a dispersive instrument requires 3000 seconds to
collect a spectrum, whereas an interferometer needs only
about 60 seconds to collect an IR spectrum with the same
signal to noise ratio. (M equals about 3000 and the
observation time is about 1 sec/element) (53).
A complete IR investigation, when possible, can enable
one to determine the structure of the molecule of interest.
The IR spectrum allows one to determine force constants of
the various bonds and from that information the bond
strengths can be determined. The bending frequencies even
enable one to determine the bond angle between the atoms
involved in the bending motion. The shift in both stretching
frequencies and bending frequencies caused by the
substitution of isotopes into a molecule is very useful
towards this purpose since the amount of the shift is
dependent on the change in mass when the isotope is
substituted into the molecule.

CHAPTER II
METAL CARBONYLS
ESR of VCOn Mole cules
Introduction
Transition-metal carbonyl molecules continue to be of
great interest, partially because of their relevance to
catalysis. The simplest molecules, those containing only one
metal atom, have been studied spectroscopically, and electron
spin resonance (ESR) has been applied successfully in some
cases, specifically to V(CO)4, V(CO)5 (55), V(CO)6 (56-59),
Mn(CO)5 (60). Co(CO) 3 , Co(C0)4 (61,62), CuCO. Cu(C0)3
(63,64), and AgCO , Ag(C0)3 (65.66). (Ionic carbonyls have
also been observed via ESR (67.68) but will not be explicitly
discussed here.) Theoretical discussions of the geometries,
ground states, and bonding in these types of molecules have
been given by several authors beginning perhaps with Kettle
(69) and then by DeKock (70), Burdett (71,72), Elian and
Hoffmann (73), and Hanlan. Huber, and Ozin (74). Although a
number of ab initio calculations have been made on such
carbonyls, the vanadium molecules considered here apparently
have not been treated in detail.
The background for the present investigation was
provided by the matrix work of Hanlan, Huber, and Ozin (74)
who observed the infrared spectra of V(C0)n where n equals 1
79

80
to 5, in the solid rare gases. Most notably, those authors
concluded, from experiment and theory, that [1] VCO is
nonlinear, [2] V(C0)2 exists in linear, cis, and trans forms
in all three matrices, argon, krypton, and xenon, [3] V(C0)3
is probably of D3^ trigonal planar geometry. It should be
emphasized that the supporting theory usually assumed
low-spin ground states.
Morton and Preston have prepared V(C0)4 and V(C0)5 in
krypton matrices by irradiation of trapped V(C0)g. From ESR
they assign V(C0)4 as a high-spin 6Aj in tetrahedral (T^)
symmetry and V(C0)5 as 2B2 with distorted trigonal bipyramid
(C2V) symmetry. The V(C0)6 molecule is a well known stable
free radical which has been rather thoroughly researched by
infrared (75), MCD (76), ultraviolet (77), electron and X-ray
diffraction (78), and ESR. It is presumably a Jahn-Teller
distorted octahedral (2T2g) molecule at low temperatures
O
leading to a B2g ground state.
Our ESR findings are only for V(C0) , where n equals 1
to 3, and are not always in agreement with conclusions from
optical work and semiempirica1 theory. The most explicit
departure is in finding that VCO and V(C0)2 are high-spin
molecules .
Experimental
The vanadium carbonyls synthesized in this work were
made in situ by co-condensing neon (Aireo, 99.996% pure),
argon (Aireo, 99.999% pure), or krypton (Aireo, 99.995% pure)

81
doped with 0.1-5 mol% 12C0 (Aireo, 99.3% pure) or 13C0
(Merck, 99.8% pure) with vanadium metal [99% pure, 99.8%
51V(I=7/2)] onto a flat sapphire rod maintained at 4-6 K but
capable of being annealed to higher temperatures.
The furnace, Heli-Tran, and IBM/Bruker X-band ESR
spectrometer have been previously described (79). Vanadium
was vaporized from a tungsten cell at 1975 °C, as measured
with an optical pyrometer (uncorrected for emissivity).
ESR Spectra
VCO
Two ESR spectra of the VCO molecule were observed in
matrices prepared by condensing vanadium into CO/argon
mixtures at 4 K. We designate these two forms of VCO below
as (A) and (a). This symbolism is derived from one of their
distinguishing features: one has a considerably larger 5*V
hyperfine splitting (hfs) than the other. Only the (a) form
survived after annealing the argon matrices and only it
appeared in a krypton matrix. Only (A) was observed in solid
neon .
51VC0(A) and 51VC0(a) in argon
Upon depositing vanadium metal into an argon matrix
doped with 1.0 mol% 1 2 C 0 , we obtained the 4 K ESR spectrum
shown in Figure 11 -1 . The two sets of eight strong, sharp
lines centered near 1200 G could be attributed to separate

82
species since upon annealing one set [designated by (A)]
disappeared. The hyperfine splitting (hfs) in the
perpendicular xyj and xy3 lines of the (A) species due to
51V(I=7/2) is approximately 100G, whereas that in the (a)
species is about 60 G. The line centered at about 8100 G has
been observed with that intensity only once, but its
appearance, and disappearance upon annealing, correlates best
with the (A) molecule. Its complex hfs is indicative of an
off-principal axis line where forbidden Anij not equal to zero
transitions can also occur. The observed lines of both (a)
and (A) are listed in Tables 11-1 and 11 - 2 .
Annealing to 16 K and quenching to 4 K converted the
VCO (A) species into (a) which has the spectrum in argon in
Figure 11 — 2 . Again the xyj and xy3 lines have the same hfs,
now about 60 G, and an "extra" line appears but centered at
about 6700 G.
51V13C0 (A) and 51V13C0 (a) in argon
These same spectra can be observed when 13CO replaces
i o
C0 and the effect upon the xy1 line, which is the same
effect for (A) and (a), is shown in Figure II-3. Each line
is split into a doublet separated by about 6 G, indicating
most importantly that there is only one CO in each species.
3 ^ VCO (A) in neon
In neon only one VCO molecule appears to be trapped,
the one designated as (A) in argon with the hfs of about

83
Table II-l. Observed and calculated line positions
(In G) for VCO (X6£) In conformation (A)
i n
argon at 4 K.
{v =
9.5596 GHz)
Mj (51
V)a
xyj
xy 3
Extra
lines
9
= 10°
Obs .
Calc.
Obs .
Calc
Obs .
Calc .
7/2
797
789
5065
5082
7906
7897
5/2
882
877
5154
5170
8015
8012
3/2
974
971
5254
5262
8119
8124
1/2
1072
1072
5364
5360
8252
8234
-1/2
1174
1176
5473
5463
8346
8344
-3/2
1282
1285
5584
5573
8467
8453
-5/2
1396
1400
5692
5689
--
85 6 2
-7/2
1511
1519
5819
5814
--
8671
AM
I=+l transitions
Derived
Parameters
Obs .
Calc.
2.002(37)
7944
7938
g-j-
1 .989(5 )
7976
7970
I A„ (51V) |
247(28)MHz
8054
8052
1 A_l ( 5 1V ) 1
288(6) MHz
8083
8083
1 D I
0.603(2)cm
- 1
8161
8164
AiSo<51v>
a 274(13)MHz
8192
8194
Adip'55v>
a -14(11)MHz
8252
8274
1 Ajl( 13C) 1
17(3) MHz
8304
8304
8380
8384
8423
8413
--
8493
8514
8521
--
8603
—
8630
a Assuming A j and A _j_ are positive
() Error of the reported value

84
Table 11 -2. Observed and calculated line positions
(in G) for VCO (X6£) in conformation (a)
i n
argon at 4 K. (v =
9.5596 GHz)
Mj (51
V) a
xyi
xy3
Extra
0
lines
= 12°
Obs .
Calc. Obs.
Calc.
Obs .
Calc
7/2
940
940 4460
4461
6449
6448
5/2
1000
999 4520
4520
6530
6526
3/2
1061
1060 4581
4580
6603
6603
1/2
1124
1124 4645
4644
6684
6680
-1/2
1191
1190 4710
4709
6756
6755
-3/2
1258
1257 4777
4777
6828
6831
-5/2
1326
1327 4847
4847
6906
6907
-7/2
1396
1398 4918
4921
--
6983
AM
j=+l transitions
Dervived
Paramenters
Obs .
Calc.
gl
2.002(10)
6476
6479
go.
1.998(3)
6502
6496
! A | ( 5 1V ) I
165(14)MHz
6563
6556
! A_l(51V) 1
183(1) MHz
6590
6573
1 D I
0.452(2)cm-1
6637
6633
4iS0<51v>
a 177(5) MHz
6665
6650
4dip<51v>
a -6(5) MHz
6711
6709
! a_!_ (13 c) 1
17(3) MHz
--
6726
6782
6 78 5
6804
6802
6857
6861
6887
6877
6934
6937
—
6953
a Assuming A | and A_i_ are positive.
() Error in the indicated value

85
Figure 11 — 1 . ESR spectrum of an unannealed matrix at
4 K containing 51VCO(A), with hfs of about 100 6, and
VCO(a), with hfs of about 60 G. For the conformation
(A) two perpendicular lines and an off principle axis
line are shown, u = 9.5585 GHz.

86
Figure 11 -2. ESR spectrum of an annealed argon matrix
at 4 K containing only 51VCO in conformation (a). Two
perpendicular lines and off principal axis line are
shown, v = 9.5585 GHz.

87
6IVl3CO(a)/ARGON
XY, LINE
0.9 l.l 1.3
H(KG)
Figure I I - 3. ESR spectrum of the perpendicular xyj
of 51v13C0 in conformation (a) in an argon matrix at
4 K. v = 9.5531 GHz.
line

88
100 G. The ESR spectrum when vanadium was trapped in neon
doped with 0.1% CO is shown in Figure II-4 and the observed
lines are listed in Table I I -3. Again the xy^ line is
centered at about 1200 G, but the center of the xy3
fine-structure line is difficult to determine. This is
because the intensity of the spectrum is lower than in argon,
and the lines appear to be split by site structure which is
apparently more exaggerated in the high-field line. The off
principal axis line was not detected in neon. Annealing is
difficult in neon matrices, and it only led to loss of the
matrix here. At CO concentrations higher than 0.1% this
spectrum was not observed, presumably because the higher
carbonyls were formed in this lower melting solid.
51VCO(a) in krypton
Before annealing there are two series of eight lines of
about equal intensity, each with about 60 G hfs. one centered
at about 1138 G and the other at about 1170 G at 4 K. When
the sample was annealed to about 30 K, only the series
centered at about 1170 G (extending from 967 to 1392 G)
remained sharp at 4 K.
® ^V(^CO) 2 and ^ * V ( ^ ^C0 ) o in neon
With CO/Ne concentrations of 0.1%. in addition to
VCO(A), two additional fine-structure lines appeared centered
at about 1800 and 6400 G with 51V hyperfine splittings of

89
about 60 G. This spectrum, assigned to V(C0)2 molecules, is
shown in Figure 11-5 and the observed lines are listed in
Table 11 — 4 . With incorporation of 13CO, the line widths
appear to be almost the same, perhaps broadened by no more
than 20%. As with the monocarbonyl this spectrum is not
observed in neon at higher CO concentrations. It has also
not been observed in argon with any of the CO concentrations
used, which varied from 0.1% to 5%, nor has it been formed by
extensive annealing of any argon matrix.
51V(12CO)3 and 51V(13C0)3 in neon
Using concentrations of 0.1 to 1.0% in neon gave a
complex signal extending from 3000 to 3500 G containing a
pattern of eight strong hyperfine lines centered about
g = 2.12 with A(51V) = 50 G (see Figure II-6 and Table II-5).
There are also two very weak signals at 2948 and 3008 G (not
shown) and two at 3560 and 3643 G which appear clearly in
Figure I I -6 . These weaker lines did not appear to have the
same intensity variation from matrix to matrix as the strong
features and using CO essentially doubled the width of the
eight strong lines. The region between about 3430 and 3530 G
becomes approximately one broad line with phase down,
indicating a broadening of each of the narrow 12CO lines by a
factor of at least three. Even with extensive annealing this
spectrum was not observed in argon matrices.

90
Table I
1-3
Observed line positions (in G) for VCO (X6£) in
conformation (A) in neon at 4 K.
(v = 9.5560 GHz).
M j ( 5 1V )
xy2
7/2
796(5)
5/2
885
3/2
976
1/2
1074
-1/2
1177
-3/2
1286
-5/2
1398
-7/2
1514

91
Table 11 - 4. Observed and calculated line positions (in G)
for V(CO)g (X4£ ) isolated in neon at 4 K.
(v = 9.5560 GHz)
M!(5 4 V)a xyj
Obs .
Calc.
Obs .
Calc
7/2
1586(5)
1586
6136
6140
5/2
1646
1646
6199
6198
3/2
1707
1707
6259
6259
1/2
1766
1769
6324
6321
-1/2
1830
1833
6387
6385
-3/2
1896
1898
6452
6451
-5/2
1960
1965
6522
6519
-7/2
2030
2032
6597
6589
Derived
Parameters
g-i-
1.9908(9)
! D |
0.2995(5)cm-1
1 A,(51V) !
132(56) MHz
! A ( 5 1 V ) I
178(3) MHz
Aiso(51v)a
163(21) MHz
Adip(51v)a
-15(20) MHz
1 A ( 1 3 C ) |
< 42 MHz
a
Assuming A w and A_i_ are positive.

92
Table II-5. Calculated and observed line positions (in G)
and magnetic parameters of V(CO)3 molecule
in a neon matrix at 4 K. (v = 9.55498 GHz)
II
II
II
II
II
II
II
II
II
—
II
II
II
II
II
II
II
II
=
II
II
II
II
II
II
II
Mja
Perpendicular
Obs .
Lines
Calc.
Parallel
Obs .
Lines
Calc
+ 7/2
3067(3 )
3068
3358(?)
3356
+ 5/2
3117
3118
--
3373
+ 3/2
3167
3168
3395(?)
3391
+ 1/2
3218
3218
3411(5)
3410
+ 1/2
3269
3269
3433(5)
3430
+ 3/2
3321
3321
3451(3)
3451
+ 5/2
3373
3373
3472
3472
+ 7/2
3425
3425
3495
3495
Derived
Parameters
g-L
2.1024(9)
ga
1.9923(9)
'A1
(51V) |
55(3) MHz
I A_l
(51v)t
150(3) MHz
1a1so<51V)1a
82(3) MHz
lAdip(51v> Ia
68(2) MHz
Assuming
A | and A _¡_ are
of opposite sign.

93
6I VCO (A)/NEON
XY3
1 1 I I I 1 L_
5.3 5.5 5.7 5.9
H(KG)
Figure 11 - 4 . ESR lines in a neon matrix at 4 K attri¬
buted to 1VCO in conformation (A), v = 9.5560 GHz.

94
4X V(C0)2/NE0N
6.1 6.3 6.5
H(KG)
I 1 1 1 I I 1
1.5 1.7 1.9 9.1
H(KG)
Figure 11 - 5. ESR lines in a neon matrix at 4 K attri¬
buted to 51V(CO)2. v = 9.5560 GHz.

95
2A V(CCVNEON
3.0 32 34 36
Figure 11-6. (Top) ESR spectrum near g=2 in a neon
matrix at 4 K attributed to an axial 5^V(C0)3 molecule.
v = 9.5584 GHz. (Bottom) Simulated spectrum using g,
A(51V) parameters and linewidths given in the text.

96
Analysis
VCO, (A) and (a)
The low-field fine structure line of each of these
molecules has an effective ge - 6 and each may then be
assigned a sextet sigma ground state. This is in accord with
the further analysis shown in Tables II—(1—3). The xy ^ line
at about 1100 G in each case corresponds to the transition
within the Kramers doublet (Mg = +1/2 <-> -1/2). The other
lines in argon diverge further for the two species,
indicating that their zero-field splitting (zfs) parameters
are quite different; as the tables show these are 0.60 and
0.45 cm-1 for (A) and (a), respectively, in argon. Although
the hfs in neon indicates that the trapped molecule there is
(A), there was insufficient data for analysis. The same was
true of the krypton spectra; however in that matrix the hfs
identified the trapped molecules as (a), presumably in two
sites before annealing.
The two perpendicular-line positions in argon yield
0
good values of | b 2 ! = |D| and g_i_ for (A) and (a), and in
principle g| could then be determined reliably from
O
high-field extra lines in each case if the b4 parameter is
neglected in the spin Hamiltonian for these presumably linear
molecules (80):

97
( 11 -1 ) H = g|/3HzSz + gj./3(HxSx + HySy) + b°[Sz - (1/3)S(S+1)]
, 0 4
+ ^ | I z ® z + ( I x ® x + * y ® y ) + (l/60)b^[35Sz
2 2
- 30S(S + 1)SZ + 2 5 S z - 6 S(S + 1) + 3S2(S + 1)2]
0
where \>2 = D and the hyperfine parameters here refer to
Cl 0
V(I=7/2). The b4 parameters have been determined for at
least two axial high-spin molecules (81,9) and, although they
were small, they had a pronounced effect upon the positions
of high-field lines. This may not be the case here but it
makes the establishment of gj uncertain. However, neglecting
0
b 4 , one finds gj values of 2.039 (A) and 2.012 (a), with the
admittance of forbidden AMj = +1 transitions , gave
reasonable fits to the lines. For S = 5/2, I = 7/2, the
above Hamiltonian generates a 48 X 48 spin matrix which was
diagonalized to obtain eigenvalues and thereby magnetic
parameters which best fit the observed transitions at the
resonance frequency. If interaction with the quadrupole
moment of the 51V nucleus (-0.05b) is involved then the
coupling constant must be less than 14 MHz (A) and 6 MHz (a).
These g| values are large, and it seemed more reasonable to
see if a fit could be made with gj = ge. This necessitated a
slight alteration in the Aj hyperfine parameter, which is
very uncertain in any case, but the approximate fit of the
"extra-line" transition shown in Tables I I -1 and 11 — 2 could
0
be made. This leaves the gj and b4 parameters in
considerable doubt.

98
There is no doubt about both of these molecules being
VCO since the 5 1V and 1 3 C hfs clearly established that. The
spectra appear to be those of linear molecules since the
perpendicular lines are narrow and any splitting would have
to be very small. However, as can be seen from the lines at
about 1200 G in Figure II-l. the widths of the VCO(a) lines,
while still quite narrow (about 8 G). are about twice as wide
as those of the (A) form. This may be significant in
suggesting an unresolved splitting in the (a) molecule lines
(see below). It is also possible that the molecules are bent
but appear linear because they are rotating about axes of
least moment of inertia. However, the similarity of the
spectra in three matrix environments may be evidence against
such motional averaging.
V(C0 ) 2
The same Hamiltonian applies to a linear V(CO)2 as was
used for VCO except that S = 3/2 instead of 5/2. Again
0
neglecting b4 , one solves a 32 X 32 eigenvalue problem to
arrive at the parameters given in Table 11 - 4 . With only
perpendicular fine structure lines observed, only go.,
assuming jDI, could be derived.
vjlpq) 3
Because of the complexity of the spectrum in Figure
I I -6 near g
2.0. a simulation program for S
1/2 utilizing

99
second-order perturbation theory (82) was employed to derive
the magnetic parameters. The final fit shown in the bottom
of that Figure used the following parameters: gv = g =
x y
2.1189, gz= 2.0057; Ax = Ay = 148.0 MHz, Az = 56.0 MHz;
linewidths Wx = Wy = 25 MHz, Wz = 12 MHz for Lorentzian line
shapes: v = 9.5584 GHz. To further confirm these derived
parameters, exact diagona1 ization of the matrix was done,
yielding almost the same results, as shown in Table II-5.
There was concern about the weak lines at low and high
fields mentioned earlier in that perhaps they were part of
the V(C0)3 spectrum which implies a nonaxial molecule.
However, attempts to simulate the spectrum with all g and all
A components distinct were not successful. Also, the
observation that the intensities of these weak lines appeared
to vary relative to the strong ones when the CO
concentrations were varied, implied that the two sets of
lines belonged to separate molecules. A possible source of
the weak lines is V2C0, although, from the triplet sigma
ground state of V2 (12), one might expect the carbonyl to
also be triplet (or singlet), but a fit to an S = 1 molecule
appears unlikely. It is not the spectrum attributed to
V(C0)4 which is a "derivative-shaped line at g = 1.9583" in
Kr , and it did not grow but diminished in relative intensity
with increasing CO/Ne concentration.

100
Discussion
VCO
Both molecules observed at ge = 6 in unannealed argon
matrices are established as VCO by the 54V and 13C hyperfine
structure observed. The sharpness of the lines and the lack
of additional features indicate that their g tensors are
nearly axial and the molecules are therefore close to linear.
Trapping in neon and krypton provides no evidence to the
contrary and makes the possibility of axial spectra due to
molecular rotation, as mentioned earlier, unlikely.
Vanadium atoms have a 3d34s2 4 F ground state but the
3d44s state lies only about 2000 cm'4 (83) higher. Thus,
it is not difficult to justify S = 5/2 for the VCO molecule.
The ten valence electrons of CO plus the five of vanadium
fill the levels, as indicated in Figure II-7, such that the
3a and In provide the shared orbitals. (Figure 11 — 7 was
derived from a similar Figure for NiCO given by DeKock and
Gray (84).) The five unpaired spins are then essentially 3d
orbitals on vanadium with some hybridization of the 3da with
the 4sa and 4pa, and with some small population of CO
orbitals. This orbital picture is corroborated by the
observed hfs, as will be discussed below. It is also in
accord with the energy level scheme described by Hanlan et
al. (74), but here corrected to the high-spin case.
The unusual aspect of the VCO molecule is the
appearance of two forms of the molecule in argon, designated

101
Figure 11 — 7. Molecular orbital scheme for the VCO
molecule (modeled after Fig. 5-43 in DeKock and
Gray(84) ) .

102
as (A) and (a) here, with only form (A) appearing in neon and
only form (a) in krypton. The (A) form of the molecule is
characterized by |D| = 0.60 cm-1 and |A|(51V)| = 288 MHz and
(a) by |D| = 0.45 cm~* and |A| (51V) | = 183 MHz, as given in
Tables 11 — 1 and II-2. The derived values of AjS0(51V) in the
two cases, although less exact, also lie in that order: for
(A) it is 274 MHz and for (a) 177 MHz. For a (dx ) 2 (d<5 ) 2 ( s a) 1
configuration one would derive from 51V atomic data (85) A^so
= 1/5 X 4165 = 833 MHz, and comparison with the two above
values yields the unpaired o electron in VCO as 33% (A) and
21% (a) s character. The remainder of the a character in
each case is then 3d and 4p, and the values of Adip can also
be considered in this way. Since (ad, xd) and dd con¬
tributions to Ad^p have opposite signs, the small value of
that parameter in both VCO molecules can then be accounted
for. For example, for molecule (A) and assuming sa + pa
hybridization
(I I-2) Adlp(A) = [2/5(1/7 - 2/7) + 1/5* 0.67•2/5]•438
= -2 MHz
where 438 MHz is the atomic radial factor (81), as compared
to the observed value of -14 (55) MHz.
Only A_j_(13C) = 6 G was definitely observed but there is
no indication of distinct A| (13C) splittings (see Figure
I 11 - 3) so that the A(*3C) tensor of VCO may be assumed to be

103
approximately isotropic. Then, accounting for the 2S spins,
one finds that the s character at 13C is only 5*6*2.8/3777 =
0.02, where the atomic Also factor for 13C is from Morton and
Preston's table (85). (Corresponding values in Cu13C0 and
Ag13C0 were ps = 0.0510, and pg = 0.01, pp = 0.0212,
respectively.) Spin density on the CO ligand is then
apparently quite small, although of course measurements of
the hfs at the oxygen nucleus are needed to confirm that
presumption.
The effective distortion of these approximate 3d3
electrons from spherical symmetry leads to both the large zfs
parameters and the shifts in the g components from ge. If
the orbital angular momentum in the ground state is coupled
to the same excited states to produce |D) and g then one
should find that (86)
( 11 — 3 ) D = +J/2[g| - gj_]
where Á is the spin-orbit coupling constant of the vanadium
atom with S = 5/2. The spin-orbit coupling constant, X , is
difficult to estimate for a d5 vanadium but might be taken
the same as for Cr+ as 190/5 = 38 cm-1 so that
( 11 -4 ) D = +1 9 [ 2.002 - 1.989] = +0.25 cm-1
as compared to 0.60 cm ^ observed.

104
The idea that VCO (A) and (a) might be isomeric VCO and
VOC can be dismissed because AJL(13C) is the same for both
forms. One would expect quite different spin densities on
C for these isomers. Of course, the ESR spectra,
particularly in the absence of spin density information on
oxygen, cannot eliminate the possibility that VOC and not VCO
is being observed, but bonding considerations indicate that
the metal-carbon bond is favored.
Earlier it was noted that the line widths differ for
the two forms in Figure 11 — 1. The increase in line width of
(a) could be due to a slight bending of VCO in that form.
This implies that a third g tensor component and a second
zero-field parameter, E, are strictly required in the
analysis of the VCO (a) spectra, but the effect is too small
to make any significant change in the analysis. However, if
(a) is a bent form of (A), the electronic parameters are very
sensitive to angle, since the zfs and A(51V) are considerably
lowered and the g tensor made more isotropic. (This
concomitant decrease in |D| and g_i_-g| is in accord with Eq.
11 — 1 . ) A decrease in so character in the bent molecule is
not unexpected since it implies decreased sa + pa
hybridization which in the linear molecule helps to lower the
energy by placing some unpaired spin density on the side of
the metal atom away from the CO.
Then one can understand the detection of two forms of
VCO if the V-CO potential energy curve is relatively flat

105
with two shallow, but apparently distinct, minima. A
rationale for the preference of particular forms (A) or (a)
for particular matrices or matrix conditions might be given
as follows: If (A) contains the more distorted vanadium, as
judged by the larger s hybridization and larger zfs, then it
is understandable that it would be the form found in
unannealed strained sites in argon and in neon where the
sites are smaller and less accommodating. Upon annealing,
the (a) form becomes the preferred species in argon,
presumably now being surrounded by a more relaxed
environment. It is then reasonable that this form would also
be found in solid krypton where the sites are larger than in
argon. If asked which form would VCO take in the
hypothetical gas phase at 4 K, one would the choose (a), the
o
bent °A molecule.
If the V-CO bond is relatively weak, then the CO
stretching frequency would be expected to be relatively high,
as Hanlan et al. (74) have observed. However, in an
unannealed argon matrix one might also expect to observe two
C-0 stretching frequencies from VCO (A) and (a). These
apparently were not observed by those authors, but perhaps
this could be the result of differences in experimental
conditions during preparation of the matrices (74), since the
sapphire rod was always cooled by liquid helium in these ESR
studies, or perhaps to the low concentrations of CO used
here .

106
V(C0)2
The molecule observed here definitely contains only one
vanadium atom, but the number of attached CO's is not
definite since only line broadening was observed when 13C0
was substituted. However, the addition of one CO molecule to
S = 5/2 VCO can be expected to lower the spin to S = 3/2.
The only possible evidence of any nonlinearity in the
molecule is the small splittings of about 10 G on each of the
xy hyperfine lines in neon (see Figure II-5). but this could
also be due to multiple sites in the matrix. With the lower
spin, the molecule also has lower values of |DI = 0.30 cm-*
and Aiso(51) = 160 MHz compared to the monocarbonyl. The
spin density, ps. at the vanadium nucleus is calculated to be
160*3/4165 = 0.12, considerably smaller than in VCO.
Although the ESR spectra are not definitive, it seems
very likely from the observed quartet multiplicity that the
molecule is at least slightly bent. If the usual o bonding
and k back-bonding (84) applies to each attached CO so that a
completely double-bonded structure is obtained, then one can
O
only assume the unpaired spins to be essentially (d5) which
would yield only a doublet state. Bending the molecule
avoids this problem since it removes the degeneracies in the
d orbitals. Then the about 10 G splitting in the lines could
be due to a small zero-field splitting E term. If the bent
symmetry is C2y then the ground electronic state might be
^B2 • Our observations are not in agreement with the IR

107
assignments in Ar. Kr, and Xe matrices (74) where the
presence of three forms of the molecule was inferred.
YICOJ3
As with V(C0)2> the assignment of the spectrum to a
tricarbonyl is somewhat arbitrary since 1^CO substitution
K 1
only led to broadening of each of the V hyperfine lines.
However, the molecule does contain only one vanadium atom,
and the spectrum does not correspond to any of those observed
for the higher carbonyls (55-59). There is no ambiguity in
the analysis of the spectrum as that of a doublet axial
molecule with Ago. large and positive. The parameters are
reminiscent of a d Cu‘ ion with the unpaired spin in a dz2
orbital in a distorted octahedron (88). A similarly large g
tensor anisotropy is found for the linear CuFg molecule.
Here, of course, the molecule is considered as planar Dgjj or
p »» p
pyramidal C 3 V with its lowest state being or Aj. The
addition of four more CO electrons to VCO has resulted in
lowering the spin to S = 1/2.
No matter what the relative signs of A ,¡ and A_l, the
small percent s character at the vanadium atom (<3%) implies
that the unpaired electron occupies an almost pure dz2
orbital and that the molecule is probably of planar Dgjj
symmetry. Then Adjp should be about 2/7*438 = +125 MHz. If
the observed A_i_ is chosen as negative and Aj as positive,
Adip = íaj_a-l)/3 = +68 MHz. which is of the right sign but

108
half the calculated magnitude perhaps indicating a slightly
higher spin density of CO in this molecule. This is in
accord with the increased line width in V(13C0)3 relative to
V(12C0)g. One can, in fact, crudely justify about 50% of the
spin population in three C(px) orbitals if Aj_(13CO) = -50 MHz
and A^(13CO)= -70 MHz (from estimated line widths) since then
one calculates Adip(13C) = -7 MHz compared to 0.50*(l/3)
• (-1/5) *268 = -9 Mhz, where the angular factor is from Morton
and Preston (85 ) .
The large gj_ value must imply a low lying electronic
state, presumably 2Ej, involving essentially excitation of
(50% of) a dx electron into the do "hole". If the spin-orbit
constant is taken as 95 cm~* then one finds AE(2Ej - 2Aj) =
1400 cm- . Such a low lying state can also be used, in
conjunction with Tippens' second-order theory (90), to yield
gI = 1.9954, versus the observed 1.9923.
Conclusion
The unexpectedly high spin S = 5/2 and relatively
large zero-field splitting (0.45 cm-1) of VC0 is decreased by
each addition of a CO ligand, first to V(C0)2 with a quartet
ground state, |D| = 0.30 cm-1, and then to V(C0)3 with
probable D3^ symmetry and a 2Aj ground state. The VCO
molecule has two conformations of almost equal stability, one
is linear and the other slightly bent, with rather different
electronic parameters. The deduced geometries of these

109
carbonyls are not in complete agreement with theory, but the
latter does also not always explicitly consider high-spin
cases.
Infrared Spectroscopy of
First Row Transition Metal Carbonyls
Introduction
There has been considerable interest in the area of
metal-carbonyls, in order to understand their bonding and
their activity as catalysts. This type of molecule is also a
prototype for chemisorption on metal surfaces. To understand
these systems, it is first necessary to understand what
occurs when a metal atom is bound to a single carbonyl group.
Our work suggests that in order to form a first row
transition metal carbonyl (MCO), the 4s orbital must be half
empty. New data shows a good correlation between the
strength of the metal carbonyl bond and promotion energies of
a 4s electron into a 3d orbital. There are now a large
number of theoretical papers concerning the electronic and
bonding properties of these molecules (91).
Experimental
The experiments were done using a standard infrared
matrix set up. An Air Products DS-202 closed cycle helium
refrigerator was used to cool the deposition window to about
12 K. The chromium and manganese carbonyls were made by

110
codepositing argon (Aireo, 99.996% pure) doped with various
amounts of 12C0 (Aireo, 99.3% pure). The amount of CO in the
argon varied anywhere from one part in 1000 to one part in
100. Chromium (Spec flake, lOOppm max.) was heated in a
tantalum cell at about 1260 °C measured using an optical
pyrometer without making any corrections for emissivity. The
manganese (Spex flake, metal impurities lOOppm max.) was
heated in a tantalum cell which was resistively heated to the
desired temperatures. Depositions temperatures varied from
950 °C to about 1300 °C (uncorrected for emissivity)
depending on the concentration of manganese desired in the
matrix. Deposition times were usually held to about 1 hour.
The spectra were taken using a Nicolet 7100 Series FT-IR.
Thirty-two scans were usually taken and added together in
order to produce a spectrum.
Spectra
Chromium (Figure 11 -7 ) and manganese (Figure 11-8)
were studied using FT-IR and stretching frequencies were
obtained for CrCO, Mn^CO, and MngCO. The product bands
observed in these experiments were not in agreement with
those previously reported (92,93). We feel that those
reported here are the correct assignments for the carbonyls
in question.
Although the product band at 1850 cm'^ was previously
thought to be the position of the CO stretch in the MnCO

111
complex (92), concentration studies done by varying the
concentration of Mn in the matrix, showed that this
stretching frequency was not due to a single manganese atom
attached to a carbonyl, but rather a carbonyl attached to an
aggregate of manganese atoms because the product peaks grew
in and became more intense as the concentration of manganese
was increased. The amount of manganese was crudely gauged by
the amount of metal which was deposited on the furnace heat
shield. At low temperatures and when there was only a small
amount of manganese in the matrix (no clusters), no product
peaks were observed. It is interesting to note that previous
work (13) done involving manganese showed a critical
dependance on the temperature of the manganese cell and the
amount of cluster formation. Manganese is rather unique in
that it easily forms clusters. We were also unable to assign
a definitive stretching frequency for the MnCO species since
none of the observed product bands remained when the amount
of manganese was decreased in the matrix, or decreased when
the manganese concentration was increased.
The carbonyl stretching frequency of the CrCO molecule
is in disagreement with previously reported results (Table
I 1 — 6 ) (92,93 ). Again, the concentration of the chromium and
the amount of CO doped into the matrix gas was varied. At
low concentrations of both chromium and CO only one strong
product peak at 1977 cm-1 was observed (top trace. Figure
II — 8) . This was assigned to the CO stretching frequency of

11 2
Table II-6. Carbonyl stretching frequencies for the
first row transition metal carbonyls.
Metal
Scandium
cm 1(2 )
Titanium
--
Vanadium
1890a
Chromium
1 9 7 7 b
Manganese
2 1 4 0 c
Iron
1 898d
Cobalt
1952a
Nickel
1 9 9 6 e
Copper
2010a
() Uncertainty in line position
-- good line positions are not available
a Ref . 92
b This work
c free carbonyl stretching frequency
d Ref. 91
e Ref. 70

ABSORPTION
113
Figure 11 - 8. Infrared spectrum of CrCO using both 12C0
and 13C0 in argon. The top trace has a 1:200 CO/Ar
concentration and the bottom has a 1:1:200 12C0/13C0/Ar
concentration.

ABSORPTION
114
Figure 11-9. Infrared spectru* of Mn and CO codeposited
Into an argon matrix. The bottom trace Is after annealing
the matrix to about 30 K and cooling back down to 14 K.

115
chromium monocarbonyl. When a 1:1 mixture of 12C0 and 13C0
In argon was used as the matrix gas, the bottom spectra was
taken. A second strong peak at 1928 cm-1 has grown In and
was assigned to the CO stretch in the Cr CO molecule. The
shift due to the carbon 13 isotope is on the order of what
one would expect for this molecule. As the concentrations of
both Cr and CO were increased, the intensity of the peaks due
to the monocarbonyl decreased and other peaks such as the
lines around 1800 cm-1 grew in.
Discussion
To understand how a metal bonds to a carbonyl, more
data than vibrational frequencies are necessary. ESR is
invaluable in giving this type of information, but
unfortunately the only ESR data available for MCO type
complexes of the first row transition metal carbonyls, are
for VCO (94) and CuCO (64). Vanadium, which has a ground
state electron configuration of 4s 3d , forms a complex with
a ground state electron configuration containing 5 unpaired
electrons, 4s1 3d4. It seems that promotion of a 4s electron
is necessary in complex formation, when the 4s orbital is
filled. The CuCO work also shows that the unpaired spin
density in this molecule resides essentially in a 4s orbital.
In order to form first row transition metal carbonyls
our data seems to indicate that the 4s orbital of the metal
must be at least half empty. The reason for this is that,

1 1 6
since the 4s orbital projects about twice as far into space
as the 3d orbital, having a filled 4s orbital would result in
repulsion of the carbonyl rather than it being attracted to
the metal. Having a half empty 4s orbital, would allow the
carbonyl to be attracted to the metal, and gives the pair of
electrons being donated by the carbonyl an available orbital.
This gives a molecular orbital which contains three
electrons, two in a bonding sigma orbital and one in the
antibonding sigma orbital. The electron in the high energy
sigma antibonding orbital will want to reside in a lower
energy orbital, if possible, and will therefore go into a 3d
orbital (91).
For seven of the first row transition metal carbonyls
the first step in being able to form a metal carbonyl is the
promotion of one of the 4s electrons into a 3d orbital. A
look at how promotion energies (Figure 11 — 10) vary across the
row should predict, to a certain extent, how tightly bound
the carbonyl will be to the metal. Also, the strength of
interaction (Figure II-9), as shown by the CO stretch in the
metal carbonyl, should vary with the promotion energy. The
stronger the interaction between the metal and the CO, the
lower the promotion energy for the metal, and the closer the
CO frequency gets to the double bond value of 1740 cm'1.
The properties of first-row transition metals usually
exhibit a characteristic "double hump". Our results hint at
this, but do not clearly show this trait. Unfortunately,

117
Figure 11-10. Plot of the CO stretching frequencies in
the first row transition metal monocarbonyl molecules MCO
(circled points are tentative). Also shown is the
variation of the energy of promotion corresponding to
4s23dn 2 to 4s13dn_1, where n is the number of valence
electrons(91).
Promotion Energy (IO3 cm

118
looking at just the promotion energy is too simplistic. One
also has to consider the pairing energy of electrons within
the d orbitals, as well as the repulsion caused by having
filled orbitals. From this, one would predict that vanadium
forms the strongest metal carbonyl. This is because vanadium
has a low energy of promotion for the 4s electron, no
repulsion from filled d orbitals, and no pairing energy
(Figure 11-10). Chromium, which has a 4s1 3d5 ground state,
is less tightly bound than vanadium or iron because of the
pairing energy necessary when the electron in the sigma
antibonding orbital goes into the 3d orbital, which is lower
in energy. Manganese carbonyl is probably very weakly bound
because of its very large promotion energy. The promotion
energy is about twice that of any other first row transition
metal carbonyl. This also explains the small difference in
CO stretching frequencies between NiCO (4s1 3d9) and CuCO
(4s1 3d10), since both have essentially filled d orbitals.
The theory also correctly predicts that Fe will form the
second most tightly bound first row transition metal
carbonyl, because of its low pairing energy, low promotion
energy, and a small amount of repulsion from a single filled
d orbital.
The trends between promotion energies and carbonyl
stretching frequencies of the metal carbonyls match up well
for the first few metals. When one gets to chromium, pairing
energies and repulsion from the filled d orbitals begin to

119
play a part in the bonding. Pairing of the first d electron
will cost the most energy. One would expect that the bonding
energies of nickel and copper carbonyl would be almost the
same since they have no open d orbitals even if pairing were
possible.
Theoretical studies have been done on FeCO (91) and
NiCO (91). The iron-carbonyl study shows the low energy
configuration of the molecule to have 4 unpaired electrons,
which is in agreement with what is predicted by our theory.
The NiCO study predicts either a triple or singlet state for
the nickel carbonyl. The triplet state probably is lower in
energy than the singlet state. Both of these theoretical
studies predict promotion of one of the 4s electrons into a d
orbital, in agreement with our scheme. The theory put forth
here, also correctly predicts the number of unpaired
electrons in the metal-carbonyl complex.
Conclusion
From the ESR data it is obvious that a half filled 4s
orbital is necessary in order to form the monocarbonyl.
Also, we feel that MnCO is so weakly bound that the metal
prefers to dimerize and polymerize before reacting
successfully with the carbonyl. Using the new value obtained
for CrCO, the graph of the CO stretching frequencies in the
MCO complex is in good agreement with the plot of the
promotional energies of the 4s electrons, and the plot

120
exhibits the feature that so many graphs of properties of the
first row transition metals do, a double dip.

CHAPTER III
E SR STUDY OF A SILVER SEPTAMER
Introduction
Silver is a Group IB metal and therefore it is expected
that Agy would be the transition-metal counterpart of the
known alkali-metal (Group IA), Liy, Nay, and Ky clusters. In
a series of classic electron spin resonance experiments
Lindsay, et al., have generally established the electronic,
magnetic, and structural properties of these clusters and
also of Li3, Na3, and Kg (95,96). Theory has agreed with
those findings (97). (It is noteworthy that the pentamers
within that series have not been detected (98).)
Correspondingly, the Group IB clusters Cug, Agg, and Aug were
trapped in matrices by Howard, Mile, Sutcliffe, et al., and
the ESR spectra revealed that their properties were very
similar to those of the Group IA trimers (99-101). Those
authors also report the detection and analyses of the ESR
spectra of the pentamers Cu5, Ag5, CUgAgg (102,103), and
CuAg4. Although we have not investigated the copper
containing clusters, the parameters for Agy given here, as
obtained from an ESR spectrum in a solid neon matrix, are
almost the same as those assigned to Ag5 by Howard, and
121

122
coworkers (103). This suggests that those authors were
actually observing Ag7 and that the putative Cu5 , Cu2Ag3, and
CuAg4 clusters may also be septamers; however, that remains
to be proven. (Also, recent theoretical calculations by
Arratia-Perez and Malli do not support the proposed
Jahn-Teller distortion of Ag5 from a trigonal bipyramidal
structure (104).)
We have convincing experimental evidence that the
cluster composed of seven silver atoms has the structure of a
pentagonal bipyramid (Figure 111 -1 ) with the single unpaired
electron spin predominantly confined to the two axial atoms.
This structure is a section of an icosahedron and can be
visualized as five slightly distorted tetrahedra meeting at
an edge to form a decahedron, thereby having a pentagonal
axis. Silver and gold particles of decahedral and
icosahedral geometry were first observed by Ino using
transmission electron microscopy (105). There has been
considerable controversy over the internal strain and the
compensating lower surface energy In these so-called
"multiply-twinned particles" (MTPs) (106). Ino proposed a
critical radius above which the icosahedral form of the
particle would transform to the cubooctahedron. The silver
septamer then corresponds to the smallest known MTP.
Experimental
Silver cluster molecules were formed by the
co-condensation of neon (Aireo, 99.996% pure) and silver

123
atoms on a sapphire or copper rod cooled to 4 K via a liquid
helium Heli-Tran system. The ESR spectrometer and furnace
assembly have also been previously described (79). Silver
was vaporized from a silver wire wound on a 1.0 mm diameter
tungsten wire resistively heated to about 925 “C, or in the
case of isotopically enriched silver powder (99.26% atomic
abundance of 199Ag from Oak Ridge National Laboratories),
from a tantalum cell resistively heated to 1290 °C.
Temperatures were measured with an optical pyrometer and were
not corrected for surface emissivity. Deposition times were
of the order of an hour with matrix gas flow rates of 12-18
mmole/hr. The matrices were not very stable and often
inadvertently annealed themselves, resulting in the loss of
trapped atoms and the formation of silver clusters.
ESR Spectra
Figure 11 I -2 shows an ESR spectrum obtained of 109Ag
enriched silver trapped in solid neon at 4 K after an
inadvertent annealing in which most of the 109Ag atom signals
near 3000 and 3700 Gauss (107) disappeared. Traces of those
signals are seen on the low field lines centered at 3006 G in
the Figure .
Figure I I I — 3 shows the ESR spectrum from the same
experiment, but before any annealing was done to the matrix.
The extremely intense lines at about 3000 G are due to the Mj
= 1/2 transition of the ^"Ag atoms. These lines completely

124
obscure the low field lines of the silver septamer. The
other two sets of lines at 3237 G and 3476 G are clearly
visible. It is not until the matrix has been annealed
strongly (close to the melting point of neon) that the three
sets of lines become clear (Figure 111 — 2 ) .
The four groups of lines indicated in Figure 111 - 2 are
produced by hyperfine interaction (hfi) of the one unpaired
electron with two equivalent 109Ag (1=1/2) nuclei. The hfi
is large enough (about 240 G) that the second order effects
lead to a small 17 G splitting of the central line (108).
Each of the four lines consists of six hyperfine lines
separated by 8.7 G with intensity ratios 1:5:10:10:5:1 (to
within a few percent) corresponding to a much weaker hfi with
five equivalent ^09Ag nuclei. The intensities of the hf
pattern in the central group of lines are accounted for as
partial overlapping of two groups of six lines to yield eight
lines with intensities in the ratio of 1:5:11:15:15:11:5:1 as
indicated in Table 111 -1 . Each of the eight central lines
was examined on a greatly expanded scale of the magnetic
field and at extremely low modulating fields in order to
detect any splitting in the individual lines. None was
detected. The linewidths in the central group were the same
as those in the two outer groups, about 2 G FWHM. It must be
reasoned that the second order splitting of 17 G is
(fortuitously) almost exactly twice the hf splitting within

125
Table 111 — 1. Calculated and observed ESR lines (in G) of
109Ag7 in solid neon at 4 K. (v = 9.5338 GHz)
Observed Lines
Calculated Lines
Relative
Center of
Intensity
a
hf Pattern
IJ.Mj>
II
II
II
II
II
II
II
II
II
II
It
II
II
II
II
It
II
II
II
============
II
II
II
II
II
II
II
II
II
II
II
II
II
II
II
II
II
II
II
II
II
II
II
II
II
II
11
II
1
2983.9(3)
2983.9
5
2992.5
2992.5
10
3001 . 4
3001 . 2
10
3009.9
3005.6
|1.1>
3009.8
5
3018.6
3018.5
1
3026.8
3027.1
1
3214.0
3214.4
5
3223.0
3223.0
11
3231.6
3236.0
O
V
3231 .7/3231 . 6
15
3240.3
3240.3/3240.2
15
3248.9
3253.2
! o, o>
3249.0/3248.9
11
3257.6
3257.6/3257.5
5
3266.2
3266.2
1
3274.8
3274.8
1
3462.2
3462.1
5
3470.7
3470.8
10
3479.6
3479.4
10
3488.1
3483.8
1 i .-i>
3488.1
5
3469.9
3496.7
1
3505.5
3505.5
a
Measured intensities are within 5% of those tabulated.

126
Figure 111 — 1 . The pentagonal bipyramid structure ascribed
to Ag7 In its 2A2 ground state. It has D5^ symetry with
two equivalent atoms along the axis and five equivalent
atoms in the horizontal plane.

127
matrix at 4 K (v = 9.5338 GHz). The top trace Is the
overall spectrum, and the bottom traces are expansions of
the three regions of Interest after annealing. Notice the
large intensity of the silver atom lines at 3000 G before
annealing.

128
3236 G 3253 G
Figure 111 -3. The ESR spectru* of 109Ag? in a solid neon
matrix at 4 K {v =» 9.5338 GHz). The fields indicated are
the positions of the four hyperfine lines corresponding
to |J,Mj> = ) 1 , 1> . |1,0>, | 0,0> , and |1,1> (see Table
111 — 1 ) . The spacing within each of the four 6-line
patterns is uniformly 8.7 G. The few extra lines in the
background of the lines centered at 3006 G are due to
residual 109Ag atom signals.

129
the six line pattern. This, in fact, is found to be the case
upon detailed analysis of the spectrum.
The spectrum is then assigned to the axial molecule
shown in Figure 111 — 1 where the Ag^ molecules are randomly
oriented in the matrix. The strength and shape of the lines
indicate that they correspond to "perpendicular" transitions
(24) where the "parallel" components lie up field of each
line and were not observed either because of their low
intensity or because they were obscured by other ESR lines.
Analysis and Discussion
The analysis of the spectrum utilized the axial spin
Hamiltonian
( 111 -1 ) H = g|0HzSz + g^/S(HxSx + HySy)
+ A|SZJZ + A_J_(SXJX + Syjy)
where, for two equivalent nuclei with Ij = I2 = 1/2, the
appropriate quantum numbers are J = |Ij + I2I I Ij - I2I
and Mj = J, J-l,..., -J. This yields here, for S = 1/2, an
8X8 matrix from which the four observed transitions |J,Mj>
in Table I I I -1 were calculated to better than 0.1 G by
varying g_t_, A j_, and A» . The reasonable assumption was made
that g| equals ge in this axial molecule; gj < go. is
indicated by the shapes of the observed perpendicular lines.
The hf splittings in the ring of five equivalent atoms of

130
8.65(5) G was a constant spacing to within the experimental
error in the spectrum. It was then used in finding the
calculated line positions in the last column of Table 111 — 1 .
Calculated and observed line positions differ at most by
0.4 G .
The derived magnetic parameters of 109Ag7 are given in
Table I 11 — 2. The A y (2) parameter for the axial atoms has a
higher uncertainty because it is derived indirectly from the
perpendicular line positions. The s electron spin densities
at the axial (2) and ring (5) nuclei are derived from A^so
values in the usual way by comparison with the free atom
109Ag values (85). To do this for the ring (5) atoms it was
necessary to assume that A_i_(5) = A y (5) = Aiso(5); however,
consideration of Ago. = g_L - ge (see below) indicates that
there is unpaired p and/or d electron character on those
atoms .
As indicated by the ps in Table I I I -2 . 65% of the spin
is in an (antibonding) orbital on the two equivalent axial
atoms in Ag7, just as in Na? and K7. The s character on the
five equivalent Ag atoms may arise from spin polarization and
could be negative so that it would then total -6.0%. The
rest of the spin, about 40%, is then distributed in p and/or
d hybridization.
Lindsay, et al., have discussed the electronic
properties of the alkali-metal septamers and place the
unpaired spin in an a2 molecular orbital with the next lower

131
Table
111-2. Magnetic parameters and s-electron spin
densities for 109Ag7 cluster In Its
2A2 ground state.
g-L
2.094 ( 3 )
2.0 0 2 3 b
! Aj_( ^ 09Ag ) 1
(2)
700
(3)
MHz
1 A K (109Ag) 1
(2)
654
(30)
MHz
I Ao.( 109Ag) |
(5)
25
• 4 (1)
MHz
Aiso<109^)
(2)C
685
(12)
MHz
Adip(109Ag)
(2)c
15
(11 )
MHz
PS (109Ag)
(2)
0 .
3 2 4 d
ps (109Ag)
(2)
+ 0 .
0 1 2 d ’ e
a (2) and (5) indicate the two equivalent axial and the five
equivalent ring atoms, respectively.
b Assumed.
c A_i_ and Aj have been taken as positive in calculating Aiso
and Adi (see ref. 118, page 55). This neglects the sign of
the nuclear moment which is negative.
ps(i ) are the s-electron spin densities calculated as the
ratio of Ajso(i) to that of the free atom (2114 MHz (119)).
Assuming Aj_(5) = A j ( 5 ) = Als(J(5).
e

132
filled orbital as . This Hlickel model calculation has been
recently discussed in more detail in two separate papers by
Wang, George, Lindsay, and Beri (109). Others have made
extensive calculations, also justifying pentagonal bipyramid
structures (99).
The simplest assumption to account for the observed
positive shift in A g_j_ (= +0.092) is that it results from
spin-orbit coupling of the ‘A2 ground state with the
low-lying 2Ej excited state produced by exciting one of the
four e^ electrons into the singly-occupied a2 orbital. Then
( 111 - 2 ) Ago. = ( - 2/1 / AE ) where AE = E-'-E." and A is taken as the spin-orbit coupling
nl a2
constant for a 5p electron (about 615 cm-1) (103) and/or for
a 4d electron (about 1800 cm-1) (87) on atomic Ag. According
to the Hueckel model of Lindsay, et al. (109), AE = 0.7B =
4000 cm-1 where B for Ag was taken as 1/8 (Fermi energy) (97)
which is about 0.7 eV (111). Then to estimate the required
matrix elements one must consider the M0's formed from s, p.
and d electrons in D5h symmetry. These have been considered
in detail for a ring of five Mn atoms (13), and one then
deduces that the non-zero matrix elements for the
"perpendicular'' lx operator, involving only the five
circumferential silver atoms of Ag?, are

133
= i
and
= * (112).
Here, at each ring atom, the x axis points toward the center
of the ring and the z axis is parallel to the principal
five-fold axis of the molecule. The p or d spin density on
the central two axial atoms does not yield non-zero matrix
elements.
Then to check the reasonableness of the measured Ag via
Eq. 111 - 2 , one can consider the limiting cases of
contribution of either all p character or all d character to
the wavefunction, where the coefficient of that AO is
(0.4) ' in the a2 MO. If one also assumes that all such
non-s character lies at the ring atoms, then one finds from
Eq. 111 - 2 that the fraction of px character in the 2e'1
excited state must be 0.75. On the other hand, with much
larger d-electron spin-orbit coupling the dx fraction drops
to the more reasonable value of 0.26 if the unpaired electron
is in an s-d hybrid. These are. of course, very crude
calculations, meant only to justify the magnitude of the
observed shift.
The ESR spectrum in Figure I I I - 2 is very similar to
that obtained by Howard, et al. (105), when 107Ag was trapped
in a deuterated cyclohexane matrix at 77 K, but the small
hyperfine splittings are completely resolved here. Those

134
authors attributed the "superhyperfine" structure to five
lines (rather than the six observed here) and assigned their
spectrum to Ag5 with a distorted trigonal bipyramid
structure. However, our derived parameters (corrected to the
107Ag nuclear moment) are essentially the same as theirs (see
Table 111 -3) except for their "superhyperfine" analysis, so
that it is clear that the molecule they were observing is
Ag7 .
Perhaps of greatest overall interest is the conclusion
from this work that Group IA (alkali-metal) and Group IB
clusters are closely related. This is emphasized by a
comparison of spin densities among the M7 cluster, as shown
in Table 111 — 4. This is not surprising and confirms the view
that both series of atoms may be treated as having one s
electron interacting by a suitable pseudopotential with an
inner closed shell core.

135
Table 111 - 3. Comparison of the magnetic parameters of
107Ag7 (this work) with those of Howard,
et al.'s *07Ag5 cluster.
Parameter
107Ag5
in CgD j £
107Ag?
in Neon
g-L
2.085
2.094
A_iJ 107Ag)
( 2 ) c
201 G
204 G
A_l( 1 07Ag)
(5)c
5.5 G
7.5 G
a Reference 102.
k Ai values obtained here for 109Ag7
l97Agrj values using the ratio 109ju/107p
have been converted to
= 1.1543.
c
(2) and (5) indicate axial and ring atoms, respectively.

136
Table I I I - 4 .
Spin densities (s-electron) compared for the
2A2 ground states of the Na7. K?, and Agy
clusters.
Na7
K 7
Ag?
°s
(2)c
0.374
0.371
0.325
ps
(5)c
-0.021
-0.022
+0.012
a Ref. 98
13 This work .
c (2) and (5) indicate axial and ring atoms, respectively.

CHAPTER IV
ESR OF METAL SILICIDES
ESR of MnSi and AgSi
Introduction
Silicon has become important in recent years because of
the semi-conductor industry, and is also interesting to the
chemist as an analogue of carbon. Various small silicon
containing molecules have been studied already in this
laboratory: HSiO, SiH3, SiCO, and Si2 (113,114). We consider
here the silicon analogs of transition-metal carbides. A
major difference between carbon and silicon atoms, other than
the larger nucleus and a closed shell of electrons for
silicon, is the availability of empty d orbitals to silicon.
Therefore we undertook a study of silicon and various first
row transition metals and coinage metals, with special
emphasis on the known metal carbide species (115). We were
able to isolate only two species which contain only silicon
and another metal, which we assign as AgSi and MnSi.
Experimental
These experiments were carried out in the usual way.
The metals were vaporized from tantalum cells using water
cooled copper electrodes. Silver (1=1/2) (200 mesh powder,
99.9% pure from Aesar) was heated to approximately 1250 °C
137

138
and manganese (100%, 1=5/2) (Spex flakes, metal impurities
100 ppm max.) was heated to approximately 1100 °C. Silicon
(95.3% 1=0, 4.7% 1=1/2)(99.9% pure, 20 mesh from Union
Carbide) was also vaporized from a tantalum cell at about
1700 °C. The metal vapor was codeposited with argon (Aireo,
99.999% pure) which was introduced to the system at a flow
rate of approximately 0.1 mmole/hour, and deposited on a
sapphire rod at approximately 14 K. All vaporization
temperatures reported here are surface temperatures of the
cells and have not been corrected for emissivity. Normal
deposition times ranged from 45 to 75 minutes. The ESR
spectra were taken using a Varian E-Line Century series EPR
spectrometer modified to operate with a Bruker BH-15 Field
Controller for the manganese work and a Varian VFR-2503 Field
Dial for the silver work. The matrices were annealed to
various temperatures and pressures without any significant
change in the ESR spectrum.
ESR Spectra
AgSi
Two doublets were observed for this molecule. These
were due to the two naturally occurring isotopes of silver
(107Ag 51.82%. 109Ag 48.18%) which have slightly different
nuclear moments. Lines at 3321 and 3375 gauss were assigned
to AgSi and lines at 3317 and 3379 gauss were assigned to
109AgSi (Figure IV-1). Unfortunately no parallel lines have

139
been observed for this molecule. The observed perpendicular
lines have been fit to within one gauss. We found that gj. =
1.9981 and A_i_ = 53.2 gauss for *07AgSi and Aj_ = 61.2 gauss
for 10 9AgSi (Table IV-1).
MnSi
A series of six lines centered at about geff = 4 are
observed for this molecule (Figure IV-2 ) . Several
experiments were done in which the concentration of silicon
in the matrix was varied in order to determine whether we
were observing MnSi or possibly a larger cluster. The same
was done for manganese and the only lines that grew in were
due to Mng and Mn5 (13). Higher manganese concentrations
caused the signals due to MnSi to decrease and they disap¬
peared altogether at high manganese concentrations. No new
lines attributable to a higher-order MnSi cluster were
observed. Table IV-2 summarizes the hyperfine parameters for
MnSi .
Analysis and Discussion
AgS i
From the ESR spectrum the ground state of AgSi has been
determined to be doublet sigma. This is consistent with the
10 2 2
idea of a sd ground state for silver and s p ground state
for silicon. Because of the small hyperfine splitting due to
the silver nucleus, most of the unpaired spin density

140
Table IV-1. Observed and calculated line positions (in Gauss)
for
AgSi
in argon at 14
K . (v = 9.380
Perpendicular
Lines
«T
1/2
ÍAg).
(107)
Obsd(2)
3321
Ca 1 cd(2 )
3321
1/2
( 107 )
3375
3375
1/2
(109)
3317
3317
1/2
(109)
3379
3378
Derived Parameters
g_L. 1.9981
g| 2.0023a
(Ajl! 149 MHz
! A | I 149 MHz b
a Assumed equal to gg
b Assumed equal to Aj_
() Error in the line positions.

141
Table IV-2. Observed and calculated line positions (in Gauss)
for MnSi in argon at 14 K.(u = 9.380 GHz)
Perpendicular Lines
Mj(Mn)
5/2
3/2
1/2
- 1/2
- 3/2
- 5/2
Obsd(2)
1424
1513
1607
1703
1804
1906
Calcd ( 2 )
1425
1513
1606
1702
1802
1906
() Error in the line positions.

142
Figure IV-1. The ESR spectrui of AgSi is an argon matrix
at 12 K. The line positions of the impurities (CH3 and
SiH3) are noted, y = 9.380 GHz.

143
Figure IV-2. The ESR spectrum of MnSi in an argon matrix
at 12 K. v = 9.380 GHz.

144
probably resides in a p orbital on the silicon. The hyper-
fine parameters as well as g were fit for both isotopes. The
difference in the hyperfine parameters that arise between the
two molecules is due to the fact that the nuclear moments are
slightly different for 1Q,7Ag and 109Ag. The ratio of the
hyperfine parameters was found to be approximately equal to
the ratio of the nuclear moments. Since no parallel lines
were observed, we had three unknowns to fit to only two
lines, the two observed lines gave two equations with which
to determine the hyperfine parameters. The Aj parameter was
assumed to be equal to A_j_ in order to solve the equations.
This introduced a certain amount of error into the derived
parameters for AgSi.
The molecule was fit to a spin Hamiltonian with axial
symmetry such as the one below (46),
(IV-1) H = gBSzHz + K S zIz + X~(S+I+ + S“I~)
+ Xj + S I J )
which was modified for an S = 1/2 and I = 1/2 system. A
4 X 4 matrix was set up for all of the possible combinations
of nij and ms. This matrix was then diagonalized using a
program which fits the hyperfine parameters to an unrotated
Hamiltonian similar to (24):

145
(IV-2)
H = g|í3HzSz + g^(HxSx + Hy Sy)
+ A„IZSZ + A-i- ( I xS x + IySy)
The hyperflne parameters were then adjusted so as to give the
best fit to the observed line positions. The calculations
were made assuming that 0 = 90 degrees. This assumption was
made because of the shapes of the observed lines.
Because no parallel lines were observed, it was not
possible to determine an independent value for Aj. This has
also made it impossible to determine a value for A^so or
Adip. Without these parameters a value for the spin density
on the silver atom cannot be determined.
MnSi
MnSi was found to have a ground state. This implies
a double bond between the manganese and the silicon since the
atoms have a s d and s p ground state electron
configurations, respectively. If the two unpaired p
electrons bonded with two of the unpaired d electrons in
manganese, this would leave three unpaired d electrons, which
are most likely in d 7r (2) and a do molecular orbitals. Again,
no other lines were observed for this molecule. This was
either due to their low intensity or the parallel lines were
obscured by other lines that occur at 3400 G such as SiH3,
which were much more intense.

146
The molecule was also fit to an axial spin Hamiltonian
which was modified for a S = 3/2 and I = 5/2 system. This
produces a 24 X 24 matrix which is then diagonalized and fit
to the observed lines in order to determine the hyperfine
parameters for this molecule. The fitting program utilizes a
non-rotated spin Hamiltonian in order to fit the differences
of eigenvalues to hi; by varying gj_, A_¡_ , and A j . This program
was also utilized in determining the errors of the calculated
hyperfine parameters. Because we observed six lines for this
molecule (Mn: mj=5/2, . . ,-5/2) , we were able to fit the lines
to within the experimental error of the lines (2 gauss). The
interesting thing to note about this species is the large
zero-field splitting of 2 cm-1 (not so unusual if one
remembers that MnO has a similar D value (116)).
Since six lines were observed, we had more equations
than parameters allowing determination of Aj independent from
Aj_. Even though no parallel lines were observed from which
Aj could be directly determined, the calculated value is
still adequate for calculating Aiso and Adip. This allowed
us to calculate a value for the spin density of the unpaired
electrons on the manganese atom ( Table IV-3 ).
As in the case of MnO only one set of lines was
observed for MnSi. This makes it difficult to assign an
accurate gj, and D value to the molecule since the two values
are interdependent on each other. In order to unequivocally
determine the parameters, it would have been necessary to

O' 03
147
Table IV-3. Hyperflne parameters and calculated spin
densities for MnSi in argon at 14 K.
(v = 9.380 GHz )
Derived Parameters
gj. 2.0080
gli
2 . 0023a
1 Ao.|
270 MHz
' A ¡ 1
350 MHz
Ai s 0
297 MHzb
Adip
80 MHzb
Spin Densities
(>S
for Manganese
0.12
i02da
1 . 35
Assumed equal to ge.
b Assuming that Aj_ and A | are
both positive.

148
observe a set of high field lines. Unfortunately, as in the
MnO case, none have been observed. The parameters g_i_ and D
were varied in order to determine their relative effects on
each other, as well as to find the best fit for the observed
product lines. The final hyperfine parameters are listed in
Table IV-3. A zero field splitting of 2 cm 1 is a reasonable
for MnSi when considering other manganese containing
molecules (117,118).
ESR of Hydrogen-Containing
Scandium-Silicon Clusters
Introduction
Clusters of various sizes have been successfully
produced with scandium (14,9). In a series of experiments
involving first row transition metal carbides ScC was not
observed. It was of interest therefore whether a ScSi
species could be made. Several attempts were made to produce
such a molecule, all of which showed no evidence of the
molecule being trapped in an argon matrix. Instead a variety
of other molecules containing both silicon and scandium were
observed. A typical blank involving only scandium produced
signals which were apparently due to a Sc-H20 molecule which
has been observed by other workers (119). A typical silicon
blank usually yields several species containing silicon such

149
as SiHg, SiCO, and Si2 (113,115). When silicon and scandium
were codeposited into an argon matrix several sets of new
bands appeared.
Experimental
Standard methods for producing the metal containing
argon matrices were used in this series of experiments. The
scandium and silicon metals were vaporized from a furnace
flange onto which two tantulum cells were mounted on seperate
sets of electrodes, so that it was possible to heat the cells
to different temperatures. The scandium (100%, 1=7/2) (Alfa
Products, 99.9% pure metal shavings) was vaporized from a 40
mil tantalum cell at about 1265 °C. The deposition
temperature for the scandium was rather critical since too
high a temperature would produce scandium clusters which
tended to obscure the product lines, and a temperature that
was too low would fail to yield any product lines at all.
Silicon (95.3% 1=0, 4.7% 1=1/2) (99.9% pure, 20 mesh from
Union Carbide) was vaporized from a tantalum cell at about
1700 °C. The matrix gas (argon, Aireo, 99.9996% pure) was
flowed in at the rate of about 12 to 18 mmole/hour. The
sapphire rod was kept at about 14 K during the experiment
utilizing an Air Products Displex closed cycle refrigeration
system. The matrix was analyzed using a Varian E-line
Century EPR modified to operate with a Bruker BH-15 Field
Control unit. Utilizing this type of a set up we were able

150
to reduce the uncertainty in our line positions to about 2
Gauss. Deposition of the matrix usually took about 60
minutes.
ESR Spectra
HScSiHn
The ESR signal attributed to this molecule consists of
a set of eight doublets centered at 3530 G (Figure IV-3).
Unfortunately not all eight lines are clearly visible. Three
of the lines (3400G, 3470G, and 3699G) (Figure IV-3) are
almost completely obscured. The lines are only visible when
the flat surface of the rod is parallel to the pole faces of
the magnet (Figure IV-4). The lines almost completely
disappeared when the matrix was slightly annealed (Figure
IV-5). This indicates that the molecule is highly oriented
within the matrix trapping site. We were therefore able to
identify those lines which were overlapping or very close to
other lines. The doublets were only observed when both
silicon and scandium were codeposited. The set of 8 lines is
listed in Table IV-4, the center of the doublet was used to
fit each of the lines. A list of the parameters calculated
for this molecule can be found in Table IV-5. It was not
possible to resolve any hyperfine structure due to silicon.
Therefore n could not be determined accurately.

151
Table IV-4. Observed and calculated line positions (in
Gauss) for HScSiHn in argon at 14 K.
(v = 9.380 GHz)
Perpendicular Lines
Mj(Sc)
7/2
Obsd(2)
3204
Calcd(2 )
3204
5/2
3265
3265
3/2
3330a
3330
1/2
3398a
3398
- 1/2
3469
3469
- 3/2
3543
3543
- 5/2
3620a
3620
- 7/2
3699
3699
a Not possible to assign a line position from the spectrum
because of a large number of other lines in the same region
() Error in the line positions.

152
Table IV-5. Hyperfine parameters and calculated spin
densities for HScSiHn in argon at 14 K.
(v = 9.380 GHz )
Derived Parameters
g-L
1.9386
gi
2.0023a
|Aj.|
192
MHz
|Afl 1
345
MHz
Ai so
243
MHz
Adi p
51
MHz
Spin Densities for Scandium
pS
0.09
^3da
0.74
a No parallel lines were observed, so gj was
set equal to 2.0023.
b
Assuming that Aj_ and A> are both positive.

153
Figure IV-3. The ESR spectrui of Sc codeposited with Si
Into an argon matrix at 12 K. The eight sets of doublets
are shown for HScSiH
n •
= 9 . 380 GHz .
v

154
Figure IV-4. The *j= -1/2 and -3/2 transitions for
HScSiHn at 12 K. Two different rod orientations are
shown. The top is with the rod parallel to the field
and the bottom trace is for the rod perpendicular to
the field, v = 9.380 GHz.

155
/-/pScS/^
Figure IV-5. The ESR spectrum in the g=2 region after
annealing a matrix containing both Si and Sc (v =
9.380 GHz). The doublets due to HScSiHn have disappeared.
The only remaining lines are due to impurities and
H2ScSiHn (noted) .

156
HqScSIHh
Four sets of eight triplets were also observed when
scandium and silicon were codeposited into an argon
matrix.Seven of the four sets of eight triplets are shown in
Figures IV-6 through 9. The 1:2:1 triplet intensity pattern
observed is what one would expect for a molecule containing
two equivalent hydrogens. Again, lines were obscured by
other lines but in this case it occurred in the 3400G region
of the spectrum only. These lines were assigned on the basis
of belonging to the same molecule (due to the similar triplet
structures on all of the lines), but trapped in two different
matrix sites. The most intense lines (A) belong to the
trapping site of the majority of the H2ScSiHn molecules, and
(a) the weak set of lines which belong to H2ScSiHn trapped in
a secondary site. The first set of lines (A) were most
intense when the flat surface of the rod was parallel to the
pole faces of the magnet (bottom trace in Figures IV-(6-9)),
and the intensity of the lines decreased to almost zero when
the rod was turned perpendicular to the pole faces (top trace
in Figures IV-(6-9)). A second, somewhat less intense set of
lines due to the (A) site, were observed growing in when,
upon turning the rod, the other lines disappeared. This set
of triplets also exhibited broader linewidths than the most
intense set of (A) lines, and the lines were assigned as the
parallel lines for the (A) site. Line positions for the
perpendicular and parallel lines of (A) can be found in Table

157
IV-6. Both sets of lines were centered at approximately g =
2. The large change in intensities upon rotating the rod
indicates that the molecule being observed is highly oriented
in the matrix. ESR parameters for this molecule were
calculated and can be found in Table IV-7.
Two other sets of triplets (a) were also observed in
the experiments with silicon and scandium. These were
significantly weaker than the first set and can be seen close
to the (A) lines in Figures IV-(6-9). The perpendicular
lines showed some orientation but not to the extent of the
first set. The parallel lines were much weaker and broader
and observed only when the rod was perpendicular to the pole
faces of the magnet. The parallel and perpendicular line
positions for (a) can be found in Table IV-8. These lines
were also centered around g = 2, but were found within the
highly oriented molecule's hyperfine splitting (Figures IV-
(6-9)). The hyperfine parameters for (a) site can be found
in Table IV-9. As expected, they are just slightly different
than those found in Table IV-7.
Analysis and Discussion
HScSJJn
The set of eight doublets have been fit using a 16 X 16
matrix developed for an unrotated spin Hamiltonian. The
variables g j_, A j , and Ao. were fit. The gp parameter was set
equal to ge which is equal to 2.0023. Because no parallel

158
Table IV-6. Observed and calculated line positions (in Gauss)
for HgScSiHjj, the (A) site, in argon at 14 K.
(v = 9.380 GHz)
Perpendicular Lines
Mj(Sc)
7/2
Obsd(2)
2733
Ca1cd(2 )
2733
5/2
2877
2877
3/2
3035
3035
1/2
3206
3206
1/2
3391a
3391
3/2
3589
3589
5/2
3802
3801
7/2
4027
4026
Parallel Lines
Mj ( Sc )
7/2
0s bs(2)
2516
Ca1cd(2)
2515
5/2
2720
2720
3/2
2935
2934
1/2
3159
3159
1/2
3394a
3394
3/2
3638
3638
5/2
3893
3893
7/2
4157
4158
a Not possible to assign a line position from the
spectrum because of a large number of other lines
in the same region.
() Error in line positions.

159
Table IV-7. Hyperfine parameters and calculated spin
densities for H2ScSiHn, site (A),
in Argon at 14 K.(v = 9.380 GHz)
Derived Parameters
g_L 1.9695
g| 1.9983
1 A^!
507
MHz
IAlll
653
MHz
Aiso
557
MHz
Adip
48
MHz
Spin Densities for Scandium
Ps 0.20
p3dcr °’70
a
Assuming that A_¡_ and A« are both positive.

160
Table IV-8. Observed and calculated line positions (in
Gauss) for H2ScSiHn> the (a) site,
in argon at 14 K.(v = 9.380 GHz)
Perpendicular Lines
Mj (Sc )
7/2
Obsd(2 )
2759
Ca 1 cd(2)
2758
5/2
2899
2898
3/2
3051
3050
1/2
3216
3216
1/2
3393a
3393
3/2
3583
3584
5/2
3786
3786
7/2
4001
4001
Parallel Lines
M-fl-ScJ
7/2
Obsd(2 )
2548
Ca1cd(2)
2548
5/2
2745
2746
3/2
2953
2953
1/2
3169
3169
1/2
3394a
3394
3/2
3630
3630
5/2
3874
3874
7/2
4127
4127
a Not possible to assign a line position from the spectrum
because of a large number of other lines in the same region
() Error in line positions.

161
Table IV-9. Hyperfine parameters and calculated spin
densities for H2ScSiHn, site (a),
in Argon at 14 K.(v = 9.380 GHz)
Derived
Parameters
So.
1.9703
gl
1.9985
iLi
489 MHz
i a 11
631 MHz
A • *
iso
536 MHz
Adip
47 MHz
Spin Densities for Scandium
ps 0.19
p3da 0.69
a
Assuming that A_i_ and A. are both positive.

162
Figure IV-6. The ESR spectrum (mj=7/2 and 5/2) for
H2ScSiHn in argon at 12 K after annealing to about 30 K.
The top trace is for the rod perpendicular to the field
and the bottom trace is for the rod parallel to the
field. v = 9.380 GHz.

163
Figure IV-7. Same as Figure IV-6 except the mj = 3/2 and
-3/2 transitions are shown.

164
Figure IV-8. Sane as Figure IV-6 except the mj = 1/2
transition is shown.

165
Figure IV-9. Same as Figure IV-6 except the *j=-5/2 and
-7/2 transitions are shown.

166
lines were directly observed, A j was fit indirectly by
varying the parameters with 9 = 90 degrees. This causes
somewhat more uncertainty in A ^ than is found in either A_i_ or
g-L.-
It was found that gj_ is equal to 1.9386 which is
somewhat lower than gg . This indicates that some spin-orbit
coupling with a low lying excited state is probably
occurring. The 5 G splitting which is observed between the
doublets is consistent with what others have found for
hydrogen attached to metal atoms (120).
H2ScSiHn
Two sets of eight triplets have been observed in these
experiments. Both sets were fit using a 16 X 16 eigenvalue
matrix which was diagonalized in order to fit the hyperfine
parameters to the observed lines. The center line in each of
the triplet patterns was used in the fitting routine since
the observed triplet was most likely due to two equivalent
hydrogens attached to a scandium. This is an acceptable
approximation since the center of the triplet pattern should
be close to where the transition would occur for the scandium
hyperfine without any interaction due to the spin of the
hydrogen nucleus. Both sets were fit to within 1 G of the
observed (center) line positions (for those lines which were
not obscured by other transitions or in the case of weak
lines, specifically the (a) parallel lines, by the background
noise).

167
For the most intense set of lines (A), g_j_ was found to
be equal to 1.9695. Because a set of parallel lines was
observed, it was possible to calculate g| independently from
the perpendicular lines. The g| parameter was calculated by
leaving A _i_ and A | unchanged from the calculation of g _j_, but
changing the value of 0 to 0 degrees. From this calculation
g| was found to be equal to 1.9983. Assuming that Aj_ and A |
were positive, we found Aiso = 557 MHz and Adip = 48 MHz.
The unpaired spin density ps on the scandium was found to
be 0.33.
That the majority of the molecules formed are so highly
oriented is somewhat unusual. When a matrix is deposited,
the trapped species are generally randomly oriented, and
there is not such a dramatic change in the ESR spectrum when
the rod is turned. But this type of trapping has been
observed by other workers (13). Because of the large
intensity of the orientation sensitive lines, it seems that
the majority of the H2ScSiHn molecules are trapped with their
axes perpendicular to the plane of the deposition surface.
The lines are a bit broader than one would expect for a
single type of trapping site. Also very weak perpendicular
lines can be observed for only the strongest perpendicular
lines when the rod is parallel to the pole faces of the
magnet. This would seem to indicate that the molecules are
trapped not exactly perpendicular to the surface but rather a

168
random selection of molecules would trace out a conical
surface with the apex pointing toward the deposition surface.
The second set of eight triplets (a) would appear to
belong to H2ScSiHn molecules which have been trapped out
parallel to the deposition surface. This is indicated by the
reduction of intensity of the perpendicular lines when the
rod is turned and the weak appearance of the parallel lines.
Both sets of lines show the characteristic triplet pattern
one would expect for two equivalent hydrogen atoms. Because
of this and since only parallel and perpendicular lines are
observed, the molecule attains a pseudo linear configuration
as far as the ESR was concerned.
Hydrogen containing scandium compounds have been
studied previously by other workers (119,120). Both H2Sc and
Sc-H20 have been reported by Knight and coworkers. Of
interest is that Sc-H20 can be observed by directly
vaporizing scandium out of a tantalum cell as was found by
Weltner and coworkers when they produced discandium (9).
Adding that to the knowledge that scandium easily adsorbs
water, it is possible that when scandium metal chips are
vaporized not only scandium atoms make up the vapor
composition, but also hydrated scandium atoms are present in
the vapor. When this is mixed with hot silicon atoms, it is
very possible that the hydrated scandium species become
hydrogenated si1 icon-scandiurn species, as is observed in
these experiments.

169
The other possibility in forming these hydrated
scandium silicides is an insertion of a scandium atom into a
silane like molecule. Several workers have reported this
type of a mechanism for organic molecules, usually methane
(121-126). Many first row transition metals have been
reported to form an insertion product with methane. The
activation of methane in a matrix has also been reported for
group VI elements A1, Ga, and In (121). In the case of
aluminum trapped in a methane matrix the insertion occurs at
10 K. If the matrix is photolyzed, the aluminum atom picks
up a second hydrogen from a different methane molecule
forming H2A1CH3. With at least two possible methods of
forming hydrogen containing scandium silicides, we turn to
the ESR spectra for help in determining what is happening in
these experiments.
The exact structures of the two molecules is unclear.
It is obvious from the experimental work that the molecules
contain both silicon and scandium and the ESR spectrum
presents a clear indication of how many hydrogens are
attached to the scandium end of the molecule. What can not
be determined is whether any hydrogens are attached to the
silicon. For HScSiHn we know that n cannot equal zero since
that would result in either a singlet or triplet ground state
for the molecule. The ESR spectra indicate that the molecule
has a doublet ground state. This necessitates that n be odd.
In all experiments involving silicon there is always present

170
In the ESR spectrum transitions due to SiH3, which indicates
the presence of silane (ESR invisible) in the matrix. With
the knowledge that metal atoms can insert into methane, it
seems reasonable that scandium could insert into a silane
molecule. This would form HScSiH3 which is a doublet
molecule.
The other set of observed lines are those of a molecule
which contains one scandium atom, most likely a single
silicon atom, and at least two hydrogen atoms attached to the
scandium. We also know from the ESR spectrum that H2ScSiHn
is a doublet molecule. This puts a limit on what values of n
are valid. If n is odd, the molecule will have either a
singlet or triplet ground state. In order for the molecule
to have a doublet ground state n needs to be even or zero.
This can be envisioned as occurring via two possible
pathways. The simplest is a silicon reacting with a scandium
attached to two hydrogen atoms to produce HgScSi. Even
though this is an obvious method because of scandium's
hydrophilic nature, no H2Sc is observed in the spectrum,
which means that the silicon has to be directly involved in
the reaction process. Because SiH3 is present in the matrix,
it is also possible that a scandium hydride molecule (ESR
invisible) inserts into a SiH3 radical to form H2ScSiH2>
Because HSc has a singlet ground state, it is impossible to
determine if any is present in our matrices.

171
Determining the number of hydrogens attached to the
silicon was not possible in these experiments since the
natural abundance of 29Si (1=1/2) is only about 4.5%, and
therefore hyperfine splittings due to silicon were not
observed. Unfortunately because of the presently exorbitant
price of the silicon 29 isotope, we were not able to run any
experiments with this isotope. This also made it impossible
for us to rule out the possibility of more than one silicon
in this molecule. In the experiments typically only a small
amount of Si2 is observed. The intensity of the observed Si2
line in the experiments with both silicon and scandium was
not significantly different when compared to the experiments
where only silicon was deposited into an argon matrix at
equivalent deposition temperatures. This seems to indicate
that a species containing scandium and two or more silicones
is very unlikely.

CHAPTER V
CONCLUSION
Matrix isolation has been utilized along with two
spectroscopic techniques to establish the electronic ground
states as well as the structures of a variety of metal
carbonyls and metal clusters. The ground state of VCO was
found to be 6£. This means that the molecule contained five
unpaired electrons. Since the ground state of vanadium
contains only three unpaired d electrons it became obvious
that in order to form the monocarbonyl, promotion of an s
electron into a d orbital was necessary. Even though this
bit of information was mute in the study of CrCO, it became
important when analyzing the negative results of the MnCO
studies.
From the literature it seemed obvious that these types
of molecules could be produced for all of the first row
transition metals (91). That MnCO could not be observed in
either ESR or FTIR was therefore thought at first to be an
anomaly of the experiment. Other workers had made tentative
assignments in the IR for the molecule (92). Upon closer
examination the assigned stretching frequency for CrCO proved
wrong by over 100 cm-1 and the assignment for MnCO could not
172

173
be reproduced under a large variety of experimental
conditions. What became obvious from our experimental work
was that MnxCO was rather easily formed. Upon analyzing the
ESR data from the VCO experiments it became obvious why MnCO
could not be produced under our experimental conditions.
Promotion of one of the 4s electrons in manganese into a d
orbital was not possible because of the promotion energy
(over 22,000cm-1). Combining the negative results obtained
from the MnCO experiments with the information obtained from
the ESR experiments with VCO, allowed development of a
reasonable explaination of how the monocarbonyls for the
first row transition metals were formed. The explaination is
reasonable in that fits in well with the known properties of
these metals, and further experimental evidence provided by
other researchers confirms our hypothesis.
A major reason for attempting to gain an understanding
of the bonding of metal carbonyls is the light such work may
shed on catalysis. Many catalytic systems contain metals
bound to carbonyls. We know that these species aid in
reducing the activation energy of many types of reactions but
unfortunately very little is known about the bonding of these
molecules. With work such as this, a fundamental
understanding has been gained of the interactions between the
metal and the carbonyl.
Metal clusters are also thought to be important in
catalytic activity. Again, many metal clusters are known to

174
have catalytic activity but a fundamental understanding of
what is occurring on a molecular level is lacking. Studying
silver clusters seemed to be an obvious choice because of the
variety of its applications in chemistry, its ease of
vaporization (about 1200 °C), its low nuclear spin (S=l/2),
and the availability of the 109 isotope of silver (with
reasonable purity and at a reasonable cost).
We were able to isolate and identify a silver cluster
containing seven atoms. From the ESR spectrum it was
possible to determine both the ground state (^£) of the
cluster as well as the structure (pentagonal bipyramidal) of
the molecule. It had been thought that metals which
contained an unpaired s electron with the remainder of the
orbitals either completely empty or completely filled (such
as the Group IA and Group IB metals) should have similar
properties (97-105). Our study of the silver septamer gave
results that correlated well with those found for the
septamers of several Group IA metals. A pentamer for silver
had been reported in the literature but no pentamers for any
of the Group IA metals have been observed. Upon closer
examination of the ESR data it became apparent that the
reported pentamer was actually the septamer. This was shown
by comparison of the hyperfine parameters and spin densities
determined for Ag? and those reported for the pentamer.
It is somewhat strange that only the silver septamer
was observed in our experimental work. One would have

175
expected the smaller clusters of silver to be present also.
We found that Ag7 was formed only after annealling the
matrix. It remained even after the matrix had been strongly
annealed (close to the melting point of the matrix). This
shows that we were dealing with a very stable molecule. It
is possible that the other clusters were simply not stable
enough to be trapped in the neon matrix. The transitions due
to the smaller clusters may also have been obscured by the
very intense lines due to silver atoms (which disappear after
annealing the matrix) or by transitions due to impurities in
the matrix such as CHg.
Since Ag7 was not observed immediately after the matrix
had been deposited, it was reasonable to assume that it was
not formed during the vaporization of the metal. Strong
signals due to silver atoms were however observed. It was
therefore assumed that the vapor consists predominantly of
atoms and possibly a few dimers (which are ESR invisible).
The nucleation in this case seemed to occur not in the vapor
but rather in the condensed phase of the matrix. And after
the matrix had been annealed several times only the most
stable molecule(s) survived. In this case it was Ag7 .
Further work was done with silver and with first row
transition metals codepositing them with silicon in order to
form clusters. This proved successful in only two cases,
MnSi and AgSi. We had some success with scandium forming
hydrogen containing si 1 i con-scandiurn clusters. The problems

176
encountered with this work exemplifies exactly how little
cluster formation is understood. In situations were the
carbide had been formed (115) we were not able to form the
silicide, even though the properties of carbon and silicon
should be similar since they are both Group IVA elements.
It became apparent that this was not the case. Why other
species were not observed is difficult to ascertain. It is
possible that there were clusters formed but their ground
states were such that they were not observable via ESR
spectroscopy. We were able to isolate AgSi and determine
that the molecule has a 2£ ground state which indicates that
there is a single bond between the silver and the silicon.
In experiments where manganese and silicon were codeposited
manganese hyperfine was observed and assigned to MnSi which
was found to have a 4£ ground state. This indicated that the
species was doubley bonded.
For scandium, clusters were observed that also
contained hydrogen. Whether a bare scandiurn-si 1icon molecule
is possible is unclear. What we were able to determine was
the number of hydrogens on the scandium from the splitting on
the scandium hyperfine lines. The ground states of these
molecules have also been determined. Both were found to be
£ molecules. One had a single hydrogen attached to the
scandium and the other molecule had two hydrogens attached to
the scandium end of the molecule.

177
From these experiments we were able to determine the
structures and ground states of several metal carbonyls and
metal clusters. In isolating and indentifying these species
we have been able to further our understanding of small metal
containing molecules as well as correct previous
misconceptions. We have been able to develop a basic
understanding of how the first row transition metal
monocarbonyls are formed. We were also able to add to the
growing body of evidence that supports the theory that the
properties of the alkali metals are similar to the coinage
metals, substantiating the belief that a closed shell of
electrons can be considered as an empty shell would be, thus
simplifying theoretical calculations on larger molecular
systems. With this work we have laid the ground work for
studies in several areas. The other coinage metals, copper
and gold need to be investigated to see if they also conform
to the theory. We were able to finally explain why certain
metal carbonyls of the first row transtion metals can not be
observed. This work needs to be pushed on so as to encompass
the other transition metals (second and third row) even
though the difficulties in vaporizing these metals can be
considerable.

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BIOGRAPHICAL SKETCH
Stephan Bach was born on November 4, 1959, in
Knoxville, Tenn., to Dr. and Mrs. Bernd B. Bach. He
graduated with Honors from Anderson High School in
Cincinnati, Ohio, in June of 1977. In June of 1983 he
graduated from the University of Cincinnati having earned a
Bachelor of Science in chemistry, Bachelor of Arts in German
literature, and a Certificate in Business Administration.
Since August of 1983 he has attended the University of
Florida pursuing a course of study leading to a Doctor of
Philosophy degree in chemistry.
187

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.
(
t
.(U
k
/SC-
c±C
v.
William Weltner, Jr., Chairman
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.
IHaaAuhJ* VaMu
Martin T. Vala
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.
k.Xh\
Eyler
r of ClVemi stry
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.
Carl R . Stouf er ¿y
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.
11'- -x ^ ' *
Jerry to1. Williams
Assistant Professer of Materials
Science and Engineering
This dissertation was submitted to the Graduate Faculty
of the Department of Chemistry in the College of Liberal Arts
and Sciences and to Graduate School and was accepted as
partial fulfillment of the requirements for the degree of
Doctor of Philosophy.
December, 1987
Dean, Graduate School

UNIVERSITY OF FLORIDA
3 1262 08553 5473



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