Magnetic circular dichroism and absorption spectroscopy of matrix isolated transition metal atoms

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Title:
Magnetic circular dichroism and absorption spectroscopy of matrix isolated transition metal atoms
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xiv, 182 leaves : ill. ; 29 cm.
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English
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Roser, Dennis, 1962-
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Magnetic circular dichroism   ( lcsh )
Absorption spectra   ( lcsh )
Transition metals   ( lcsh )
Matrix isolation spectroscopy   ( lcsh )
Gases, Rare   ( lcsh )
Chemistry thesis Ph. D
Dissertations, Academic -- Chemistry -- UF
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non-fiction   ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1992.
Bibliography:
Includes bibliographical references (leaves 178-181).
Statement of Responsibility:
by Dennis Roser.
General Note:
Typescript.
General Note:
Vita.

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University of Florida
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Full Text









MAGNETIC CIRCULAR DICHROISM AND ABSORPTION SPECTROSCOPY
OF MATRIX ISOLATED TRANSITION METAL ATOMS
















By

DENNIS ROSER


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

1992


Fi FL 1CW,. L'5,rF'S












ACKNOWLEDGEMENTS


I would like to extend my gratitude and appreciation to my research advisor, Dr.

Martin Vala, without whose guidance and suggestions this endeavor would not have been

completed. Dr. William Weltner and Dr. Richard Van Zee also deserve thanks for many

helpful discussions and for various samples lent to this investigator over the last few

years.

A special note of appreciation is given to Dr. Bryce Williamson for information

which allowed temperature calibrations to be made. Dr. Robert Pellow is also thanked

for his calculations of theoretical spin orbit reduction factors of Mo atoms.

The entire support staff within the chemistry department is graciously

acknowledged for their unending support. Special thanks are extended to Joe Shalosky

for his timely design advice and the many "minor modifications" to instrumentation he

performed on a moment's notice. Russ Pierce also deserves a special thanks for the

electronics help he has provided and for the many times he has re-explained the operation

of certain circuits to the author.

I also wish to thank my coworkers, Bill, Jan, T.M., Bob and Marc, for their many

helpful discussions, of all sorts, over the past six years. Mitch and Kathi Cheeseman,

Steve and Trish Bach, Ngai Wong and Larry Chamusco also deserve special mention for

their support and encouragement.












TABLE OF CONTENTS



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

LIST OF TABLES ............................................ v

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

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

CHAPTER I
INTRODUCTION ....................................... 1
M atrix Isolation .................................... 3
Magnetic Circular Dichroism ........................... 6
Aims of this Investigation ............................. 7

CHAPTER II
MAGNETIC CIRCULAR DICHROISM THEORY ................ 9
Introduction ...................................... 9
Circularly Polarized Light ............................. 9
Basic MCD Equations ............................... 10
M om ents ........................................ 22

CHAPTER III
APPARATUS AND EXPERIMENTAL TECHNIQUES ............. 25
Introduction ...................................... 25
Matrix Isolation Equipment ............................ 25
Spectroscopic Apparatus .............................. 32
Calibration Procedures ............................... 43

CHAPTER IV
ABSORPTION AND MCD OF MATRIX ISOLATED SILVER AND GOLD
ATOM S ..... ...... .............. .... ............. 47
Introduction ...................................... 47
Experim ental ...................................... 48
Results ......................................... 49
D discussion ....................................... 85







CHAPTER V
MOLYBDENUM ATOMS IN RARE GAS MATRICES ............. 90
Introduction ...................................... 90
Experimental ...................................... 91
Results .......................................... 92
Discussion .. ... .................................. 103


CHAPTER VI
SPECTRA OF MATRIX ISOLATED COBALT
Introduction ...................
Experimental ...................
Titanium ......................
Cobalt .......................


AND TITANIUM ATOMS110
...................110
. . ... 111
................... 113
................... 124


CHAPTER VII
FUTURE STUDIES ................................... .. 152

APPENDIX
COMPUTER PROGRAMS ................................ 156

REFERENCE LIST ........................................... 178

BIOGRAPHICAL SKETCH ................... ................ .182












LIST OF TABLES


Table Page

4.1 Observed Absorption Band Positions (in cm-1) and Parameters Derived
from the Moments Analysis for Ag Atoms in Rare Gas Matrices. ....... 53

4.2 Observed Absorption Band Positions (in cm-1) and Parameters Derived
from the Moments Analysis for Au Atoms in Rare Gas Matrices. ....... 59

4.3 Selected Excited States, Configurations and Gas Phase Energies of
A u A tom s. ............................................ 64

4.4 Crystal Field Model: Absorption and MCD Parameters. ............. 71

4.5 Comparison of Experimental and Theoretical SO Coupling "Reduction"
Factors for the Noble Metals in Rare Gas Matrices ................ 87

5.1 Observed Absorption Band Positions (in cm-1) and Parameters Derived
from the Moments Analysis for Mo Atoms in Rare Gas Matrices. ....... 96

5.2 Gas Phase Absorption Band Positions and gf Values for Allowed and
Spin-Forbidden or Orbitally Forbidden Transitions for Mo Atoms ...... 99

5.3 Comparison of Experimental and Theoretical SO Coupling "Reduction"
Factors for Molybdenum Atoms in Rare Gas Matrices. .............. 109

6.1 Theoretical Co/Do (MCD) Terms for the Atomic Transitions J' J ..... 115

6.2 Gas Phase Data for Titanium Atoms .......................... 116

6.3 Assignments for Titanium Atoms in an Ar Matrix ................ 122

6.4 Gas Phase Data for Cobalt Atoms ........................... 125

6.5 Band Assignments, Matrix Shifts and Observed MCD Sign for Co Atoms
in a Xenon M atrix. ..................................... 132






6.6 Band Assignments, Matrix Shifts and Observed MCD Sign for Co Atoms
in a Krypton Matrix. ...................................... 139

6.7 Band Assignments, Matrix Shifts and Observed MCD Sign for Co Atoms
in an Argon Matrix. ..................................... 145

6.8 Energy Levels, Spacings and Land6 Interval Rule Constants for the
z 4F and z 4G States of Co Atoms. ............................ 149












LIST OF FIGURES


Figure Page

2.1 Resolution of circularly polarized light into electric and magnetic field
vectors which vary sinusoidally but with one retarded by X/4. A line
connecting the resultant vectors will trace a helical path of circular
cross-section. .......................................... 11

2.2 (a) Passage of circularly polarized beam L parallel to a magnetic field B
through sample S.
(b) A circularly polarized photon of the correct energy inducing a
electronic transition between ground state A and excited state J of a
sample molecule. Neighboring states K may affect the transition probability
by magnetic field induced mixing with the ground or excited state ...... 13

2.3 Appearance of MCD terms.
(a) Zero field absorption and MCD for a positive A1 term. The positive
lobe lies at higher energy.
(b) B0 terms may be positive or negative with the maximum coincident with
the absorption maximum.
(c) Co terms may be positive or negative with the maximum coincident with
the absorption maximum and will show a temperature dependence. ....... 21

3.1 Cutaway side view of furnace and Knudsen cell assembly used for
resistively heated samples. ................................. 27

3.2 Cutaway side view of cryostat with attached laser vaporization source. 30

3.3 Diagram of closed-cycle helium refrigerator (Displex) expander section. 33

3.4 Schematic representation of matrix gas delivery manifold ........... 34

3.5 Schematic representation of optical bench used for simultaneous recording
of MCD and absorption spectra. .............................. 36







3.6 Details of specially constructed chopper wheel and timing signals. Absorption
control signals are derived from outer notches while MCD control signals are
triggered by the abs/MCD slot. ............................... 38

3.7 Circuit diagram of the absorption board detailing circuitry used to subtract
the zero signal and the logarithmic amplifier .................... 41

3.8 Block diagram of the MCD signal path from PMT ouput to chart recorder and
A/D converter. .......................................... 42

4.1 Experimental MCD (top) and absorption (bottom) spectra of Ag atoms in a
Ar m atrix at 5.9 K. ...................................... 50

4.2 MCD (top) spectra of Ag atoms in a Kr matrix showing temperature dependence
of the signal. Absorption (bottom) spectra at 5.8 K ............... 51

4.3 Experimental MCD (top) and absorption (bottom) spectra of Ag atoms in a
Xe matrix at 6.5 K. ....................................... 52

4.4 Reduced MCD first moment plots vs. inverse temperature for the three Ag/RG
systems. For clarity, the Ag/Kr and Ag/Xe plots have been shifted by -5
and -10 y axis units, respectively. ............................. 54

4.5 Experimental MCD (top) and absorption (bottom) spectra of Au atoms in a
Ar matrix at 10.5 K. ..................................... 56

4.6 MCD (top) spectra of Au atoms in a Kr matrix showing temperature dependence
of the signal. Absorption (bottom) spectra at 10.3 K. ................ 57

4.7 Experimental MCD (top) and absorption (bottom) spectra of Au atoms in a
Xe matrix at 12.0 K. ..................................... 58

4.8 Reduced MCD first moment plots vs. inverse temperature for the three Au/Rg
systems. For clarity, the Au/Kr and Au/Xe plots have been shifted -5
and -10 y axis units, respectively ............................ 60

4.9 Reduced MCD second moment plots vs. inverse temperature for the three
Au/Rg system s. ........................................ 61

4.10 MCD zeroth moment plots vs. inverse temperature for the three Au/Rg
system s. .............................................. 62

4.11 Ordering of the spin-orbit split levels of the excited 2P state in octahedral
(Oh) and distorted tetragonal (D4) fields ........................ 70






4.12 MCD (top) and absorption (bottom) spectra of Ag atoms in a Ar matrix at
6K (solid curves). Simulation using the CF model with variable bandwidths
(dotted curves). Simulation using the CF model with bandwidths determined
from eq. 54 (dashed curves). Simulations are normalized to lowest
energy experimental absorption band ......................... 72

4.13 MCD (top) and absorption (bottom) spectra of Au atoms in a Xe matrix at
10.5K (solid curves). Simulation using the CF model with variable
bandwidths (dotted curves). ................................. 73

4.14 Temperature dependence of the cubic c and noncubic Nc bandwidth
contributions of Ag/Ar. Solid line fit follows the relation:
NC = 1.6x10" coth(32.1/2kT), in cm-1 ..................... 77

4.15 Temperature dependence of the cubic c and noncubic NC bandwidth
contributions of Ag/Kr. Solid line fit follows the relation:
NC = 1.5x10 coth(35.8/2kT), in cm-1 ..................... 78

4.16 Temperature dependence of the cubic c and noncubic NC bandwidth
contributions of Ag/Xe. Solid line fit follows the relation:
NC = 6.9x104 coth(24.2/2kT), in cm-1 ..................... 79

4.17 Temperature dependence of the cubic and noncubic bandwidth contributions
for the three Au/RG systems.
Legend: (NC values: 0 Au/Ar; U Au/Kr; A Au/Xe;
c values: + Au/Xe; V Au/Kr; Au/Ar) ................... 80

4.18 Band peak position vs. temperature for Au/Xe. The solid line fit follows
the relation: v0 = 39283 148coth(29.5/2kT), in cm-1 ............. 82

4.19 Reduced absorption second moment plots vs. temperature for the three
Au/RG systems. Lines are least squares fits .................... 83

5.1 Experimental MCD (top) and absorption (bottom) spectra of Mo atoms
in a Ar matrix at 10.3 K. ................................... 93

5.2 Experimental MCD (top) and absorption (bottom) spectra of Mo atoms
in a Kr matrix at 10.9 K. ................................... 94

5.3 Experimental MCD (top) and absorption (bottom) spectra of Mo atoms
in a Xe matrix at 11.3 K. ................................... 95

5.4 MCD temperature dependence for the z 7p 7S transition of Mo atoms
in a Ar m atrix. ......................................... 97

ix







5.5 Expansion of MCD from a concentrated Mo/Kr matrix. Bands marked with
a may be due to forbidden transitions. (+) band for 5p 7S
and (-) band for 7D *- 7S. No absorption was visible for either band. 100

5.6 Reduced MCD first moment plots vs. inverse temperature for the three
M o/RG systems. ........................................ 101

5.7 Temperature dependence of the cubic c and noncubic NC bandwidth
contributions of Mo/Ar. Solid line fit follows the relation:
NC = 1.9x105 coth(44.7/2kT), in cm-1 ................. .. 104

5.8 Temperature dependence of the cubic c and noncubic NC bandwidth
contributions of Mo/Kr. Solid line fit follows the relation:
NC = 1.7x105 coth(47.7/2kT), in cm-1 ..................... 105

5.9 Temperature dependence of the cubic c and noncubic NC bandwidth
contributions of Mo/Xe. Solid line fit follows the relation:
NC = 1.8x105 coth(43.2/2kT), in cm-1 ..................... 106

6.1 Absorption spectra of Ti atoms in an Ar matrix.
(a) Multiple sites from laser vaporization with continuous gas flow.
(b) Single site from laser vaporization with pulsed gas ...... ........ 118

6.2 MCD spectra of Ti atoms in an Ar matrix.
(a) Multiple sites from laser vaporization with continuous gas flow.
(b) Single site from laser vaporization with pulsed gas ............. 119

6.3 (a) Absorption spectrum of Ti atoms in an Ar matrix, 410-250 nm.
(b) Simulated absorption spectrum produced from gas phase band positions
and intensities. ......................................... 120

6.4 (a) MCD spectrum of Ti atoms in an Ar matrix, 410-250 nm.
(b) Simulated MCD spectrum produced from gas phase band positions
and intensities. ......................................... 121

6.5 (a) Absorption spectrum of Co atoms in a Xe matrix, 380-280 nm.
(b) Simulated absorption spectrum produced from gas phase band positions
and intensities. ......................................... 127

6.6 (a) MCD spectrum of Co atoms in a Xe matrix, 380-280 nm.
(b) Simulated MCD spectrum produced from gas phase band positions
and intensities. ......................................... 128






6.7 (a) Absorption spectrum of Co atoms in a Xe matrix, 270-220 nm.
(b) Simulated absorption spectrum produced from gas phase band positions
and intensities. ......................................... 130

6.8 (a) MCD spectrum of Co atoms in a Xe matrix, 270-220 nm.
(b) Simulated MCD spectrum produced from gas phase band positions
and intensities. ......................................... 131

6.9 (a) Absorption spectrum of Co atoms in a Kr matrix, 380-280 nm.
(b) Simulated absorption spectrum produced from gas phase band positions
and intensities. ......................................... 134

6.10 (a) MCD spectrum of Co atoms in a Kr matrix, 380-280 nm.
(b) Simulated MCD spectrum produced from gas phase band positions
and intensities. ......................................... 135

6.11 (a) Absorption spectrum of Co atoms in a Kr matrix, 270-220 nm.
(b) Simulated absorption spectrum produced from gas phase band positions
and intensities. ......................................... 136

6.12 (a) MCD spectrum of Co atoms in a Kr matrix, 270-220 nm.
(b) Simulated MCD spectrum produced from gas phase band positions
and intensities. ......................................... 137

6.13 (a) Absorption spectrum of Co atoms in an Ar matrix, 380-280 nm.
(b) Simulated absorption spectrum produced from gas phase band positions
and intensities. ......................................... 140

6.14 (a) MCD spectrum of Co atoms in an Ar matrix, 380-280 nm.
(b) Simulated MCD spectrum produced from gas phase band positions
and intensities. ......................................... 141

6.15 (a) Absorption spectrum of Co atoms in an Ar matrix, 270-220 nm.
(b) Simulated absorption spectrum produced from gas phase band positions
and intensities. ......................................... 142

6.16 (a) MCD spectrum of Co atoms in an Ar matrix, 270-220 nm.
(b) Simulated MCD spectrum produced from gas phase band positions
and intensities. ......................................... 143







6.17 Experimental and simulated spectra of Co atoms in a Xe matrix. The
simulations have been shifted to align with the experimental spectrum.
(a) Simulation using gas phase data published in Ref. 20.
(b) Experimentally observed spectrum.
(c) Simulation with 4Gl1/2 and 4F7/2 energy levels exchanged.
(d) Simulation with newly assigned 4G11/2 shifted 50 cm- to higher
energy. .............................................. 147

6.18 Experimental and simulated spectra of Co atoms in a Xe matrix. The
simulations have been shifted to align with the experimental spectrum.
(a) Simulation using gas phase data published in Ref. 20.
(b) Experimentally observed spectrum.
(c) Simulation with the unassigned J = 7/2 sublevel changed to a
J = 11/2 sublevel. ....................................... 151

7.1 Cutaway top view of pulsed valve, laser vaporization cluster source. .... 155












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

MAGNETIC CIRCULAR DICHROISM AND ABSORPTION SPECTROSCOPY
OF MATRIX ISOLATED TRANSITION METAL ATOMS


By

Dennis Roser

December 1992

Chairperson: Martin Vala
Major Department: Chemistry

Magnetic circular dichroism (MCD) and absorption spectroscopies have been used

to study Ag, Au, Mo, Ti and Co atoms trapped in rare gas matrices. Band moment

analyses have been performed for the 2p 2S transition of Ag and Au atoms and matrix

induced changes in their spin-orbit (SO) splitting have been assessed. The 614 cm-1 SO

splitting of gas phase Ag atoms is found to increase to 783 cm-1 and 638 cm-1 in Ar and

Kr matrices, respectively. A reduction to 524 cm-1 is observed in Xe matrices. For Au

atoms, the observed matrix splitting (Ar: 3354 cm-1, Kr: 3110 cm-1, Xe: 2655 cm-1) is

greater than the gas phase in all cases. These experimental values are compared to values

predicted from a model in which the isolated metal atom is considered to occupy a

tetredecahedral hole formed by twelve nearest neighbor rare gas atoms. A similar

analysis for the z 7p .7S transition of Mo atoms revealed an increase in Ar matrices







(126 cm-1) from the gas phase value of 101 cm-1. Reductions to 84.5 cm-1 and 57.5

cm-1 were noted in Kr and Xe matrices, respectively. The model is extended to the many

electron system of Mo atoms with good results. The analysis for all three atoms also

revealed considerable Jahn-Teller activity in the excited state which for the Ag and Au

atoms results in a further splitting of the 2p3/2 level. This results in the observation of

three absorptions in matrices where only two are seen in the gas phase.

The observed transitions for matrix isolated Ti and Co atoms have been assigned

by comparing the experimental spectra to simulations produced from gas phase data. For

Ti atoms in an Ar matrix, this was found to be straightforward with the predicted

spectrum matching the experimental one. For Co atoms in Xe matrices, several observed

MCD bands were found to have opposite sign from the predicted bands. Further

investigation revealed that three bands had been misassigned in the original gas phase

work. The same MCD patterns were observed in Kr and Ar matrices, but multiple

trapping sites complicated the assignment of transitions.












CHAPTER I
INTRODUCTION



The ability of magnetic circular dichroism (MCD) spectroscopy to provide

information about excited states has produced much interest in the technique. The excited

states of highly reactive species may be probed using MCD if they can be trapped in a

frozen rare gas matrix. Magnetic circular dichroism studies of the electronic and

structural configurations of small transition metal clusters, which are becoming increasing

important in catalysis and microelectronics,1 have been hindered by an incomplete

understanding of matrix induced changes in the spectra of trapped species. The study of

matrix isolated atoms to characterize and quantify these matrix induced spectral changes

is necessary before MCD characterization of clusters may begin.

The introduction of matrix isolation by Whittle, Dows and Pimentel2 in 1954 has

allowed a large number of unstable or highly reactive species to be isolated in a frozen

gas lattice and studied spectroscopically. Many standard spectroscopic techniques,

including infrared, UV-Visible absorption and emission, Raman, M6ssbauer and electron

spin resonance, have been used to probe these molecules. As a first approximation,

interactions between the matrix and sample are assumed to be nonexistent and the

observed spectra are expected to be equivalent to gas phase. By comparing matrix spectra

for species where gas phase data are available a number of matrix induced spectral







2

changes have been noted. Typically there are slight shifts in transition energies when a

species is trapped in a matrix, but these generally do not prevent correlation with gas

phase data. Multiple trapping sites (different micro-environments within the matrix) may

result in overlapping bands. These sites can often be removed by careful warming of the

matrix (annealing) to allow the crystal lattice to rearrange to a more stable configuration.

Jahn-Teller distortions and lattice mode interactions may also lead to changes in the

matrix spectra.

The 2p 2S transition of the noble metals, Cu, Ag and Au, has been extensively

studied in matrices.3-19 The transition is particularly sensitive to the matrix environment.

In the gas phase the 2P state is spin-orbit (SO) split into 2P3/2 and 2p1/2 multiplets20

resulting in two observed bands. Trapping these molecules in the various rare gases may

produce profound changes in the magnitude of the SO splitting. For Cu in matrices the

SO constant has been shown to drop21'22 from the gas phase value of 166 cm-1 to 124

cm-1 in Ar, 95 cm-1 in Kr and to -23 cm-1 in Xe. Additionally, the matrix spectra

invariably exhibit three absorption maxima attributable to a splitting of the 2P3/2 state by

a dynamic Jahn-Teller effect.21'22 Absorption spectra for matrix isolated Au atoms

indicate17 that the SO coupling is always greater than in the gas phase. The spectra of

matrix isolated alkali metals,23-26 which also have a dominant 2p : 2S transition, show

similar matrix induced changes from the gas phase spectra.

For a species trapped in a frozen noble gas (the most commonly used matrix

material), the temperature is normally maintained near 10K to prevent softening of the

matrix which could lead to diffusion of the sample. At this temperature the sample







3

molecule is vibrationally and rotationally cold resulting in a great simplification of the

observed spectra. Also, since the trapped species are generally in their electronic ground

state, conventional spectroscopic probes yield no information about the excited states of

the species. Magnetic circular dichroism (MCD) provides a means of extracting

information about excited states based on polarization dependent selection rules. MCD

is the measurement of the differential absorption of left- and right-circularly polarized

(LCP and RCP, respectively) light when a sample is place in a magnetic field parallel to

the propagation direction of the light. The theoretical development of this technique was

given by Buckingham and Stephens27 in 1966. The first application of MCD to matrix

isolated species was reported by Douglas, Grinter and Thomson28 at the University of

East Anglia in 1973.


Matrix Isolation


Matrix isolation involves the trapping of a sample species within a large excess

of frozen host gas at a dilution ratio high enough to prevent (or minimize) reactions

between the guest molecules. The matrix (host) gas is usually chosen to be non-reactive

(typically neon, argon, krypton or xenon) but in some instances where a reaction is

required to produce the desired sample or wider temperature ranges for annealing studies

are necessary other gases (CH4, C3H8, SF6) may be used. Several recent texts29-32

provide more detailed descriptions of the varied techniques and procedures employed in

matrix isolation than the brief description given below.







4

The choice of matrix gas determines the method of cooling necessary to freeze the

gas on the sample substrate. To prevent diffusion of the sample through the matrix the

temperature is generally maintained lower than 40% of the melting point of the matrix

gas. Liquid N2 (bp 77K) and liquid He (bp 4.2K) are commonly used cryogenic liquids,

but only liquid He provides enough cooling to form rigid noble gas matrices. Liquid H2

will freeze all but neon but has been abandoned due to the fire risk involved. The use

of liquid cryogens requires specially constructed dewars and appropriate safety

precautions. The introduction of closed cycle refrigeration units employing He has

spurred many applications of matrix isolation. These units are capable of reaching -10K

which allows them to be used with Ar, Kr and Xe matrices. The Heliplex, marketed by

APD Cryogenics, uses a standard refrigeration unit coupled with a Joule-Thompson

expansion to allow cooling to 4K, enabling work with neon matrices. These systems are

typically equipped with thermocouples for monitoring temperature of the substrate and

a resistance heater for annealing studies or for stabilizing the matrix at a temperature

higher than the lowest attainable by the refrigerator. Requiring little maintanence and no

handling of cryogenic liquids, these units have become the mainstay of many matrix

isolation experiments.

The choice of cold substrate also plays an important role in the matrix isolation

technique. Two primary considerations are thermal conductivity and transparency of the

substrate to the probing radiation. For transmission techniques, a window is usually

mounted in a copper holder which is attached to the cold finger of the refrigeration unit.

Alkali metal halides are used in the infrared region while quartz, CaF2 or sapphire are







5

employed in the UV-visible regions. The windows are mounted in the holder using

indium seals to insure good thermal transfer from the copper to the window. In Raman

spectroscopy, the cold surface is often a polished Cu or Al block attached directly to the

cold finger. Single crystal sapphire or Cu rods are routinely employed in ESR

investigations.

The deposition system and cold surface must be maintained in a vacuum (typically

< 10-5 torr) to prevent condensation of atmospheric gases onto the cold surface and to

prevent possible reactions of the sample with the gases. For gaseous samples or those

with a high vapor pressure at room temperature premixing of the sample and matrix gas

may be done prior to deposition. Host:guest ratios of 103:1 to 105:1 are typically used.

For samples with lower vapor pressures, heating may be employed to produce a molecular

or atomic beam which may then mix with a continuous flow of matrix gas before

condensing on a sample window. Both resistive and inductive heating methods have been

employed. The availability of high power, low cost lasers has led to a new technique for

vaporization of refractory materials. The output of a laser (often a Q-switched Nd:YAG

operating at 532 nm) is focused onto a solid target within the vacuum chamber. The

ablated sample is then mixed with either a continuous flow of matrix gas or with a pulse

of gas timed to coincide with the firing of the laser. Deposition times may range from

minutes to hours depending on the volatility of the sample and the concentration of

sample necessary for spectroscopic study.









Magnetic Circular Dichroism


Circular dichroism results when the absorption coefficients for RCP and LCP light

differ for a medium. This inequality may occur naturally as a result of low symmetry for

a molecule or unit cell in the case of crystals. Placing the medium within a magnetic

field parallel to the direction of light propagation will also produce a difference in the

absorption coefficients. The differential absorption of RCP and LCP light in the presence

of the magnetic field is termed magnetic circular dichroism. This results in a signed

spectrum (both positive and negative bands are observed) that is governed by polarization

dependent selection rules. The observed transitions can provide ground state information

about atoms and molecules but are particularly useful in extracting excited state

information that is otherwise unavailable.

In practice, the sample is placed in a magnetic field colinear with the propagation

direction of alternating RCP and LCP light. The differential absorption is detected by a

photomultiplier tube whose output is connected to a phase sensitive detector. The MCD

spectrum is then displayed as a wavelength function of differential absorption. Additional

requirements for successful measurement of MCD spectra are that all optical components

are non-birefringent and that the sample does not cause depolarization of the circularly

polarized light by scattering.

The MCD spectrum is actually the difference between the RCP and LCP

longitudinal Zeeman spectra and the same information is available from the Zeeman

spectra if all Zeeman components are resolved. Resolution of these components is often

difficult and requires high magnetic fields. MCD requires only modest fields (-5000







7

gauss in the present study) and has increased sensitivity due to phase sensitive detection

techniques. The signed nature of the MCD signal may allow unresolved absorptions to

be discovered if the MCD selection rules dictate oppositely signed signals for the

transitions. The temperature dependence of some MCD signals also provides additional

information for molecules with degenerate ground states.


Aims of this Investigation


The matrix-induced changes in the SO coupling of matrix isolated Ag and Au

atoms and the origin of the tri-peaked structure of the spectra will be investigated by

obtaining the MCD and absorption spectra and subjecting the data to a band moment

analysis. The analysis will be used to quantitatively extract SO coupling constants and

the relative contributions of totally symmetric (cubic) and Jahn-Teller active nontotally

symmetric (noncubic) modes to the spectral bandwidth. The derived SO coupling

constants will be used to confirm a recent model proposed by Pellow and Vala33 (PV) to

explain the wide variation in the SO splitting of the 2p 2S transition of the alkali and

noble metals in matrices. The origin of the three maxima will be shown to result from

a dynamic Jahn-Teller effect. A similar analysis will be performed for the 7p 7S

transition in matrix isolated Mo atoms. The results will be compared with a theoretical

prediction derived from an extension of the PV theory.

The MCD and absorption spectra of Co atoms and Ti atoms in several matrices

will also be presented. Electronic transitions will be assigned via a comparison to

simulations based on gas phase data. Analysis of the MCD bandshapes will be used to







8
diagnose several previously misassigned transitions. The study of transition metal

diatomics using the MCD technique will be suggested as future work and modifications

to the apparatus to produce these species will be outlined.












CHAPTER II
MAGNETIC CIRCULAR DICHROISM THEORY


Introduction


The theoretical basis for the MCD phenomenon and the equations necessary to

extract useful information from experimental data will be developed in this chapter. An

outline of Stephens' 34,35 derivation of the parametric MCD equations will be presented

to detail the approximations and limitations of the method. The extraction of excited state

information will employ the method of moments originally pioneered by Henry,

Schnatterly and Slichter.36 Osborne and Stephens37 have recast the theory in more

general terms and applied it to MCD. The formalism of their derivation will be used in

this work.


Circularly Polarized Light


A description of circularly polarized light will be given to aid in understanding its

interactions with a sample. A more thorough description may be found in reference 38.

Unpolarized light consists of a electric vector, E and a magnetic vector, B which vary

sinusoidally in the direction of propagation but with random direction. In plane polarized

light the vectors still vary sinusoidally in the direction of propagation but their direction

is constant. If this plane polarized light passes through a transparent birefringent material






10

where the speed of light depends on the direction of polarization then one part of the

beam will be retarded with respect to the other. By passing the plane polarized beam

through the medium at 450 to the perpendicular axes of the differing refractive indices

projections of the E and B vectors will show components of equal magnitude phase

shifted relative to one another. The resultant electromagnetic vectors will trace helical

paths as they emerge from the medium. A clockwise tracing of the helix as an observer

looks toward the light source is defined as right elliptical polarization. For elliptical

polarization the E and B vectors of the emergent light vary both in direction and

magnitude. Two special cases can occur in this process. If the phase shift is equal to .

the resultant beam is returned to plane polarization. If the phase shift is X/4 the light is

termed circularly polarized because the cross section of the helical trace is a circle (Fig

2.1). In this case the E and B vectors vary in direction but are constant in magnitude.

In MCD the phase shift must be carefully controlled to provide circular polarization

throughout the spectral region of interest.

If left (LCP) and right circularly polarized (RCP) light are absorbed in differing

amounts by a substance the material exhibits circular dichroism. If a magnetic field is

present along the axis of light propagation all materials within the magnetic field will

exhibit a circular dichroism termed magnetic circular dichorism (MCD).


Basic MCD Equations


Consider a sample with ground state, A, and excited states, J and K, placed in a

magnetic field that is irradiated by circularly polarized light collinear with the magnetic















































Figure 2.1 Resolution of circularly polarized light into electric and magnetic field
vectors which vary sinusoidally but with one retarded by X/4. A line
connecting the resultant vectors will trace a helical path of circular cross-
section. (ref. 38)






12

field. This situation is represented schematically in Figure 2.2. The intensity of the light

at any point z is given by the Poynting vector:




c 2 -2Ekz
I(z) = n(EO)2 e-xp2Ekz
4(1)
-0 -2!Ekz
0It exp




where k, represents the absorption coefficients of right(+) and left(-) circularly polarized

light, E=hv is the photon energy, I' is Planck's constant divided by 2n, n, are the complex

refractive indices for LCP and RCP light, Eq is the electric field at z=0 and I1 is the

incident light intensity.

The amount of energy absorbed per unit time at z can be expressed as -0I(z)/Oz

and is dependent on the photon energy E, the number of sample species, Na, and the

transition probability, Pa-j"


-aI(z) = E Na Pa-j (z) E (2)
az a,j



The above probabilities can be related to the electric dipole transition moments

using time dependent perturbation theory if the effective Hamiltonian H1o is assumed to

be a sum of independent components. Considering only electric dipole transitions


























II


tmn

N


a


-4.)
ua
5
o .o
I-
2 >=
2-0
&o .
> ca







*- 0O

-U Wa t
is







&E .
I..J



~O

o ueo
-0 ., ^
*** BO Wo


ra4
E .S o






$00
o-
-- 0* BO


4- ^-'*

ag c a



4.)
4. = -
? 8 ii E


= 0 -S u *

C O *t tl
N
N
s U O




00
*Z










'0 = 0 + (3)



where H0 is the Hamiltonian in the absence of light and SHj is the Hamiltonian for the

perturbation induced by the light. At this point the external magnetic field is not yet

considered. This is denoted by the subscript 0. This approach yields




Pa-j (z) = a E,(z)2 || 2 6Eja-E) (4)



where
are the transition moments, m. is the electric dipole transition moment

operator for RCP and LCP light, Eja = Ej Ea, 6 is the Kronecker delta operator arising

from the neglect of transition lifetimes and a is the Lorentz effective field correction

factor which relates the electric field due to the light at the absorption center to the

macroscopic electric field.

By differentiating (1) and employing (2) and (4) the absorption coefficients can

now be expressed as


k, = 2 2a2 E
26(Eja-E) (5)
T1 a,j


Transforming (5) to absorbance units gives










A. + N
-A = -cz = y a
2 (Eja-)cz (6)
E E a,j N

where


Non 22 logl0e (7)
250hcT1




Na/N is the relative population of the ground state A, No is Avogadro's number, c is the

speed of light, E. is the molar absorption coefficient and c is the concentration of

absorbers. This result assumes that Beer's law applies and is not valid for non-linear

effects produced by intense light. The MCD is expressed as


AA = AL-AR = A-A+ (8)



which (using (6)) gives


A = Y[
12 E j a,N



This equation (9) is general and applies to natural CD of optically active materials. MCD

is not a perturbation of natural optical activity but an additive effect resulting from

differences in polarizabilities in the presence of a magnetic field.

To reflect the actual bandwidths the rigid shift model is used. This assumes that

the zero field absorption (ZFA) band shifts along the energy axis upon introduction of the







16

magnetic field but does not change shape. The model requires that the Born-

Oppenheimer approximation hold for both the ground and excited states. Separating the

electronic wavefunctions into nuclear and electronic terms yields


IAaa> = WPAa(r,R)Xa(R) a = 1 to dA (10)




I JJ> = )W (r,R)Xj(R) = 1 to dj (11)



where r is the electronic coordinate, R is the nuclear coordinate, Xa and Xj are the

vibrational wavefunctions and da and dj are the degeneracies of the ground and excited

states. To further simplify the matrix elements the Franck-Condon approximation that

most electronic transitions occur at R near the equilibrium nuclear separation Ro is

embraced.

Applying the rigid shift model and summing over all vibronic bands leads to an

equation for the ZFA


A0
= y Do f(E) c z (12)
E^


where z is the pathlength, c is the concentration and










Do 1 I02 + I0 2 (13)
2dA a,k



Vibrational overlaps are explicit in the lineshape function f('E).



f(E) = a
2 jaE ) (14)





fo f(E)dE = 1 (15)




Equations (14) and (15) show that the lineshape is temperature dependent due to the

Boltzmann term but that the integrated intensity is temperature independent.

The rigid shift model is now applied to molecules in a magnetic field.

Considering only electronic terms the perturbation of the system Hamiltonian may be

expressed as


H' -tzB = gB(Lz + 2Sz)B (16)



where uz is the electronic magnetic moment along z and tB is the electronic Bohr

magneton. The orbital and spin angular moment along z are represented by Lz and Sz,

respectively. Equation (16) describes the Zeeman splitting induced by the magnetic field.

If the electronic wavefunctions are chosen to diagonalize Rz, then H will be diagonal






18
in the Franck-Condon approximation. Stephens35 now explicitly includes intermixing of

additional states K to yield a better approximation of the transition moments.

The ground state Zeeman splitting leads to population changes. In the case where

the Zeeman splitting is small compared to kT, the Boltzmann term can be expressed as

a Taylor expansion which yields


Na = 1{1 I'BB/kT} (17)
N da


Combining the assumptions of the rigid shift model and applying them to (9)

produces the parametric equation for the MCD of the A J transition



AA =y A1 ())+ BO + (E) }RBBCZ (18)



The terms A1, 1Bg and Co are given by


S= + 1 E [ 2 12]
a 2S> (19)


x [ (19)











O 2 Re{ E [
S a a,X KJ


o o
K -W


+ [

K A







Co = -1 2
da a,X


x (21)



where Wa, Wj and Wk are the energies of the states and the other terms are as previously

defined.

Experimental forms of the A1, Bo and Co terms are shown in Fig. 2.3. The A,

term arises when either the ground or excited states are degenerate. The two lobes, which

arise from the small Zeeman splitting of the degenerate level, are always oppositely

signed. The A1 term intensity is influenced by the sharpness of the absorption band,

following its dependence on the derivative of the lineshape function, and by the difference

in magnetic moments of the ground and excited states. It the moments are equal no Al







20

term will appear. A positive Al term is defined when the high energy lobe is of positive

sign.

Degeneracy of the ground state is necessary for the appearance of CO terms. These

depend on the magnetic moment of the ground state and on the circularly polarized

transition moments. A CO term may be identified by its 1/T intensity dependence.

A Bo term is present for all materials as a result of magnetic field induced mixing

of electronic wavefunctions. These terms are particularly difficult to assess because the

energies and multiplicities of all states near A and J must be known. Fortunately, these

are also the least intense MCD bands.

The MCD spectrum of a species can be deconvoluted into contributions from each

of these three terms. Also, if A1, B0 and CO can be calculated the MCD spectrum can be

predicted. It is useful to determine the relative contribution of each term to the overall

MCD. The maximum contributions from each of the three terms is


A, :S :C _- Z : Z Z (22)
F AW kT

where Z is the Zeeman energy, F is the bandwidth of the electronic transition, AW is the

order of magnitude of an electronic energy gap, k is the Boltzmann constant and T is the

temperature. For a matrix isolated sample, the assumptions F 200cm-1, kT 10cm-1

and AW 2000cm-1 may be used, leading to


A1 : B : C0 10 : 1 : 200 (23)

which indicates that CO terms should dominate the spectrum if they are present.


















+
4-

AA 0-














A


- T low


- T high


E-


Figure 2.3 Appearance of MCD terms.
(a) Zero field absorption and MCD for a positive A1 term. The
positive lobe lies at higher energy.
(b) BS terms may be positive or negative with the maximum coincident
with the absorption maximum.
(c) C0 terms may be positive or negative with the maximum coincident
with the absorption maximum and will show a temperature
dependence.








Moments


The general absorption and MCD moments are defined as


n = f(A /v)(v -v0)n dv (24)


n = f(AA/vXv-v0o) dv (25)

where the integration is over the entire band (i.e., 2P1/2 and 2p3/2 components); A and AA

are the optical absorbance (A) and differential (MCD) absorbance per Tesla. The average

energy of the zero field absorption is given by


vo = fAdv/f(A /v)dv (26)

where v is the photon frequency.

The "reduced" moment form represents the division of the nth MCD moment by

the zeroth absorption moment and has the general form


nn Cn B B (27)
n n Dn kT D

where An, Bn, Cn and 'D are as defined in Osborne and Stephens37 and the other terms

are as previously defined. The moment equations relevant to the present analysis,

assuming harmonic vibrational frequencies, lowest order in SO coupling and first order

electron-lattice interactions are









1 /
o = 2BB(gorb as /kT) (28)


2/o = c + NC + ast2 (29)


3/
o = 6PBB(grb as/kT)(c + NC/2 + as2 /2) (30)


o = 0 (31)

Here as is defined39 as



as = -(kT/VBBX1/(2S+1))E mexp(-msgitBB/kT) (32)
ms

which in the limit kT >> ms g 1iBB for S = 1/2 yields as = 1/2. c and NC

represent the cubic and noncubic lattice mode contributions to the observed bandwidths.

t is the SO coupling constant of the excited 2P state (the actual splitting between 2P1/2

and 2P3/2 multiplets is A = 3/J2), and gorb is the excited 2P state orbital g factor.

From (28), the slope of the plot of 1/
o vs. 1/T yields the SO coupling

constant, ,, which upon insertion into (29) and (30) permits the determination of c

and NC. It is expected that for a system exhibiting the Jahn-Teller (JT) effect in the

2p state, the value of NC will be nonzero. Acting on a suggestion by Stephens,

Schatz and coworkers24 have shown that a crystal field-induced splitting (derived from

a distorted site symmetry) may be differentiated from JT activity by the temperature

independence of its
2/o plot. For an active JT effect, the ratio 2/o (and

thus the NC component) should show a temperature dependence3 according to









NC = NC coth(vi / 2kT) (33)

where c is the contribution of the noncubic lattice vibration modes to the

bandwidth with T approaching OK. Here


NC + (34)

where or are given by



= E (i2/2k i)vi coth(vi /2kT) (35)


in which ei is the linear electron-lattice coupling parameter, ki the ground state force

constant and vi the frequency of the contributing mode.












CHAPTER III
APPARATUS AND EXPERIMENTAL TECHNIQUES



Introduction


The process of studying matrix isolated species using MCD is conveniently

divided into three sections: matrix isolation of the species of interest, spectroscopic study

of the sample and calibration of the absorbance, MCD and temperature. This also

provides an effective means of detailing the apparatus and techniques used in the present

work. The first section will deal with the matrix isolation assembly and matrix

preparation procedures, the second will describe the optics and electronics of the

spectrometer, while the third will discuss calibrations. Individual experimental details will

be given for each species in their respective chapters.


Matrix Isolation Equipment


To prevent the condensation of atmospheric contaminates on the cold sample

window, the entire sample preparation and isolation setup must be maintained under high

vacuum conditions. The high vacuum system employed consisted of a Alcatel pumping

station which included a roughing pump (12 m3/hr), diffusion pump (150 L/sec), liquid

nitrogen trap, three-way control valve and internal butterfly valve. The pumping station

was connected to the furnace-cryostat assembly via a Edwards rotary high-vacuum valve

25







26

and a length of corrogated stainless-steel tubing. All connections were made with

Kwik-Flange connectors. In experiments where powdered samples were vaporized, rapid

initial pumping could result in the powder being blown out of the sample cell by the

outrush of trapped atmosphere. The rotary valve allowed for fine control of rough

pumping speed. System pressure was monitored by thermocouple (Alcatel model CA

101) and Penning ionization (Alcatel model FA 101) gauges, both of which were mounted

on the pumping station control area.

Sample preparation followed one of two distinct routes. For metals with relatively

low melting points, vaporization was accomplished by resistive heating. A small stainless

steel furnace (4 inch diameter) was constructed to allow the combined furnace/cryostat

assembly to remain inside the pole faces of the electromagnet and to bring the source of

the metal beam to within four inches of the sample window. The furnace was fabricated

from a single piece of stainless-steel which was then covered with another stainless-steel

tube. This tube was heliarc welded to the outside of the furnace can and fitted with inlet

and outlet connections to allow water cooling of the furnace body and the internal heat

shield. This system is shown in figure 3.1. This system corrected an earlier problem of

cooling water leaks into the vacuum space as all welds were external.

Metal powders were placed into a one-inch-long section of tantalum tubing

(0.015" wall thickness) with a small hole drilled midway along the body. The ends were

sealed with solid tantalum endplugs and fitted with angled tantalum brackets. This

Knudsen cell was secured to water cooled copper electrodes mounted on a stainless steel

flange that closed the back end of the furnace (also shown in Fig 3.1). The exit hole of










28

the Knudsen cell was carefully positioned to be colinear with the center of the sample

window. One of the electrodes was electrically isolated by using a teflon washer and

teflon screws for mounting.

Resistive heating of the Knudsen cell was accomplished by passing an AC current

of up to 300 Amps, 60 Hz through the electrodes. The temperature of the Knudsen cell

was monitored by a IRCON digital pyrometer (model 220) thru the pyrometer veiwport

in the electrode flange. These samples generally required outgassing to drive off adsorbed

H20 and any contaminants more volatile than the sample. The displex head was rotated

to protect the sample window from any vaporized contaminants and the cell was heated

to approximately 3/4 of the expected deposition temperature. This temperature was

maintained for 20-30 minutes. For depositions the sample cell was typically heated to

a temperature that resulted in a vapor pressure of 10-3 torr for the sample. The viewport

was equipped with a magnetic shutter which was opened only to read the temperature.

This procedure prevented metal from being deposited on the viewport window which

would cause a reduced temperature reading.

Highly refractory samples were more easily vaporized by direct laser ablation

using the second harmonic (532 nm) of a pulsed Nd:YAG laser (Spectra Physics model

DCR-11). A variety of sample forms were available including rods, ingots, wire or discs.

These discs were made by compressing a quantity of metal powder in a stainless steel die

using a hydraulic press. In most cases, the sample was rotated using a small electric

motor to continuously provide a clean surface and to prevent drilling through the sample

with the laser. Since resistive heating was not required a simpler sample holder was built.






29

A small brass block that could be attached directly to the cryostat vacuum shroud was

bored in three directions to allow sample insertion, matrix gas and laser beam

introduction. This method of sample vaporization is diagramed in Fig. 3.2.

For resistively heated samples, initial system pump down was controlled using the

rotary valve on the pump stack. Slow rough pumping of the system insured that the

powder was not blown out of the Knudsen cell. Approximately 25-40 minutes were

required to fully open the roughing valve after filling (or refilling) a Knudsen cell. For

laser vaporized samples, more rapid roughing of the system was possible. After the

pressure in the system reached -2x10-2 mbar, the three way valve was set to diffusion

pump and the internal butterfly valve was opened. For powdered samples the pressure

was allowed to decrease to the 10-5 mbar range before outgassing of the cell was

performed. Generally, pumping of the system was allowed to continue overnight. With

this arrangement, ultimate system pressures typically were recorded as 2x10-6 mbar with

the liquid N2 trap filled and the cryostat off. With the cryostat cold the pressure

generally read 5x10-7 mbar.

The cold surface for sample condensation was either a CaF2 or sapphire window.

The sapphire window was used whenever possible due to its greater thermal conductivity.

Only sapphire windows cut on the C axis of a single crystal were used to avoid

birefringent signals from the window overlapping the sample signals. The window was

held in a holder made from oxygen-free high conductive (OFHC) copper. The windows

used were 2.54 cm in diameter and 3 mm thick. The window holder was designed to

allow optical access through a 1.25 cm diameter area at the center of the window. The




















SAPPHIRE WINDOW


ROTATING TARGET



S- GAS IN






VACUUM SEALED SPINDLE


Nd:YAG LASER BEAM


Cutaway side view of cryostat with attached laser vaporization source.


Figure 3.2







31

remaining area of the window was covered by the copper holder to insure maximum

cooling. Indium gaskets were used to insure good contact between the window and the

holder. The holder was screwed into the copper cold tip of either an Air Products (now

APD Cryogenics) Displex or Heliplex. Indium gaskets were again used to provide good

thermal contact between the cold tip and the window holder. The Displex is a two stage

closed-cycle He refrigerator capable of cooling to 10 K while the Heliplex is a three stage

refrigeration unit capable of cooling to 4 K by use of the Joule-Thompson expansion in

conjunction with a standard refrigeration cycle. An internal copper heat shield surrounded

the cold finger and window holder. This shield was maintained at approximately 60-80K

to minimize radiant heat transfer to the cold window. A thermocouple (Au(0.07%Fe) vs.

Chromel) was mounted in a small hole drilled in the copper window holder using Crycon

grease. The temperature was monitored using an APD-E control unit with digital

readout. This control unit also provided power for the 30 watt resistive heater used for

controlling the temperature of the window during measurement of temperature dependent

spectra.

The head of the refrigeration unit was rotatable on O-ring seals within the vacuum

shroud. This allowed sample preparation at 900 to the optical path. The shroud had five

openings to allow access to the cold finger. Three of these were covered with Suprasil

windows to allow access to the optical path and for viewing or photolysis of the matrix.

A Kwik-flange adapter was mounted over the fourth opening to allow connection of the

furnace. The fifth access in the bottom of the shroud was blanked off during experiments

with the furnace but was used for pumping when the laser vaporization source was used.






32

Since no gate valves were used between the sample source and the shroud, samples could

not be changed without bringing the cryostat to room temperature and breaking vacuum.

A diagram of the Displex is given in Fig. 3.3.

The high purity (Matheson Research Grade, 99.9995%) matrix gas was introduced

from a stainless steel manifold designed to have a very small hold volume. A standard

two stage regulator was connected to an analogue pressure meter, a pumping port and a

needle valve using 1/8" O.D. stainless steel tubing. A small rotary vacuum valve allowed

the pumping port to be closed until a gas change was necessary. The largest contributor

to the total volume was the pressure gauge. A coil of 1/8" O.D. stainless steel tubing on

the outlet side of the needle valve was used for trapping any residual water or other

contaminants in the matrix gas. Typically this coil was immersed in a Dewar flask

containing a slush of acetone/ liquid nitrogen. The setup is shown in Fig. 3.4. Flow rates

of 0.25 to 0.33 torr per minute were used to produce the matrices and were easily

controlled by adjustment of the needle valve.


Spectroscopic Apparatus


Previous attempts to study the MCD of Ag atoms in matrices40 have shown that

the quantity of Ag atoms decreases from one scan of the spectrum to the next. From

Ozin's work41'42 this is now known to be the result of cryophotoclustering. Since ratios

of MCD and absorption moments are required for the moment analysis of the bands a

new instrument was built to allow the simultaneous recording of MCD and absorption

spectra. With this approach the continual decrease in signal intensity did not affect the












ELECTRICAL




He GAS





THERMOCOUPLE
and
HEATER WIRES





EXPANDER
1st STAGE


VACUUM
CONNECTION




- ROTATABLE
JOINT









VACUUM
SHROUD


RADIATION SHIELD


Diagram of closed-cycle helium refrigerator (Displex) expander section.


Figure 3.3





















I- n






S-









1 0
0



c z




>o I






ca >
0






I




___________________________ (






35

analysis since ratios of MCD and absorption moments were available for each scan of the

spectrum. This section describes the optics, electronics and computer control of this

psuedo-double beam spectrometer.

The optical system is represented schematically in Fig. 3.5. The output of a 300

watt xenon lamp fitted with an internal parabolic reflector and sapphire window (Eimac)

was directed onto the entrance slit of a 3/4 meter Czerny-Turner monochromator (Spex).

The wavelength scan of the monochromator was driven by a 200 step/revolution stepper

motor. Pulses to drive the motor were produced on a digital I/O line of a Metrabyte Dash

16 D/A interface board controlled by a IBM PC clone (80286 processor). A gaseous N2

purge of the monochromator housing was maintained during operation to prevent

oxidation of atmospheric contaminants by the UV output of the lamp and subsequent

degradation of the mirrors and grating.

Circular polarization was provided by focusing the output of the monochromator

onto a Glan-Thomson prism oriented a 450 to the modulation axis of the photoelastic

modulator (Morvue PEM-3). To maintain circular polarization throughout the scanned

wavelength region the retardation voltage applied to the piezoelectric oscillator was

changed. The spectrometer control program (see appendix) calculated a digital value for

each wavelength which was then applied to the remote modulation control input of the

PEM as an analog voltage from D/A channel 0 of the Dash-16 board.

The emerging beam was then chopped to provide reference and sample beams.

A second lens allowed focusing of the sample beam at the center of the gap between the

magnet pole faces. An axially bored magnet (Alpha Scientific model 4600) allowed the






















0


'I 0
o =
z 8
I z
wu 0



2,


'U cc







1. ---/--- ---















I CO-


a
I-
Q.
U)





0
U)

.0
CO






















.C
U


0




















O
0.,















U
o-
Uo


0
u


'3
E



.0

(4-1

.0

.2


4-
E0
0

a
U)



Cu
U/
.0
U


2
I-






37

beam to be collinear with the magnetic field. The maximum attainable field with the pole

pieces adjusted to allow the displex shroud to slip between them was approximately 4750

gauss for initial experiments. Later experiments utilized a newer magnet (Alpha Scientific

model 4800) capable of reaching approximately 5500 gauss for the same pole gap. After

passing through the sample window at the center of the pole gap the beam passed through

the second pole and impinged upon the photomultiplier tube (PMT) (EMI 9973QB). The

reference beam was directed around the magnet using mirrors and focused onto the same

PMT. All mirrors were front surfaced to allow measurement to near 200 nm.

A specially designed optical chopper wheel, shown in Fig 3.6, provided both

pseudo-double beam operation and timing signals for spectrometer control and data

collection. The mirrored sections directed light around the magnet for the reference

beam, the blackened areas prevented light from the monochromator from reaching the

PMT and provided a zero signal while the large open areas allowed light to pass through

the wheel and strike the sample matrix. During the open periods both sample absorption

and MCD were recorded.

The square notches in the outer edge of the wheel triggered opto-interrupters

which provided control signals to switch the spectrometer interface between reading

sample, reference and blank signals. A second opto-interrupter was triggered by the

inner absorption/MCD slot and caused the interface to begin recording MCD. The signal

timings are shown schematically in Fig 3.6.

The trigger signals were routed to the gating logic board. Each signal passed

through two Schmidt triggers to produce a clean signal for a monostable multivibrator.
























z z

0 0



z00
w z a_

wU W~
U.


w
N
















CC


0J



0


I-
U

0
2
0
'0
U
I-
U
*0
U
I-



(fl

I-.

0
U
0


0




*~L)



~o c~
.2




U
04)
U ~O




0.



U *~
U -
- -

U


U
00
~






39

The absorption control signals passed through a JK flip-flop network arranged as a divide

by three counter. The three output signals were connected to three separate switch control

inputs on a ADG-202 quad switch on the absorption board. The MCD control signal

passed directly from the multivibrator to the signal switch on the absorption board. A

clear pulse for the JK flip-flop network was also derived from the opening of the MCD

gate.

The absorption and MCD signals followed two distinct paths and each will be

described. The absorption board is shown in Fig. 3.7. The voltage input from the PMT

housing was amplified and fed to three signal input positions of the quad switch. The

timing signals from the logic board closed the appropriate switch and sample, reference

and zero signals were sent to their respective amplifiers. The zero signal was then

electronically subtracted from the sample and reference signals. These zero corrected

sample and reference signals were then connected to the inputs of a logarithmic amplifier

(Burr-Brown #4127) whose output, the absorbance signal, was recorded on one line of

a dual pen strip chart recorder (Soltec) and digitized for computer storage by one A/D

channel (12 bit resolution) of the Dash-16 board.

To prevent the MCD signal from being influenced by changes in the single beam

absorption of the sample the DC portion of the PMT output, which contained the

absorption information, was held constant by a feedback circuit driven by the sample

minus zero signal. Holding this voltage constant insured that the AC portion (50 kHz

modulation) of the PMT signal was not divided by the DC portion. The feedback circuit







40

controlled the high voltage input to the PMT through a programmable high voltage power

supply (Bertan PMT-20A-N).

For MCD measurement, the PMT signal was not amplified but fed directly to the

fourth position of the quad switch. During the MCD measurement window the output of

the switch was routed to a sharp bandpass filter (50 kHz 2 kHz) and then to an

amplifier circuit fitted with a variable set of feedback resistors to control the gain. This

signal then passed directly to the lock-in amplifier (Ithaco model 353) phase locked to

the 50 kHz reference signal from the PEM. The DC output of the lock-in was amplified

and recorded on the second pen of the strip chart recorder. The second D/A channel of

the Dash-16 board was used to digitize the MCD signal for disk storage.

The MCD channel was often found to be extremely noisy which resulted in

unusable data. This problem was traced to ringing induced in the filter circuit when the

switch for MCD closed. The instantaneous application of a voltage caused the filter to

be unstable and large oscillations to appear in the output of the lock-in. This problem

was corrected by feeding the PMT signal directly to the filter circuit and from there to

the quad switch. Since the filter was now active at all times no oscillations were induced

when the switch closed. After passing through the switch the signal was again sent to the

variable gain amplifier and then on to the lock-in. The present setup is shown in Fig.

3.8.








41




































_5



00


0
U
-5
5.0





'0
ca




Cu
*E

o
Cu




0
I
4.S

N




















S2~
' A


Lul


I-

0
0








Calibration Procedures


Wavelength calibrations were accomplished by passing the 632.8 nm line of a

HeNe laser through the monochromator and adjusting the wavelength readout to 632.8 nm

at maximum throughput. This procedure was performed occasionally throughout the

course of this work and whenever the monochromator was moved. It was also done when

new mirrors and the cleaned grating were installed in the monochromator.

Calibration of the magnetic field was done with a portable gaussmeter (F.W. Bell

model 640). The probe was mounted securely in the center of the pole gap. The probe

was then covered with a mu metal shield and the meter zeroed. The mu metal was

removed and current was applied to the magnet. This was done whenever the pole gap

of the magnet was changed.

Aqueous solutions of (+) Co(en)3Cl tartrate (en = ethylenediamine) and d10 -

camphorsulphonic acid (CSA) were used to calibrate the absorption and MCD spectra.

The absorbance maximum of each of these solutions was measured using either a Cary

17D or Hewlett-Packard diode array spectrometer. The spectra of these solutions was

then run on the MCD apparatus along with a sample of deionized water to serve as a zero

absorption. The digital value of the water baseline at kmax was then subtracted from the

digitized value of the sample at max to give an absorbance value in digital units. The

known O.D. from the Cary or Hewlett-Packard runs was then divided by this digital

value to give a calibration factor in O.D./byte which was then used by the moments

program (see appendix) to convert digital data units to O.D. units.






44

The circular dichroism of each of these standard solutions was also measured and

stored by the computer. Using the relation AAmax/Amax = 0.225 determined by

McCaffery and Mason43 for (+) Co(en)3Cl tartrate the AO.D. was determined and

divided by the peak height (in digital units) to give a calibration factor in AO.D./byte.

Calibration of the CD using CSA was more involved. The concentration, c, of the

solution was determined from


O.D. = ecl (36)

where O.D. is the measured absorbance, I is the pathlength and E is the molar absorption

coefficient. The molar ellipticity of CSA at 291 nm is 7800 degree cm2/decimole44 and

is related to the observed rotation, 0, and the concentration by


[01291 = x 100. (37)

A value for 0 was determined and the AO.D. was calculated from




0 = 33 x AO.D. (38)

This AO.D. value was again divided by the zero corrected digitized intensity of the CSA

circular dichroism to give a calibration factor in AO.D./byte.

Uncertainty in absolute temperature of the sample represents a large source of

error in values derived from plots of moment ratios vs. 1/T. Sample temperature was

monitored with a thermocouple (chromel/Au (0.07% Fe)) mounted in the copper window

holder. These temperatures were corrected using a procedure reported previously40 which






45

uses the matrix-isolated metal itself as a probe of the temperature of its own

environment. For a paramagnetic species the temperature dependence of the moment ratio

may be expressed as


o /
o = (Co/Do)(gBB/kT) (39)

For two temperatures (T2 > T1),


T2 =T1 + AT. (40)



Denoting the moment ratio as X and using the ratio x2/x1, it can be shown that a plot of

AT vs. {(Xz/X2)-1} will have a slope equal to the inverse of the lowest temperature (T1-1)

attainable. The interval AT is taken from the thermocouple readings and the moment ratio

from the lowest energy component of the three peaks observed for both Ag and Au

containing matrices. This procedure was performed for each matrix and the difference

between the calculated lowest temperature and the recorded lowest temperature was used

as a correction factor for all temperatures. The Displex thermocouple reading was

generally about 0.5K too low, while the Heliplex thermocouple reading was consistently

about 2.0K too low. This procedure was verified in the following manner. A

polyvinylalcohol (PVA) film containing K3Fe(CN)6 was deposited from solution directly

onto the sample window. Absorption and MCD spectra were recorded over the range 10-

40K. After temperature correction (using the above procedure) a plot of AAo/(ARoBB)

vs. 1/kT for the 400 nm Fe(CN)63- MCD band was found to be linear with a slope of

0.84. A similar study by Bryce Williamson at the University of Canterbury, New Zealand






46

using a free-standing PVA film containing K3Fe(CN)6 in a immersion cryostat from 1.5

to 300K found a slope of 0.86 for the same plot. In this case the film was surrounded

either by liquid He (4.2K and below) or by thermally equilibrated He gas (above 4.2K)

ensuring that the film was at the temperature indicated by the vapor pressure of the liquid

He. This suggests that after calibration our temperatures may still be -0.2K too low.

This uncertainty will translate to a 3-6% uncertainty in the SO coupling constants

reported later. Additionally, the temperature dependence of the MCD from a ground state

spin-doublet such as possessed by Ag or Au is expected to vary as tanh(tLBB/kT) which

for kT >> pgB becomes -tgBB/kT. The temperature variation at a fixed magnetic field

followed within 3.5% what would be expected from the latter limiting expression. These

observations provide confidence that the temperatures used in the moment analyses are

accurate to a reasonable degree.












CHAPTER IV
ABSORPTION AND MCD OF MATRIX ISOLATED
SILVER AND GOLD ATOMS


Introduction


The origin of the three absorption maxima observed when the noble metals are

isolated in rare gas matrices has stimulated much discussion. Early studies10'13 favored

a distorted site model where an axial distortion of the matrix cage atoms surrounding the

metal induces a static "crystal field" splitting of the 2P excited state. An ESR study by

Kasai and McLeod8 showed that Cu, Ag and Au atoms sit in single, substitutional,

octahedral (i.e. nondistorted) sites in the matrix. These contradictory conclusions were

reasonably reconciled by suggestions15-19'45'46 involving simultaneous SO and dynamic

Jahn-Teller (JT) coupling in the 2P state. These suggestions were proven for Cu atoms

in rare gas matrices21'22 by subjecting temperature dependent MCD and absorption data

to a moments analysis. Noncubic (Jahn-Teller active) lattice modes were found to be the

major contributors to the observed bandwidth indicating that a dynamic JT effect was

operating within the matrix environment. The effect of matrix isolation on the SO

constants was also assessed. The SO constant for Cu was found to decrease from 166

cm-1 in the gas phase20 to 124cm-1 in Ar, 95 cm-1 in Kr and reverse sign in Xe, to -23

cm-1. Early studies of Au atoms in matrices10 indicated from studies of absorption

spectra that the SO constant increased over its gas phase value20 of 2543 cm- .

47









Experimental


Matrices containing Ag and Au were prepared using the resistively heated

Knudsen cell. For Ag, powdered metal (Spex) was placed in the Knudsen cell and after

outgassing was allowed to pump overnight. All subsequent deposits were made without

refilling the cell. The cell was heated to 900-950C and deposited with excess rare gas

for 30-60 minutes. The Heliplex was used to cool the sample window for all Ag

containing matrices. To prepare gold containing matrices the Knudsen cell technique was

again used but Au wire (Spex) was used instead of metal powder. This cell was heated

to 1200-12500C during depositions which also lasted from 30-60 minutes. A Displex

was used to maintain the cold window during all Au experiments. These matrices were

annealed (to -20K for Ar and -25K for Kr and Xe) prior to recording data to eliminate

possible interference from multiple sites.

For Ag matrices, moments were calculated directly from the digitized spectra. The

Au matrices showed a large background absorption, which is most likely attributable to

Rayleigh scattering by the matrix itself. Below 220 nm the absorption signal declined

rapidly. This was due to a decrease in reference signal caused by reflectivity losses in

the chopper wheel mirrors. The background of each Au absorption spectrum was

corrected by fitting the baseline to a 6th order polynomial and subtracting the calculated

fit. Normal moments calculations were then performed on the baseline corrected spectra.








Results


Spin-Orbit Interactions in the 2P State


The absorption and MCD spectra of Ag atoms in Ar, Kr and Xe matrices are

shown in Figs. 4.1-4.3 with the observed band positions listed in Table 4.1. Temperature

dependent C terms dominate the spectra as shown in the figures. The Ag/Xe system

shows the four band structure that has been observed previously.4,11,18 The origin of this

structure is still unsettled although several proposals have been introduced that will be

discussed later.

The SO coupling constant, ,, for Ag in the three rare gases was extracted from

the slope of a plot of the reduced first MCD moment vs. 1/T. Fig. 4.4 shows the plots

which are straight lines as expected from (28). In Ar and Kr matrices, the extracted s

were found to be greater (Ar: 783 cm-1, Kr: 638 cm-1) than the gas phase value20 of 614

cm-1, while in Xe a reduction to 583 cm-1 was noted. These values are also listed in

Table 4.1.

In deriving the equations for determining the SO constants second-order effects

were neglected. The importance of these effects can be assessed in two ways. First,

using the relation


2/
o = asRBB(',)2/kT (41)

second-order effects can be shown to be small if the obtained is close to that obtained

from (28). The !' represent the combined contributions from first and second-order

effects. The values shown in Table 4.1 show that the t obtained from this expression are











Ag/Ar


30000 31000 32000 33000 34000


FREQUENCY / cm-1


Figure 4.1 Experimental MCD (top) and absorption (bottom) spectra of Ag atoms in
a Ar matrix at 5.9 K.































0-

30000


31000 32000

FREQUENCY / cm


33000


MCD (top) spectra of Ag atoms in a Kr matrix showing temperature
dependence of the signal. Absorption (bottom) spectra at 5.8 K.


Figure 4.2










Ag/Xe


30000 31000

FREQUENCY / cm-1


32000


Experimental MCD (top) and absorption (bottom) spectra of Ag atoms in
a Xe matrix at 6.5 K.


01

29000


Figure 4.3






53
Table 4.1 Observed Absorption Band Positions (in cm-1) and Parameters Derived from
the Moments Analysis for Ag Atoms in Rare Gas Matrices.


Gasa Ar Kr Xe


Excited State

2p1/2

2P1/2


b/cm-1

I'c/cm-1


O /cm-2

v d/c-1


31606

32733
33278

783

766

1.6x105

4.9x104

32.1


29842

30481
30611
30888
583

524

0.7x105

1.1x104

24.2


aValues from Ref. 20.
bFirst order, obtained from (28).
CSecond order, obtained from (41).
dValues from fitting (33).


29552

30473


614

614


30902

31807
32216

638

616

1.5x105

2.0x104

35.8









0


-10


-20


-30


-40


4 8 12


16


20


102 T


Reduced MCD first moment plots vs. inverse temperature for the three
Ag/RG systems. For clarity, the Ag/Kr and Ag/Xe plots have been shifted
by -5 and -10 y axis units, respectively.


O
0


Figure 4.4


-50-


-60
0







55

within experimental error (-10%) of those obtained from (28). Secondly, while the zeroth

MCD moment is expected to be zero to first order it should become nonnegligible and

vary linearly with 1/T if second-order effects are present. Plots of o/
o vs. T-1

with Bo/D0 (intercept) values of the order 10-9 10-10 and Co/Do (slope) values of about

10-8 indicate that second-order SO coupling is negligible for Ag in Ar, Kr and Xe

matrices.

Baseline corrected absorption and MCD spectra for Au in the three gases are

shown in Figs. 4.5-4.7 and are again dominated by temperature dependent C terms. The

band positions, listed in Table 4.2, agree well with those reported by Gruen et al.10

Straight lines were obtained for plots of ,/
o vs. 1/T, shown in Fig. 4.8, from

which the SO coupling constants were extracted. These constants are listed in Table 4.2.

In this case the extracted values (Ar: 3354 cm-1, Kr: 3110 cm-1, Xe: 2665 cm-1) were

all greater than the gas phase20 value of 2543 cm-1.

Second-order effects were again assessed using (41) which is shown plotted in

Fig. 4.9. The C values obtained are listed in Table 4.2 and are not close, for Au/Ar and

Au/Kr, to the first order values obtained from (28). For Au/Xe the difference in the

calculated s is within the experimental error (-4%) but the difference for Au/Kr is -17%

and is near 30% for Au/Ar. This is also reflected in the zeroth MCD moment plots

shown in Fig. 4.10. While considerable scatter is present in all three plots the Au/Xe and

Au/Kr plots appear temperature independent but the Au/Ar plot shows a distinct

temperature dependence (i.e., linear with 1/T). The importance of second-order spin orbit

effects appears to decrease in going from Ar to Xe matrices.












Au/Ar


40000 42000 44000


FREQUENCY / cm 1


Experimental MCD (top) and absorption (bottom) spectra of Au atoms in
a Ar matrix at 10.5 K.


cN
0

F-
N


38000


Figure 4.5










10.3 K

13.8 K
16.8 K


Au/Kr


38000 40000 42000 44000


FREQUENCY / cm -


MCD (top) spectra of Au atoms in a Kr matrix showing temperature
dependence of the signal. Absorption (bottom) spectra at 10.3 K.


Figure 4.6












Au/Xe


38000 40000

FREQUENCY / cm-1


Experimental MCD (top) and absorption (bottom) spectra of Au atoms in
a Xe matrix at 12.0 K.


36000


42000


Figure 4.7



















37359

41174


2543

2543


38895

43365
43937

3354

2357

0.44:0.90

2120

1.2x106(g)

-1.7x106


38124

42301
42790

3110

2572

0.85:0.52

2577

1.3x106(g)

-1.1x106


59
Table 4.2 Observed Absorption Band Positions (in cm-1) and Parameters Derived from
the Moments Analysis for Au Atoms in Rare Gas Matrices.


Gasa Ar Kr Xe


Excited State

2P1/2

2P3/2


b/cm-1

t'c/cm-1

a:bd

t!/cm-1

OC/Cm-2

/cm-2

vif/cm-1


___________________ I ______ 1 _________ L _________ ________


aValues from Ref. 20.
bFirst order, obtained from (28).
CSecond order, obtained from (41).
dCoefficients of mixing: ap'(2P3/2) + b(4P32.
elst SO parameter, calculated from (44).
fValues from fitting (33).
gAverage values no fit performed.


36644

40258
40734

2655

2555

0.98:0.20

2534

0.3x106

-0.1x106

23.2














-20- 0 Au/Kr
A Au/Xe
-40
O

S-60 \

<1 -80 -X.


-1 00 -


-1 20
0 2 4 6 8 10 12


102


Figure 4.8


T


Reduced MCD first moment plots vs. inverse temperature for the three
Au/Rg systems. For clarity, the Au/Kr and Au/Xe plots have been shifted
-5 and -10 y axis units, respectively.













*. Au/Ar
a Au/Kr
A Au/Xe


0 2 4 6 8 10 12


102


Reduced MCD second moment plots vs. inverse temperature for the three
Au/Rg systems.


140

120

100


'


0







0


80

60

40

20


/


/ A
A


T- /K-


Figure 4.9


,/
,,,K











o Au/Ar
* Au/Kr
A u/Xe


o o


L
A M &A N
Zal. 6 P


0 2 4 6 8 10 12
0 2 4 6 8 10 12


102 T


/K


Figure 4.10


MCD zeroth moment plots vs. inverse temperature for the three Au/Rg
systems.


18


14


0



0


10


6







63

The fact that second-order SO interaction in Au/RG decreases in the order RG =

Ar > Kr > Xe shows the dramatic effect the matrix material can have on this quantity.

Second-order SO coupling may arise from either out-of-state mixing of the Au 6p

orbital with the appropriate orbitals on nearby rare gas atoms and/or with other Au atom

excited states. Mixing with higher-lying p orbitals on the rare gas neighbors can be

immediately discounted since the trend in the energies of the appropriate mixing states20

is opposite to the observed trend. Table 4.3 lists the energies of the states for Au. Note

that the energy of the 21P3/2 multiple (the average of the two bands) increases for Au/Ar

and Au/Kr compared to the gas phase, whereas for Au/Xe it decreases. This multiple

may second-order SO couple to the 4P3/2 multiple. Coupling of the 2P1/2 state with the

4P1/2 state was neglected here due to the significantly larger energy separation. The 4P3/2

state was assumed to be unshifted in the various matrices because no information on its

location was available from this study (it lies at shorter wavelengths than the present

apparatus can reach). It can then be seen that the energy spacing between the 2P3/2 and

4P3/2 multiplets decreases in the order Xe (-6500 cm-1) > Kr (-4500 cm-1) > Ar (-3300

cm-1). On this basis, a larger second-order SO coupling would be predicted in Au/Ar

than in Au/Xe. By way of contrast, the spacing of the Ag 2P3/2 and 4P3/2 multiplets is

in the 28,000 cm-1 range, effectively precluding any appreciable second-order mixing.

The second-order SO mixing between excited states of a matrix-isolated atom or

ion may be explicitly determined using a procedure that has been previously reported.39'47

Rivoal and Vala and coworkers39,47 showed that for the mixing of an allowed state ip' and

a forbidden state Vp" with mixing coefficients, a and b, respectively, the zeroth MCD







64
Table 4.3 Selected Excited States, Configurations and Gas Phase Energies of Au
Atomsa


aFrom Ref. 20
bTaken as average of two split bands, cf. Table 4.2.
Av v GAS (4P3/2) RG (2P31, in cm-1.


Au
State Configuration v/cm-
Gas Ar Kr Xe
21/2 5dl06s 0 0 0 0
2P/2 5dlo6p 37358.9
23/2 5d0o6p 41174.3 43651b 42546b 40496
4P3/2 5d96s6p 47004.4
4P 5d96s6p 53197.5
AvC 13353 4458 6508








moment, ' for the allowed band, is given by


(2J+3Xa2-1)m2 (J+1X2J+1)

where J is the total angular momentum of the ground state, m is the transition dipole

moment matrix element and is the thermal average over the Zeeman-split ground

state levels. The value of m2 was obtained from
0 = m2, the zeroth absorption

moment over the entire band. ' and were calculated at each temperature

and were combined with m2 in (42) to give a value for a2. The mixing coefficient a was

taken from the square root of the average of all a2 values. From a2+b2=1, the value of

b was calculated. Finally, using the perturbed first moment MCD expression39'47


,E = [2gttBB + 2']m2 (43)


where


b2. (2J+3) AW (44)
2 (J+1X2J+1)

the first order SO constant t for the allowed 2P state was extracted from the usual MCD

first moment plot. The experimental SO constants (t', which include first and second

order contributions) for the Au/Ar, Au/Kr and Au/Xe cases have been given previously

(cf. Table 4.2). Using b2 and AW (the energy separation between allowed and forbidden

partners) along with (44) the first order SO constant was calculated. The values found

for the a and b coefficients and the and constants are given in Table 4.2. If the

mixing partners proposed here are valid, the t values obtained should be close to the ones






66

determined from (41). These values were found to lie within 3-10% of each other:

Au/Ar (2120 cm-1 vs. 2357 cm-1), Au/Kr (2577 cm-1 vs. 2572 cm-1), and Au/Xe (2534

cm-1 vs. 2555 cm-1). The a and b coefficients for Au/Ar (a = 0.44, b = 0.90) indicate

that the 2P3/2 and 4P3/2 are thoroughly mixed by SO interaction. The slight discrepancy

between the two t values may arise from other states such as 2P1/2, 4P1/2 not included in

the calculation or from the inaccuracy of the assumed energy separations (AW). In any

event, the close correspondence found strongly indicates that the second-order SO effect

arises primarily from the mixing between the P3/2 and 4p3/2 states. This also establishes

that the intra-atomic SO coupling in gold is strongly influenced by the matrix material

with the largest effect occurring in Ar and the smallest in Xe.


Origin of the Observed Band Structure


Two primary explanations have been offered for the appearance of three bands in

the spectrum of the 2P 2S transition of matrix isolated noble and alkali metals: a static

distorted site model or a dynamic Jahn-Teller (JT) effect. Lund et al.24 have shown that

absorption spectra and MCD spectra may be combined to conclusively establish the

dynamic JT effect as the source of the three bands for the matrix isolated alkali metals.

The present spectra for matrix isolated Ag and Au atoms differ from the alkali metals in

several ways. The measured SO constants for Ag and Au are much larger than the alkali

metal SO constants and do not change sign from their gas phase values, indicating that

the 2P3/2 multiple remains at higher energy than the 2P1/2 multiple. Also, the 2P1/2 band

is well-resolved and separated from the 2P3/2 doublet.







67

Previous authors have proposed explanations for the observed band structure of

matrix-isolated Au atoms. Gruen and coworkers10 proposed that an axial site distortion

was responsible for the splitting. Forstmann, Kolb, Leuthoff and Schulze,13 following

Gruen, also proposed such an origin for the appearance of the three peaks. Weinert et

al.,48 used a moments analysis on the absorption bands of the individual multiplets within

the extended configuration coordinate model, but noted a number of problems with this

approach. They suggested in a subsequent paper49 that a moments analysis utilizing

MCD and absorption would yield valuable information. In the following, a distorted site

model will be tested and shown to be incapable of reproducing the observed spectra, and

thereafter, a moments analysis of the MCD and absorption data will be presented to

confirm the presence of JT activity.

Following the procedure used by Lund et al.,24 the metal atom was assumed to

reside in a site of D4 (or D3) symmetry. A crystal field calculation on the 2P state then

yielded the energies of the three split levels as a function of t, the one electron SO

coupling constant, and A, the crystal field (or tetragonal10) parameter as


1
El(bE') = -1(- +A+2S)


E2(E") = (-+A) (45)


E3(aE') = -.(-+A-2S)
4


where








1
S = (9a + 3A+ 9t2)2 = E3-EI>0. (46)
4 2 4

The state descriptions in parentheses refer to the D4 double group (D4). For the correct

ordering of energy levels for the Ag/RG and Au/RG cases, where the 2P3/2 (U') SO

multiple lies above the 2P1/2 (E') level, the expressions of Lund et al.24 have been

modified by substituting -t for C and -A for A. The energy levels are shown

schematically in Fig. 4.11. Solving the above equations for t and A yields

1 (47)
= a-(a2-q)

1 (48)
A = a+(a2-q)



where

a = [(E2-E3) +(E2-E1)]/3 (49)


q = 2[(E2-E1)(E2-E3)]/3. (50)

The relevant MCD parameters, (A 0Bo, o, Do), defined in Lund et al.,24 were calculated

and are given for Ag/RG and Au/RG in Table 4.4.

Using these parameters the MCD and absorption spectra were simulated from



AA'/e = 152.5 -A(i) + + (kT)) fi(E) ce (51)
i=1 ae (kT) I


and









3
A/e = 326.6 Do(i)fi(e)cR (52)
i=1

where AA' is the MCD per tesla, e is the photon energy (in cm-1), c the sample

concentration and 6 its pathlength. The band shape, fi(e), was taken as a normalized

Gaussian


fi(e) = (1/6i')exp(-(e-ei)2/b). (53)

As seen in Table 4.4, the MCD parameters A 0, and Co are completely determined by

the two crystal field parameters, t and A, which in turn are determined by the absorption

band peak positions. Most importantly, the scaling of the simulated MCD spectrum is

completely fixed by the experimental absorption band intensity. For the present

simulations, both simulated and experimental absorption spectra were normalized on the

lowest energy (bE') band.

Using this procedure absorption and MCD spectra were simulated for both Ag and

Au atoms in the three rare gases. The best fit simulations are compared with

experimental spectra in Fig. 4.12 (Ag/Ar) and Fig. 4.13 (Au/Xe). The bandwidths for

each band (i=1-3) were adjusted to best match the absorption spectra contours and then

retained when simulating the MCD spectra. For Ag/Ar the absorption spectrum is

matched reasonably well except for the highest energy band whose intensity is not well-

reproduced. The Ag/Ar MCD simulation shows three distinct bands, as observed, all of

which are predicted to be too intense. Similar observations hold for the Ag/Kr and Ag/Xe

cases, with absorption being simulated well but with even larger discrepancies between

predicted and observed MCD intensities.













aE'


U2 /E
P/


\ E'

'-- bE'
55


Oh


D4


Figure 4.11


Ordering of the spin-orbit split levels of the excited 2p state in octahedral
(Oh) and distorted tetragonal (D4) fields.







Table 4.4 Crystal Field Model: Absorption and MCD Parametersa


E'(2S) -* bE' E" aE'


Ib x+y 1/3 x-y

Bb B21 + B31 -B21 + B32 -B31 B32

C'ob 1/6 + u -1/3 1/6 u

Dob 1/3 1/3 1/3



aThis table is taken from Ref. 24.
bAll MCD and absorption parameters are in units of the reduced transition moment matrix
element squared. The symbols in the Table are defined as:


CF


W~F + 1 _5CF + ACE. U 3 'CF +
2S 2 12-lSCF 4SCE' 4 SCF
CF


ACE
4SCF


9AC 2 3ACFC 2~
S CF C__ ___ + 9t__ = E3 -E,
4 2 4


-Bj's given in Ref. 24.










15-


10-


5-

0-

-5-


-10



3


I
0


A
!^ Ag/Ar



I I
! I
I 1





15


30000 31000 32000 33000 34000 35000

FREQUENCY / cm1
FREQUENCY / cm


Figure 4.12


MCD (top) and absorption (bottom) spectra of Ag atoms in a Ar matrix at
6K (solid curves). Simulation using the CF model with variable
bandwidths (dotted curves). Simulation using the CF model with
bandwidths determined from eq. 54 (dashed curves). Simulations are
normalized to lowest energy experimental absorption band.


0
I-


<1










Au/Xe


' I
I


38000


40000


FREQUENCY / cm


Figure 4.13


MCD (top) and absorption (bottom) spectra of Au atoms in a Xe matrix
at 10.5K (solid curves). Simulation using the CF model with variable
bandwidths (dotted curves).


36000


42000






74

In the case of Au/Xe, similar results were obtained. The intensities of both higher

energy bands (E" and aE') were not reproduced well by the crystal field model. The

MCD simulation again shows intensities which are too strong for all bands. Furthermore,

the bandwidths necessary to produce the absorption simulation result in a MCD

simulation with only two distinct bands. The two higher energy bands show no evidence

of separation in the simulated MCD. This model produced considerably less accurate

simulations for the other Au/RG cases. Overall, the crystal field model does not correctly

simulate the amplitudes of the absorption and MCD spectra of any of the Ag/RG or

Au/RG cases.

Another approach to the crystal field model, introduced by Lund et al.,24 starts

with a specific D4 (or D3) model and develops moment equations for MCD and

absorption, which are then equated to the experimental moments. This approach was

applied to Ag in the rare gases. The parameters, t and A, are then deduced from these

moments, the MCD and absorption are simulated and finally compared to the

experimental spectra. Lund et al.24 found that (28) is still valid if gorb is set equal to one

and 2NC is replaced by A2, where A is the tetragonal crystal field parameter defined

in (48). The standard first MCD moment plot was used to deduce The value of A was

taken as the square root of 20NC obtained from (29) and (30), vide infra. These

values have been listed in Table 4.2. With and A, the band energies (Ei) were

calculated using (45) and thence the A 1 (i), B 0 (i), C 0 (i) and D 0 (i) obtained from the

definitions in Table 4.4. The bandwidths were not varied arbitrarily to fit the absorption

widths (as in the previous model), but instead the relation used was









2 = 6 i

This form is dictated since the only source of line broadening in the crystal field model

comes from cubic lattice modes (i.e., C) and because the dipole strengths 0 0 (i) for

transitions to each of the levels are identical. The values of deduced from (29)

and (30) are given in Table 4.2. The simulations using bandwidths determined from (54),

shown as a dashed curve in Fig. 4.12 for Ag/Ar, generally fit the spectra very poorly.

(This procedure was not performed for Au/RG due to the negative values of C

obtained from the experimental data, vide infra.) Indeed, neither approach using the

crystal field model is able to fit both MCD and absorption well. The inability of the

crystal field model to reproduce the observed spectra agrees with the conclusions of Kasai

and McLeod8 that the atoms sit in a substitutional site and requires that a different

explanation for the tri-peaked appearance be found.

In earlier work on Cu in the rare gases21'22 and the alkali metals in the rare

gases,23-26 which also feature a 2p 2S transition, it was conclusively established that

the Jahn-Teller effect is operative in the excited 2P state and that, together with the SO

splitting of the 1/2 and 3/2 J components, it is responsible for the tri-peaked appearance

of the absorption band. The assumption that a similar mechanism holds true for the Ag

and Au cases is warranted since a matrix-dependent SO splitting has been shown and the

transition involved, 2p 2S, is identical. The proof of the existence of JT activity in

matrix-isolated atoms rests on two major experimental observations, viz., that the

contributions of noncubic lattice vibrations to the bandwidths (i.e. Nc) are

nonnegligible and that their values vary with temperature as the coth(vi/2kT) function.






76

To test this assumption (29) and (30) were used to determine the cubic, c,

and non-cubic, Nc, contributions to the bandwidths. Plots of c and NC

vs. T for the Ag/RG cases are shown in Figs. 4.14-4.16. The NC and c values

found, together with the effective lattice frequencies (vi), obtained by fitting (53), have

been listed in Table 4.1. The c terms are all small compared to the NC.

Furthermore, all the NC data fit a coth function reasonably well, although with

considerable scatter. These observations fit the criteria for JT activity in the 2P state and

support the assumption that the tri-peaked appearance of the 2p 2S transition for

matrix isolated silver atoms is a result of simultaneous SO splitting and a dynamic JT

effect.

Confirmation of the JT effect in the Au/RG cases was similar but not without

some complications. Figure 4.17 shows plots of NC and c as a function of

temperature for Au atoms. For Au/Xe, expression (33) was fit well with C= 3.0

x 105 cm-1 and vi = 23 cm-1. However, the c values for Au/Xe are negative (a

physically unrealistic result) and, furthermore, became increasingly negative at higher

temperatures. For Au/Ar and Au/Kr, the NC and c plots are problematic. They

show practically no T-dependence although their values for
c. These anomalous results may arise from anharmonicity and/or higher order

electron phonon coupling terms not specified in the moments derivation and are discussed

further below. However, since the crystal field model could not correctly simulate the

observed absorption/MCD (recall that the Au/Xe case was better simulated than either the

Au/Ar or Au/Kr case) and the calculated NC values are substantial, it appears that

the JT effect is active in the three Au/RG cases.










Ag/Ar


35

30

25

20

15

10

5

0

-5


10


00 00


20 30


T/K


Figure 4.14


Temperature dependence of the cubic c and noncubic NC
bandwidth contributions of Ag/Ar. Solid line fit follows the relation:
NC = 1.6x15 coth(32.1/2kT), in cm-1.


E

0


CMj
v/


qptPbh 00
ct9


40









35

30

25


E

0
d-

C

Ag/Kr


20

15

10-

5-

0 -

-5-
0


03
, 000


10


0 _0


20


30


40


T/K


Figure 4.15


Temperature dependence of the cubic and noncubic NC
bandwidth contributions of Ag/Kr. Solid line fit follows the relation:
NC = 1.5x105 coth(35.8/2kT), in cm-1.


0DO











Ag/Xe


dPo 00
00EfflEFw0


0 0
0 0 0
0


20 30


40


T/K


Figure 4.16


Temperature dependence of the cubic and noncubic NC
bandwidth contributions of Ag/Xe. Solid line fit follows the relation:
NC = 6.9x104 coth(24.2/2kT), in cm-1.


25


20


15


10


E
O
C.)
r0)
C


(N
w


-5


10


50









20

15 U "

10- o 0 A

o 5

0
+ + + + + + +

-5 +

V
-10 v v

-15 -

-20 -'--'--'--
0 9 18 27 36 45

T/K



Figure 4.17 Temperature dependence of the cubic and noncubic bandwidth
contributions for the three Au/RG systems.
Legend: (NC values: 0 Au/Ar; U Au/Kr, A Au/Xe; c values:
+ Au/Xe; V Au/Kr; O Au/Ar).






81

The expressions given in (28) (34) were derived under a number of limiting

assumptions: harmonic ground state vibrational wavefunctions, first order SO coupling,

and linear electron-phonon coupling.37 In relaxing the latter condition and allowing

quadratic electron-phonon coupling, expression (29) becomes37


2/o = 2/2 + 1(2 1 2 (55)
2 41.



Here C2 involves only linear electron-phonon coupling and is equivalent to (34). The

additional term, -1/4o)12, incorporates the influence of quadratic electron-phonon mixing,

which is given by37


01 = E i/2( k i)vi coth(vi/2kT) (56)



where Ki is the quadratic electron-photon coupling parameter and other terms are as

defined previously. The magnitude of (o may be determined from the variation with T

of the barycenter energy, v0 (as defined in (26)):


v0 = Vp + 11 = v0 + Npcoth(vi/2kT) (57)




A plot of v0 vs. T is shown in Fig. 4.18 for Au/Xe. Knowing the magnitude of o1 at

various temperatures now permits a qualitative understanding of the form of the Au/RG

2/o vs. T curves. Figure 4.19 shows that Au/Ar decreases at higher T, while both

Au/Kr and Au/Xe increase at higher T. This behavior can be interpreted as arising from





























0 10


Figure 4.18


Band peak position vs. temperature for Au/Xe. The solid line fit follows
the relation: v0 = 39283 148coth(29.5/2kT), in cmn1.


39.3


39.2


Au/Xe


E
C)
0
I


39.1


39.0


38.9


38.8


20


30


40


50


T/K































20 30


T/K


Figure 4.19


Reduced absorption second moment plots vs. temperature for the three
Au/RG systems. Lines are least squares fits.


6.0


5.5


0
<\C

N
<(


0
to


5.0


4.5


4.0


3.5


3.0-
0


10


40


50






84
a partial cancellation of the 0o2 and 0o, terms, with the 01, term larger in Au/Ar and the

02 term larger in the Au/Kr and Au/Xe samples. However, as expected, the SO term
dominates in all three cases. The intercept (T=0) in these plots should equal t2/2, and

does. The values observed are (in parenthesis the t values from first moment MCD

slopes): Au/Ar: 3350 cm-1 (3354 cm-1); Au/Kr: 3200 cm-1 (3110 cm-1); Au/Xe: 2650

cm-1 (2655 cm-1).

The question of why the c curves are negative, and increasingly so at higher

temperatures, can be assessed qualitatively in the following manner. Labelling the LHS

of (29) as R and the ratio of the temperature dependent parts of (30) and (28) as P, i.e.,


R =
2/0 = c + NC + 2/2 (58)


P = 3/1 = 3c + 3NC/2 + 3t2/4 (59)

and rearranging, gives expressions for c and NC:


NC = 2R-2P/3-t2/2 (60)


c = 2P/3-R (61)

Thus if R > 2P/3, c can become negative. The question is now, under what

conditions can c be expected to be negative. Recall that R = t2/2 + 1/2m2 1/4(012

(cf. (55)). Knowing that 01, -304.6 cm-1 at 10K (from the v0 vs. T plot) and that its

(negative) contribution to R is only -3% of the total value (at 50K it climbs to -16%),

the value of R will increase with T, but not sufficiently if only linear electron-coupling

terms are included in the c2 term. The fitting of the
2/0 curve shows this is to

be the case. Thus, it appears clear that higher order coupling effects and/or anharmonicity







85

terms should be included in (02 to account for the further decrease of c below zero

with increasing temperature. This, of course, demonstrates that the values of NC and

c obtained above are only approximate. Still, the determination of non-negligible

NC values provides strong evidence that the Jahn-Teller effect is operative in these

systems.

The appearance of four bands in the Ag/Xe absorption and MCD spectra deserves

further comment. The crystal field (CF) model by itself is incapable of explaining this

observation. Previous authors11 have proposed that the fourth band arises from the CF-

split 2p3/2, 3/2, level which interacts with the Xe 6s level in a Ag-Xe molecule. Others

have suggested18 that it is the result of a resonant interaction of the 2p3/2 multiple with

a near-lying 2D5/2 state, coupled by nontotally symmetric vibrations of the lattice.

Having confirmed the importance of the JT effect in this sample, it is possible to

speculate that the additional structure arises directly from transitions to the three JT-SO

excited state potential manifolds whose inherent sharp band structure is not completely

smoothed out by coupling to the symmetric modes. A computation of the band contours

which may lead to this situation would be very interesting and would possibly lead to a

conclusive argument for the origin of the fourth band.


Discussion


Spin-Orbit Coupling


Recently, a theory of spin-orbit coupling in the 2P excited state of alkali metal

and noble metal atoms in rare gas matrices was proposed.33 The theory assumed a model

in which the metal atom resides at a tetradecahedral substitution site surrounded by a first