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Absorption and magnetic circular dichroism of matrix isolated metal atoms and small clusters

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Absorption and magnetic circular dichroism of matrix isolated metal atoms and small clusters a study of atom-matrix interactions
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Zeringue, Kyle J., 1954-
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English
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xii, 201 leaves : ill. ; 28 cm.

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Absorption spectra ( jstor )
Atoms ( jstor )
Eigenvalues ( jstor )
Electronics ( jstor )
Ground state ( jstor )
Magnetic fields ( jstor )
Magnetism ( jstor )
Matrices ( jstor )
Orbitals ( jstor )
Temperature dependence ( jstor )
Chemistry thesis Ph. D
Circular dichroism ( lcsh )
Dissertations, Academic -- Chemistry -- UF
Matrix isolation spectroscopy ( lcsh )
Metals -- Effect of high temperatures on ( lcsh )
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bibliography ( marcgt )
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non-fiction ( marcgt )

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Thesis:
Thesis (Ph. D.)--University of Florida, 1983.
Bibliography:
Includes bibliographical references (leaves 196-200).
Additional Physical Form:
Also available online.
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Typescript.
General Note:
Vita.
Statement of Responsibility:
by Kyle J. Zeringue.

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ABSORPTION AND MAGNETIC CIRCULAR DICHROISM
OF MATRIX ISOLATED METAL ATOMS AND
SMALL CLUSTERS: A STUDY OF ATOM-MATRIX INTERACTIONS












BY

KYLE J. ZERINGUE






















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

1983































To Jan Olson-Zeringue















ACKNOWLEDGEMENTS


The author would like to thank Dr. Martin Vala for his guidance in this research. A great debt is owed to Dr. Robert Ferrante for the training he provided in high vacuum technology and matrix isolation.

The invaluable assistance of Dr. Jean-Claude Rivoal in calibration and design and construction of electronics is greatly appreciated. Thanks are also due to Dr. Joseph Baiardo for many helpful discussions and his computer interfacing expertise. Thanks are also extended to Dr. Richard Van Zee, Dr. Marek Kreglewski, and Dr. Robert Pyzalski for helpful and informative discussions. For assistance in data collection the author thanks Mr. Bill Copeland.

The author greatly appreciates the craftsmanship of Mr. Art Grant, Mr. Rudy Strohschein, and Mr. Chester Eastman,shown in the fabrication of the apparatus.

The author thanks Mrs. Laura Griggs for her diligence and attention to detail in preparing this dissertation.

The seemingly unending patience, understanding, and assistance of Jan Olson-Zeringue are most deeply appreciated.

Funding for this research has been provided by the National Science

Foundation and the Graduate School. Partial support by the Division of Sponsored Research is also appreciated.















TABLE OF CONTENTS


Page

ACKNOWLEDGEMENTS ................................................... iii

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

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

ABSTRACT ........................................................... xi

CHAPTER I INTRODUCTION ........................................ 1

CHAPTER 11 THEORY OF MAGNETIC CIRCULAR DICHROISM ............... 9

Basic Equations ..................................... 10
Magnetic Circular Dichroism Calculation for Atoms ... 25 Effect of Reduced Site Symmetry ..................... 42
The Adiabatic Model ................................. 46
Band Moment Analysis ................................ 49

CHAPTER III EXPERIMENTAL ........................................ 52

Sample Preparation .................................. 52
Spectroscopic Apparatus ............................. 59

CHAPTER IV RESULTS ............................................. 77

Copper in Argon ..................................... 82
Copper in Krypton ................................... 115
Copper in Xenon ..................................... 131
Gold in Argon ....................................... 138
Gold in Krypton and Xenon ........................... 153
Results for Lead Experiments ........................ 170
Further Studies ..................................... 176

APPENDIX A ORBITAL OVERLAP CALCULATIONS ........................ 178

APPENDIX B PROGRAMS ............................................ 182


iv









Page

APPENDIX C TEMPERATURE CALIBRATION ............................. 190

REFERENCES ......................................................... 196

BIOGRAPHICAL SKETCH ................................................ 201















LIST OF TABLES

Page

Table 4.1 Calculated eigenvalues, eigenfunctions and MCD Co 105
and Do parameters for Cu atoms in Ar. Ei's are
eigenvalues measured from the excited state center of gravity; ci's are coefficients of the adiabatic
wavefunctions [see equation (58)]. For Cu/Ar, X = 124 cm-', t = 115 cm'-, and z = 220 cm-1.

Table 4.2 Calculated eigenvalues, eigenfunctions and MCD Co 125
and Do parameters for Cu atoms in Kr. Ei's are
eigenvalues measured from the excited state center of gravity; ci's are coefficients of the adiabatic
wavefunctions [see equation (58)]. For Cu/Kr X = 95 cm-', t = 111 cm-1, and z = 152 cm-.

Table 4.3 Calculated eigenvalues, eigenfunctions and MCD Co 143
and 0Do parameters for Cu atoms in Xe. Ei's are
eigenvalues measured from the excited state center of gravity; ci's are coefficients of the adiabatic
wavefunctions [see equation (58)]. For Cu/Xe X = -23 cm-1, t = 86 cm-', and z = -174 cm-'.

Table 4.4 Calculated eigenvalues, eigenfunctions and MCD Co 156
and Do parameters for Au atoms in Ar. Ei's are
eigenvalues measured from the excited state center of gravity; ci's are coefficients of the adiabatic
wavefunctions [see equation (58)]. For Au/Ar X = 3165 cm-1, t = 45 cm-1, and z = 300 cm-1.

Table A.1 Data used in orbital overlap calculations. 179

Table A.2 Orbital overlaps and predicted spin orbit reduction 181
factors.


vi















LIST OF FIGURES


Page

Figure 2.1 The appearance of terms predicted by MCD theory 24
(a) The zero field absorption and MCD for a transition with a positive A, term. The positive lobe lies at higher energy.
(b) A Bo term may be positive or negative, the maximum coinicident with the absorption maximum.
(c) A negative Co term at two temperatures, Thigh and Tlow, may be positive or negative with its maximum coincident with the absorption maximum.

Figure 2.2 Polarized transition to an atomic P state and mag- 27
netic field splittings. Transition a is right circularly polarized, transition c is left circularly
polarized, and transition b is polarized parallel
to the magnetic field.

Figure 2.3 Magnetic field splitting in degenerate ground and 30
excited states illustrating the origin of A0 and Co
terms.

Figure 2.4 Splittings in free atom 'S and 2p orbitals for 36
(a) an octahedral site
(b) spin orbit interaction
(c) Zeeman splitting.

Figure 2.5 The state splittings and allowed transitions for an 40
atom in an octahedral field showing the effect of
spin orbit and Zeeman splitting.

Figure 2.6 The predicted MCD and absorption patterns for the 44
2p 2S transition in an octahedral field.

Figure 3.1 (a) Diagram of the furnace assembly. 54
(b) Diagram of Knudsen cell used for metal vaporizati on.

Figure 3.2 Detail of furnace-cryostat assembly used in matrix 58
isolation experiments.

Figure 3.3 Optics for absorption experiment 61


vii









Page

Figure 3.4 Schematic of absorption experiment. 64

Figure 3.5 Optics for MCD experiment. 67

Figure 3.6 Schematic of MCD experiment. 69

Figure 3.7 Magnetic field dependence of an MCD signal. 75

Figure 4.1 The splittings induced in free atom 'S and 2P 79
states. Note dependence upon the order of application of various interaction in calculation.

Figure 4.2 The eigenvalues and C0/V0 values predicted for a 81
reduction of pure 0 h site symmetry to D3.

Figure 4.3 Absorption and MCD spectra observed for Cu isolated 85
in Ar.

Figure 4.4 Temperature dependence of the Cu atom Co term in an 87
Ar matrix. The intensity decreases with increased
temperature.

Figure 4.5 Experimental plot of o/o vs. l/T for Cu atoms 89
in an Ar matrix.

Figure 4.6 Experimental plot of 1/
o vs. l/T for Cu atoms 92
in an Ar matrix. The spin orbit splitting, A, is obtained from the slope and the excited state gor
is obtained from the intercept,.r

Figure 4.7 Experimental plot of B/
o vs. l/T for Cu atoms 96
in an Ar matrix.

Figure 4.8 Experimental plot of
2/0 vs. T for Cu atoms in 98
an Ar matrix.

Figure 4.9 Diagram of the degenerate modes of the e lattice 103
vibration.

Figure 4.10 Plot of calculated C0 term as a function of lattice 107
motion z holding lattice motion t = 115 and X constant (from moment plots) for Cu atoms in Ar matrix.

Figure 4.11 Plot of calculated Co term as a function of lattice 109
motion t holding lattice motion z = 220 and X constant
(from moment plots) for Cu atoms in an Ar matrix.

Figure 4.12 Composite drawing showing the effect of varying ill
contributions from lattice vibrational modes.

Figure 4.13 The effect of varying the magnitudes of the t2 and 114
e modes on absorption profile. B represents the e
mode and C the t2 mode.

viii









Page

Figure 4.14 Absorption and MCD spectra for Cu atoms isolated 117
in a Kr matrix.

Figure 4.15 Temperature dependence of the Cu atom Co term in 120
a Kr matrix. The intensity decreases with
increased temperature.

Figure 4.16 Experimental plot of 1/
o vs. 1/T for Cu 122
atoms in a Kr matrix.

Figure 4.17 Experimental plot of 3/
0 vs. 1/T for Cu 124
atoms in a Kr matrix.

Figure 4.18 Cu absorption and MCD bands in the range 220 nm to 127
340 nm.
Figure 4.19 Appearance of Cu/Kr spectrum after prolonged depo- 130
sition from 230 nm to 290 nm.

Figure 4.20 The Cu2 band in the range 330 nm to 450 nm. 133

Figure 4.21 Absorption and MCD bands for Cu in a Xe matrix. 135

Figure 4.22 Plot of /
O vs. 1/T for Cu in Xe. 137

Figure 4.23 Plot of 3/
o vs. 1/T for Cu in Xe. 140

Figure 4.24 Plot of
2/o vs. 1/T for Cu in Xe. 142

Figure 4.25 Relative positions of Cu MCD in Ar, Kr and Xe. 145
Note the reversal of MCD term sign in Xe.

Figure 4.26 Absorption and MCD for Au in Ar. 148

Figure 4.27 Plot of 1/
o vs. 1/T for Au in Ar. 150

Figure 4.28 Plot of 3/
o vs. 1/T for Au in Ar. 152

Figure 4.29 Plot of best fit for Au in Kr of (peak separation)2 = 155
4 hwEjTcoth (t)

Figure 4.30 Absorption and MCD for Au in Kr. 158

Figure 4.31 Plot of 1/
O vs. l/T for Au in Kr. 160

Figure 4.32 Plot of 3/
0 vs. 1/T for Au in Kr. 163

Figure 4.33 Absorption and MCD spectra for Au in Xe after a 165
high temperature metal vaporization.
Figure 4.34 Spectra obtained in a 1300'C Au deposition into Xe. 167


ix









Page

Figure 4.35 Absorption and MCD for Ag in Ar. 169

Figure 4.36 Absorption and MCD for Pb in Kr between 220 nm and 173
280 nm.

Figure 4.37 Absorption bands for Pb clusters in Kr. 175

Figure C.1 The Au/Ar band and equations used to calibrate the 193
lowest T attained on the Displex.

Figure C.2 Plot of MCD and thermocouple tracking of tempera- 195
ture fluctuations. Note lag less than one second.
The arrows indicate times at which the temperature
cycling period was changed. The right most portion shows the temperature stability at the lowest
temperature.




































x















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


ABSORPTION AND MAGNETIC CIRCULAR DICHROISM OF MATRIX ISOLATED METAL ATOMS AND SMALL CLUSTERS: A STUDY OF ATOM-MATRIX INTERACTIONS By

Kyle J. Zeringue

April 1983


Chairman: Dr. Martin T. Vala
Major Department: Chemistry


Copper, silver, gold and lead have been vaporized and codeposited with argon, krypton and xenon on a cold surface. Magnetic circular dichroism and zero field absorption spectra are presented. Data are digitized and stored on a microcomputer for analysis.

A brief introduction to matrix isolation and the magnetic circular dichroism (MCD) technique is given. The theoretical background for the MCD experiment is outlined. Calculations of predicted absorption and MCD spectra for copper atoms trapped in rare gas lattices are presented for various site symmetries and interactions with the surrounding matrix cage.

The cause of the triplet structure of the 2p _~ 2S transition for group IB metals is discussed in terms of 0 h symmetry, D3 symmetry, spin orbit coupling, Zeeman splitting, and ultimately, a model involving simultaneous spin orbit and Jahn-Teller interaction of the









isolated metal atom with host lattices. On the basis of comparison of calculated to observed absorption and MCD spectra, several of the excited state splitting models can be excluded, and the simultaneous spin orbit and Jahn-Teller model is shown to be the explanation of observed spectra.

Calculations for a detailed moment analysis are presented for

copper atoms isolated in an argon matrix. Moment analysis results are also presented for copper in krypton and xenon as well as for gold in argon and krypton. The spin orbit coupling constants are shown, for copper, to be reduced as compared to the gas phase. For copper atoms

X=124 cm-', 95 cm-1, and -23 cm-1 (gas phase = 166 cm-1) when isolated in argon, krypton and xenon, respectively. The spin orbit reduction is discussed in terms of atomic orbital overlaps. Overlaps for approximated metal atom excited state valence orbitals with matrix gas outer shells are computed for copper, silver and gold with argon, krypton and xenon. I

The absorption and MCD spectra of several small cluster bands are presented. On the basis of the type of MCD term observed and comparison to expected bands due to state degeneracies, bands are assigned to dimers or trimers and comparison is made to literature assignments.

The absorption and MCD spectra of lead atoms and dimers confirm

literature assignments. The anticipated positive A term is observed for the 3K -.-- 3p0 lead atom transition (AJ =+1).

A new technique for measurement of the temperature of matrix

samples is introduced. The measurement involves the temperature dependence of an MCD band of a paramagnetic species and accurate measurement (by a thermocouple) of temperature differences.

xii















CHAPTER I

INTRODUCTION


Molecular spectroscopy, the primary tool utilized to study details of molecular geometry and electronic structure, has been applied routinely to many stable chemical species in the solid, liquid and gaseous phases. The study of short-lived or unstable species has been aided greatly by high-speed electronic instrumentation. There are, however, many species yet very difficult or impossible to observe due to reactivity, short lifetime, or method of preparation. Among these are high temperature atoms or molecules that exist only in extreme conditions such as stellar atmospheres or in arcs and radicals or fragments with such high reactivity that production of quantities sufficient for normal analyses is difficult or impossible. Even when high temperature species are observed, analysis of their spectra is difficult due to their population distribution in various electronic, vibrational and rotational states. This is often the case in laboratory generation of such fragments via flash photolysis, plasmas, arcs, etc. Employment of the matrix-isolation technique can circumvent many of these difficulties.

Norman and Porter 1 and Whittle et al. 2 independently proposed the technique of matrix-isolation spectroscopy in 1954. Since that time a vast literature has evolved which includes excellent reviews by Chadwick, 3 Downs and Peake, 4 and Jacox, 5 as well as books by Meyer, 6 Ozin and Moskovits, 7 and more recently by Barnes et al. 8 Matrix-isolated samples are prepared by codeposition of "guest radical fragments,


1







2

reactive molecules, or high temperature species in inert, transparent solids (matrices) at cryogenic temperatures.

A basic assumption in matrix isolation is that there is little or no interaction between the matrix and the isolated species, and essentially gas-like species is obtained. Though this assumption is valid as a first approximation, matrix interactions do occur which cause shifts in the energies of spectra. The sample can also be trapped in multiple sites in the crystalline lattice (examples are substitutional or interstitial sites) which lead to band broadening and multiples due to differing energies of the various sites. These site effects can often be removed by warming the matrix to allow controlled diffusion and thus permit the sample species to settle into the more stable sites resulting in more simplified spectra. Lattice modes and JahnTeller distortions due to matrix-sample interactions have also been observed. Mowery et al.9 have observed Jahn-Teller distortions in the magnetic circular dichroism spectra of matrix isolated magnesium atoms.

The matrix material can be any non-reactive gas which can be rigidly solidified. Many substances have been used for this purpose including N2, CH4, CO, the freons, SF6, CS2, and 02, as well as large organic molecules. More often, though, the solid rare gases Ne, Ar, Kr and Xe are used as these elements are relatively chemically inert and transparent over a broad spectrum, and provide a rather broad selection of melting points and atomic sizes. Neon is expected to perturb a guest specimen least, as it is least polarizable. However, neon requires temperatures below 10 K and has a lower trapping efficiency compared to other rare gases. It is usually easier to trap samples in Ar, and it is most widely used as a host gas. Krypton and Xe are found to perturb trapped







3

molecules to a greater extent but provide a broader temperature range for matrix isolation than do Ne and Ar.

Temperatures sufficiently low to condense matrix gases can be

achieved by mechanical closed-cycle refrigerators utilizing Joule-Thompson expansion of high pressure hydrogen or helium gas. Alternatively physical refrigerants such as liquified nitrogen, hydrogen or helium may be employed. Liquid nitrogen (boiling point 77.4 K) is plentiful and inexpensive. Although it is adequate for the more stable matrix materials, much lower temperatures are necessary for the better rare gas matrices. Liquid H2 (boiling point 20.4 K) has been used, but it entails a fire hazard in addition to the normal dangers associated with cryogenic fluids. The most useful refrigerant is liquid He (boiling point 4.2 K). It is also the only refrigerant useful for condensation of Ne which melts at 24 K and allows solid state diffusion at less than half that temperature (which is a general rule by which the temperature required for controlled diffusion may be apprixmated). Closed-cycle refrigerators which can attain temperatures near the liquid He boiling point are available commercially.

The main advantages of the refrigerators include convenience, low operating cost after the initial investment, and relief of the requirement to replenish cryogenic fluids during experiments.

A deposition substrate is chosen that is transparent in the spectral range of interest. Some common materials are CaF2, quartz and sapphire for the visible and ultraviolet regions; CsI, NaCl and KBr for the infrared region; and some nonconducting material such as sapphire for microwave spectroscopy. A polished crystal plate is mounted on a cold block (often copper) which makes good thermal contact with the







4

cryogenic fluid reservoir or the expansion chamber of the Joule-Thompson refrigerator.

Several methods have been employed for generation of guest species. The simplest method involves a gas phase sample mixed with the matrix gas at the desired guest-host ratio in an external container and subsequent introduction of the mixture into the vacuum chamber, condensing the mixture onto the cooled substrate. This, of course, is not useful in the study of high temperature samples. The vaporization of nonvolatile substances has been approached in different ways. One interesting method recently employed by Bondybey and Englishio involves irradiation of the sample with a powerful laser, thus introducing the necessary energy for vaporization. A more widely employed method is vaporization from a high temperature Knudsen cell in a vacuum furnace. These cells can be constructed of carbon, or a refractory metal such as Ta, W or Mo. In some cases it is necessary to prevent cell degradation by including a liner, usually of C, BN or A1203. The cells are heated either by induction or resistance to temperatures as high as 2900 K. The vapor effuses in a crude molecular beam through a small orifice in the cell and is introduced simultaneously with isolant gas onto the target. Molar ratios of matrix gas to sample used are anywhere from 100:1 to 10,000:1. Another technique used to introduce gas samples involves passing the sample through a heated inlet tube, the resulting thermolysis products then being matrix isolated. Unstable species and fragments are generated by exposing a parent molecule to photolysis with ultraviolet lamps, electron bombardment, gamma rays, or plasmas, again cocondensing the products with matrix gas.






5


Matrix isolation spectroscopy displays a number of advantages over gas phase studies. Conventional spectrometers can be used to study samples unavailable under standard conditions due to high reactivity or instability. A big advantage in the study of high temperature species is that all trapped molecules are in theIr ground electronic and vibrational states. This enhances sensitivity as the originating level of spectroscopic transitions is always the ground state. With matrix temnperatures below 20 K the thermal energy is below 15 cm-1 "Hot" bands are thus eliminated. Very long depositions are possible allowing buildup of low abundance species and species of low absorption coefficient. Controlled diffusion experiments allow matrix reactions to form new species or clusters. It is also sometimes possible to observe species with preferential orientation in matrices as is done in single crystal work. More detailed discussions of the matrix isolation technique can be found in recent reviews 4,6,11-21 and references therein.

A large array of spectroscopic techniques have been employed in matrix work, including infrared and Raman, electron spin resonance, Mb5ssbauer, and visible and ultraviolet absorption and emission. More recently magnetic circular dichroism of matrix isolated samples was introduced by Douglas et al.22 at the University of East Anglia. Magnetic circular dichroism has its roots in the work of Michael Faraday when in 1845 he first observed the phenomenon now known as the Faraday effect. When plane polarized light traverses any transparent medium collinearly with an externally applied magnetic field, the plane of polarization is rotated.

Linearly polarized light consists of equal components of right circularly polarized (RCP) and left circularly polarized (LCP) light.






6


If in some medium the indices of refraction for RCP and LCP light are different, optical rotation occurs. If the absorption coefficients for some transition differ for RCP and LCP light, circular dichroism (CD) is said to be present.

There are two sources for these inequality. Natural optical:

activity arises in a molecule of low symmetry or unit cell in the case of crystals, and its wavelength dependence is known as optical rotary dispersion (ORD). The quantum mechanical theory ascribes the ORD of a molecule to electronic transitions which have parallel or antiparallel electric and magnetic transition moments. 23 The second source of inquality is application of an external magnetic field, H, in the direction of light propagation. In this magnetic optical rotation, the right- and left-handed circular motions around fl do not interact equivalently with

the medium, and the absorption coefficients of RCP and LCP light in regions of absorption differ in the presence of the magnetic field. This gives rise to magnetic circular dichroism (MCD) which is the differential absorbance of RCP and LCP light. The increase in information content

offered by polarization-dependent selection rules for optical absorptions makes MCD a very powerful complement to conventional spectroscopic methods in electronic structure determination.

Magnetic circular dichroism can provide information on the ground states of atoms and molecules although the prime utility of MCD has been in extracting excited state information otherwise unavailable. Excited state magnetic moments and g values are attainable as well as spin-orbit coupling constants and information on static and dynamic Jahn-Teller interactions. 24

The same information is available from Zeeman spectra if all Zeeman components are resolved. This resolution is often difficult, requiring







7

very high magnetic fields. The advantage of MCD is that it is a signed technique (i.e., positive and negative bands are seen) not requiring high magnetic fields. In this work a 5500 Gauss field was employed. Overlapping, thus unresolved absorptions may be resolved in MCD if the MCD for one of the overlapping components is much larger due to MCD selection rules or if the transitions have opposite MCD signs. An example is the differentiation of tyrosine and tryptophan where absorptions overlap. 25'26 Typical limits of detectability are 10-3 OD for absorption and 10-5 OD for MCD. The expected situation of a detectable MCD with an absorption too weak for observation sometimes arises as in the example of spin-forbidden transitions of octahedral and tetrahedral Co(II) species 27'28 and for impurities in optical grade CaF2 plates cooled to 13 K, vide infra. The fact that some MCD transitions display a temperature dependence (to be discussed in detail later) makes application of the matrix isolation technique to MCD very appealing.

Matrix isolated samples studied by MCD since the work by Douglas etal. 22 are few. Atomic species Hg; 29gru IatmMGCandS;3

Ta; 31 diatomic Cl2 32 and 02; 29 Xe halides; 33 diatomic oxides of Ti, Zr, Hf, V, Nb and Ta; 34and benzene,3 0S04 36and acrolein 37are included.

The present research involves matrix isolated samples of atoms and/or clusters of Pb, Cu, Ag and Au. Primary reasons for studying these systems are the roles of small clusters in fundamental processes such as heterogeneous catalysis, 38 nucleation 39 and photography. 40 Another compelling reason to study the electronic spectra of these systems is the increasing number of optically pumped lasers being developed involving them. 41Also of basic interest is the observation that matrix isolated Cu, Ag and Au atoms, all involving 2p _~- 2S transitions,






8


reveal a triplet structure. while the corresponding gas phase spectra display only doublet structure. The on-going controversy as to the origin of the matrix triplet structure can be resolved by a moment analysis of the MCD spectra as is shown later.















CHAPTER II

THEORY OF MAGNETIC CIRCULAR DICHROISM


The theoretical treatment and pertinent equations as developed by Stephens 42-44 and Buckingham and Stephens 45 are outlined. The treatment has gained wide acceptance and is employed in this work. It is convenient to begin with consideration of circularly polarized light. Various suggestions have arisen recently to explain the anomalous structure of the 'P 2S transitions of matrix isolated atoms. The quantum mechanical equations necessary for evaluation of these theories are also developed here.

Unpolarized light consists of an electric field vector, t, and a magnetic field vector, H, both with random direction and both varying sinusoidal'ly with the direction of propagation. In plane polarized light
A
the vectors E and H vary in magnitude but are constant in direction. If now plane polarized light traverses a transparent birefringent medium where the speed of light depends upon the direction of light polarization, then part of the beam will be delayed with respect to the other, depending upon the thickness of the medium and the difference in the indices of refraction. If the plane-polarized beam enters the birefringent medium oriented at 45' relative to two perpendicular axes of
A
different refractive index, components of the projection of the E and H vectors of equal magnitude will be phase shifted relative to each other. If this phase shift is equal to the light wavelength, X, the emergent beam is restored to plane polarization. If, however, the phase shift

9







10

is not equal to X, the resultant electromagnetic vectors will trace helical paths upon emergence. If the helix is traced clockwise while looking toward the source, the beam is said to be right polarized. The emergent light is elliptically polarized. If the phase shift is just equal to an integral multiple of X/4, the light is said to be circularly polarized as the cross section of the helix will be a circle. The t and H vectors in circularly polarized light vary in direction but are constant in magnitude, while in elliptically polarized light both direction and magnitude vary.

If in some medium left and right circularly polarized light are propagated with differing absorption, the medium exhibits circular dichroism. In the presence of a magnetic field along the direction of propagation of circularly polarized light, all matter exhibits circular dichroism, known as magnetic circular dichroism (MCD).


Basic Equations


Consider a light beam traversing a sample with ground state A and excited states J and K in the presence of a magnetic field H in the direction of light propagation. The Poynting vector can be used to express the light intensity at a point z:



I+(z) C n+(E 0)- exp -2-6--- (1)


1 0 exp -29c+


where c = hv is the photon energy, k+ represents the absorption coefficients for left (-) and right (+) circularly polarized light, h is Planck's constant divided by 27r, c is the speed of light, E' is the







11

electric field at z = 0, n are the complex refractive indices for LCP and RCP light, and I' is the incident light intensity. Differentiating and solving for k+,


h -(2)(z)
+ nIE+(z)l2 6z (2)



where

o -2Ek~z1


The quantity -Iz.
Tz expresses the energy absorbed per unit time at z which is dependent upon the number of sample species, Na, the photon energy E, and the transition probability Pa j.


6 Na Pa-j (z) E (4)
Sz
a,j


If electric quadrupole and magnetic dipole interactions are ignored and we consider only electric dipole transitions, the above probabilities can be related to the electric dipole transition matrix elements through time-dependent perturbation theory if the assumption that the effective Hamiltonian H, is a sum of independent components is embraced.


Ho = Ho + H (5)

where Ho is the Hamiltonian for the system with no light, and H0' is the
0
Hamiltonian for the perturbation due to a radiation field. The subscripts denote the absence of an extPrnal magnetic field.


Pa-j (z) = a,2-IE(z)j2I2(Eja-E) (6)
-IF j(6)







12
where are electric dipole transition moments, E. = E.-Ea, a is j a Ej a ,(
a Lorentz effective field correction factor which relates the electric field due to the light at the absorption center to the macroscopic electric field, m is the transition dipole moment operator for LCP and RCP transitions, and 6 is the Kronecker operator which arises because transition lifetimes are neglected. The absorption coefficients can now be expressed as


k+ 2n2c2 Naj12j(Eja-E) (7)
a,j


This equation can be expressed in terms of absorbance


exp (-2kz) -A I(z) 10-ecz (8)
expM c 1 : o = 8



where A = absorbance, e' is the molar extinction coefficient, and c is now the concentration of absorbing species. The absorbance is


A = e cz =Na )cz (9)
a,jN mIj>Ka(Eja


where


No T2C21lo oe
250 cn+ (10)


No is Avogadro's number, Na/N is the relative population of ground state a, and e is the Naperian log base. This equation assumes Beer's law is obeyed and does not apply for the non-linear effects present for intense light. The difference in LCP and RCP light dichroism, LA, is expressed


AA = A. A+ (11)







13

Substituting into equation (9)


AA Y+ Ij N j2 l 6(c. a-)cz (12)
F_ a,j Nj


The summations are over all sublevels a and j of the ground and excited states, and the integrals are electric dipole transition moments. Equation (12) is general and applies to natural CD as seen in optically active media. Magnetic circular dichroism is not a perturbation of natural optical activity but rather arises from different polarizabilities which are zero when no external magnetic field is present. The natural and magnetically induced phenomena are additive. In a system possessing no natural optical activity in a region absent of a magnetic field,AA = 0 and IjK = ll2. In this case the zero-field absorption, ZFA, is defined as

A0 0 = I A
A A+ A- : (Ao + A) (13)


At this point it is convenient to introduce the rigid shift model

in order to modify these results to reflect the actual bandwidths in the presence of a magnetic field. The rigid shift model requires adherence to the Born-Oppenheimer approximation in the ground and excited states. Separation of electronic wave functions under the Born-Oppenheimer approximation into nuclear and electronic terms may be denoted by a product of wave functions


IA~a> = YA (r,R)Xa(R) 1 to dA (14)
a

lJxj> = YJX (rR)xj(R) X = 1 to dd (15)



where p indicates electronic wavefunctions with dependence upon the







14

instantaneous nuclear configuration, Xa and Xj are vibrational wavefunctions dependent upon the particular electronic configuration and the nuclear coordinates R, r is the electronic coordinate, and dA and dj are the degeneracies of states A and J. The eigenfunction equations are
HoA a> = 6aIA a> (16)



HolJxj> = ejlJXj>


The Franck-Condon approximation that most electronic transitions occur at R near the equilibrium nuclear separation R, is employed to simplify the transition matrix elements.


= 0 (17)


The lower case letters refer to the vibrational wavefurctions, and the superscript indicates evaluation of electronic matrix elements at R = Ro. If the transition is only weakly allowed, the Franck-Condon approximation is inadequate, and further account of the R dependence of electronic wavefunction must be taken. Equation (12) now becomes


A 0
E AA
2] (18)
L A a,X


LI Naja



Assuming y to be constant for all vibronic transitions and integrating over the whole band yields

f dE = y7 L ~ ~
I2CZ (19)







15

Equation (18) now can be written

0
= yD0f(E)cz (20)


where


Do Im. J >0>2
dcA ,X a X


_2dA I
o 2 + JI21 (21)


and


f(s) = Na (Eja -E:) (22)
a,j

with


f( )dE = 1

The ZFA as given in equation (20) has a shape originating in the ground and excited state vibrational wavefunctions and an integrated intensity dependent only upon the electronic wavefunctions, evaluated at equilibrium position Ro. The line shape is temperature dependent due to the Boltzmann term Na/N, but the integrated intensity is temperature independent.

If a magnetic field is applied, the absorption coefficients, k+, display a field dependence. The eigenfunction and eigenvalues of the system's Hamiltonian must now be obtained as explicit functions of the magnetic field. This is only feasible in an analytical form when perturbation theory may be employed to treat field-dependent terms.







16

The assumption here is that the magnetic field energy is small compared to the zero field separation of the states. A perturbation term is added to the system Hamiltonian [equation (5)]:


H = Ho + H' (23)


Considering only electronic contributions to the first order magnetic field perturbation,


HI 2 zi + 2siH (24)



where the summation runs over all electrons, i of mass m and charge e. The magnitude of the magnetic field is given by H and is directed along the z axis. The projection of the angular momentum of the i th electron onto the z axis is given by kz. and the projection of the spin onto the
i
z axis is given by szi. Summation over all electrons yields


H' = -PHEB(Lz + 2Sz)H (25)


where is the electronic Bohr magneton (= 4.6681x1O-cm'/gauss), and Iz is the electronic magnetic moment along z. The corresponding orbital and spin angular momenta along z are given by Lz and Sz. Equation (25) ignores interaction with the nuclei since nuclear magnetons are at least three orders of magnitude smaller than electronic magnetons. Within the ground and excited state manifolds, H' is diagonal in the Franck-Condon approximation:


= -H'aaa, (26)


= -0H6XX,6 ji,






17

if the electronic wavefunctions at Ro are chosen to diagonalize pz. So, if mixing of electronic states by H' is neglected the wavefunctions in the magnetic field are IAaa> and JXj> with energies

EA a = a H (27)

E'jXj = H


In this first approximation the Zeeman splitting of each vibronic state is independent of vibrational level and is identical to the pure electronic splitting at Ro. As a better approximation Stephens includes intermixing of different electronic states, K, with states A and J:


H
J j>' = IJj>- IK > K (28)
K k K jk
K
(K/J)

H
JA a>' = Aa> [K >
a' = K k K ak
K
(KfA)

where the primes denote wavefunctions in a magnetic field. The intervals Eak and Ejk are large compared to Zeeman energies and again use the Franck-Condon approximation. If it is assumed that the vibrational levels k contributing to the sums in equation (28) are such that the intervals are approximated as

E = W 0 (29)
ak A k

0 0
S= W0 Wk
where the values are energies for the various states, then

where the WO values are energies for the various states, then







18

equation (28) becomes



IJi >1 = Ij j> xI j~> xx K /J W ~WK
K 3


Aa>' = JAa> >1 IK a> 0H
a K K/A K W 0- W0
K A K


To first order in H there is no energy contribution from these wavefunction perturbations. The transition moments become


1 (31)



+ (KJ '0
0- w0




K K A WK W A)jaIi


E
0 + ']H Ground state Zeeman splitting also leads to population changes.


N' A a exp(-E'A a /kT)

N exp(-cE'a /kT) (2


exp(-F-a/kT) exp(
0H/kT) Z exp(-ca /kT) exp(0 H/kT) d,a


At large T where Zeeman energies are small relative to kT,



exp(
0H/kT) %' 1 + H(3






19

so that

N'A a exp(- /kT) 1
oH
a a 1 + 0. z a (34)
N I exp(-ca/kT) dA kT
a

N'A ( +
oH
1 + k
N kT

Since under Zeeman splittings the center of gravity is retained,

H = 0 (35)


This shows that the fractional change of population in IAaa> is not dependent upon vibrational level and is the same as obtained in a purely electronic system at R0.

With these effects of the magnetic field on transition energies and

moments and on ground state populations, the circularly polarized absorption MCD can be derived.

From equation (9),

N'
A + N A Caj > 1 6
= --i-- 'K6('JjA a e) cz (36)

E ~ ~ < I __A >oHA
o ,j


1 allz Aa> H
= 7 .---(1 +0 \
a,X A kT

2
x o + 'H f '0 (C) cz

Here,


fa) j
126(J [' o]H c) (37)
a aj N ja






20

is a line shape function identical to f(c) but shifted rigidly along the E axis by the At J1 Zeeman shift

-[o O]H


If a band is broad, the Zeeman shift is a very small perturbation, and the shifted lineshape function can be expressed in terms of the unshifted lineshape function by a Taylor expansion:


fV (E) = f(E) + [ 0]H f() (38)


if terms above the first order in H are dropped. Substituting into equation (36) and collecting terms of zero and first order in H is obtained


,A+ AA A
+ Y I
[ (39)


] Df
a z CS

+ I -Re[
o1*]f(c)

oX
+ 1 m J >02f( ))cz
X A kT < m+X>Icz


From the manner in which the circularly polarized light absorption is modified by the magnetic field and the above considerations, an expression for the MCD is written as


LA = A A+ = y(Ai + O + ]f(c) )Hcz (40)







21

where


A [I
012 o12] (41)
A 2,X

X [o 0]


80 2 Re K [
O0 o]
A a,A K J

x + [
o
W Wj K VA
K J K
o
o< mIK>] x z
Wo W0
K A


Co [l
012 02]0
A a~,X

The effect of an applied magnetic field on the circularly polarized absorption is shown in equation (36). Each of the component transitions A JX contributes absorption identical in shape to that at zero field. The intensity is modified by the ground state Zeeman effect and intermixing of the zern-field electronic wavefunctions,and the energy of the band is changed by the Zeeman shift. Each of these changes is the same as that obtained with nuclei located at Ro configuration. The term "rigid shift" is used because the absorptions shift in an applied magnetic field without change in shape.

The total MCD and CP absorption is the sum of contributions from all Zeeman components Aa JX* On inspection equations (39) and (41) show that at high temperature and large band width the intensity and energy changes of the Zeeman components of the transition due to the magnetic field contribute additively and linearly in H to the change in







22


MCD and CP absorption. Other contributions to Zeeman splitting or intensity changes due to either ground state redistribution or intermixing of electronic states are physically separable through their dependence on E or T. The relative magnitudes of the A, B and C terms determine the overall MCD. The A terms require either ground or excited state degeneracy; B terms can exist under any condition of ground and excited state degeneracy; and C terms require the ground state A to be degenerate. Calculation of these terms can be used to predict the sign and shape of the MCDrj dispersion. The maximum contribution to the MCD of the three terms are related as


A1:B:C0lu ZZ Z(42) F*AWkT


where 1' is the bandwidth of an electroniic transition, AW is the order of magnitude of an electronic energy gap, k is the Boltzmann constant, Z is the Zeeman energy, and T is the temperature.

The experimental form of A, B, and C0 terms is illustrated in

Figure 2.1. The A, terms occur if there is a degeneracy in either the ground or excited state. In positively signed A1 terms, the high energy lobe is of positive sign and the low energy lobe of negative sign. In A, terms the two lobes are always oppositely signed and of equal magnitude. Since the two lobes are separated by a small Zeeman splitting of the degenerate level involved, the derivative-shaped term arises. The intensity of allowed A1 terms is influenced by the sharpness of the absorption band as indicated by the 3f/3E factor. The A1 term size is also affected by the difference in magnetic moments for the ground and excited states. If these are equal, no A1 term is observed.






















Figure 2.1. The appearance of terms predicted by MCD theory.

(a) The zero field absorption and MCD for a transition with a positive A, term. The positive lobe lies at higher energy.

(b) A Bo term may be positive or negative, the
maximum coincident with the absorption
maximum.

(c) A negative Co term at two temperatures,
Thigh and Tjow, may be positive or negative with its maximum coincident with the absorption maximum.















(---Thigh







25

Terms of B0 are a general property of all MCD spectra and arise from magnetic field mixing of neighboring electronic states with either the ground or excited state of a transition. These terms have the same shape as the absorption spectrum and can be positively or negatively signed. It is generally difficult to calculate B0 terms as knowledge of multiplicities and energies of all states near A and J must be known.

Only when the ground state is degenerate can C. terms exist.

Population changes induced by magnetic field splitting are demonstrated by the inverse temperature dependence of the parametric equation. The C, terms may have either sign and have the same shape as the absorption band.


Magnetic Circular Dichroism Calculation for Atoms


Photons possess well-defined values of angular momentum and are absorbed or emitted by systems which are characterized by well-defined values of their angular momenta.46 The selection rules characterizing transitions involving photons with angular momenta must account for the conservation of angular momentum.

Consider transitions occurring in an isolated atom with total angular momentum J. The degeneracy of the state is given by 2J+1, corresponding to the number of distinct eigenvalues m J, The field around an atom is spherically symmetric so there is no preferential directionality of the angular momentum. Under an external magnetic field this degeneracy is lifted via the space quantization imposed by the direction of the magnetic field. Figure 2.2 shows the Zeeman splitting of the eigenstates of atoms with total angular momentum J = 0 and J = 1 in a magnetic field and the possible transitions.




























Figure 2.2. Polarized transition to an atomic P state and
magnetic field splittings. Transition a is right circularly polarized, transition c is left circularly polarized, and transition b is polarized parallel to the magnetic field.





27










m


0 0 0
H 0 H O






28

It is possible to calculate the probability for the absorption of a photon for a transition from states a to j. The probability is proportional to the square of the transition dipole moment matrix element

along the direction of the photon polarization,





where is the unit vector determining light polarization and $ i. is the electric dipole moment. Selection rules for the transitions in Figure 2.2 can be derived considering the three possible light polarizations (x, y and z) in equation (43) and the properties of the wavefunctions as described by spherical harmonics. 4

First, considering polarization in the z direction (parallel to the applied magnetic field), equation (43) is non-zero if AJ = 1 and AM3 0. Since this is the direction of light propagation in the MCD experiment, it is not available. The two possible polarizations u x and
4-x
u for light propagating along z are more conveniently examined in the linear combinations u x1u y corresponding to circular polarizations. The sum is RCP and the difference LGP. For RCP equation (43) is non-zero if Am j = m 31-m 31 = -1 and the non-zero LCP values arise for Am j = +1. For both cases AJ = 1. Transition b in Figure 2.2 is thus not observed. Transition a corresponds to RCP and c to LCP. In this case circularly polarized light corresponds to electric dipole photons of J = 1. and m= -1 for RCP and +1 for LCP. Similar selection rules apply for any system due to conservation of angular momentum.

To illustrate how the various magnetic field splittings give rise

to the MCD A, and C0 terms, Figure 2.3 shows MCD transitions with either ground or excited state degenerate. Two cases are shown with only the





























Figure 2.3. Magnetic field splitting in
degenerate ground and excited
states illustrating the origin
of Ao and Co terms.







ML ML
+1
/G+
1P ... 71S...
T T


-S is "//

0 P -0-0 ... 0 o0o







AA AA Z AA
I N


AA A

A Term: Temp. C Term: Temp.
Independent Dependent







31

ground state split. At low temperature the population of the lowest magnetic sublevel is much greater than that of the higher sublevels, and the observed MCD will be similar to that at the right of the figure. Increasing the temperature depopulates the lowest state thus decreasing the MCD at the higher energy transition and increasing the MCD transition at lower energy (dashed curve higher T). If all the sublevels are equally populated the MCD will be as in the middle spectrum. The populations are governed by Boltzmann statistics. A C0 term such as the middle spectrum appears to have the A, term derivative shape and is sometimes referred to as a "pseudo A term."

Consider the transition of an electron in a free atom of 'S ground state to a 2 P excited state. If the atom is placed in an octahedral field, the representation of these states must be determined in group 0 h*


Full Rotation Group 0 h





Note that for group 0 the F representations are r, = A1, r 2 = A 2, F3 = E, r= F11 r5 =T, F6 = El F 7 E"V, and F. = U'.7Tuin0hte2
4 Ths in0 te2
state representation is Al, and the 2P state representation is Ti. Using Koster's table of compatibility for orbital angular momentum, 47 the representations for 0 and 1 are D. and D1, respectively. Both states are spin -I, and again from Koster's tables D1 '2 -P 6 (E'). The spin-orbit coupling effect in these states can be determined taking cross products of the spin and orbital representations. For 2S,


F 1 0 I 6 = F6 = E







32

and for 2p,


r 4 6 = + F8 = El + U'


The energies of the spin-orbit states can now be found. The 2T, states are

<2TjtTIHS.0.12 TJtT> (44)


where 2Ti is the representation of the excited state, t is either E' or U T is the component of t (for E', T= a' or ', and for U', =K', ', W' or v'), and Hs.o. represents the spin-orbital Hamiltonian. Following Griffith,48 equation (44) can be rewritten in terms of a reduced matrix element R.


<2TtjIHs 2TJt> = Qd, TI) x R



The Q values are taken from Griffith. For t E' the energy is

<2T1Hs.0. 112T,>, and for t = U' the energy is -<2T1Hs.o. II2T,>. If


k <2T1 02T1>


the splitting in the excited state becomes

E'
2T, -2k

U'-k




There is also a Zeeman splitting to consider for each state in a magnetic field. It is convenient to choose a basis set which yields a






33

matrix where all off-diagonal terms are zero for the Zeeman Hamiltonian. This facilitates determination of Zeeman energies. Such a basis set is obtained by reference to Griffith's book.49 The spin orbit basis can be expressed in the form lm ms>.
I
Ground state: 2A E',> = 10 > (45)
1 2
Excited States: 2T E'o'> = 0 + > 2 1 >
1
2T E'B'> 1 + > 0 >


2T U'K> = Ii +->
_1
2T U'X'> = ~ > + 1 >

1 1
TU ' > = -5 -1 + > + | 0 >

2T U'v'> = -1 >


The wavefunctions in equation (45) are found by taking cross products of orbital and spin representations in group Oh such as F4F6 FT eE for
1
the excited state, so the appropriate table (A20 for TjE) is consulted in Griffith's book.49
The Zeeman operator is Lz+2Sz,so matrix elements of the form

<2TiE'c'ILz+2Sz12TiEal> (46)


are calculated. The results of applying these operators are


Szms> = msIms> if 4 = 1

L zmZ> = mzlmz> if t = 1







34

Since there is some reduction in angular momentum if the system is not a free atom, integrals of the form

<1ILzIl> =


rather than 1. To facilitate approximation of MCD and absorption intensities, the p can be approximated as 1. The integrals in equation (46) for the excited state are

<2TIE'V'|Lz+2Sz12TiE'a'> = + (p-i) (47)


<2 TiE'B' Lz+2Sz12TE'B'> -- (p-1)


<2 TiU'V' Lz+2Sz2 TU'K'> = -p + 1

<2T1U'' Lz+2Sz12TU'v'> = -p I1


<2TiU'X' Lz+2SzI2T1U'X'> = 3 + 3(-I)


<2TiU'p' Lz+2Sz 2T U'p'> = (-i) and for the ground state

< 2AiE''Lz+2Sz 2AiE''> = +1 (48)

< 2AE'B' Lz+2Sz 2A E'B'> = -1


The energy level diagram in Figure 2.4 can now be drawn.

In order to predict MCD and absorption spectra it is also necessary to calculate electric dipole transition moment integrals. In the octahedral point group the dipole moment operator transforms as the T, symmetry representation. The integrals are of the form in equation (48)




























Figure 2.4. Splittings in free atom 2S and 'P
orbitals for:

(a) an octahedral site

(b) spin orbit interaction

(c) Zeeman splitting.






36











a


E/1/








-2/
K
j0


a
2 S - - - A FREE ~ ~ ~ OhX' EEA
ATOM ORI SPLITTIN
(uit Uf G)/






37

= [-1]a+at V at ct b


where a and c are the ground and excited states, g represents the mTi dipole moment operator, and V is a vector coupling coefficient found in Griffith's tables.49 These integrals are calculated over the wavefunctions given in equations (45) above. In order to have a non-zero matrix element the spin must be the same in each wavefunction in the integral. The m operators of interest for MCD transitions are step-up and stepdown operators m+ and m_. It is possible to consider all possible transitions from the ground state to each excited state function and determine which are + and a-.

I > 22 0,
<2AIE'' mI2TiE'a'> = T0+ > -<2AlOH m_2T1L- > (50)

1
<2A OIm_2T 0>


= [-1]TIV A T, Ti)
0 0

= 0




v'2
1
= 1- T 1A m -2


_12 1 ~
= -1]Ti VA TT1 0 1 1
VI 1 -T
-3=77 1

'2 < 2A 1m_ T11 T >

2 ~ ~ ~ +1 -/2 I T 1

<2AiE'WI'm TIE'B'> = T







38

<2AE'8' mI2TE'B'> = 0

< 2Al E'am- TU'K'> +1 < + A |m T lT >
V 0
<2A1E' ml2TU'K'> = 0 <2A1E'cY' m2TU'v'> = 0

< A E' m+ Ti U'V'> = + <2Al m+T 12T,>


<2AIE'~ mT M12TU''> = 0 T 1

<2AzE'' mTzU'A'> = + -< AI m_T 2T >

<2AE'a' m+12T1U'p'> + 2<2All m+T1 2Ti>

<2 AE'8' mI2TU'p'> = 0

Note that the bra is the ground state and the ket the excited state. The energy level diagram in Figure 2.4 can be redrawn including the sign of light polarity of each transition and the square of transition probabilities as in Figure 2.5. It is interesting to note that the polarity of a transition will be u+ for the m+ step-up operator and a step-down operator.

Having determined the integrals above and the transition probabilities, the Co and Do expressions in equations (21) and (41) can now be evaluated. Recall equation (41):


Co = -d []2
12]


and equation (21):

D 1 I J
0 d dA a,X































Figure 2.5. The state splittings and allowed transitions for
an atom in an octahedral field showing the effect
of spin orbit and Zeeman splitting.







40















E
/2/,V/'3I-1I1/2> -1,/3Io- 1/2>



1//2

/







K2A E- 0- 11 A,0 1/2>

2/9fx 1/Fvf31 1/9F 2>+/Ii/

OhSIN / -ORBIT







41

Now, for the transition from 2AlE' to 2TlE':


c 1 11<2A El 'Jm_12T EV> 2 <2A El 'JL +2S Z12 AlEW> (51)
0 2 1 1 1 1 z

1<2 AlEVIm+12TP 1>1 2 < 2 AlEla'ILZ+2S Z12 AEl(xl>]

1 [2 Ffl 2 2 Fn2($H)]
2 9 9

2. rn 2
9


Do L ,2 F2
2 9 7 (52)


Thus,


Co/Do = +2 (53)


For the transition from 2 AE' to 2 TIU': I [1< 2 A Elall M_12 T U11<1>12<2 AlEVIL +2SZI 2 A Elal> (54) CO 2 1 1 z 1

I < 2 AlEls' JM+12 TlU'v'>l 2 <2AlEWILZ +2SZ12AElsl> + 1<'-AIE' JM_12 Ti UIX1>1 2 <2 AlEWILZ +2S Z12 AlEl '>

1<'AE'a' JM+12 TlUl p 1>11<2 AEYIL z +2S Z12 AIE'a'>


c '. j_ [I 2 (M) I V (-M) + 1 V (-M) 1- W (M) I
0 2 3 3 9 9

2 -2
M


and


D ff'2 + ffi2] = 2 (55)
0 3 9







42


Thus,


C0/o= -1 (56)


The predicted MCD and absorption transitions of 2P 2S in an octahedral field can be diagrammed as in Figure 2.6.


Effect of Reduced Site Symmetry


Another possible cause of MCD C terms which must be explored arises through a reduction of the octahedral site symmetry described above. The most likely reduced symmetries are due to displacement of the copper from the center of the surrounding octahedral rare gas atoms resulting in a D3 symmetry and a change in the distance of the "axial" octahedral distance resulting in a D4 symmetry. Either of these distorted matrix sites yields a further splitting in the 2TIU'(2P3/2) octahedral state. The predicted MCD term signs can then be compared with experimental results. The distorted symmetry approach can be illustrated by considering a static trigonal distortion (D3) and calculation of the eigenvalues, eigenfunctions and C0/V0 values. The 3x3 energy matrix for the D3* case is given as5052


12E,I, > 12E,I, > 12A2,0, > (57)
A + X s 0 0



0 A X
7- f E

0 X-A-Fi



where A denotes the trigonal field distortion parameter. The matrix consists of lxi (2EE" state) and 2x2 (the 2A2E' and 2EE' states)






























Figure 2.6. The predicted MCD and absorption patterns for
the 2P 2S transition in an octahedral field.





44















1/9 m ABS 2/9m 2








+2






MCD






45

submatrices. The eigenvalues and eigenfunctions in the m,,ms basis are:

A+X
2EE"{ ,}> = 12E,1, > with el 2

12A2E'{ '}> = C2 12E,1,+ -> C312A2,0,'2 >


and

2E E'{ ,}> = C212E,1, > + C3s2A2,0, >


with

2 2XA + A2 (X+A) + 3
2,3 4 4

where


C2 C42 + -,'- 2

C3c 42
C2C=
(2/2 + C42

C A X for i = 1,2,3
2 -i


In the limit where the trigonal field distortion parameter, A, is zero, the functions reduce to those obtained above for octahedral symmetry.

Using these eigenfunctions and Piepho's tables53 for the D3* group, the Co and Do terms may be calculated from the standard formulae53 for randomly distributed anisotropic centers:
i
1 2~iii~
Co = 1 { +12 + 2P+om0 _I f m +1 + m_1 + meo 2}
Do 3d







46

where d is the ground state degeneracy; 8 is the Bohr magneton; and +, 0, mo, m+, and m_ represent integrals between states (for example, the 2A2E' + 2AE' transition):

1
-+ = -1 <2AE'a ,i(L++2S+)12AE'B'>
v/2

PO = <2AzE'a' -iB(Lz+2Sz)2AE'a'>


mo = <2AiE'a' m 2A2E'c'> m+ = <2AE'a' m+ 2A2E'B'> ._ = <2AIE'' m_2 A2E'a'> In the case of trigonal distortion


Co (C2mE) + 2C2C3mAmE
6 3

S (C2mE)2 + (C3mA2)2
Do=
6

where E = and mA2 = are reduced matrix elements for the electric dipole transition moment. Possible eigenvalues and values of Co/Do could be estimated if a value for the spin orbit constant, X, was chosen (see, for example, the discussion of the method of moments for Cu in an Ar matrix) and the trigonal field distortion parameter, A, was varied (vide infra). A similar treatment can be followed for a D4 distorted octahedral site.

The Adiabatic Model

From the band moment analysis it was shown that both spin orbit interaction and noncubic vibrational modes of the matrix cage are







47

important to the spectroscopic appearance of the 2P -- 'S transition in matrix isolated Cu, Ag and Au. Three components of the 2P state are apparent in the experimental MCD and absorption spectra. The observed C terms are positive, negative, and negative (with the exception of Cu isolated in Xe) as energy increases. The band separations in all three metals are much larger than the spin orbit splitting deduced from band moments. Because of similarities of these systems to the much studied 54 F center case (although in several F center crystals the triplet is not resolved 55 ), it is possible to compare these results with theoretical calculations done within the framework of the adiabatic approximation. In particular the effect of the two degenerate components of the noncubic e mode on the MCD C terms and band separations are considered.

Because of the noncubic vibrational activity which mixes the firstorder spin orbit split states, it is not possible to describe the component states by a simple JM i (or other) description. The first-order states become coupled by vibronic interaction. Any calculation of the sign and magnitude of the C terms of the transitions to each component of the 2p state must account for this coupling. To do this Moran's 56 adiabatic model of vibronic and spin orbit interactions in an excited 2T1(2P) state is examined. Moran considered the effect of simultaneous first-order spin orbit coupling and vibronic interaction via the tetragonal e mode only. The effect of the t mode will be to modify the existing band shapes but not the splitting pattern (i.e., the triplet of bands). 56 In the Moran model the wavefunctions are


= ~~TiUI{! ,> + Ci 2T UI{>}:> + C 12TEI1 :}> (58)


where i runs from 1 to 3 and the coefficients are given by







48


= ( 2 + 32 + 1 (59)
3pli P li


P3i C
C2i ps



C. ---C
P~i

li p i 3i


and


pli = -v/[z(X/2 + z ci) t2] (60)


P2i = [t(X/2 z Ei) tz]


p i = 26z + t(X + c.)


In equation (60) t and z represent the degenerate pair of lattice coordinate displacements belonging to the e vibration, and X is the experimentally determined 2p spin orbit coupling constant. Using these expressions and the Wigner-Eckart theorem for the transition probabilities in the 0* group as in previous cases, an expression for Co/Do can be found.


i 2(3C 2 C 2i 2C3i2 2v'2C2iC 3i)
C0/V0i 23o 2 21i (61)
(30 + C2 2 + 2C 2 + 2/C Ci ) (3C11 2+ C2i 3 1 3i


The influence of the e mode components on the spectral splitting pattern and MCD sign behavior can be determined by diagonalization of Moran's 3x3 interaction varying the t and z displacements while keeping X constant (and equal to the experimental value). For the case of large spin orbit coupling, the effective Hamiltonian is given by:






49

H = Ho + XL.S + Hel + HL


where


Hel =-y( L.L)S Y3(3Lz2 L.L)Z y3',7(Lx2 Ly)T


Setting s = -y1S, t = -yT, and z = -y3Z the excited state Hamiltonian matrix is


3/2- '/2 > 3/2 1/2 > 12 /

E+ X + z + A t -/2t


t E + X z + s
-42t -V-z E X + s


The Kramers degeneracy is apparent from the above matrix. Two criteria are imposed on the diagonalization: 1) that the interband spacings match the experimental ones at low temperature, and 2) that the signs of the C0 terms match the observed ones. Further discussion of the evaluation of results under this model is presented with the spectra and analyses of the individual cases studied.

Band Moment Analysis


Returning to the subject of dispersion calculations [see equations

(13) through (22)], the most drastic assumption made there is that the Born-Oppenheimer approximation holds for ground and excited electronic states. In the Jahn-Teller theorem all spatial-symmetry-derived electronic degeneracy is broken by at least some nuclear displacement, and therefore the potential surfaces emanating from a degenerate state do not remain exactly degenerate. The Born-Oppenheimer approximation then







50

breaks down, and it is no longer possible to associate a vibronic state with only one electronic state. The calculation of zero field absorption and MCD becomes very much more difficult. The diagonality of H' in equation (26) is not maintained, and the magnetic field perturbation scrambles different vibronic levels of the same electronic state. The calculation of the Zeeman effect within an electronic state is then dependent on the details of the Jahn-Teller phenomenon. In such situations where the absorption and MCD are evaluated with difficulty, it is of interest to look at alternative methods of analysis that enable more complex models to be treated without dispersion calculations. The method of moments is such an approach. The method of moments was developed by Henry et al. 54in work formulating the theoretical framework for the relationship between the moments of F center bands and the changes in these moments with applied perturbations to the interactions (spin orbit, vibronic) within an excited 'T, state. Osborne and Stephens 55 modified this work for treatment of F centers in LiF. The moment analysis performed here follows closely the equations as developed by Osborne and Stephens. The various absorption and MCD moments are obtained from


n A (v-v O) "dv (62)





where A and LA are the optical absorbance and differential absorbance, A LA R3 respectively, and the average frequency of the zero field absorption is given by


f Adv
0fAd







51

The ratio of the nth MCD moment to the zeroth absorption moment is given by:

( C n PB B
An + B + (63)



where PB is the Bohr magneton; B is the magnetic field strength; and the MCD parameters An, Bn, C n, and Do are defined as in Osborne and Stephens.55 The MCD parameters of interest in this study are:


Co/Do = Bo/D0 = 0 (64)

AI/D = 2gorb (65)

C1/0 = -2,/3 (66)

A3/D0 = 6gorb[ + { + + 2(A/3)2}] (67)

C3/Do = -2A[ + { + + 2(A/3)2}] (68)

D2/Do = + ( + ) + 2(A/3)2 (69)


where gorb = <2T ;M L=ILz12T1;ML=1>, A is the spin orbit splitting of the 2Ti excited state (positive when the M' component lies highest), and ( + ) represent the contributions to the band width (second absorption moment) from the cubic and noncubic lattice modes, respectively, and include linear and quadratic coupling or anharmonicity. The moments were calculated from digitized data by application of Simpson's rule for numerical integration by the CBM 8032 microcomputer. Further discussion of application of the moment analysis to Cu and Au results appears in the respective sections.















CHAPTER III

EXPERIMENTAL


Sample Preparation


Detailed descriptions of the furnace assembly as well as the absorption and MCD apparatus are outlined. Figure 3.1a shows the furnace assembly used in these experiments.

Metal beams were generated from a resistively heated Knudsen cell which is shown in Figure 3.1b. The cell was constructed of 0.15-0.020 in wall thickness, 0.25 in outer diameter tantalum tubing. The cell was closed on either end by solid tantalum endcaps and strapped to two water cooled copper electrodes. One of the electrodes was electrically isolated from the furnace while the other was in contact with the furnace assembly. Alternating current as high as 300 amp, 60 Hz could be run through the cell allowing temperatures in excess of 2300'C. The furnace was cooled by water flowing through 0.25 in diameter copper tubing soldered onto the exterior surface of the furnace. A Leeds and Northrup optical pyrometer was used to measure the cell's surface temperature by sighting the cell via a magnetic shutter on the furnace. The magnetic shutter prevented metallic depositions on the surface of the viewing window and associated inaccuracies in temperature measurement.

In order to prevent heating of the cryogenic window by heat radiating from the Knudsen cell, a water cooled shield was installed in the furnace. It is worth noting that this radiation shield could be removed when generating vapors at temperatures below 1000% allowing a greater 52





























Figure 3.1. (a) Diagram of the furnace assembly.

(b) Diagram of Knudsen cell used for metal vaporization.







54









(a)



KNUDSEN CELL







PYROMETER VIEWPORT WATER COOLED HEAT SHIELD
I t
FURNACE O- RING MOUNTING
COOLING GROOVE FLANGE
WATER




(b)

To CELL



-l-- oo" ----0 .75"
To END CAP O0.375" ,

Ta STRAP I--70"----







55

flux of metal toward the cryostat. The heat shield is a 0.25 in diameter copper tube spiral between two 0.125 in copper plates. A 0.125 in diameter hole drilled at the center of the shield also served to collimate the metal beam. This provided the added benefit of reducing the thermal load of hot metal striking parts of the cryostat other than the cold window. Careful alignment of the Knudsen cell effusion orifice with the heat shield hole was necessary to ensure that the metal beam was directed properly toward the cold window.

The metal beam was codeposited with an inert gas onto one face of the cold CaF2 plate. The temperature of the cold window was maintained by an Air Products Displex R Model CS 202 closed-cycle helium refrigerator capable of cooling to approximately 13 K. The temperature of the window was set using an Air Products APD-B temperature controller and monitored by use of a chromel-Au, 0.07% Fe thermocouple mounted near the middle of the copper window frame and referenced to liquid nitrogen. The stability of the temperature controller was rated at better than 2 K at the set point but at times performed to better than 1 K from 13 K to 40 K. In later experiments a Lakeshore Cryotronics Model DRC-80C Digital Cryogenic Thermometer/Controller utilizing silicon diode detectors with a rated stability of 0.1 K was employed. The detectors were mounted in holes drilled into the copper window frame. The window frame assembly was made from high purity oxygen-free copper and had a -1,"-28 thread stud for mounting to the second stage of the refrigerator. The entire piece was machined from a single block of copper and indium gaskets smeared with Cry-con R grease were used between all metal junctions on the copper window assembly to ensure good thermal contact.

The cold window was a one inch diameter, 4 mm thick CaF2 plate. It proved necessary to use an ultraviolet grade window since the lower







56

purity infrared grade window originally used contained an impurity which had a temperature dependent MCD band overlapping the copper and silver atomic bands. The corresponding impurity absorption band was too weak for observation. The cold window temperature was controlled by a 10 W variable duty cycle heater in a feedback loop with a second thermocouple.

The isolant gas inlet nozzle was constructed from a 16 gauge Yale stainless steel needle silver soldered to a 0.25 in diameter stainless steel tube which was in turn silversoldered through a hole in the wall of the short brass tube which joined the furnace to a gate valve. A 0.25 in vacuum quick connect joined the nozzle assembly to a 0.25 in diameter stainless steel tube which was joined to a glass inert manifold. Inert gas was bled into the vacuum system through a Nupro extra fine metering valve. The gas manifold was pumped by a 3 in Varian M2 diffusion pump charged with 100 mL of Dow corning 704 silicone oil. Inert gas flow rate was monitored using a standard mercury side-arm manometer.

The Air Products Displex is a two-stage, closed-cycle He refrigerator which makes use of the Joule-Thompson effect as compressed gas at 300 psi is expanded with a pressure drop in excess of 200 psi. The cryotip unit (shown in Figure 3.2) is constructed of stainless steel, with the exception of the final expansion chamber. A nickel-plated copper shroud attached to the first stage, maintained at 40-60 K acts as a heat shield fo-r the lower stage and copper window holder. Two openings cut 180' apart in the shield allow matrix deposition and, as the whole unit is rotatable, also allow alignment with two ports in the external vacuum housing. The second expansion stage terminates in a copper cold tip which accepts the window frame threaded stud. The cryostat assembly is connected to the furnace assembly by a second gate valve and can be






























Figure 3.2. Detail of furnace-cryostat assembly used in
matrix isolation experiments.





58




ELECTRICAL .

He GAS
-- ROTATABLE
JOINT
THERMOCOUPLE I and MATRIX
HEATING WIRES GAS
INLET
EXPANDER
Ist STAGE VACUUM
2nd STAGE I PUMPS


COPPER COLD TIP TARGET WINDOWRADIATION SHIELD

GATE VALVES
FURNACE
ASSEMBLY







59

removed and rolled along rails into an electromagnet for MCD measurements. When joined to the furnace assembly, the entire assembly is pumped by a 2 in oil diffusion pump backed by a mechanical forepump and equipped with a liquid N2 cold trap. Pressures below 1x106 ,torr are attainable. Pressures are monitored by thermocouple and ionization gauges connected to a Granville-Phillips Series 270 gauge controller.


Spectroscopic Apparatus


A diagram of the optics used in absorption measurements is shown in Figure 3.3. The apparatus operates as a "pseudo double beam" spectrometer. The reference beam was not passed through a matched cell but rather reflected around the cryostat onto the photomultiplier tube. Light scattering from matrices caused some drift in the baseline at higher energy wavelengths, but the Xe lamp emission spectrum was quite effectively nulled over most of the spectral range. Spectra were obtainable over the range of 8500 to 2200 A. The lamp was a 300 W Eimac R xenon lamp made by Varian Associates and operated at a pressure of 115 atm and had a built-in parabolic reflector and a sapphire window yielding an intense, well-collimated beam. The lamp was enclosed in a small hood for removal of the ozone generated during operation. The lamp housing was attached to a Spex 0.75 m Ozerny-Turner Spectrometer with a grating blazed at (1200 lines/mm) 3000 A. and an f-number of 6.8. The slits were set for a spectral band pass of less than 6 A.

The beam emerging from the monochromator slit was spread by a 3 in quartz lens (f/3) and then passed through two sets of slots on a spinning wheel. The wheel was driven by a hysteresis-synchronous motor at 1800 rpm. Five outer and nine inner slots in the wheel gave chopping



























Figure 3.3. Optics for absorption experiment.










M errors
_____ _____ ____M 2

Mo nochrometer XeSureMl
Jp PM *
______ _____ __ 9 Sar ple1
Chopper Electronics



Sample
CryoStat
*M1



Sl it







62

frequencies of 150 Hz and 270 Hz. These frequencies were selected to minimize ac powerline pick-up since they were not integral multiples of ac line frequency, 60 Hz.

The beam chopped at 270 Hz traversed the matrix and arrived at the photocathode of an EMI 9683 QB photomultiplier tube. The beam chopped at 150 Hz was reflected around the cryostat by two Edmund Scientific aluminized front-surface mirrors and onto the same photomultiplier tube. An iris allowed attenuation of the reference beam.

The chopping wheel assembly was equipped with two light emitting

diodes and two phototransistors located on opposite sides of the chopping wheel from the LEDs so the signals from the phototransistors were used as reference signals for the two chopping frequencies. The LEDs were powered by a 15 V supply. Both signals were amplifed by RCA 3140 operational amplifiers. A diagram of the absorption electronics is shown in Figure 3.4.

The current output of the photomultiplier tube (%10-7 amp) was converted to a voltage by a 15 ko resistor connected to the ground. Part of the signal was amplified by a factor of 100 using an Analog Devices 52 k low-drift operational amplifier and sent to an oscilloscope for monitoring the wave form during the experiment. The rest of the signal was introduced in parallel to two lock-in amplifiers--an Ithaco Dynatrac 391A Lock-in Amplifier and an Ithaco Model 353 Phase-lock Amplifier. The Ithaco 353 was locked to the 150 Hz reference frequency from the chopper, and its output was proportional to the lamp emission spectrum, monochromator dispersion characteristics, and the photomultiplier tube spectral response. The Ithaco 391A was locked to the 270 Hz reference, and its output was proportional to the absorption spectrum of the matrix

























Figure 3.4. Schematic of absorption experiment.












'- F ------ PM TUBE
MONOCHROMATOR --- PM TUE
SAMPLE IM ] PEDANCE
TA'EADAPTOR
WIDE HAND
____ AMP
STEPPI NG
MOTOR DRIVE
I GA IN LOG AMP

_LOCK-IN B LOCK-IN A LEVEL
( IK- SHIFTER REF
AMP
INTERFACE IMP.
ADAPT. SAM.



MA/B. ERROR
SSWITCHAMP


CHART RECORDER PM HV
VOLT, SUPPLY
DISKSCOPE
DRIVESCP







65

in addition to the factors mentioned above. Both outputs were connected to a Log Amplifier which took the log of each signal and performed an analog subtraction to give an output in the form of the ratio of sample to reference intensities. This output was connected in parallel to a Soltec 1242 series two channel strip-chart recorder and the computer interface.

All MCD experiments were performed with the same light source and monochromator. The light source and monochromator were rolled on casehardened steel rails into position for the MCD experiment without disturbing the chopper assembly (which is permanently fixed on the optical bench to aid easy alignment). Figure 3.5 shows the optics for the MCD experiment. The beam emerging from the monochromator is focused by the same lens onto a Glan-Thomson prism oriented at an angle of 450 to the modulation axis of a Morvue Electronic Systems PEM-3R photoelastic modulator.

With the cryostat situated in the light path and in the field of an Alpha Model 4600 electromagnet, a single beam MCD experiment was performed. The magnet had a 0.75 in hole collinear with the magnetic field in each of the adjustable-gap pole faces.

The MCD electronics are illustrated in Figure 3.6. The signal

from the photomultiplier tube was fed into an Ithaco Model 391 Lock-in Amplifier which was locked to the 50 kHz photoelastic modulator frequency. The amplifier's bipolar output was level shifted to yield only positive voltages which were suitable inputs for the computer interface and chart recorder. The output from the Analog Devices 52 k operational amplifier was fed into an error amplifier-feedback circuit. The feedback circuit employs a Bertan PMT-20, option 3


























Figure 3.5. Optics for MCD experiment.














Magnet

Monochrometer Xe Source
______---'PM Linear Polarizer
Photoelastic Modulator Sample MCD
Electronics


























Figure 3.6. Schematic of MCD experiment.













Lt2 MTB
MONOCHROMATORJ I
____________SAMPLEQ I MPEDANCE E
AD)AP TOF
N IDE BAND A x100
STEPPINMG________ ___MOTOR DRIVE
)R I :VEVOLTAGE N MH

R EG ULATORre





dc
LEVEL
SHIFTER




TO



DISK MCD







70

programmable high voltage power supply. The gain of the photomultiplier tube is controlled in an inverse relation to the dc output by the feedback circuit. The photomultiplier tube signal consists of a relatively small 50 kHz ac component riding on a larger dc component that is proportional to both the xenon lamp emission spectrum and the absorption of the sample. Background effects in the MCD spectrum are automatically corrected for by maintaining a constant dc level with the feedback circuit. In later absorption experiments the feedback circuit was also used. This was facilitated by passing the lock-in output through another operational amplifier used as an impedance adaptor and then into the feedback circuit.

Both the absorption and MCD experiments were controlled by a

Commodore CBM 8032 computer. The monochromator was driven by computer pulsing a SL0-SYNR Model MOGI-FD-301 stepper motor attached to the wavelength scan control. The motor was stepped 200 times per revolution. This allowed 0.25 A steps of the monochromator.

The data was digitized using a Datel Systems, Inc., ADC-EK8B

analog-to-digital converter of 8 bit resolution. The operating program allowed data collection at 1, 0.5 or 0.25 A intervals. After collecting a spectral scan, the data was stored on a floppy disk. The data collection and storage program is listed in the appendix.

The computer was also used to control the photoelastic modulator

which was synchronized with the wavelength drive. The modulator's wavelength of quarter-wave retardation depended upon the amplitude of stress applied to the quartz crystal which was linearly dependent upon the modulator's input voltage. The program calculated the correct voltage for the running wavelength after each 0.25 A step, and this output was







71

sent to the modulator through a Date] Systems, Inc., mode] DAC-IC8BC digital-to-analog converter. This device was also used when another program read data from a floppy disk for output to the chart recorder.

For matrix preparation a tantalum cell was filled with metal powder as fully as possible, but some of the fine powder invariably blew out of the effusion orifice into the vacuum chamber during pump down and degassing of the furnace.

The Knudsen cell was mounted, in the tantalum straps, onto the

water-cooled electrodes making certain the effusion hole of the cell was aligned with the collimating hole in the heat shield and the CaFz target window. This alignment could be checked by sighting the tantalum cell, when mounted in the furnace, through a window on the outer vacuum shroud of the cryostat into the furnace.

The furnace was rough pumped for a number of minutes (as long as 30 min for very finely divided powders) using a bypass line which isolated the diffusion pump and liquid nitrogen trap. The pumping was continued until a pressure below 200 pi was shown on the thermocouple gauge at which time the gate valve to the diffusion pump was gradually opened and the bypass closed. The system was then pumped to below 2x10-5 torr with the diffusion pump.

The tantalum cell was then gradually heated to the deposition

temperature while keeping the pressure below 2-4x10-5 torr. With rapid heating, material blew out of the cell as a powder and resulted in weakly absorbing matrices. The outgassing process took as long as 2 hr in some cases. During this procedure the DisplexR was rotated so the CaF2 window was shielded from the Knudsen cell to prevent metallic film deposition on the target.







72

The CaF2 window had to be cleaned with acetone and ethanol (to

prevent residue from evaporated acetone) between subsequent experiments in order to obtain transparent matrices. Simply allowing heating of the window and loss of the matrix and then recoiling for another deposition resulted in cloudy matrices.

After the outgassing process, the DisplexR compressor was started and the CaF2 window cooled to deposition temperature. In order to achieve transparent matrices, the window was cooled to 14 K for argon work and 20 K for krypton and xenon work. Depositions below these temperatures resulted in cloudy matrices. After cooling to the proper temperature, the window was rotated into deposition position and a flow rate of rare gas was set to about 1-3 mmol/hr with the needle valve. Gas was deposited for 10 min before heating the Knudsen cell to deposition temperature. Initial estimates of the correct tantalum cell temperature were set as the temperature required to maintain a vapor pressure of the sample at ulxlO-3 torr. Depositions continued anywhere from 5 to 120 min. At intervals during the deposition, the CaF2 window was rotated through 90' so the absorption could be measured. Deposition continued until the bands of interest showed absorption of 0.5 to 0.95 OD. Deposition temperatures for each metal can be found in the respective sections discussing results.

Both MCD and absorption spectra were obtained on a matrix at 13 K and 20 K. If temperature dependence was exhibited, three scans were stored at each temperature from 13 K to the highest allowed by the matrix gas in 1 K intervals. For argon spectra were observed to 25 K, for krypton to 28 K, and for xenon to 32 K.






73

The monochromator was calibrated with He-Ne and argon ion lasers and scans were always run from low to high energy to prevent stepping motor assembly backlash and maximum photomultiplier tube sensitivity.

All MCD spectra were run at 0.55 Tesla as determined by an

F. W. Bell Model 640 Gaussmeter. Zero-field circular dichroism spectra were recorded to determine the zero-field line in the MCD. With the magnet power turned off, a residual field of %60 Gauss was measured. A test of the linear dependency of the MCD signal upon the magnetic field yielded the expected result (see Figure 3.7).

The MCD apparatus was calibrated for each matrix using aqueous

solutions of [Co(en)3]Cl-(d-tartrate) made such that the absorbance at 4690 A was near 1 OD as measured by a Cary 17 Spectrometer. The procedure was similar to that of Tacon,57 and the circular dichroism of the standard solution was measured at 4930 A. McCaffery and Mason58 measured the ratio of AA max/A max = 0.0225. The same solution was used to calibrate the absorption experiment. Digitized absorption data were calibrated in optical density units through use of the relation


KA
A I A


where KA is the number of OD units per digital data unit, C is the concentration of the standard solution in optical density, and IA is the sample absorption band intensity in arbitrary units as stored on the floppy disk. Calibration of digitized MCD data was done through the relation


KM (C)(0.0225) S s
IM Sc

































Figure 3.7. Magnetic field dependence of an MCD
signal.






75







O/






z0






U)D
z
c>- ozLd >
2












.. .I II
0 I 2 3 4 5 6

MAGNETIC FIELD STRENGTH (KILOGAUSS)







76

where K M is the number of OD units per digital data unit, C is the concentration of the standard solution in optical density, IM is the sample MCD band intensity in arbitrary units as stored on the floppy disk, and Ss and Sc are the lock-in amplifier sensitivities for the sample and standard solution scans, respectively.

The signature of bands was cross checked by measuring the MCD of a solution of K3[Fe(CN)61 which was known to have a positive MCD band centered at 4250 A. A check for any depolarization due to the matrix was run by noting any difference in the intensity of the CD spectrum of the spectrum of the standard solution placed before and after the matrix. No measurable depolarization was noted in most experiments.















CHAPTER IV

RESULTS


Figure 4.1 shows .the expected splitting pattern of the isolated 'S and 2p states under the various perturbations one might expect in the matrix environment. The left section of the diagram shows the effect on the free atom states, first when placed in an octahedral field. The state labels refer to the 0 h group. Operating on the basis set with the spin orbit Hamiltonian causes a splitting in the 2 T, state. This splitting still cannot account for the observed triplet structure (vide infra) of group lb metals in rare gas matrices. If, then, the effect of a distorted octahedral field (possible trigonal D3 and tetragonal D4 reduced symmetries) is considered, a further splitting is induced. Diagonalization of the trigonal field distortion matrix in equation (57) holding the spin orbit coupling constant at the value obtained through a moment analysis and varying the trigonal distortion parameter, A, results in eigenvalues which can be plotted as functions of A. The top panel in Figure 4.2 shows that there are no values of A (positive or negative) which reproduce the observed peak positions given below (for the Cu/Ar experiment). Even more decisive in excluding the trigonal site model are the predicted C0/V0 values (see the bottom panel in Figure 4.2). The value of C0/V0 for the lowest energy peak (2A2E') is positive only for A < -180 cm'1, but in this range the value for the highest energy peak ('EE') is also positive, contrary to experiment (refer, for example, to Figure 4.3). For no values of the trigonal


77































Figure 4.1. The splittings induced in free atom 2S and 2P
states. Note dependence upon the order of
application of various interactions in calculation.






79









E M


Mp 2 p





E M: Atom 0h S.O* J.T S.O. 0h Atom































Figure 4.2. The eigenvalues and Co/Do values predicted
for a reduction of pure Oh site symmetry
to D3.





81





52


E 2 EE
u







4

2 2 EE


i0 2 A2E
2EB


-4 ___-500 0 500

A (c m)







82

distortion is the observed combination of C0/V0 signs found. Values for

CI were also calculated as a function of X. For no value of X in the range of 10 cm-1 to 500 cm'1 (for Cu in Ar) was the experimental MCD sign combination found. Thus it can be unambiguously concluded on the basis of energy level separations and MCD sign combinations that the trigonally distorted site model is not a valid explanation of the observed Cu/Ar absorption and MCD results. This conclusion prompted calculations outlined as splittings shown in the right half of Figure 4.1. This scheme is pursued here,

Included after a somewhat detailed treatment of Cu isolated in Ar is included a concise presentation of results for Cu in Kr (including a spectrum of the region from 340 nm to 210 nm) and Cu in Xe as well as the results of a moment analysis for Au isolated in Ar, Kr and Xe. Following these are the atomic spectra obtained for matrix isolated silver and, finally, the results obtained for Pb and Pb2 isolated in Kr.


Copper in Argon


The absorption spectra of copper atoms isolated in rare gas matrices have been studied extensively6'50'51',5961 and the triplet of bands at 310 nm attributed to a number of different causes. These include spin

orbit splitting and static axial site distortion, multiple matrix sites, 6exciplex formation between the metal and a single matrix atom, long-range metal-metal interactions, 60and a Jahn-Teller effect resulting from matrix cage atom vibrations interacting with the excited state of the metal. 61While this work was in progress, Armstrong et al. 52and Grinter et al. reported on the magnetic circular dichroism of Cu atoms in Ne, Ar, Kr and Xe matrices and concluded that their results were







83

consistent with either the distorted site mode] or the Jahn-Teller interpretation. One of the primary results of this work is that the triplet of bands in matrix isolated Cu, Ag and Au arise from simultaneous spin orbit and Jahn-Teller interactions in the 'P excited state. The simple nature of the 2S ground state (no orbital moment) allows a detailed interpretation of the experimental moments of absorption and MCD bands. Excited state spin orbit coupling constants, orbital g factors, and contributions to the band width from cubic and noncubic matrix lattice modes can be deduced.

Copper metal (Spex) was vaporized at 1100'C and codeposited with matrix gas onto a CaF2 window typically cooled to 15 K for Ar and Kr and 20 K for Xe. Typical absorption and MCD spectra are shown in Figure 4.3. The spectra agree well with those reported by Grinter et al. 62 Spectra were run in triplicate at 1 K intervals from 13 K to 25 K. Each spectrum was digitized every 1.0 A, transferred to a Commodore CBM 8032, and recorded on a floppy disk for storage and calculations. Figure 4.4 shows the temperature dependence of the Cu MCD band. A detailed moment analysis was performed on the Cu C term. Figure 4.5 shows a plot of 0/
0 vs. l/T from which the parameters 0 /Bo and

CIOwere obtained (cf. Chapter II). The slope of the plot yields

C0/P0 = -8(3)x10-', and the intercept yields A./B. = 4(3)x10-'. Both these quantities are expected to be zero based on a consideration of only first order intrastate (2P) interactions. There are several second order spin orbit interactions which might account for the nonzero values. They include excited Cu atom states mixed into either the Cu 'P or 2 states or excited matrix atom states mixed (via orbital overlap) with the 'P or 'S states. It will be shown below that the former interaction































Figure 4.3. Absorption and MCD spectra observed for Cu
isolated in Ar.







85








0.6


Cu/Ar




0.4







0.2







0


0.5




0 --------0.5




28 I 0I I 1/n
280 300 320 X/nm






























Figure 4.4. Temperature dependence of the Cu atom Co term
in an Ar matrix. The intensity decreases with
increased temperature.





87









Cu/Ar AA










290 300 310 320
































Figure 4.5. Experimental plot of o/
o vs. 1/T for
Cu atoms in an Ar matrix.




Full Text
Figure 2.1. The appearance of terms predicted by MCD theory.
(a) The zero field absorption and MCD for a
transition with a positive Ai term. The
positive lobe lies at higher energy.
(b) A 80 term may be positive or negative, the
maximum coincident with the absorption
maximum.
(c) A negative C0 term at two temperatures,
T^igh and Tgow, may be positive or negative
with its maximum coincident with the
absorption maximum.


79
E" M
Id
u
Gl
OJ
M
V
/ \ 2 p
/
/ \ /
' /
\ -T i
' 11
'u
\
\ E'
w
M
Ifld
^j
/
/
/
H
2S
\
\ 2a
\ A'i E
h -
h -
H
2S
E' 2A1 /
Atom S.O. J.T. S.O. Atom


186
38520 PRINTS,A$CHR$(13)
38530 CLOSEl
38540 0PEN2,6
38550 INFUT#2,G$,R$,P$,S$,T$
38560 CL0SE2
38570 PRINT:PRINT
38580 PRINT"gain ";G$
38590 PRINT"reset ";R$
38600 PRINT"panel ";P$
38610 PRlNT"set point ";S$
38620 PRINT"teinper£ture ";T$
38625 PRINT:PRINT:PRINT:PRINT
38630 RETURN
38700 END


112
modes. That information can be obtained from the Monte Carlo integration
67
done by Cho. Cho calculates the expected band shapes using Moran's
model without limiting the degree of freedom of the lattice vibration to
ax and e modes. Because it is known from the moment analysis that in
matrix isolated Cu there is little or no coupling with the totally sym
metric mode, the experimental band shape can be compared to the results
67
of Cho's Figure 11, which is reproduced here as Figure 4.13. It is
clear that neither the e mode nor the t2 mode can be active alone. The
best agreement is reached when both the parameters which describe the
coupling with the e and t2 modes are roughly equal and furthermore of
the same order of magnitude as A.
63
Kasai and McLeod point out in their ESR study of Cu isolated in
Ar that each observed ESR signal is extremely sharp and isotropic
indicating little deviation, if any, of symmetry of the trapping site
from octahedral. They also indicate the variance of their results with
those of optical matrix isolation studies which reveal the triplet band
structure. The conclusion drawn in this research reconciles the finding
by Kasai and McLeod of an octahedral ground state symmetry with the
optical triplet as the triplet is shown to arise from an excited state
dynamical distortion resulting from nontotally symmetric cage vibrations.
The spin orbit interaction in the excited state also contributes to the
triplet structure. For Cu in Ar the matrix value for the spin orbit
coupling constant is 25% lower than the gas phase value. As mentioned
above this reduction cannot be accounted for by the intrastate vibronic
coupling. It is more likely a consequence of the interaction (i.e.,
overlap) of the Cu 4p orbital with the 3p Ar atom orbital. Ammeter and
68
Schlosnagle have done a careful and in-depth study of the ESR spectra


109


Figure 4.10. Plot of calculated C0 term as a function of
lattice motion z holding lattice motion t = 115
and A constant (from moment plots) for Cu
atoms in an Ar matrix. Eigenvalues increase
energy from Ei to E2 to E3.


Figure 4.36. Absorption and MOD for Pb in Kr between
220 nm and 280 nm.


Figure 4.21. Absorption and MCD bands for Cu in a Xe matrix.


CHAPTER IV
RESULTS
Figure 4.1 shows the expected splitting pattern of the isolated 2S
and 2P states under the various perturbations one might expect in the
matrix environment. The left section of the diagram shows the effect
on the free atom states, first when placed in an octahedral field. The
state labels refer to the 0^ group. Operating on the basis set with the
spin orbit Hamiltonian causes a splitting in the 2TX state. This split
ting still cannot account for the observed triplet structure (vide infra)
of group lb metals in rare gas matrices. If, then, the effect of a
distorted octahedral field (possible trigonal D3 and tetragonal D4
reduced symmetries) is considered, a further splitting is induced.
Diagonalization of the trigonal field distortion matrix in equation (57)
holding the spin orbit coupling constant at the value obtained through a
moment analysis and varying the trigonal distortion parameter, A,
results in eigenvalues which can be plotted as functions of A. The top
panel in Figure 4.2 shows that there are no values of A (positive or
negative) which reproduce the observed peak positions given below (for
the Cu/Ar experiment). Even more decisive in excluding the trigonal
site model are the predicted C0/V0 values (see the bottom panel in
Figure 4.2). The value of Ca/V0 for the lowest energy peak (2A2E') is
positive only for A < -180 cm-1, but in this range the value for the
highest energy peak (2EE') is also positive, contrary to experiment
(refer, for example, to Figure 4.3). For no values of the trigonal
77


Figure 4.8. Experimental plot of 2/0 vs. T for Cu atoms
in an Ar matrix.


41
Now, for the transition from 2A1E to 2T1E':
C0 = [|<2A1E,31|m_|2TiE'a,>|2<2AlEl3l|Lz+2Sz|2A1E'3
- |<2A1E'a'|m+|2T1E,3,>|2<2A1E,al| Lz+2Sz | 2AX E V>]
= j [| m2(-3H) | m2(3H)]
= |m2
vo = J'J2 = |m2
Thus,
C0/VQ = +2
For the transition from 2A1E to 2T1U1:
C0 = [|<2AiE'al |m_|2T1UV>|2<2A1E,a|Lz+2Sz|2A1E'a
- |<2A1E'3i|m+|2TlU'vl>|2<2A1E,3'|Lz+2Sz|2A1E'3'>
+ |<2A1E,3'|m_|2TlU,A,>|2<2A1E,3|Lz+2Sz|2A1E'3,>
- |<2A1E,al|m+|2T1Ulul>|2<2A1E'a'ILZ+2SZ|2A:E'a'>
C0 = | m2(3H) y m2(-3H) + } m2(-3H) | m2(3H)]
2 2
g m
and
Vc = = |ni2
> (51)
(52)
(53)
'> (54)
(55)


20
is a line shape function identical to f(c) but shifted rigidly along the
e axis by the A -* J, Zeeman shift
a a.
-[
]H
A1 z1 A a1 z1 a J
If a band is broad, the Zeeman shift is a very small perturbation, and
the shifted lineshape function can be expressed in terms of the unshifted
lineshape function by a Taylor expansion:
f'ca'E> f + WxlKzlV MV W <38>
if terms above the first order in H are dropped. Substituting into
equation (36) and collecting terms of zero and first order in H is
obtained
e
A
Ei+ 37 l0l2t -
a,A A
]
a|Hz' of J 9e
If
+ Zj Re[
'*]f(e)
4\ dn L a1 ' X a'A J v
a, A A
If
a,A aA

a1 z 1 a
kT
l0|2f(e)^CZ
(39)
From the manner in which the circularly polarized light absorption is
modified by the magnetic field and the above considerations, an expres
sion for the MCD is written as
= A_ A+
3f(e)
3e
r co'
So + kT
\
f(e)
/
AA
3Hcz (40)


87
290
300
310
320 X(nm)


APPENDIX B
PROGRAMS
The program used to control absorption and MOD measurements follows.
OO
The program is a modification of the version utilized by Powell for
use on the Commodore 8032 computer. Modifications were made by
Dr. Martin Vala, Dr. Jean-Claude Rivoal, Dr. Joseph Baiardo, and the
author.
The second program is used to calculate absorption and MCD moments.
The program is an expansion of the Simpson's rule integration algorithm
written by Dr. Marek Kreglewski.
182


56
purity infrared grade window originally used contained an impurity which
had a temperature dependent MOD band overlapping the copper and silver
atomic bands. The corresponding impurity absorption band was too weak
for observation. The cold window temperature was controlled by a 10 W
variable duty cycle heater in a feedback loop with a second thermocouple
The isolant gas inlet nozzle was constructed from a 16 gauge Yale
stainless steel needle silver soldered to a 0.25 in diameter stainless
steel tube which was in turn silver soldered through a hole in the wall
of the short brass tube which joined the furnace to a gate valve. A
0.25 in vacuum quick connect joined the nozzle assembly to a 0.25 in
diameter stainless steel tube which was joined to a glass inert manifold
Inert gas was bled into the vacuum system through a Nupro extra fine
metering valve. The gas manifold was pumped by a 3 in Vari an M2 diffu
sion pump charged with 100 mL of Dow corning 704 silicone oil. Inert
gas flow rate was monitored using a standard mercury side-arm manometer.
The Air Products Displex is a two-stage, closed-cycle He refrigera
tor which makes use of the Joule-Thompson effect as compressed gas at
300 psi is expanded with a pressure drop in excess of 200 psi. The cry-
otip unit (shown in Figure 3.2) is constructed of stainless steel, with
the exception of the final expansion chamber. A nickel-plated copper
shroud attached to the first stage, maintained at 40-60 K acts as a heat
shield for the lower stage and copper window holder. Two openinqs cut
180 apart in the shield allow matrix deposition and, as the whole unit
is rotatable, also allow alignment with two ports in the external vacuum
housing. The second expansion stage terminates in a copper cold tip
which accepts the window frame threaded stud. The cryostat assembly is
connected to the furnace assembly by a second gate valve and can be


MAGNETIC FIELD STRENGTH (KILOGAUSS)
MCD INTENSITY
(ARBITRARY UNITS)
o
i
OJ
-f*
cn
-^1
cn
CD
O


Figure 4.12. Composite drawing showing the effect of varying
contributions from lattice vibrational modes.


10
is not equal to A, the resultant electromagnetic vectors will trace
helical paths upon emergence. If the helix is traced clockwise while
looking toward the source, the beam is said to be right polarized. The
emergent light is elliptically polarized. If the phase shift is just
equal to an integral multiple of X/4, the light is said to be circularly
polarized as the cross section of the helix will be a circle. The and
H vectors in circularly polarized light vary in direction but are con
stant in magnitude, while in elliptically polarized light both direc
tion and magnitude vary.
If in some medium left and right circularly polarized light are
propagated with differing absorption, the medium exhibits circular
dichroism. In the presence of a magnetic field along the direction of
propagation of circularly polarized light, all matter exhibits circular
dichroism, known as magnetic circular dichroism (MCD).
Basic Equations
Consider a light beam traversing a sample with ground state A and
excited states J and K in the presence of a magnetic field H in the
direction of light propagation. The Poynting vector can be used to
express the light intensity at a point z:
2ek+z
I(z) = ^ n(E0)2 exp
o -2ekz
= J exP "T
(1)
where e = hv is the photon energy, k+ represents the absorption coeffi
cients for left (-) and right (+) circularly polarized light, h is
Planck's constant divided by 2tt, c is the speed of light, E is the


Page
Figure 3.4 Schematic of absorption experiment. 64
Figure 3.5 Optics for MCD experiment. 67
Figure 3.6 Schematic of MCD experiment. 69
Figure 3.7 Magnetic field dependence of an MCD signal. 75
Figure 4.1 The splittings induced in free atom 2S and 2P 79
states. Note dependence upon the order of applica
tion of various interaction in calculation.
Figure 4.2 The eigenvalues and C0/V0 values predicted for a 81
reduction of pure 0^ site symmetry to D3.
Figure 4.3 Absorption and MCD spectra observed for Cu isolated 85
in Ar.
Figure 4.4 Temperature dependence of the Cu atom C0 term in an 87
Ar matrix. The intensity decreases with increased
temperature.
Figure 4.5 Experimental plot of o/
0 vs. 1/T for Cu atoms 89
in an Ar matrix.
Figure 4.6 Experimental plot of x/
o vs. 1/T for Cu atoms 92
in an Ar matrix. The spin orbit splitting, A, is
obtained from the slope, and the excited state g ^
is obtained from the intercept.
Figure 4.7 Experimental plot of 3/
o vs. 1/T for Cu atoms 96
in an Ar matrix.
Figure 4.8 Experimental plot of
2/0 vs. T for Cu atoms in 98
an Ar matrix.
Figure 4.9 Diagram of the degenerate modes of the e lattice 103
vibration.
Figure 4.10 Plot of calculated C0 term as a function of lattice 107
motion z holding lattice motion t = 115 and X con
stant (from moment plots) for Cu atoms in Ar matrix.
Figure 4.11 Plot of calculated Co term as a function of lattice 109
motion t holding lattice motion z = 220 and X constant
(from moment plots) for Cu atoms in an Ar matrix.
Figure 4.12 Composite drawing showing the effect of varying 111
contributions from lattice vibrational modes.
Figure 4.13 The effect of varying the magnitudes of the t2 and 114
e modes on absorption profile. B represents the e
mode and C the t2 mode.
vi i i


120
~h
.A
300 315 330


72
The CaF2 window had to be cleaned with acetone and ethanol (to
prevent residue from evaporated acetone) between subsequent experiments
in order to obtain transparent matrices. Simply allowing heating of the
window and loss of the matrix and then recooling for another deposition
resulted in cloudy matrices.
D
After the outgassing process, the Displex compressor was started
and the CaF2 window cooled to deposition temperature. In order to
achieve transparent matrices, the window was cooled to 14 K for argon
work and 20 K for krypton and xenon work. Depositions below these
temperatures resulted in cloudy matrices. After cooling to the proper
temperature, the window was rotated into deposition position and a flow
rate of rare gas was set to about 1-3 mmol/hr with the needle valve.
Gas was deposited for 10 min before heating the Knudsen cell to deposi
tion temperature. Initial estimates of the correct tantalum cell temper
ature were set as the temperature required to maintain a vapor pressure
of the sample at 'vlxlO-3 torr. Depositions continued anywhere from 5 to
120 min. At intervals during the deposition, the CaF2 window was rotated
through 90 so the absorption could be measured. Deposition continued
until the bands of interest showed absorption of 0.5 to 0.95 0D. Depo
sition temperatures for each metal can be found in the respective
sections discussing results.
Both MOD and absorption spectra were obtained on a matrix at 13 K
and 20 K. If temperature dependence was exhibited, three scans were
stored at each temperature from 13 K to the highest allowed by the
matrix gas in 1 K intervals. For argon spectra were observed to 25 K,
for krypton to 28 K, and for xenon to 32 K.


156
Table 4.4. Calculated eigenvalues, eigenfunctions and MCD C0 and V0
parameters for Au atoms in Ar. E.'s are eigenvalues meas-
ured from the <
coefficients of
axcited state
the adiabatic
center of gravity; c.'s
wavefunctions [see
are
equation
z = 300
(58)].
cm-1.
For Au/Ar A
= 3165 cm-1, t
= 45 cm'
-1, and
Ei
CH
2i
C3i
c0
c0/p0
-3206
0.012
0.094
0.996
0.251
0.125
2.00
1318
0.089
-0.992
0.093
-0.080
0.042
-1.87
1888
-1.00
-0.088
0.020
-0.330
0.166
-2.00


REFERENCES
1.I. Norman and G. Porter, Nature, 174, 508 (1954).
2. E. Whittle, D. A. Dows, and G. C. Pimentel, J. Chem. Phys., 22,
1943 (1954).
3. B. M. Chadwick, Mol. Spectrosc., 3_, 281 (1975).
4. A. J. Downs and S. C. Peake, Mol. Spectrosc., 1_, 523 (1973).
5. M. E. Jacox, Rev. Chem. Intermed., 3_, 1 (1979).
6. B. Meyer, "Low Temperature Spectroscopy," Elsevier, New York, 1971.
7. G. Ozin and M. Moskovits, eds., "Cryochemistry," Wiley-Interscience,
New York, 1976.
8. A. J. Barnes, W. J. Orvi11 e-Thomas, A. Mller, and R. Gaufrs, eds.,
"Matrix Isolation Spectroscopy," D. Reidel, Boston, 1981.
9. R. L. Mowery, J. C. Miller, E. R. Krausz, P. N. Schatz, S. M. Jacobs,
and L. Andrews, J. Chem. Phys., 70_, 3920 (1979).
10. V. E. Bondybey and J. H. English, J. Chem. Phys., 74_, 6978 (1981).
11. A. J. Barnes, "Vibrational Spectroscopy of Trapped Species,"
(H. E. Hallam, ed.), Wiley, New York, 1973, p. 133.
12. S. Cradock and A. J. Hinchcliffe, "Matrix Isolation, A Technique for
the Study of Reactive Inorganic Species," Cambridge University Press,
Cambridge, 1975.
13. A. M. Bass and H. P. Broida, "Formation and Trapping of Free
Radicals," Academic Press, New York, 1960.
14. W. Weltner, Jr., Science, 155, 155 (1967).
15. J. W. Hastie, R. H. Hauge, and J. L. Margrace, "Spectroscopy in
Inorganic Chemistry," Vol. 1 (C. N. R. Rao and J. R. Ferraro, eds.),
Academic Press, New York, 1970, p. 57.
16. W. Weltner, Jr., "Advances in High Temperature Chemistry," Vol. 2
(L. Eyring, ed.), Academic Press, New York, 1970, p. 85.
17. A. J. Barnes, Rev. Anal. Chem., 1_, 193 (1972).
196


Figure 3.7. Magnetic field dependence of an MCD
signal.


71
sent to the modulator through a Datel Systems, Inc., model DAC-IC8BC
digital-to-analog converter. This device was also used when another
program read data from a floppy disk for output to the chart recorder.
For matrix preparation a tantalum cell was filled with metal powder
as fully as possible, but some of the fine powder invariably blew out
of the effusion orifice into the vacuum chamber during pump down and
degassing of the furnace.
The Knudsen cell was mounted, in the tantalum straps, onto the
water-cooled electrodes making certain the effusion hole of the cell was
aligned with the collimating hole in the heat shield and the CaF2 target
window. This alignment could be checked by sighting the tantalum cell,
when mounted in the furnace, through a window on the outer vacuum shroud
of the cryostat into the furnace.
The furnace was rough pumped for a number of minutes (as long as
30 min for very finely divided powders) using a bypass line which iso
lated the diffusion pump and liquid nitrogen trap. The pumping was
continued until a pressure below 200 y was shown on the thermocouple
gauge at which time the gate valve to the diffusion pump was gradually
opened and the bypass closed. The system was then pumped to below
2><105 torr with the diffusion pump.
The tantalum cell was then gradually heated to the deposition
temperature while keeping the pressure below 2-4x10~5 torr. With rapid
heating, material blew out of the cell as a powder and resulted in weakly
absorbing matrices. The outgassing process took as long as 2 hr in some
R
cases. During this procedure the Displex was rotated so the CaF2 window
was shielded from the Knudsen cell to prevent metallic film deposition on
the target.


0xicr
163
l/T (K-)


104
criteria were imposed on the solution: 1) that the interband spacings
match the experimental ones at 12.9 K, and 2) that the signs of the
C terms match the observed ones. The final computed results are shown
in Table 4.1 and show for Cu in Ar that the first order spin orbit
split states are thoroughly mixed by the vibronic interaction.
Figure 4.10 shows, for Cu in Ar, the variation of C0 with z mode
coordinate for a fixed t mode displacement. At z = 220 cm-1 and
t = 115 cm-1, one positive and two negative C0 terms are predicted for
transitions to states whose energy separations correspond closely to
the experimental intervals (calculated AE's are 476 cm-1 and 410 cm-1
as compared to the experimental 479 cm-1 and 402 cm-1). From the C0-z
space plot (see Figure 4.10) it is shown that only for z > 70 (at
t = 115) is the C0 of the lowest energy peak positive and the upper two
negative. From a similar C0-t space plot (shown in Figure 4.11), only
for 10 < |t| < 380 (at z = 220) can we obtain a similar combination of
C0 term signs. This plot also shows that the C0 term variation is
independent of the sign of the t mode displacement, whereas this is not
the case in z space. The ranges of allowed z and t displacements are
substantially narrowed to z = +2205 and t = 1155 when the criterion
of matching the observed band intervals is superimposed on the above
MCD sign criterion. A composite drawing for the transition energies vs.
t and z is shown in Figure 4.12. Thus it can be concluded that the
Moran model is applicable to the case of matrix isolated Cu atoms and
that the simultaneous spin orbit and vibronic interactions in the 2P
excited state can explain the observed C0 term signs and absorption band
separations. The initial limitations of this model do not, however,
yield any information about the respective influence of the e and tz


17
if the electronic wavefunctions at R0 are chosen to diagonalize y So,
if mixing of electronic states by H is neglected the wavefunctions in
the magnetic field are |A a> and JJ j> with energies
Ot A
£
A a
a
-
a1 Hz
A > H
a
(27)
ej In this first approximation the Zeeman splitting of each vibronic state
is independent of vibrational level and is identical to the pure elec
tronic splitting at R0. As a better approximation Stephens includes
intermixing of different electronic states, K, with states A and J:
uxj>
K k
(k5j)
K >
K
H
£jk
(28)
IA a>'
1 a
A a>
1 a
K >
K k
(KfA)
H
eak
where the primes denote wavefunctions in a magnetic field. The intervals
eal< and are large compared to Zeeman energies and again use the
Franck-Condon approximation. If it is assumed that the vibrational
levels k contributing to the sums in equation (28) are such that the
intervals are approximated as
e
ak
e
Jk
(29)
where the W
o
values are energies for the various states, then


170
72 73
observed by Mitchell and Ozin and Mitchell et al. With the appartus
utilized in these experiments it was therefore not possible to accurately
measure the MCD temperature dependence and obtain values for a moment
analysis. Even without this information it is possible to conclude,
from the triplet structure, that the same Jahn-Teller/spin orbit model is
effective in these systems. Orbital overlaps can be employed as in Cu
and Au matrices to estimate a spin orbit reduction factor and therefore
approximate the matrix spin orbit constants. The calculated spin orbit
reduction factors for Ag in Ar, Kr and Xe are listed in Table A.2 in
Appendix A.
Results for Lead Experiments
The matrix absorption spectra of Pb and Pb2 were first studied by
74
Brewer and Chang. Two bands were discovered for the dimer (508 nm
A X, and 244 nm E X). A band at 261.4 nm was assigned to the
3Pi - 3 P0 atomic transition in a Kr matrix. The Pb2 spectrum had been
75 76
studied previously in the gas phase by Shawhan' and then by Weniger.
The absorption and laser induced emission of Pb2 in solid Ne, Ar and Kr
77 78
was reported by Teichman and Nixon. Bondybey and English revised
Weniger's analysis of the 500 nm dimer band, determined a 112 cm-1
vibrational frequency in the ground state, and reported evidence for
six Pb2 states below 500 nm. They also suggested that transitions to
the 500 nm state be assigned as F0+ + X0+. This was the first symmetry
o g
assignment proposed for any Pb2 transition.
For preparation of Kr matrices containing Pb, a Ta Knudsen cell was
filled with Pb (Spex) powder and thoroughly outgassed at approximately
800C. Resistively heating the cell to 875C, a metal beam was produced
which was codeposited with Kr onto the CaF2 window at 20 K. For Pb


49
H = H, + AL-S + H + H.
u e I L
where
Hel = -Y^kt-hs Y3(3Lz2 L*L)Z y3/3(Lx2 Ly2)T
Setting s = -y1S, t = -y T, and z = -y3Z the excited state Hamiltonian
matrix is
%3/2>
3/z V2 >
E + hX + z + A
=
t E + JgA-z + s
-/2t -S2z
I 1/21/2>
-S2t
E A + s
The Kramers degeneracy is apparent from the above matrix. Two criteria
are imposed on the diagonalization: 1) that the interband spacings
match the experimental ones at low temperature, and 2) that the signs of
the C0 terms match the observed ones. Further discussion of the evalua
tion of results under this model is presented with the spectra and anal
yses of the individual cases studied.
Band Moment Analysis
Returning to the subject of dispersion calculations [see equations
(13) through (22)], the most drastic assumption made there is that the
Born-Oppenheimer approximation holds for ground and excited electronic
states. In the Jahn-Teller theorem all spatial-symmetry-derived elec
tronic degeneracy is broken by at least some nuclear displacement, and
therefore the potential surfaces emanating from a degenerate state do
not remain exactly degenerate. The Born-Oppenheimer approximation then


153
51
by Forstmann et al. (which had been photographically enlarged). A
typical plot is shown in Figure 4.29. The points plotted are the values
51
measured from work by Forstmann et al. while the line through the
points is a non-linear least-squares fit to the hyperbolic cotangent
relation. As discussed by Englman^ this behavior is indicative of
Jahn-Teller coupled transitions. The agreement of plotted data with
the coth fit as well as the indicated dominance of noncubic lattice
modes is strong justification for application of the Moran model to the
gold-matrix interaction analysis. Table 4.4 lists the results of the
Moran treatment for Au in Ar. The degenerate t and z modes were varied
with A held at 3165 cm-1. Inspection of the coefficients in the eigen
functions indicates little interaction between the high energy doublet
with the lower energy band. This situation is treated by Sturge.^
In such systems the spin orbit constant can be determined by measurement
of the energy separation of the center of gravity of the high energy
doublet and the position of the low energy band (3215 cm-1)- This is
50
the same measurement made by Gruen et al., but here it arises from a
50
different basis. Gruen et al. assumed a distorted octahedral D3 site
symmetry which is indicated in this work to be erroneous.
Gold in Krypton and Xenon
The absorption and MOD of Au isolated in Kr are shown in Figure 4.30.
There is perhaps some indication of a broad cluster band centered between
the atomic components. From the 1/
0 vs. 1/T plot in Figure 4.31,
a spin orbit constant of 316265 cm-1 is obtained. The intercept yields
gQrb ~ 7.710. The spin orbit reduction factor calculated for Au in Kr
is k^ = 0.953 and k^. ,
sub mt
= 0.869, compared to the experimental


185
3030 X%=A%(I)
3040 PRINT#8,X%
3050 IF DSO0 THEN PRINT DS$:STOP
3060 NEXT I
3070 DCL0SE#8
3071 PRINT" DO YOU WISH TO CHANGE THE MATRIX TEMPERATURE?(YES=1,NO=0)"
3072 INPUT Z8
3073 IF Z8=l THEN GCSUB 38499
3074 FOR 11=1 TO NT
3075 POKE 36866,10
3076 POKE 36866,11
3078 NEXT II
3090 PRINT "FINISHED"
5000 END
32000 V=0.105E-03*(WL/2)*255+0.5: REM MODULATOR VOLTAGE
32500 Dl=INT(V)
33000 POKE 36874,Dl
33500 RETURN
34000 FOR Kl=l TO D:REH CHART RECORDER STEPPER MCTOR
34100 POKE 36866,9
34200 POKE 36866,25:GOSUB 38499
34300 NEXT Kl
34400 RETURN
36000 X1=0:REM SIGNAL AVERAGING
36100 FOR KS=1 TO E
36200 Xl=Xl+PEEK(36864)
36300 NEXT KS
36400 A%(II)=INT(Xl/E)
36500 RETURN
38000 POKE 36866,57:REM CHART RECORDER EVENT MARKER
381C0 FOR 19=1 TO 50
38200 NEXT 19
38300 POKE 36866,25
38350 GOSUB 32000
38400 RETURN
38499 PRINT:PRINT:PRINT:PRINT
38500 PRINT "TO SET TEMP., ENTER A#lB#2CA WHERE #1 IS THE DESIRED t (A 3-DIGIT"
38501 PRINT "NUMBER) AIT) #2 IS A SINGLE DIGIT FROM 1 TO 9. iF THE t-CONTROLLER"
38502 PRINT"IF THE t CONTROLLER IS NOT UNDER COMPUTER CONTROL"
38503 PRINT"ENTER A#lB#2CAD TO SWITCH CONTROL "
38504 PRINT"OVER TO THE pet. aNOTHER D ENTERED IN THE SUBROUTINE WILL SWITCH"
38505 PRINT"CONTROL BACK TO THE FRONT PANEL."
38506 PRINT:PRINT:PRINT:PRINT
38510 INPUT"ENTER t CHANGE ";A$
38515 OPENl,6


Figure 4.2. The eigenvalues and C0/V0 values predicted
for a reduction of pure 0^ site symmetry
to D3.


195
low T
high T
t t
THERMOCOUPLE
highT
low T


Figure 4.31. Plot of i/
0 1/T for Au in Kr.


LIST OF TABLES
Table 4.1
Table 4.2
Table 4.3
Table 4.4
Table A.l
Table A.2
Page
Calculated eigenvalues, eigenfunctions and MCD C0 105
and Vo parameters for Cu atoms in Ar. E^'s are
eigenvalues measured from the excited state center
of gravity; c. 's are coefficients of the adiabatic
wavefunctions [see equation (58)]. For Cu/Ar,
X = 124 cm-1, t = 115 cm-1, and z = 220 cm-1.
Calculated eigenvalues, eigenfunctions and MCD C0 125
and Vo parameters for Cu atoms in Kr. E.'s are
eigenvalues measured from the excited state center
of gravity; c^'s are coefficients of the adiabatic
wavefunctions [see equation (58)]. For Cu/Kr
X = 95 cm-1, t = 111 cm-1, and z = 152 cm-1.
Calculated eigenvalues, eigenfunctions and MCD C0 143
and V0 parameters for Cu atoms in Xe. E.'s are
eigenvalues measured from the excited state center
of gravity; c.'s are coefficients of the adiabatic
wavefunctions [see equation (58)]. For Cu/Xe
X = -23 cm-1, t = 86 cm-1, and z = -174 cm-1.
Calculated eigenvalues, eigenfunctions and MCD C0 156
and V0 parameters for Au atoms in Ar. E-'s are
eigenvalues measured from the excited state center
of gravity; c.'s are coefficients of the adiabatic
wavefunctions [see equation (58)]. For Au/Ar
X = 3165 cm-1, t = 45 cm-1, and z = 300 cm-1.
Data used in orbital overlap calculations. 179
Orbital overlaps and predicted spin orbit reduction 181
factors.
VI


82
distortion is the observed combination of C0/£>0 signs found. Values for
C0/VQ viere also calculated as a function of X. For no value of X in the
range of 10 cm"1 to 500 cm'1 (for Cu in Ar) was the experimental MOD
sign combination found. Thus it can be unambiguously concluded on the
basis of energy level separations and MOD sign combinations that the
trigonally distorted site model is not a valid explanation of the
observed Cu/Ar absorption and MOD results. This conclusion prompted
calculations outlined as splittings shown in the right half of Figure 4.1.
This scheme is pursued here.
Included after a somewhat detailed treatment of Cu isolated in Ar
is included a concise presentation of results for Cu in Kr (including a
spectrum of the region from 340 nm to 210 nm) and Cu in Xe as well as
the results of a moment analysis for Au isolated in Ar, Kr and Xe.
Following these are the atomic spectra obtained for matrix isolated
silver and, finally, the results obtained for Pb and Pb2 isolated in Kr.
Copper in Argon
The absorption spectra of copper atoms isolated in rare gas matrices
have been studied extensively0' 5 1 and the triplet of bands at
310 nm attributed to a number of different causes. These include spin
50
orbit splitting and static axial site distortion, multiple matrix
c
sites, exciplex formation between the metal and a single matrix atom,
60
long-range metal-metal interactions, and a Jahn-Teller effect resulting
from matrix cage atom vibrations interacting with the excited state of
61 52
the metal. While this work was in progress, Armstrong et al. and
CO
Grinter et al. reported on the magnetic circular dichroism of Cu atoms
in Ne, Ar, Kr and Xe matrices and concluded that their results were


125
Table 4.2. Calculated eigenvalues, eigenfunctions and MCD C0 and Vo
parameters for Cu atoms in Kr. E.s are eigenvalues meas
ured from the excited state center of gravity; c.'s are
coefficients of the adiabatic wavefunctions [see
equation
(58)].
For Cu/Kr X
= 95 cm-1,
t = 111 cm-i,
and
z = 152
cm-1.
E.
i
CH
C2i
CSi
C0
Po
C q/Vq
-317
0.070
0.691
0.719
0.323
0.163
1.98
- 36
0.621
-0.594
0.511
-0.127
0.065
-1.94
+353
-0.781
-0.411
0.471
-0.196
0.105
-1.86


Page
APPENDIX C TEMPERATURE CALIBRATION 190
REFERENCES 196
BIOGRAPHICAL SKETCH 201
v


Figure 2.4. Splittings in free atom 2S and 2P
orbitals for:
(a) an octahedral site
(b) spin orbit interaction
(c) Zeeman splitting.


181
Table A.2. Orbital overlaps and predicted spin orbit reduction factors.
rab
Subst.
Site
System
S
IT
So
?X^M
7.098
CuAr
0.031677
0.106869
5.687
0.865
7.098
AgAr
0.036205
0.120881
1.564
0.953
7.098
AuAr
0.036791
0.127865
0.370
0.988
7.541
CuKr
0.031602
0.114655
20.96
0.476
7.541
AgKr
0.036040
0.130665
5.668
0.816
7.541
AuKr
0.036229
0.138423
1.368
0.953
3.193
CuXe
0.030587
0.118135
36.63
0.078
8.193
AgXe
0.034614
0.135470
9.902
0.676
8.193
AuXe
0.034145
0.142835
2.391
0.918
RAB
Interst.
Si te
System
IT
5.020
CuAr
0.111841
5.020
AgAr
0.122093
5.020
AuAr
0.124467
5.333
CuKr
0.118540
5.333
AgKr
0.130220
5.333
AuKr
0.132900
5.794
CuXe
0.122040
5.794
AgXe
0.134965
5.794
AuXe
0.137596
Sc
h'h
kX
0.218277
5.687
0.587
0.215312
1.564
0.882
0.213195
0.370
0.972
0.245030
20.96
-0.846
0.246968
5.668
0.463
0.247182
1.368
0.869
0.268690
36.63
-2.713
0.277948
9.902
-0.125
0.282058
2.391
0.719


73
The monochromator was calibrated with He-Ne and argon ion lasers
and scans were always run from low to high energy to prevent stepping
motor assembly backlash and maximum photomultiplier tube sensitivity.
All MCD spectra were run at 0.55 Tesla as determined by an
F. W. Bell Model 640 Gaussmeter. Zero-field circular dichroism spectra
were recorded to determine the zero-field line in the MCD. With the
magnet power turned off, a residual field of ^60 Gauss was measured. A
test of the linear dependency of the MCD signal upon the magnetic field
yielded the expected result (see Figure 3.7).
The MCD apparatus was calibrated for each matrix using aqueous
solutions of [Co(en)3]Cl(d-tartrate) made such that the absorbance at
o
4690 A was near 1 0D as measured by a Cary 17 Spectrometer. The proce
ed
dure was similar to that of Tacn," and the circular dichroism of the
standard solution was measured at 4930 A. McCaffery and Mason^ measured
the ratio of AA max/A max = 0.0225. The same solution was used to cali
brate the absorption experiment. Digitized absorption data were cali
brated in optical density units through use of the relation
where is the number of 0D units per digital data unit, C is the
concentration of the standard solution in optical density, and 1^ is
the sample absorption band intensity in arbitrary units as stored on
the floppy disk. Calibration of digitized MCD data was done through
the relation
K (C)(0.0225) Ss
^M L. S


5
Matrix isolation spectroscopy displays a number of advantages over
gas phase studies. Conventional spectrometers can be used to study
samples unavailable under standard conditions due to high reactivity or
instability. A big advantage in the study of high temperature species
is that all trapped molecules are in their ground electronic and vibra
tional states. This enhances sensitivity as the originating level of
spectroscopic transitions is always the ground state. With matrix tem
peratures below 20 K the thermal energy is below 15 cm-1. "Hot" bands
are thus eliminated. Very long depositions are possible allowing build
up of low abundance species and species of low absorption coefficient.
Controlled diffusion experiments allow matrix reactions to form new
species or clusters. It is also sometimes possible to observe species
with preferential orientation in matrices as is done in single crystal
work. More detailed discussions of the matrix isolation technique can
be found in recent reviews^^^-^ and references therein.
A large array of spectroscopic techniques have been employed in
matrix work, including infrared and Raman, electron spin resonance,
Mossbauer, and visible and ultraviolet absorption and emission. More
recently magnetic circular dichroism of matrix isolated samples was
22
introduced by Douglas et al. at the University of East Anglia. Mag
netic circular dichroism has its roots in the work of Michael Faraday
when in 1845 he first observed the phenomenon now known as the Faraday
effect. When plane polarized light traverses any transparent medium
colli nearly with an externally applied magnetic field, the plane of
polarization is rotated.
Linearly polarized light consists of equal components of right
circularly polarized (RCP) and left circularly polarized (LCP) light.


Magnet


(a)
(b)
(c)


7
very high magnetic fields. The advantage of MCD is that it is a signed
technique (i.e., positive and negative bands are seen) not requiring
high magnetic fields. In this work a 5500 Gauss field was employed.
Overlapping, thus unresolved absorptions may be resolved in MCD if the
MCD for one of the overlapping components is much larger due to MCD
selection rules or if the transitions have opposite MCD signs. An
example is the differentiation of tyrosine and tryptophan where absorp-
tions overlap. Typical limits of detectability are 103 OD for
absorption and 10-s OD for MCD. The expected situation of a detectable
MCD with an absorption too weak for observation sometimes arises as in
the example of spin-forbidden transitions of octahedral and tetrahedral
27 28
Co(II) species 5 and for impurities in optical grade CaF2 plates
cooled to 13 K, vide infra. The fact that some MCD transitions display
a temperature dependence (to be discussed in detail later) makes applica
tion of the matrix isolation technique to MCD very appealing.
Matrix isolated samples studied by MCD since the work by Douglas
22 29 30
et al. are few. Atomic species Hg; group 11A atoms MG, Ca and Sr;
31 32 29 33
Ta; diatomic Cl2 and 02; Xe halides; diatomic oxides of Ti, Zr,
Hf, V, Nb and Ta;^ and benzene,^ OsO^ and acrolein^ are included.
The present research involves matrix isolated samples of atoms
and/or clusters of Pb, Cu, Ag and Au. Primary reasons for studying
these systems are the roles of small clusters in fundamental processes
38 39 40
such as heterogeneous catalysis, nucleation and photography.
Another compelling reason to study the electronic spectra of these
systems is the increasing number of optically pumped lasers being devel-
41
oped involving them. Also of basic interest is the observation that
matrix isolated Cu, Ag and Au atoms, all involving 2P <- 2S transitions,


51
The ratio of the nth MCD moment to the zeroth absorption moment
is given by:

^A>
n
o
A + 8
(63)
where pin is the Bohr magneton; B is the magnetic field strength; and
the MCD parameters An, 8n, Cn, and VQ are defined as in Osborne and
55
Stephens. The MCD parameters of interest in this study are:
c0/p0
II
03
o
33
o
II
O
(64)
VPo
^orb
(65)
Ci/Po
= -2A/3
(66)
A3/Po
= 69orbt + }2{ + + 2(A/3)2}]
(67)
c3/v0
= -ZACo^ + %{ + + 2 (A/3)2} ]
(68)
= + ( + ) + 2(A/3)2
(69)
where gorb = , A is the spin orbit splitting of the
2J1 excited state (positive when the M' component lies highest),
and ( + ) represent the contributions to the band width (second
absorption moment) from the cubic and noncubic lattice modes, respec
tively, and include linear and quadratic coupling or anharmonicity.
The moments were calculated from digitized data by application of
Simpson's rule for numerical integration by the CBM 8032 microcomputer.
Further discussion of application of the moment analysis to Cu and Au
results appears in the respective sections.


Figure 4.13. The effect of varying the magnitudes of the t2 and e
modes on absorption brofile. B represents the e mode
and C the t2 mode.


Figure 4.16. Experimental plot of i/
0 vs. 1/T for
Cu atoms in a Kr matrix.


145
300 310 320
n
290
X (nm)
~i
330
r~
340


115
of matrix isolated A1 and Ga atoms (2P ground states). They orthogonal -
ized the metal orbitals with the rare gas cage atom orbitals by calcu
lating the a and it overlap integrals (S^ and S^) and evaluated a spin
orbit coupling constant reduction factor, k\ through the relation (for
nondistorted octahedral sites)
kA = 1 KAwA..-1 (2S S -S 2)
where K = 2 for an interstitial (MX6) site and K = 4 for a substitutional
(MX12) site, and A^ and A^ are the rare gas and metal spin orbit coupling
constants, respectively. Since Hartree-Fock calculations are not avail
able for the metal excited state configurations, the wavefunctions
were approximated from double zeta metal ground state functions. Using
= 941 cm-1 and A^ = 166 cm-1 (gas phase), the kAsub = 0.86 for the
substitutional octahedral site and kA-n^. = 0.59 for the interstitial
site. The observed kAQbs = 124 cm-1/166 cm-1 = 0.75. Both results
show that overlap of the matrix atom orbitals with Cu 4p orbitals can
reasonably explain the observed reduction in spin orbit in an Ar matrix.
Further support for this interpretation comes from the observation that
the A's for Cu in Kr and Xe are each further reduced, vide infra, with
the A in Xe actually becoming negative. This trend reversal can be
predicted from the above relation since the quantity A^/A^ increases
dramatically in going to Kr (20.96) and Xe (36.63).
Copper in Krypton
Figure 4.14 shows the absorption and MCD spectra for Cu atoms iso
lated in Kr. As for Ar experiments the Cu was vaporized from a cell
heated to ~1100C and codeposited with Kr at a pressure of 3-4xl0"5 torr


155
T(K)


isolated metal atom with host lattices. On the basis of comparison of
calculated to observed absorption and MCD spectra, several of the
excited state splitting models can be excluded, and the simultaneous
spin orbit and Jahn-Teller model is shown to be the explanation of
observed spectra.
Calculations for a detailed moment analysis are presented for
copper atoms isolated in an argon matrix. Moment analysis results are
also presented for copper in krypton and xenon as well as for gold in
argon and krypton. The spin orbit coupling constants are shown, for
copper, to be reduced as compared to the gas phase. For copper atoms
A = 124 cm-1, 95 cm-1, and -23 cm-1 (gas phase = 166 cm-1) when isolated
in argon, krypton and xenon, respectively. The spin orbit reduction is
discussed in terms of atomic orbital overlaps. Overlaps for approxi
mated metal atom excited state valence orbitals with matrix gas outer
shells are computed for copper, silver and gold with argon, krypton and
xenon.
The absorption and MCD spectra of several small cluster bands are
presented. On the basis of the type of MCD term observed and comparison
to expected bands due to state degeneracies, bands are assigned to
dimers or trimers and comparison is made to literature assignments.
The absorption and MCD spectra of lead atoms and dimers confirm
literature assignments. The anticipated positive A term is observed for
the 3Pj - 3P0 lead atom transition (AJ = +1).
A new technique for measurement of the temperature of matrix
samples is introduced. The measurement involves the temperature depen
dence of an MCD band of a paramagnetic species and accurate measurement
(by a thermocouple) of temperature differences.
XT 1


191
interval AT. To find xjxl an argon isolated Au band was chosen since
Au has one component of its 2P - 2S transition completely resolved from
the other two (see Figure C.l). The quantity AT is simply found by
noting the difference in thermocouple readings (in yV) at the two
temperatures and dividing by the thermocouple sensitivity (in yV/K).
This procedure is dependent on the similarity in time response of
the thermocouple and the MCD signal of the sample. This was measured
by plotting the thermocouple output and the MCD signal (of Fe atoms in
an Ar matrix, A = 266.2 nm) simultaneously on a dual-pen strip chart
recorder as the temperature was cyclically raised and lowered. The
result is shown in Figure C.2. It is clear that both signals tracked
the temperature variation together and with a time lag less than one
second. The lowest temperature on the apparatus was found to be 10.2 K
by this method.


135
290
300
310
320
330


Figure 4.9. Diagram of the degenerate modes of the e lattice vibration.


32
and for 2P,
r6 = r6 + r8 = e1 + u1
The energies of the spin-orbit states can now be found. The 2TX
states are
<2T1Jtx|Hs [2 T!Jtx> (44)
where Z11 is the representation of the excited state, t is either E or
U', t is the component of t (for E', x = a' or 3', and for U1, t = K, A1,
y' or v'), and Hs Q represents the spin-orbital Hamiltonian. Following
48
Griffith, equation (44) can be rewritten in terms of a reduced matrix
element R.
<2T1Jtx|Hs<0J2T1JtT> = tZj x R
The fl values are taken from Griffith. For t = E' the energy is
c2T11 |H ||2T1>, and for t = U1 the energy is --i-<2T1 | |H ||2TX>.
J SvOe O o (j o
If
k
s.o.
?Tr
the splitting in the excited state becomes
E1
' U' "k
There is also a Zeeman splitting to consider for each state in a
magnetic field. It is convenient to choose a basis set which yields a


14
instantaneous nuclear configuration, y^ and y. are vibrational wavefunc-
a J
tions dependent upon the particular electronic configuration and the
nuclear coordinates R, r is the electronic coordinate, and d^ and dj are
the degeneracies of states A and J. The eigenfunction equations are
:uxi>
e A a>
a1 a
(16)
The Franck-Condon approximation that most electronic transitions occur
at R near the equilibrium nuclear separation R0 is employed to simplify
the transition matrix elements.
=
a 1 1 X 1 a1 1 X
(17)
The lower case letters refer to the vibrational wavefurctions, and the
superscript indicates evaluation of electronic matrix elements at R = R0.
If the transition is only weakly allowed, the Franck-Condon approximation
is inadequate, and further account of the R dependence of electronic
wavefunction must be taken. Equation (12) now becomes
e
Y
Na
N
|26(eja-e)
cz
(18)
Assuming y to be constant for all vibronic transitions and integrating
over the whole band yields
I
2
CZ
(19)


184
250 IF J2<>2 GCTO 215
255 IF J2=2 GOTO 210
258 IQ=I2/100
260 IF IQ =INT(IQ) THEN 270
265 GOTO 275
270 C-OSUB 38000
275 NEXT II
290 GOTO 400
300 N4=NT/4
302 FOR 11=1 TO N4
305 J3=0
310 GOSB 36000
315 POKE 36866,24
320 VJL=WL-.25
330 POKE 36866,25
335 GOSUB 34000
340 J3=J3+1
345 IF J3<>4 GOTO 315
350 IF (11/50) =1171(11/50) THEN 360
355 GOTO 365
360 GCSUB 38000
365 NEXT II
370 GOTO 400
400 PRINT"SAVE DATA? YES=1,N0=0
410 INPUT B
415 IF B=0 THEN 3072
1000 DATA "SAMPLE: ", "MATRIX: ", "DEPOS.TEMP. : ", "MATRIX TEMP.: ", "INITIAL WVL.
1002 DATA "FINAL WVL:","RESOLUTION:","CYCLES FOR SIG. AVG.:"
1003 DATA "PTE. PER ANG. AND GAIN"DATE:"
1004 PRINT"INPUT FILE NAME"
1006 INPUT A6$
1010 DOPEN#8,(A6$) ,W
1020 IF DSO0 THEN PRINT DS$:STOP
1030 PRINT ENTER DATA INFORMATION"
1040 FOR 1=1 TO 10
1050 READ F$
1060 PRINTF?;:INPUT DA$(I)
1070 NEXT I
1080 RESTORE
1090 PRINT"ENTER Y TO RECORD, N TO RE-ENTER";
1100 GET Y$: IF Y$<>"Y" AND Y$<>"N" THEN 1100
1110 PRINTY$
1120 IF Y$="N" THEN 1030
2000 FOR 1=1 TO 8
2010 PRINTtr8 ,DA$(I)
2020 NEXT I
2030 IF DSO0 THEN PRINT DS$:STOP
3010 N=4*(X-Y)/C


Page
Figure 4.35
Absorption and MCD for Ag in Ar. 169
Figure 4.36
Absorption and MCD for Pb in Kr between 220 nm and 173
280 nm.
Figure 4.37
Absorption bands for Pb clusters in Kr. 175
Figure C.l
The Au/Ar band and equations used to calibrate the 193
lowest T attained on the Displex.
Figure C.2
Plot of MCD and thermocouple tracking of tempera- 195
ture fluctuations. Note lag less than one second.
The arrows indicate times at which the temperature
cycling period was changed. The right most por
tion shows the temperature stability at the lowest
temperature.
x


Figure 4.11. Plot of calculated C0 term as a function of
lattice motion t holding lattice motion z = 220
and X constant (from moment plots) for Cu
atoms in an Ar matrix. Eigenvalues increase
in energy from Ex to E2 to E3.


58
ELECTRICAL-
ge
He GAS
53
o
THERMOCOUPLE
and
HEATING WIRES
EXPANDER
1st STAGE
U

2nd STAGE
COPPER COLD TIP
TARGET WINDOW
RADIATION SHIELD
GATE VALVES
ROTATABLE
JOINT
MATRIX
GAS
INLET
VACUUM
PUMPS
FURNACE
ASSEMBLY


107
z


173
220 250 280
X/nm


Figure 4.34. Spectra obtained in a 1300C Au depositi
into Xe.


/ 2
142
T (K)


Figure 3.3. Optics for absorption experiment.


Figure 4.6. Experimental plot of i/
0 vs. 1/T for Cu
atoms in an Ar matrix. The spin orbit splitting,
A, is obtained from the slope, and the excited
state g k is obtained from the intercept.


Energy/cm
in
Cu/Ar
-500


A Term: Temp.
Independent
G+ G_
- 0
T >
r
.1
doo
o
/
/
/
/
/
/
/
n
OOP
OQQ
\
\
\
\
\
\
_ 1
OQQ
GOOOQ
i
C Term: Temp.
Dependent


O/WN / l/WV7\
137


1Q0
important as one calculates higher moments because the wings of the
band make an increasingly important contribution. Therefore AR is most
susceptible to error. It is interesting to consider two values of F,
namely 1 and 0. For F = 1 the ratio is very sensitive to experimental
uncertainties (AR varying as 3). If AR varies 15%, F will run from
2.9 to 0.5. Thus accurate values of F cannot be determined without
extraordinarily accurate measurements of R and particularly AR if cubic
and noncubic modes contribute comparable amounts. Fortunately the case
observed for matrix isolated Cu where F = 0 is much more favorable.
For F = 0 a 15% variation in AR yields F values from -0.09 to 0.11. From
these considerations it is difficult to say much about the cubic contri
bution although it does appear that it is nonexistent or quite small. It
is, however, possible to conclude that the noncubic contribution is
significant. This conclusion is central to the claim that the
Jahn-Teller effect is operative in this system since both the and
56
modes are Jahn-Teller active.
Having obtained evidence that the Jahn-Teller effect is operative
in this system it is interesting to determine the effect of different
lattice modes on the spectrum as well as the extent to which the excited
state components are mixed through spin orbit coupling. The Moran model
as previously discussed can be applied to the matrix isolated Cu atom
in Ar, Kr and Xe. The above analysis showed that both spin orbit inter
action and noncubic vibrational modes of the matrix cage are important
to the appearance of the 2P <- 2S transition in matrix isolated Cu. Three
components of the 2P state are apparent (see Figure 4.3) in the experi
mental absorption and MCD spectra. The observed C terms are positive,
negative and negative (increasing energy), and the separations between


89
!I I 1
0 0.02 0.04 0.06 0.08
I
0.10
l/T (KH)


Mirrors


Figure C.l. The Au/Ar band and equations used to calibrate
the lowest T attained on the Displex.


54
COOLING
WATER
GROOVE
FLANGE
(b)
To CELL
.] G4 l?a5"
t
V

I IOO
Ta END CAP
Ta
STRAP^
-0.70


_0ix /£
152
l/T(K)


3 /
0 XIO
124
l/T (K'1)


I I I I I I I 1 1 1 1 I I I I I L
300 350 400 450
WAVELENGTH jnmj


To Jan 01son-Zeringue


143
Table 4.3. Calculated eigenvalues, eigenfunctions and MCD C0 and V0
parameters for Cu atoms in Xe. E.'s are eigenvalues meas-
ured
from
the excited state center of gravity
", c 1 s
are
coefficients of
the adiabatic
wave functions
[see
equation
(58)].
For Cu/Xe X :
= -23 cm-1, t =
86 cm'
-1, and
2 = -
-174
cm-1.
Ei
CH
C2i
C3i
^ 0
C0/VQ
-324
0.733
-0.406
0.545
-0.164
0.097
-1.69
- 25
-0.680
-0.449
0.580
-0.139
0.085
-1.64
346
-0.010
0.796
0.605
0.303
0.152
2.00


ABSORPTION AND MAGNETIC CIRCULAR DICHROISM
OF MATRIX ISOLATED METAL ATOMS AND
SMALL CLUSTERS: A STUDY OF ATOM-MATRIX INTERACTIONS
BY
KYLE J. ZERINGUE
A DISSERTATION PRESENTED TO THE GRADUATE
COUNCIL OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
1983

To Jan 01son-Zeringue

ACKNOWLEDGEMENTS
The author would like to thank Dr. Martin Vala for his guidance
in this research. A great debt is owed to Dr. Robert Ferrante for the
training he provided in high vacuum technology and matrix isolation.
The invaluable assistance of Dr. Jean-Claude Rivoal in calibration
and design and construction of electronics is greatly appreciated.
Thanks are also due to Dr. Joseph Baiardo for many helpful discussions
and his computer interfacing expertise. Thanks are also extended to
Dr. Richard Van Zee, Dr. Marek Kreglewski, and Dr. Robert Pyzalski for
helpful and informative discussions. For assistance in data collection
the author thanks Mr. Bill Copeland.
The author greatly appreciates the craftsmanship of Mr. Art Grant,
Mr. Rudy Strohschein, and Mr. Chester Eastman,shown in the fabrication
of the apparatus.
The author thanks Mrs. Laura Griggs for her diligence and attention
to detail in preparing this dissertation.
The seemingly unending patience, understanding, and assistance of
Jan Olson-Zeringue are most deeply appreciated.
Funding for this research has been provided by the National Science
Foundation and the Graduate School. Partial support by the Division of
Sponsored Research is also appreciated.

TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS iii
LIST OF TABLES vi
LIST OF FIGURES vii
ABSTRACT xi
CHAPTER I INTRODUCTION 1
CHAPTER II THEORY OF MAGNETIC CIRCULAR DICHROISM 9
Basic Equations 10
Magnetic Circular Dichroism Calculation for Atoms... 25
Effect of Reduced Site Symmetry 42
The Adiabatic Model 46
Band Moment Analysis 49
CHAPTER III EXPERIMENTAL 52
Sample Preparation 52
Spectroscopic Apparatus 59
CHAPTER IV RESULTS 77
Copper in Argon 82
Copper in Krypton 115
Copper in Xenon 131
Gold in Argon 138
Gold in Krypton and Xenon 153
Results for Lead Experiments 170
Further Studies 176
APPENDIX A ORBITAL OVERLAP CALCULATIONS 178
APPENDIX B PROGRAMS 182
i v

Page
APPENDIX C TEMPERATURE CALIBRATION 190
REFERENCES 196
BIOGRAPHICAL SKETCH 201
v

LIST OF TABLES
Table 4.1
Table 4.2
Table 4.3
Table 4.4
Table A.l
Table A.2
Page
Calculated eigenvalues, eigenfunctions and MCD C0 105
and Vo parameters for Cu atoms in Ar. E^'s are
eigenvalues measured from the excited state center
of gravity; c. 's are coefficients of the adiabatic
wavefunctions [see equation (58)]. For Cu/Ar,
X = 124 cm-1, t = 115 cm-1, and z = 220 cm-1.
Calculated eigenvalues, eigenfunctions and MCD C0 125
and Vo parameters for Cu atoms in Kr. E.'s are
eigenvalues measured from the excited state center
of gravity; c^'s are coefficients of the adiabatic
wavefunctions [see equation (58)]. For Cu/Kr
X = 95 cm-1, t = 111 cm-1, and z = 152 cm-1.
Calculated eigenvalues, eigenfunctions and MCD C0 143
and V0 parameters for Cu atoms in Xe. E.'s are
eigenvalues measured from the excited state center
of gravity; c.'s are coefficients of the adiabatic
wavefunctions [see equation (58)]. For Cu/Xe
X = -23 cm-1, t = 86 cm-1, and z = -174 cm-1.
Calculated eigenvalues, eigenfunctions and MCD C0 156
and V0 parameters for Au atoms in Ar. E-'s are
eigenvalues measured from the excited state center
of gravity; c.'s are coefficients of the adiabatic
wavefunctions [see equation (58)]. For Au/Ar
X = 3165 cm-1, t = 45 cm-1, and z = 300 cm-1.
Data used in orbital overlap calculations. 179
Orbital overlaps and predicted spin orbit reduction 181
factors.
VI

LIST OF FIGURES
Figure 2.1
Figure 2.2
Figure 2.3
Figure 2.4
Figure 2.5
Figure 2.6
Figure 3.1
Figure 3.2
Page
The appearance of terms predicted by MOD theory 24
(a) The zero field absorption and MOD for a
transition with a positive Ai term. The
positive lobe lies at higher energy.
(b) A So term may be positive or negative, the
maximum coinicident with the absorption
maximum.
(c) A negative C0 term at two temperatures, Thigh
and T-]ow, may be positive or negative with
its maximum coincident with the absorption
maximum.
Polarized transition to an atomic P state and mag- 27
netic field splittings. Transition a is right cir
cularly polarized, transition c is left circularly
polarized, and transition b is polarized parallel
to the magnetic field.
Magnetic field splitting in degenerate ground and 30
excited states illustrating the origin of A0 and C0
terms.
Splittings in free atom 2S and 2P orbitals for 36
(a) an octahedral site
(b) spin orbit interaction
(c) Zeeman splitting.
The state splittings and allowed transitions for an 40
atom in an octahedral field showing the effect of
spin orbit and Zeeman splitting.
The predicted MOD and absorption patterns for the 44
2P 2S transition in an octahedral field.
(a) Diagram of the furnace assembly. 54
(b) Diagram of Knudsen cell used for metal vapori-
zation.
Detail of furnace-cryostat assembly used in matrix 58
isolation experiments.
Optics for absorption experiment
vi i
Figure 3.3
61

Page
Figure 3.4 Schematic of absorption experiment. 64
Figure 3.5 Optics for MCD experiment. 67
Figure 3.6 Schematic of MCD experiment. 69
Figure 3.7 Magnetic field dependence of an MCD signal. 75
Figure 4.1 The splittings induced in free atom 2S and 2P 79
states. Note dependence upon the order of applica
tion of various interaction in calculation.
Figure 4.2 The eigenvalues and C0/V0 values predicted for a 81
reduction of pure 0^ site symmetry to D3.
Figure 4.3 Absorption and MCD spectra observed for Cu isolated 85
in Ar.
Figure 4.4 Temperature dependence of the Cu atom C0 term in an 87
Ar matrix. The intensity decreases with increased
temperature.
Figure 4.5 Experimental plot of o/
0 vs. 1/T for Cu atoms 89
in an Ar matrix.
Figure 4.6 Experimental plot of x/
o vs. 1/T for Cu atoms 92
in an Ar matrix. The spin orbit splitting, A, is
obtained from the slope, and the excited state g ^
is obtained from the intercept.
Figure 4.7 Experimental plot of 3/
o vs. 1/T for Cu atoms 96
in an Ar matrix.
Figure 4.8 Experimental plot of
2/0 vs. T for Cu atoms in 98
an Ar matrix.
Figure 4.9 Diagram of the degenerate modes of the e lattice 103
vibration.
Figure 4.10 Plot of calculated C0 term as a function of lattice 107
motion z holding lattice motion t = 115 and X con
stant (from moment plots) for Cu atoms in Ar matrix.
Figure 4.11 Plot of calculated Co term as a function of lattice 109
motion t holding lattice motion z = 220 and X constant
(from moment plots) for Cu atoms in an Ar matrix.
Figure 4.12 Composite drawing showing the effect of varying 111
contributions from lattice vibrational modes.
Figure 4.13 The effect of varying the magnitudes of the t2 and 114
e modes on absorption profile. B represents the e
mode and C the t2 mode.
vi i i

Page
Figure 4.14 Absorption and MCD spectra for Cu atoms isolated 117
in a Kr matrix.
Figure 4.15 Temperature dependence of the Cu atom Co term in 120
a Kr matrix. The intensity decreases with
increased temperature.
Figure 4.16 Experimental plot of i/
0 vs. 1/T for Cu 122
atoms in a Kr matrix.
Figure 4.17 Experimental plot of 3/
0 vs. 1/T for Cu 124
atoms in a Kr matrix.
Figure 4.18 Cu absorption and MCD bands in the range 220 nm to 127
340 nm.
Figure 4.19 Appearance of Cu/Kr spectrum after prolonged depo- 130
sition from 230 nm to 290 nm.
Figure 4.20 The Cu2 band in the range 330 nm to 450 nm. 133
Figure 4.21 Absorption and MCD bands for Cu in a Xe matrix. 135
Figure 4.22 Plot of i/
0 vs. 1/T for Cu in Xe. 137
Figure 4.23 Plot of 3/
0 vs. 1/T for Cu in Xe. 140
Figure 4.24 Plot of
2/0 vs. 1/T for Cu in Xe. 142
Figure 4.25 Relative positions of Cu MCD in Ar, Kr and Xe. 145
Note the reversal of MCD term sign in Xe.
Figure 4.26 Absorption and MCD for Au in Ar. 148
Figure 4.27 Plot of i/
0 vs. 1/T for Au in Ar. 150
Figure 4.28 Plot of 3/
0 vs. 1/T for Au in Ar. 152
Figure 4.29 Plot of best fit for Au in Kr of (peak separation)2 = 155
4 hwEJTcoth^2j-y)
Figure 4.30 Absorption and MCD for Au in Kr. 158
Figure 4.31 Plot of i/
0 vs. 1/T for Au in Kr. 160
Figure 4.32 Plot of 3/
0 vs. 1/T for Au in Kr. 163
Figure 4.33 Absorption and MCD spectra for Au in Xe after a 165
high temperature metal vaporization.
Figure 4.34 Spectra obtained in a 1300C Au deposition into Xe. 167
ix

Page
Figure 4.35
Absorption and MCD for Ag in Ar. 169
Figure 4.36
Absorption and MCD for Pb in Kr between 220 nm and 173
280 nm.
Figure 4.37
Absorption bands for Pb clusters in Kr. 175
Figure C.l
The Au/Ar band and equations used to calibrate the 193
lowest T attained on the Displex.
Figure C.2
Plot of MCD and thermocouple tracking of tempera- 195
ture fluctuations. Note lag less than one second.
The arrows indicate times at which the temperature
cycling period was changed. The right most por
tion shows the temperature stability at the lowest
temperature.
x

Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of
the Requirements for the Degree of Doctor of Philosophy
ABSORPTION AND MAGNETIC CIRCULAR DICHROISM
OF MATRIX ISOLATED METAL ATOMS AND
SMALL CLUSTERS: A STUDY OF ATOM-MATRIX INTERACTIONS
By
Kyle J. Zeringue
April 1983
Chairman: Dr. Martin T. Vala
Major Department: Chemistry
Copper, silver, gold and lead have been vaporized and codeposited
with argon, krypton and xenon on a cold surface. Magnetic circular
dichroism and zero field absorption spectra are presented. Data are
digitized and stored on a microcomputer for analysis.
A brief introduction to matrix isolation and the magnetic circular
dichroism (MCD) technique is given. The theoretical background for the
MCD experiment is outlined. Calculations of predicted absorption and
MCD spectra for copper atoms trapped in rare gas lattices are presented
for various site symmetries and interactions with the surrounding matrix
cage.
The cause of the triplet structure of the 2P - 2S transition for
group IB metals is discussed in terms of 0^ symmetry, D3 symmetry,
spin orbit coupling, Zeeman splitting, and ultimately, a model involv
ing simultaneous spin orbit and Jahn-Teller interaction of the
xi

isolated metal atom with host lattices. On the basis of comparison of
calculated to observed absorption and MCD spectra, several of the
excited state splitting models can be excluded, and the simultaneous
spin orbit and Jahn-Teller model is shown to be the explanation of
observed spectra.
Calculations for a detailed moment analysis are presented for
copper atoms isolated in an argon matrix. Moment analysis results are
also presented for copper in krypton and xenon as well as for gold in
argon and krypton. The spin orbit coupling constants are shown, for
copper, to be reduced as compared to the gas phase. For copper atoms
A = 124 cm-1, 95 cm-1, and -23 cm-1 (gas phase = 166 cm-1) when isolated
in argon, krypton and xenon, respectively. The spin orbit reduction is
discussed in terms of atomic orbital overlaps. Overlaps for approxi
mated metal atom excited state valence orbitals with matrix gas outer
shells are computed for copper, silver and gold with argon, krypton and
xenon.
The absorption and MCD spectra of several small cluster bands are
presented. On the basis of the type of MCD term observed and comparison
to expected bands due to state degeneracies, bands are assigned to
dimers or trimers and comparison is made to literature assignments.
The absorption and MCD spectra of lead atoms and dimers confirm
literature assignments. The anticipated positive A term is observed for
the 3Pj - 3P0 lead atom transition (AJ = +1).
A new technique for measurement of the temperature of matrix
samples is introduced. The measurement involves the temperature depen
dence of an MCD band of a paramagnetic species and accurate measurement
(by a thermocouple) of temperature differences.
XT 1

CHAPTER I
INTRODUCTION
Molecular spectroscopy, the primary tool utilized to study details
of molecular geometry and electronic structure, has been applied rou
tinely to many stable chemical species in the solid, liquid and gaseous
phases. The study of short-lived or unstable species has been aided
greatly by high-speed electronic instrumentation. There are, however,
many species yet very difficult or impossible to observe due to reactiv
ity, short lifetime, or method of preparation. Among these are high
temperature atoms or molecules that exist only in extreme conditions
such as stellar atmospheres or in arcs and radicals or fragments with
such high reactivity that production of quantities sufficient for normal
analyses is difficult or impossible. Even when high temperature species
are observed, analysis of their spectra is difficult due to their popu
lation distribution in various electronic, vibrational and rotational
states. This is often the case in laboratory generation of such frag
ments via flash photolysis, plasmas, arcs, etc. Employment of the
matrix-isolation technique can circumvent many of these difficulties.
1 2
Norman and Porter and Whittle et al. independently proposed the
technique of matrix-isolation spectroscopy in 1954. Since that time a
vast literature has evolved which includes excellent reviews by
3 4 5 6
Chadwick, Downs and Peake, and Jacox, as well as books by Meyer,
7 8
Ozin and Moskovits, and more recently by Barnes et al. Matrix-isolated
samples are prepared by codeposition of "guest radical fragments,
1

2
reactive molecules, or high temperature species in inert, transparent
solids (matrices) at cryogenic temperatures.
A basic assumption in matrix isolation is that there is little or
no interaction between the matrix and the isolated species, and essen
tially gas-like species is obtained. Though this assumption is valid
as a first approximation, matrix interactions do occur which cause
shifts in the energies of spectra. The sample can also be trapped in
multiple sites in the crystalline lattice (examples are substitutional
or interstitial sites) which lead to band broadening and multiplets
due to differing energies of the various sites. These site effects
can often be removed by warming the matrix to allow controlled diffu
sion and thus permit the sample species to settle into the more stable
sites resulting in more simplified spectra. Lattice modes and Jahn-
Teller distortions due to matrix-sample interactions have also been
g
observed. Mowery et al. have observed Jahn-Teller distortions in the
magnetic circular dichroism spectra of matrix isolated magnesium atoms.
The matrix material can be any non-reactive gas which can be rigidly
solidified. Many substances have been used for this purpose including
N2, CH4, CO, the freons, SF6, CS2, and 02, as well as large organic mole
cules. More often, though, the solid rare gases Ne, Ar, Kr and Xe are
used as these elements are relatively chemically inert and transparent
over a broad spectrum, and provide a rather broad selection of melting
points and atomic sizes. Neon is expected to perturb a guest specimen
least, as it is least polarizable. However, neon requires temperatures
below 10 K and has a lower trapping efficiency compared to other rare
gases. It is usually easier to trap samples in Ar, and it is most
widely used as a host gas. Krypton and Xe are found to perturb trapped

3
molecules to a greater extent but provide a broader temperature range for
matrix isolation than do Ne and Ar.
Temperatures sufficiently low to condense matrix gases can be
achieved by mechanical closed-cycle refrigerators utilizing Joule-Thomp
son expansion of high pressure hydrogen or helium gas. Alternatively
physical refrigerants such as liquified nitrogen, hydrogen or helium may
be employed. Liquid nitrogen (boiling point 77.4 K) is plentiful and
inexpensive. Although it is adequate for the more stable matrix mate
rials, much lower temperatures are necessary for the better rare gas
matrices. Liquid H2 (boiling point 20.4 K) has been used, but it entails
a fire hazard in addition to the normal dangers associated with cryogenic
fluids. The most useful refrigerant is liquid He (boiling point 4.2 K).
It is also the only refrigerant useful for condensation of Ne which melts
at 24 K and allows solid state diffusion at less than half that tempera
ture (which is a general rule by which the temperature required for
controlled diffusion may be apprixmated). Closed-cycle refrigerators
which can attain temperatures near the liquid He boiling point are avail
able commercially.
The main advantages of the refrigerators include convenience, low
operating cost after the initial investment, and relief of the require
ment to replenish cryogenic fluids during experiments.
A deposition substrate is chosen that is transparent in the spectral
range of interest. Some common materials are CaF2, quartz and sapphire
for the visible and ultraviolet regions; Csl, NaCl and KBr for the
infrared region; and some nonconducting material such as sapphire for
microwave spectroscopy. A polished crystal plate is mounted on a
cold block (often copper) which makes good thermal contact with the

4
cryogenic fluid reservoir or the expansion chamber of the Joule-Thompson
refrigerator.
Several methods have been employed for generation of guest species.
The simplest method involves a gas phase sample mixed with the matrix
gas at the desired guest-host ratio in an external container and subse
quent introduction of the mixture into the vacuum chamber, condensing the
mixture onto the cooled substrate. This, of course, is not useful in the
study of high temperature samples. The vaporization of nonvolatile sub
stances has been approached in different ways. One interesting method
recently employed by Bondybey and English^ involves irradiation of the
sample with a powerful laser, thus introducing the necessary energy for
vaporization. A more widely employed method is vaporization from a high
temperature Knudsen cell in a vacuum furnace. These cells can be con
structed of carbon, or a refractory metal such as Ta, W or Mo. In some
cases it is necessary to prevent cell degradation by including a liner,
usually of C, BN or AI2O3. The cells are heated either by induction or
resistance to temperatures as high as 2900 K. The vapor effuses in a
crude molecular beam through a small orifice in the cell and is intro
duced simultaneously with isolant gas onto the target. Molar ratios of
matrix gas to sample used are anywhere from 100:1 to 10,000:1. Another
technique used to introduce gas samples involves passing the sample
through a heated inlet tube, the resulting thermolysis products then
being matrix isolated. Unstable species and fragments are generated by
exposing a parent molecule to photolysis with ultraviolet lamps, electron
bombardment, gamma rays, or plasmas, again cocondensing the products with
matrix gas.

5
Matrix isolation spectroscopy displays a number of advantages over
gas phase studies. Conventional spectrometers can be used to study
samples unavailable under standard conditions due to high reactivity or
instability. A big advantage in the study of high temperature species
is that all trapped molecules are in their ground electronic and vibra
tional states. This enhances sensitivity as the originating level of
spectroscopic transitions is always the ground state. With matrix tem
peratures below 20 K the thermal energy is below 15 cm-1. "Hot" bands
are thus eliminated. Very long depositions are possible allowing build
up of low abundance species and species of low absorption coefficient.
Controlled diffusion experiments allow matrix reactions to form new
species or clusters. It is also sometimes possible to observe species
with preferential orientation in matrices as is done in single crystal
work. More detailed discussions of the matrix isolation technique can
be found in recent reviews^^^-^ and references therein.
A large array of spectroscopic techniques have been employed in
matrix work, including infrared and Raman, electron spin resonance,
Mossbauer, and visible and ultraviolet absorption and emission. More
recently magnetic circular dichroism of matrix isolated samples was
22
introduced by Douglas et al. at the University of East Anglia. Mag
netic circular dichroism has its roots in the work of Michael Faraday
when in 1845 he first observed the phenomenon now known as the Faraday
effect. When plane polarized light traverses any transparent medium
colli nearly with an externally applied magnetic field, the plane of
polarization is rotated.
Linearly polarized light consists of equal components of right
circularly polarized (RCP) and left circularly polarized (LCP) light.

6
If in some medium the indices of refraction for RCP and LCP light are
different, optical rotation occurs. If the absorption coefficients for
some transition differ for RCP and LCP light, circular dichroism (CD) is
said to be present.
There are two sources for these inequality. Natural optical
activity arises in a molecule of low symmetry or unit cell in the case
of crystals, and its wavelength dependence is known as optical rotary
dispersion (ORD). The quantum mechanical theory ascribes the ORD of a
molecule to electronic transitions which have parallel or antiparallel
23
electric and magnetic transition moments. The second source of inqual-
/\
ity is application of an external magnetic field, H, in the direction of
light propagation. In this magnetic optical rotation, the right- and
left-handed circular motions around A do not interact equivalently with
the medium, and the absorption coefficients of RCP and LCP light in
regions of absorption differ in the presence of the magnetic field. This
gives rise to magnetic circular dichroism (MCD) which is the differential
absorbance of RCP and LCP light. The increase in information content
offered by polarization-dependent selection rules for optical absorptions
makes MCD a very powerful complement to conventional spectroscopic meth
ods in electronic structure determination.
Magnetic circular dichroism can provide information on the ground
states of atoms and molecules although the prime utility of MCD has been
in extracting excited state information otherwise unavailable. Excited
state magnetic moments and g values are attainable as well as spin-orbit
coupling constants and information on static and dynamic Jahn-Teller
24
interactions.
The same information is available from Zeeman spectra if all Zeeman
components are resolved. This resolution is often difficult, requiring

7
very high magnetic fields. The advantage of MCD is that it is a signed
technique (i.e., positive and negative bands are seen) not requiring
high magnetic fields. In this work a 5500 Gauss field was employed.
Overlapping, thus unresolved absorptions may be resolved in MCD if the
MCD for one of the overlapping components is much larger due to MCD
selection rules or if the transitions have opposite MCD signs. An
example is the differentiation of tyrosine and tryptophan where absorp-
tions overlap. Typical limits of detectability are 103 OD for
absorption and 10-s OD for MCD. The expected situation of a detectable
MCD with an absorption too weak for observation sometimes arises as in
the example of spin-forbidden transitions of octahedral and tetrahedral
27 28
Co(II) species 5 and for impurities in optical grade CaF2 plates
cooled to 13 K, vide infra. The fact that some MCD transitions display
a temperature dependence (to be discussed in detail later) makes applica
tion of the matrix isolation technique to MCD very appealing.
Matrix isolated samples studied by MCD since the work by Douglas
22 29 30
et al. are few. Atomic species Hg; group 11A atoms MG, Ca and Sr;
31 32 29 33
Ta; diatomic Cl2 and 02; Xe halides; diatomic oxides of Ti, Zr,
Hf, V, Nb and Ta;^ and benzene,^ OsO^ and acrolein^ are included.
The present research involves matrix isolated samples of atoms
and/or clusters of Pb, Cu, Ag and Au. Primary reasons for studying
these systems are the roles of small clusters in fundamental processes
38 39 40
such as heterogeneous catalysis, nucleation and photography.
Another compelling reason to study the electronic spectra of these
systems is the increasing number of optically pumped lasers being devel-
41
oped involving them. Also of basic interest is the observation that
matrix isolated Cu, Ag and Au atoms, all involving 2P <- 2S transitions,

8
reveal a triplet structure while the corresponding gas phase spectra
display only doublet structure. The on-going controversy as to the
origin of the matrix triplet structure can be resolved by a moment
analysis of the MCD spectra as is shown later.

CHAPTER II
THEORY OF MAGNETIC CIRCULAR DICHROISM
The theoretical treatment and pertinent equations as developed by
42-44 45
Stephens and Buckingham and Stephens are outlined. The treatment
has gained wide acceptance and is employed in this work. It is conven
ient to begin with consideration of circularly polarized light. Various
suggestions have arisen recently to explain the anomalous structure of
the 2P - 2S transitions of matrix isolated atoms. The quantum mechanical
equations necessary for evaluation of these theories are also developed
here.
Unpolarized light consists of an electric field vector, , and a
/\
magnetic field vector, H, both with random direction and both varying
sinusoidally with the direction of propagation. In plane polarized light
the vectors E and H vary in magnitude but are constant in direction. If
now plane polarized light traverses a transparent birefringent medium
where the speed of light depends upon the direction of light polariza
tion, then part of the beam will be delayed with respect to the other,
depending upon the thickness of the medium and the difference in the
indices of refraction. If the plane-polarized beam enters the bire
fringent medium oriented at 45 relative to two perpendicular axes of
/s i ^
different refractive index, components of the projection of the E and H
vectors of equal magnitude will be phase shifted relative to each other.
If this phase shift is equal to the light wavelength, X, the emergent
beam is restored to plane polarization. If, however, the phase shift
9

10
is not equal to A, the resultant electromagnetic vectors will trace
helical paths upon emergence. If the helix is traced clockwise while
looking toward the source, the beam is said to be right polarized. The
emergent light is elliptically polarized. If the phase shift is just
equal to an integral multiple of X/4, the light is said to be circularly
polarized as the cross section of the helix will be a circle. The and
H vectors in circularly polarized light vary in direction but are con
stant in magnitude, while in elliptically polarized light both direc
tion and magnitude vary.
If in some medium left and right circularly polarized light are
propagated with differing absorption, the medium exhibits circular
dichroism. In the presence of a magnetic field along the direction of
propagation of circularly polarized light, all matter exhibits circular
dichroism, known as magnetic circular dichroism (MCD).
Basic Equations
Consider a light beam traversing a sample with ground state A and
excited states J and K in the presence of a magnetic field H in the
direction of light propagation. The Poynting vector can be used to
express the light intensity at a point z:
2ek+z
I(z) = ^ n(E0)2 exp
o -2ekz
= J exP "T
(1)
where e = hv is the photon energy, k+ represents the absorption coeffi
cients for left (-) and right (+) circularly polarized light, h is
Planck's constant divided by 2tt, c is the speed of light, E is the

11
electric field at z = 0, n+ are the complex refractive indices for LCP
and RCP light, and 1 is the incident light intensity. Differentiating
and solving for k+>
h "6I(z)
k ne|E(z)|2 <5z
where
n /-2ek z\
|E(2}|2 = (E¡)2 oxp' ^--J (3)
The quantity ^ ' expresses the energy absorbed per unit time at z
which is dependent upon the number of sample species, Na, the photon
energy e, and the transition probability Pa -> j.
-<5I(z)
5z
Na Pa-\j
(z) e
(4)
If electric quadrupole and magnetic dipole interactions are ignored
and we consider only electric dipole transitions, the above probabilities
can be related to the electric dipole transition matrix elements through
time-dependent perturbation theory if the assumption that the effective
Hamiltonian H0 is a sum of independent components is embraced.
H0 = H0 + V (5)
where is the Hamiltonian for the system with no light, and H0 1 is the
Hamiltonian for the perturbation due to a radiation field. The subscripts
denote the absence of an external magnetic field.
= ^IL!E(z)|2||26(Eja-E)
Pa-j (z)
(6)

12
where are electric dipole transition moments, E. = E.-E a is
1 ja J a
a Lorentz effective field correction factor which relates the electric
field due to the light at the absorption center to the macroscopic elec
tric field, m+ is the transition dipole moment operator for LCP and RCP
transitions, and 5 is the Kronecker operator which arises because tran
sition lifetimes are neglected. The absorption coefficients can now be
expressed as
2tt a
2,2
a ,j
Na||26(Eja-E)
(7)
This equation can be expressed in terms of absorbance
exp
-2ekz
-tic
= 10
-A IU1
1
10
-e cz
(8)
where A = absorbance, e' is the molar extinction coefficient, and c is
now the concentration of absorbing species. The absorbance is
A
£ '
Y+
Z_i j-pl
¡ 2a(£ja-e)cz
(9)
where
NniT2ct2loqi 0e
250 ficn
(10)
N0 is Avogadro's number, Na/N is the relative population of ground state
a, and e is the Naperian log base. This equation assumes Beer's law is
obeyed and does not apply for the non-linear effects present for intense
light. The difference in LCP and RCP light dichroism, AA, is expressed
= A_ A+
AA
(11)

13
Substituting into equation (9)
= Y+ X {r I|2 ||2 fi(e-a-e)cz (12)
^ 5 j
The summations are over all sublevels a and j of the ground and excited
states, and the integrals are electric dipole transition moments.
Equation (12) is general and applies to natural CD as seen in optically
active media. Magnetic circular dichroism is not a perturbation of
natural optical activity but rather arises from different polarizabili
ties which are zero when no external magnetic field is present. The
natural and magnetically induced phenomena are additive. In a system
possessing no natural optical activity in a region absent of a magnetic
field,AA = 0 and ||2 = ||2. In this case the zero-field
absorption, ZFA, is defined as
A = A+ = A = Jg(A+ + A.) (13)
At this point it is convenient to introduce the rigid shift model
in order to modify these results to reflect the actual bandwidths in the
presence of a magnetic field. The rigid shift model requires adherence
to the Born-Oppenheimer approximation in the ground and excited states.
Separation of electronic wave functions under the Born-Oppenheimer
approximation into nuclear and electronic terms may be denoted by a
product of wave functions
|Aaa> = Ta (r,R)x (R) a = 1 to dft (14)
a
|JXJ> = Tj (r,R)x-(R) A = 1 to dj (15)
X
where ip indicates electronic wavefunctions with dependence upon the

14
instantaneous nuclear configuration, y^ and y. are vibrational wavefunc-
a J
tions dependent upon the particular electronic configuration and the
nuclear coordinates R, r is the electronic coordinate, and d^ and dj are
the degeneracies of states A and J. The eigenfunction equations are
:uxi>
e A a>
a1 a
(16)
The Franck-Condon approximation that most electronic transitions occur
at R near the equilibrium nuclear separation R0 is employed to simplify
the transition matrix elements.
=
a 1 1 X 1 a1 1 X
(17)
The lower case letters refer to the vibrational wavefurctions, and the
superscript indicates evaluation of electronic matrix elements at R = R0.
If the transition is only weakly allowed, the Franck-Condon approximation
is inadequate, and further account of the R dependence of electronic
wavefunction must be taken. Equation (12) now becomes
e
Y
Na
N
|26(eja-e)
cz
(18)
Assuming y to be constant for all vibronic transitions and integrating
over the whole band yields
I
2
CZ
(19)

15
Equation (18) now can be written
A+
= yDnf(e)cz
(20)
where
D
1
o h
>
0 dn c 1 a1 1 X
A a,A
nI 2
__1
2d
A a,A
I2 + |I2
a' 1 X 1 1 a1 1 A 1
(21)
and
f(e)
I
Na,
a,j
12S(c. -e)
Jd
(22)
with
r<
f(e)de = 1
The ZFA as given in equation (20) has a shape originating in the ground
and excited state vibrational wavefunctions and an integrated intensity
dependent only upon the electronic wavefunctions, evaluated at equilib
rium position R0. The line shape is temperature dependent due to the
Boltzmann term Na/N, but the integrated intensity is temperature inde
pendent.
If a magnetic field is applied, the absorption coefficients, k+,
display a field dependence. The eigenfunction and eigenvalues of the
system's Hamiltonian must now be obtained as explicit functions of the
magnetic field. This is only feasible in an analytical form when per
turbation theory may be employed to treat field-dependent terms.

16
The assumption here is that the magnetic field energy is small compared
to the zero field separation of the states. A perturbation term is added
to the system Hamiltonian [equation (5)]:
H = Hq + H (23)
Considering only electronic contributions to the first order mag
netic field perturbation,
' = -I +2s )H (24)
i i S'
where the summation runs over all electrons, i of mass m and charge e.
The magnitude of the magnetic field is given by H and is directed along
+ h
the z axis. The projection of the angular momentum of the i electron
onto the z axis is given by and the projection of the spin onto the
i
z axis is given by szi. Summation over all electrons yields
H = -uzH=e(Lz + 2Sz)H (25)
where 3 is the electronic Bohr magneton (= 4.6681xl0_1cm_1/gauss), and
yz is the electronic magnetic moment along z. The corresponding orbital
and spin angular momenta along z are given by l_z and Sz- Equation (25)
ignores interaction with the nuclei since nuclear magnetons are at least
three orders of magnitude smaller than electronic magnetons. Within the
ground and excited state manifolds, H' is diagonal in the Franck-Condon
approximation:
| H1
\ A ,
i a' > =
- u
A >H6
a
1 a
a
1 HZ
' a aa
| H'
i-V
.j> =
- lyZ
IV"H5aa
(26)

17
if the electronic wavefunctions at R0 are chosen to diagonalize y So,
if mixing of electronic states by H is neglected the wavefunctions in
the magnetic field are |A a> and JJ j> with energies
Ot A
£
A a
a
-
a1 Hz
A > H
a
(27)
ej In this first approximation the Zeeman splitting of each vibronic state
is independent of vibrational level and is identical to the pure elec
tronic splitting at R0. As a better approximation Stephens includes
intermixing of different electronic states, K, with states A and J:
uxj>
K k
(k5j)
K >
K
H
£jk
(28)
IA a>'
1 a
A a>
1 a
K >
K k
(KfA)
H
eak
where the primes denote wavefunctions in a magnetic field. The intervals
eal< and are large compared to Zeeman energies and again use the
Franck-Condon approximation. If it is assumed that the vibrational
levels k contributing to the sums in equation (28) are such that the
intervals are approximated as
e
ak
e
Jk
(29)
where the W
o
values are energies for the various states, then

18
equation (28) becomes
>1
H
I Jxj> Z, |K J> 4
KZJ W W
(30)
[ A a>'
1 a
, , H
A a> Zj K a>
Ot iTZn K 1,0 ,0
kk/a Wa WK
To first order in H there is no energy contribution from these wavefunc-
tion perturbations. The transition moments become
'

a1 1 X
(31)
. K /J
1 K

a1 ¡ k k1 z1 X
"k
\
rv 1 + 1 iz~ \r 1 ^ 7 1 rv
K fk
K
a1 1 k k 1 z a
WK V

= [ + ']H a1 1 X
Ground state Zeeman splitting also leads to population changes,
A a
a
exp(-c'A a/kT)
a
I exp(-e'fl a/kT)
a ,a a
(32)
exp(-ea/kT) exp( H/kT)
^ exp(-ea/kT) exp(H/kT)
a, a
At large T where Zeeman energies are small relative to kT,
exp( H/kT) ^ 1 +
H
rv I rv
kT
(33)

19
so that
Aaa exp(-ea/kT) 1
N X exp(-ea/kT) dA
(34)
N
Since under Zeeman splittings the center of gravity is retained,
(35)
This shows that the fractional change of population in |A^a> is not
dependent upon vibrational level and is the same as obtained in a purely
electronic system at RQ.
With these effects of the magnetic field on transition energies and
moments and on ground state populations, the circularly polarized absorp
tion MCD can be derived.
From equation (9),
A
Y
(36)
X,j
Y
X
+ 'H f1 (e) cz
a1 ' X a1 1 A aA '
Here,
f

20
is a line shape function identical to f(c) but shifted rigidly along the
e axis by the A -* J, Zeeman shift
a a.
-[
]H
A1 z1 A a1 z1 a J
If a band is broad, the Zeeman shift is a very small perturbation, and
the shifted lineshape function can be expressed in terms of the unshifted
lineshape function by a Taylor expansion:
f'ca'E> f + WxlKzlV MV W <38>
if terms above the first order in H are dropped. Substituting into
equation (36) and collecting terms of zero and first order in H is
obtained
e
A
Ei+ 37 l0l2t -
a,A A
]
a|Hz' of J 9e
If
+ Zj Re[
'*]f(e)
4\ dn L a1 ' X a'A J v
a, A A
If
a,A aA

a1 z 1 a
kT
l0|2f(e)^CZ
(39)
From the manner in which the circularly polarized light absorption is
modified by the magnetic field and the above considerations, an expres
sion for the MCD is written as
= A_ A+
3f(e)
3e
r co'
So + kT
\
f(e)
/
AA
3Hcz (40)

21
where
The effect of an applied magnetic field on the circularly polarized
absorption is shown in equation (36). Each of the component transitions
contributes absorption identical in shape to that at zero field.
The intensity is modified by the ground state Zeeman effect and inter
mixing of the zern-field electronic wavefunctions, and the energy of the
band is changed by the Zeeman shift. Each of these changes is the same
as that obtained with nuclei located at R0 configuration. The term
"rigid shift" is used because the absorptions shift in an applied mag
netic field without change in shape.
The total MCD and CP absorption is the sum of contributions from
all Zeeman components -* J^. On inspection equations (39) and (41)
show that at high temperature and large band width the intensity and
energy changes of the Zeeman components of the transition due to the
magnetic field contribute additively and linearly in H to the change in

22
MCD and CP absorption. Other contributions to Zeeman splitting or
intensity changes due to either ground state redistribution or inter
mixing of electronic states are physically separable through their
dependence on e or T. The relative magnitudes of the A, 8 and C terms
determine the overall MCD. The A terms require either ground or excited
state degeneracy; 8 terms can exist under any condition of ground and
excited state degeneracy; and C terms require the ground state A to be
degenerate. Calculation of these terms can be used to predict the sign
and shape of the MCD dispersion. The maximum contribution to the MCD
of the three terms are related as
A i 8 o: C q
zz_z_
T'AW'kT
(42)
where T is the bandwidth of an electronic transition, AW is the order of
magnitude of an electronic energy gap, k is the Boltzmann constant, Z is
the Zeeman energy, and T is the temperature.
The experimental form of Aj 80 and C0 terms is illustrated in
Figure 2.1. The A: terms occur if there is a degeneracy in either the
ground or excited state. In positively signed Aj terms, the high energy
lobe is of positive sign and the low energy lobe of negative sign. In
Aj terms the two lobes are always oppositely signed and of equal magni
tude. Since the two lobes are separated by a small Zeeman splitting of
the degenerate level involved, the derivative-shaped term arises. The
intensity of allowed Aj terms is influenced by the sharpness of the
absorption band as indicated by the 3f/9c factor. The Ax term size is
also affected by the difference in magnetic moments for the ground and
excited states. If these are equal, no A1 term is observed.

Figure 2.1. The appearance of terms predicted by MCD theory.
(a) The zero field absorption and MCD for a
transition with a positive Ai term. The
positive lobe lies at higher energy.
(b) A 80 term may be positive or negative, the
maximum coincident with the absorption
maximum.
(c) A negative C0 term at two temperatures,
T^igh and Tgow, may be positive or negative
with its maximum coincident with the
absorption maximum.

(a)
(b)
(c)

25
Terms of B0 are a general property of all MCD spectra and arise
from magnetic field mixing of neighboring electronic states with
either the ground or excited state of a transition. These terms have
the same shape as the absorption spectrum and can be positively or
negatively signed. It is generally difficult to calculate 80 terms as
knowledge of multiplicities and energies of all states near A and J
must be known.
Only when the ground state is degenerate can C0 terms exist.
Population changes induced by magnetic field splitting are demonstrated
by the inverse temperature dependence of the parametric equation. The
C0 terms may have either sign and have the same shape as the absorption
band.
Magnetic Circular Dichroism Calculation for Atoms
Photons possess well-defined values of angular momentum and are
absorbed or emitted by systems which are characterized by well-defined
values of their angular momenta.^6 The selection rules characterizing
transitions involving photons with angular momenta must account for the
conservation of angular momentum.
Consider transitions occurring in an isolated atom with total angu
lar momentum J. The degeneracy of the state is given by 2J+1, corre
sponding to the number of distinct eigenvalues rrij. The field around
an atom is spherically symmetric so there is no preferential direction
ality of the angular momentum. Under an external magnetic field this
degeneracy is lifted via the space quantization imposed by the direction
of the magnetic field. Figure 2.2 shows the Zeeman splitting of the
eigenstates of atoms with total angular momentum J = 0 and J = 1 in a
magnetic field and the possible transitions.

Figure 2.2. Polarized transition to an atomic P state and
magnetic field splittings. Transition a is
right circularly polarized, transition c is
left circularly polarized, and transition b
is polarized parallel to the magnetic field.

27
J
O
o
H = O
H/0

28
It is possible to calculate the probability for the absorption of
a photon for a transition from states a to j. The probability is pro
portional to the square of the transition dipole moment matrix element
along the direction of the photon polarization,
(tf-i. ) = (-
) (43)
ja
where "u is the unit vector determining light polarization and rfi- is
\J u
the electric dipole moment. Selection rules for the transitions in
Figure 2.2 can be derived considering the three possible light polariza
tions (x, y and z) in equation (43) and the properties of the wavefunc-
46
tions as described by spherical harmonics.
First, considering polarization in the z direction (parallel to the
applied magnetic field), equation (43) is non-zero if AJ = 1 and
Amj = 0. Since this is the direction of light propagation in the MCD
experiment, it is not available. The two possible polarizations u and
uy for light propagating along z are more conveniently examined in the
linear combinations ftxiu corresponding to circular polarizations. The
sum is RCP and the difference LCP. For RCP equation (43) is non-zero if
Anij = = -1 and the non-zero LCP values arise for Arrij = +1. For
both cases AJ = 1. Transition b in Figure 2.2 is thus not observed.
Transition a corresponds to RCP and c to LCP. In this case circularly
polarized light corresponds to electric dipole photons of J = 1 and
mj = -1 for RCP and +1 for LCP. Similar selection rules apply for any
system due to conservation of angular momentum.
To illustrate how the various magnetic field splittings give rise
to the MCD Ax and C0 terms, Figure 2.3 shows MCD transitions with either
ground or excited state degenerate. Two cases are shown with only the

Figure 2.3. Magnetic field splitting in
degenerate ground and excited
states illustrating the origin
of A0 and C0 terms.

A Term: Temp.
Independent
G+ G_
- 0
T >
r
.1
doo
o
/
/
/
/
/
/
/
n
OOP
OQQ
\
\
\
\
\
\
_ 1
OQQ
GOOOQ
i
C Term: Temp.
Dependent

31
ground state split. At low temperature the population of the lowest
magnetic sublevel is much greater than that of the higher sublevels, and
the observed MCD will be similar to that at the right of the figure.
Increasing the temperature depopulates the lowest state thus decreasing
the MCD at the higher energy transition and increasing the MCD transi
tion at lower energy (dashed curve higher T). If all the sublevels are
equally populated the MCD will be as in the middle spectrum. The
populations are governed by Boltzmann statistics. A CQ term such as the
middle spectrum appears to have the A: term derivative shape and is
sometimes referred to as a "pseudo A term."
Consider the transition of an electron in a free atom of 2S ground
state to a 2P excited state. If the atom is placed in an octahedral
field, the representation of these states must be determined in group 0. .
Full Rotation Group ^h
Note that for group 0 the r representations are rx = A1, T2 = A2, F3 = E,
r4 = ri5 r5 = T2, r6 = E', r7 = E", and r8 = U'.47 Thus, in 0^ the 2S
state representation is A,, and the 2P state representation is Tx.
47
Using Koster's table of compatibility for orbital angular momentum,
the representations for 0 and 1 are D0 and D1S respectively. Both states
are spin %, and again from Koster's tables Dt r.(E'). The spin-orbit
-i
coupling effect in these states can be determined taking cross products
of the spin and orbital representations. For 2S,
r. rK = r = e1
lb b

32
and for 2P,
r6 = r6 + r8 = e1 + u1
The energies of the spin-orbit states can now be found. The 2TX
states are
<2T1Jtx|Hs [2 T!Jtx> (44)
where Z11 is the representation of the excited state, t is either E or
U', t is the component of t (for E', x = a' or 3', and for U1, t = K, A1,
y' or v'), and Hs Q represents the spin-orbital Hamiltonian. Following
48
Griffith, equation (44) can be rewritten in terms of a reduced matrix
element R.
<2T1Jtx|Hs<0J2T1JtT> = tZj x R
The fl values are taken from Griffith. For t = E' the energy is
c2T11 |H ||2T1>, and for t = U1 the energy is --i-<2T1 | |H ||2TX>.
J SvOe O o (j o
If
k
s.o.
?Tr
the splitting in the excited state becomes
E1
' U' "k
There is also a Zeeman splitting to consider for each state in a
magnetic field. It is convenient to choose a basis set which yields a

33
matrix where all off-diagonal terms are zero for the Zeeman Hamiltonian.
This facilitates determination of Zeeman energies. Such a basis set is
49
obtained by reference to Griffith's book. The spin orbit basis can be
expressed in the form |rryn >.
Ground
state:
|2AX E1
ia
3'
>
= |o h>
l ,
2 .
Excited
States:
iv
'a'
>
= /y |0 +Js> "
1
1
-h>
Sz ,
1
1 2txe
'3'
'>
= ^ ll +%> -
SZ 1
0
-h>
I2TiU
V
'>
= 1 +Jg>
SZ ,
1
1 2T i U
'X
'>
- /y |0 -h> +
S3 1
1
-h>
1
SZ
l^u
V
'>
= /3 1-1 +Js>
+ S3
|0
-h>
|2TlU
V
>
= | -1 -%>
The wavefunctions in equation (45) are found by taking cross products of
orbital and spin representations in group 0^ such as r4r6 Tj @E for
the excited state, so the appropriate table (A20 for T^E) is consulted
49
in Griffiths book.
The Zeeman operator is Lz+2Sz, so matrix elements of the form
<2T1E'al|Lz+2Sz|2T1Ea'>
are calculated.
. JL
The results
of applying these operators are
S I
m >
= m,.
m >
if = 1
z1
s
s1
s
L I
z1
lv
if - = 1
(46)

34
Since there is some reduction in angular momentum if the
a free atom, integrals of the form
system is not
<1[LZ|1>
= y
rather than 1. To facilitate approximation of MCD and absorption inten
sities, the y can be approximated as 1. The integrals in equation (46)
for the excited state are
<2T1Eal|
Lz+2Sz|2T1E'a'> = ^+§(y-l)
(47)
<2T1EI6'|
Lz+2Sz|2T1E'6'> = 4-|(y-l)
<2T1U,ki1
LZ+2SZ|2T1UV> = y + 1
<2T1U1v1|
Lz+2Sz|2T1U'v'> = -y 1
<2T1U'A'1
LZ+2SZ|2T1U'A,> = j + j (y-i)
<2T1U'y'|
Lz+2Sz|2T1U'y'> = -|-|(y-l)
and for the ground
state
<2A1E'al|
L z+2S z|2Aj Ea1> = +1
(48)
<2A1E'8i1
|Lz+2Sz|2A1E'3'> = -1
The energy level diagram in Figure 2.4 can now be drawn.
In order to predict MCD and absorption spectra it is
to calculate electric dipole transition moment integrals.
hedral point group the dipole moment operator transforms
also necessary
In the octa-
as the Tx
symmetry representation. The integrals are of the form in equation (48)

Figure 2.4. Splittings in free atom 2S and 2P
orbitals for:
(a) an octahedral site
(b) spin orbit interaction
(c) Zeeman splitting.

36
FREE
ATOM
Oh
SPIN
ORBIT
ZEEMAN
SPLITTING
(units of ¡3)

37
a g y
[-l]a+a I |gbl lovf
a c
i t t
\-a y
where a and c are the ground and excited states, g represents the mj1
dipole moment operator, and V is a vector coupling coefficient found in
49
Griffith's tables. These integrals are calculated over the wavefunc-
tions given in equations (45) above. In order to have a non-zero matrix
element the spin must be the same in each wavefunction in the integral.
The m operators of interest for MCD transitions are step-up and step-
down operators m+ and m_. It is possible to consider all possible tran
sitions from the ground state to each excited state function and deter
mine which are a+ and o .
<2A1E'al|m|2T1E'a'>
1 /2~
| 2T10+h> yf <2A104is|m_|2T1l-J$> (50)
1
= <2A, 01 m_ | 2Tj 0>
= [-l]TlV
Ai h Ti'
0 0 -1.
<2A1E'B'Im|2T1E'a>
<2A1E'a'[m+12Tj E'G1>
1 /2 .
7f |2T10+%> yf <2A10-%|m_|2T1l-%>
- tI <2A10|m_|2Tx1>
C-i]Tl v|Al Tl Tl|
L -T,
" /3 m
- 4
+
/2
3
%>

38
<2A1E'3Im¡2T1E1S' > =
<2A1E'a|m_|2T1U1k'> =
<2A1E18iIm|2TU1k1> =
<2A1Elal|m|2T1U,vl> =
<2A1E'3 Im+pTjU'v^ =
<2A1E'a1|m|2T1U1A1> =
<2A1E'3iIm_|2T!UX'> =
<2A1E,a |m+|2T1UV> =
<2A1E,3|m|2TXU'y'> =
Note that the bra is the ground state and the ket the excited state.
The energy level diagram in Figure 2.4 can be redrawn including the
sign of light polarity of each transition and the square of transition
probabilities as in Figure 2.5. It is interesting to note that the
polarity of a transition will be a+ for the m+ step-up operator and o_
step-down operator.
Having determined the integrals above and the transition probabil
ities, the C0 and V0 expressions in equations (21) and (41) can now be
evaluated. Recall equation (41):
Cn = -i- [I
[2 II2]
0 dn ; L| a1 -1 A 1 1 a1 Tl X 1 J a1 z z1 a
A a,A
and equation (21):
= 37 2 l A a,A
+ /3<2A1| |m_Ti| |2V
+ 7=<2A1||m+Ti||2T1>
+ ¡r<2A, I Im Ti| I2
3 I 1 1 T1>
+ ^-<2A1||m+TM|2T1>
2

Figure 2.5. The state splittings and allowed transitions for
an atom in an octahedral field showing the effect
of spin orbit and Zeeman splitting.

nado
0*H NldS MO
<2/1 0 1 Vs I
<2/1 O *VZ I
2y>6/i 2yjc/i ^e/z
to
to
\D
-JD
to
<2/1-I-1
<2/1 0 | %/'/y* + <2/1 I- | £/V I
<2/1 -I |£/VI + <2/1 0\%/-/Zf
<2/1 11
n \
j7 vx\
's\
^ /
<2/1-0 ¡£/-/i <2/11-1 y-/y-
<2/1 I |CA/^A <2/1 O | £/-/!
D
/
Ofr

41
Now, for the transition from 2A1E to 2T1E':
C0 = [|<2A1E,31|m_|2TiE'a,>|2<2AlEl3l|Lz+2Sz|2A1E'3
- |<2A1E'a'|m+|2T1E,3,>|2<2A1E,al| Lz+2Sz | 2AX E V>]
= j [| m2(-3H) | m2(3H)]
= |m2
vo = J'J2 = |m2
Thus,
C0/VQ = +2
For the transition from 2A1E to 2T1U1:
C0 = [|<2AiE'al |m_|2T1UV>|2<2A1E,a|Lz+2Sz|2A1E'a
- |<2A1E'3i|m+|2TlU'vl>|2<2A1E,3'|Lz+2Sz|2A1E'3'>
+ |<2A1E,3'|m_|2TlU,A,>|2<2A1E,3|Lz+2Sz|2A1E'3,>
- |<2A1E,al|m+|2T1Ulul>|2<2A1E'a'ILZ+2SZ|2A:E'a'>
C0 = | m2(3H) y m2(-3H) + } m2(-3H) | m2(3H)]
2 2
g m
and
Vc = = |ni2
> (51)
(52)
(53)
'> (54)
(55)

42
Thus,
C0/P0 = -1 (56)
The predicted MCD and absorption transitions of 2P 2S in an octahedral
field can be diagrammed as in Figure 2.6.
Effect of Reduced Site Symmetry
Another possible cause of MCD C terms which must be explored arises
through a reduction of the octahedral site symmetry described above.
The most likely reduced symmetries are due to displacement of the copper
from the center of the surrounding octahedral rare gas atoms resulting
in a D3 symmetry and a change in the distance of the "axial" octahedral
distance resulting in a D4 symmetry. Either of these distorted matrix
sites yields a further splitting in the 2TiU'(2P3/z) octahedral state.
The predicted MCD term signs can then be compared with experimental
results. The distorted symmetry approach can be illustrated by consid
ering a static trigonal distortion (D3) and calculation of the eigen
values, eigenfunctions and CQ/VQ values. The 3x3 energy matrix for the
cnco
D3* case is given asJ
2E,1,%>
0
0
2 E,1,h>
0
_x
/2
-a2,o,%>
0
_X
/?
-A-ei
(57)
where A denotes the trigonal field distortion parameter. The matrix
consists of lxl (2EE" state) and 2x2 (the 2A2E and 2EE1 states)

Figure 2.6. The predicted MCD and absorption patterns for
the 2P 2S transition in an octahedral field.

44

45
submatrices. The eigenvalues and eigenfunctions in the m,ms basis are
wi th
where
2EE"{^}> = |2E,1,%> with E]
A+A
and
!A2E{,}> = C2 | 2E ,1 ,%> C 31 2 A2,0, Jg>
!2E E1{gi}>
= C2|2E,1,%> + C3|2A2>0,>5>
'2,3
(A+A) +
4 '
(A2
2AA + A2j%
2
_x
/2
r 2 +
U 2
2 \ 2
A2/2 + C4:
A A
2 £i
for i = 1,2,3
In the limit where the trigonal field distortion parameter, A, is
zero, the functions reduce to those obtained above for octahedral sym
metry.
53
Using these eigenfunctions and Piepho's tables for the D3* group
53
the C0 and V0 terms may be calculated from the standard formulae for
randomly distributed anisotropic centers:
C0 = 3f yo Im+l2 + 2y+m0m_}
V0 = i Im+12 + |m_|2 + |m012)

46
where d is the ground state degeneracy; 3 is the Bohr magneton; and p+,
do m+, and m_ represent integrals between states (for example, the
2 Aa E1 2 A i E' transition):
d+ =
<2AiE
/2
'a'|i3(L++2S+)|2AiE'3'>
0 =
<2A1E'a'
|-i3(Lz+2Sz)|2A1E'a,>
m0 =
<2A1Ea'
|m01 2A2E1 a.'>
m+ =
<2A1E'al
|m+|2A2E13>
m_ =
<2A1E'3i
|m_|2A2E'a>
In the case of trigonal distortion
(C2^r] 2C2C3mA rcv
C = 3
(C2mE)2 + (C3mA )2
Vq = 1
6
where m^ = and m^ = are reduced matrix ele
ments for the electric dipole transition moment. Possible eigenvalues
and values of C0/V0 could be estimated if a value for the spin orbit
constant, A, was chosen (see, for example, the discussion of the method
of moments for Cu in an Ar matrix) and the trigonal field distortion
parameter, A, was varied (vide infra). A similar treatment can be
followed for a Di+ distorted octahedral site.
The Adiabatic Model
From the band moment analysis it was shown that both spin orbit
interaction and noncubic vibrational modes of the matrix cage are

47
important to the spectroscopic appearance of the 2P - 2S transition in
matrix isolated Cu, Ag and Au. Three components of the 2P state are
apparent in the experimental MCD and absorption spectra. The observed
C terms are positive, negative, and negative (with the exception of Cu
isolated in Xe) as energy increases. The band separations in all three
metals are much larger than the spin orbit splitting deduced from band
54
moments. Because of similarities of these systems to the much studied
F center case (although in several F center crystals the triplet is not
55
resolved ), it is possible to compare these results with theoretical
calculations done within the framework of the adiabatic approximation.
In particular the effect of the two degenerate components of the noncubic
e mode on the MCD C terms and band separations are considered.
Because of the noncubic vibrational activity which mixes the first-
order spin orbit split states, it is not possible to describe the compo
nent states by a simple J,Mj (or other) description. The first-order
states become coupled by vibronic interaction. Any calculation of the
sign and magnitude of the C terms of the transitions to each component
56
of the 2P state must account for this coupling. To do this Moran's
adiabatic model of vibronic and spin orbit interactions in an excited
2Ti(2P) state is examined. Moran considered the effect of simultaneous
first-order spin orbit coupling and vibronic interaction via the tetrag
onal e mode only. The effect of the t mode will be to modify the exist
ing band shapes but not the splitting pattern (i.e., the triplet of
56
bands). In the Moran model the wavefunctions are
Â¥i
= C
11
+ + c3j l2T,E
i p
}>
(58)
where i runs from 1 to 3 and the coefficients are given by

48
(59)
and
pn- -/2[z(A/2 + z ei) t2]
(60)
-/2[t(A/2 z e.) tz]
psi = 26z + + £i}
In equation (60) t and z represent the degenerate pair of lattice coor
dinate displacements belonging to the e vibration, and X is the experi
mentally determined 2P spin orbit coupling constant. Using these expres
sions and the Wigner-Eckart theorem for the transition probabilities in
the 0* group as in previous cases, an expression for C0/P0 can be found.
(61)
C0'/V
The influence of the e mode components on the spectral splitting
pattern and MOD sign behavior can be determined by diagonalization of
Moran's 3x3 interaction varying the t and z displacements while keeping
X constant (and equal to the experimental value). For the case of large
spin orbit coupling, the effective Hamiltonian is given by:

49
H = H, + AL-S + H + H.
u e I L
where
Hel = -Y^kt-hs Y3(3Lz2 L*L)Z y3/3(Lx2 Ly2)T
Setting s = -y1S, t = -y T, and z = -y3Z the excited state Hamiltonian
matrix is
%3/2>
3/z V2 >
E + hX + z + A
=
t E + JgA-z + s
-/2t -S2z
I 1/21/2>
-S2t
E A + s
The Kramers degeneracy is apparent from the above matrix. Two criteria
are imposed on the diagonalization: 1) that the interband spacings
match the experimental ones at low temperature, and 2) that the signs of
the C0 terms match the observed ones. Further discussion of the evalua
tion of results under this model is presented with the spectra and anal
yses of the individual cases studied.
Band Moment Analysis
Returning to the subject of dispersion calculations [see equations
(13) through (22)], the most drastic assumption made there is that the
Born-Oppenheimer approximation holds for ground and excited electronic
states. In the Jahn-Teller theorem all spatial-symmetry-derived elec
tronic degeneracy is broken by at least some nuclear displacement, and
therefore the potential surfaces emanating from a degenerate state do
not remain exactly degenerate. The Born-Oppenheimer approximation then

50
breaks down, and it is no longer possible to associate a vibronic state
with only one electronic state. The calculation of zero field absorption
and MOD becomes very much more difficult. The diagonality of H1 in
eouation (26) is not maintained, and the magnetic field perturbation
scrambles different vibronic levels of the same electronic state. The
calculation of the Zeeman effect within an electronic state is then
dependent on the details of the Jahn-Teller phenomenon. In such situa
tions where the absorption and MCD are evaluated with difficulty, it is
of interest to look at alternative methods of analysis that enable more
complex models to be treated without dispersion calculations. The method
of moments is such an approach. The method of moments was developed by
54
Henry et al. in work formulating the theoretical framework for the
relationship between the moments of F center bands and the changes in
these moments with applied perturbations to the interactions (spin orbit,
55
vibronic) within an excited 2TX state. Osborne and Stephens modified
this work for treatment of F centers in LiF. The moment analysis per
formed here follows closely the equations as developed by Osborne and
Stephens. The various absorption and MCD moments are obtained from
(62)
where A and AA are the optical absorbance and differential absorbance,
A^-AR, resPec't've^y ar|d the average frequency of the zero field absorp
tion is given by
v

51
The ratio of the nth MCD moment to the zeroth absorption moment
is given by:

^A>
n
o
A + 8
(63)
where pin is the Bohr magneton; B is the magnetic field strength; and
the MCD parameters An, 8n, Cn, and VQ are defined as in Osborne and
55
Stephens. The MCD parameters of interest in this study are:
c0/p0
II
03
o
33
o
II
O
(64)
VPo
^orb
(65)
Ci/Po
= -2A/3
(66)
A3/Po
= 69orbt + }2{ + + 2(A/3)2}]
(67)
c3/v0
= -ZACo^ + %{ + + 2 (A/3)2} ]
(68)
= + ( + ) + 2(A/3)2
(69)
where gorb = , A is the spin orbit splitting of the
2J1 excited state (positive when the M' component lies highest),
and ( + ) represent the contributions to the band width (second
absorption moment) from the cubic and noncubic lattice modes, respec
tively, and include linear and quadratic coupling or anharmonicity.
The moments were calculated from digitized data by application of
Simpson's rule for numerical integration by the CBM 8032 microcomputer.
Further discussion of application of the moment analysis to Cu and Au
results appears in the respective sections.

CHAPTER III
EXPERIMENTAL
Sample Preparation
Detailed descriptions of the furnace assembly as well as the absorp
tion and MCD apparatus are outlined. Figure 3.1a shows the furnace
assembly used in these experiments.
Metal beams were generated from a resistively heated Knudsen cell
which is shown in Figure 3.1b. The cell was constructed of 0.15-0.020
in wall thickness, 0.25 in outer diameter tantalum tubing. The cell
was closed on either end by solid tantalum endcaps and strapped to two
water cooled copper electrodes. One of the electrodes was electrically
isolated from the furnace while the other was in contact with the fur
nace assembly. Alternating current as high as 300 amp, 60 Hz could be
run through the cell allowing temperatures in excess of 2300C. The fur
nace was cooled by water flowing through 0.25 in diameter copper tubing
soldered onto the exterior surface of the furnace. A Leeds and Northrup
optical pyrometer was used to measure the cell's surface temperature by
sighting the cell via a magnetic shutter on the furnace. The magnetic
shutter prevented metallic depositions on the surface of the viewing
window and associated inaccuracies in temperature measurement.
In order to prevent heating of the cryogenic window by heat radiat
ing from the Knudsen cell, a water cooled shield was installed in the
furnace. It is worth noting that this radiation shield could be removed
when generating vapors at temperatures below 1000C allowing a greater
52

Figure 3.
(a) Diagram of the furnace assembly.
(b) Diagram of Knudsen cell used for metal
vaporization.

54
COOLING
WATER
GROOVE
FLANGE
(b)
To CELL
.] G4 l?a5"
t
V

I IOO
Ta END CAP
Ta
STRAP^
-0.70

55
flux of metal toward the cryostat. The heat shield is a 0.25 in diameter
copper tube spiral between two 0.125 in copper plates. A 0.125 in diam
eter hole drilled at the center of the shield also served to collimate
the metal beam. This provided the added benefit of reducing the thermal
load of hot metal striking parts of the cryostat other than the cold win
dow. Careful alignment of the Knudsen cell effusion orifice with the
heat shield hole was necessary to ensure that the metal beam was directed
properly toward the cold window.
The metal beam was codeposited with an inert gas onto one face of
the cold CaF2 plate. The temperature of the cold window was maintained
by an Air Products Displex Model CS 202 closed-cycle helium refrigerator
capable of cooling to approximately 13 K. The temperature of the window
was set using an Air Products APD-B temperature controller and monitored
by use of a chromel-Au, 0.07% Fe thermocouple mounted near the middle of
the copper window frame and referenced to liquid nitrogen. The stability
of the temperature controller was rated at better than 2 K at the set
point but at times performed to better than 1 K from 13 K to 40 K. In
later experiments a Lakeshore Cryotronics Model DRC-80C Digital Cryogenic
Thermometer/Controller utilizing silicon diode detectors with a rated
stability of 0.1 K was employed. The detectors were mounted in holes
drilled into the copper window frame. The window frame assembly was
made from high purity oxygen-free copper and had a V'-28 thread stud for
mounting to the second stage of the refrigerator. The entire piece was
machined from a single block of copper and indium gaskets smeared with
Cry-con grease were used between all metal junctions on the copper
window assembly to ensure good thermal contact.
The cold window was a one inch diameter, 4 mm thick CaF2 plate. It
proved necessary to use an ultraviolet grade window since the lower

56
purity infrared grade window originally used contained an impurity which
had a temperature dependent MOD band overlapping the copper and silver
atomic bands. The corresponding impurity absorption band was too weak
for observation. The cold window temperature was controlled by a 10 W
variable duty cycle heater in a feedback loop with a second thermocouple
The isolant gas inlet nozzle was constructed from a 16 gauge Yale
stainless steel needle silver soldered to a 0.25 in diameter stainless
steel tube which was in turn silver soldered through a hole in the wall
of the short brass tube which joined the furnace to a gate valve. A
0.25 in vacuum quick connect joined the nozzle assembly to a 0.25 in
diameter stainless steel tube which was joined to a glass inert manifold
Inert gas was bled into the vacuum system through a Nupro extra fine
metering valve. The gas manifold was pumped by a 3 in Vari an M2 diffu
sion pump charged with 100 mL of Dow corning 704 silicone oil. Inert
gas flow rate was monitored using a standard mercury side-arm manometer.
The Air Products Displex is a two-stage, closed-cycle He refrigera
tor which makes use of the Joule-Thompson effect as compressed gas at
300 psi is expanded with a pressure drop in excess of 200 psi. The cry-
otip unit (shown in Figure 3.2) is constructed of stainless steel, with
the exception of the final expansion chamber. A nickel-plated copper
shroud attached to the first stage, maintained at 40-60 K acts as a heat
shield for the lower stage and copper window holder. Two openinqs cut
180 apart in the shield allow matrix deposition and, as the whole unit
is rotatable, also allow alignment with two ports in the external vacuum
housing. The second expansion stage terminates in a copper cold tip
which accepts the window frame threaded stud. The cryostat assembly is
connected to the furnace assembly by a second gate valve and can be

Figure 3.2. Detail of furnace-cryostat assembly used in
matrix isolation experiments.

58
ELECTRICAL-
ge
He GAS
53
o
THERMOCOUPLE
and
HEATING WIRES
EXPANDER
1st STAGE
U

2nd STAGE
COPPER COLD TIP
TARGET WINDOW
RADIATION SHIELD
GATE VALVES
ROTATABLE
JOINT
MATRIX
GAS
INLET
VACUUM
PUMPS
FURNACE
ASSEMBLY

59
removed and rolled along rails into an electromagnet for MCD measure
ments. When joined to the furnace assembly, the entire assembly is
pumped by a 2 in oil diffusion pump backed by a mechanical forepump and
equipped with a liquid N2 cold trap. Pressures below lxlO-6 torr are
attainable. Pressures are monitored by thermocouple and ionization
gauges connected to a Granville-Phi11ips Series 270 gauge controller.
Spectroscopic Apparatus
A diagram of the optics used in absorption measurements is shown in
Figure 3.3. The apparatus operates as a "pseudo double beam" spectrom
eter. The reference beam was not passed through a matched cell but
rather reflected around the cryostat onto the photomultiplier tube.
Light scattering from matrices caused some drift in the baseline at
higher energy wavelengths, but the Xe lamp emission spectrum was quite
effectively nulled over most of the spectral range. Spectra were
obtainable over the range of 8500 to 2200 A. The lamp was a 300 W
D
Eimac xenon lamp made by Varian Associates and operated at a pressure
of 115 atm and had a built-in parabolic reflector and a sapphire window
yielding an intense, wel1-col 1imated beam. The lamp was enclosed in a
small hood for removal of the ozone generated during operation. The
lamp housing was attached to a Spex 0.75 m Czerny-Turner Spectrometer
with a grating blazed at (1200 lines/mm) 3000 and an f-number of 6.8.
The slits were set for a spectral band pass of less than 6 A.
The beam emerging from the monochromator slit was spread by a 3 in
quartz lens (f/3) and then passed through two sets of slots on a spin
ning wheel. The wheel was driven by a hysteresis-synchronous motor at
1800 rpm. Five outer and nine inner slots in the wheel gave chopping

Figure 3.3. Optics for absorption experiment.

Mirrors

62
frequencies of 150 Hz and 270 Hz. These frequencies were selected to
minimize ac powerline pick-up since they were not integral multiples
of ac line frequency, 60 Hz.
The beam chopped at 270 Hz traversed the matrix and arrived at the
photocathode of an EMI 9683 QB photomultiplier tube. The beam chopped
at 150 Hz was reflected around the cryostat by two Edmund Scientific
aluminized front-surface mirrors and onto the same photomultiplier tube.
An iris allowed attenuation of the reference beam.
The chopping wheel assembly was equipped with two light emitting
diodes and two phototransistors located on opposite sides of the chopping
wheel from the LEDs so the signals from the phototransistors were used as
reference signals for the two chopping frequencies. The LEDs were
powered by a 15 V supply. Both signals were amplifed by RCA 3140 opera
tional amplifiers. A diagram of the absorption electronics is shown in
Figure 3.4.
The current output of the photomultiplier tube (^lO-7 amp) was con
verted to a voltage by a 15 to resistor connected to the ground. Part
of the signal was amplified by a factor of 100 using an Analog Devices
52 k low-drift operational amplifier and sent to an oscilloscope for
monitoring the wave form during the experiment. The rest of the signal
was introduced in parallel to two lock-in amplifiers--an Ithaco Dynatrac
391A Lock-in Amplifier and an Ithaco Model 353 Phase-lock Amplifier.
The Ithaco 353 was locked to the 150 Hz reference frequency from the
chopper, and its output was proportional to the lamp emission spectrum,
monochromator dispersion characteristics, and the photomultiplier tube
spectral response. The Ithaco 391A was locked to the 270 Hz reference,
and its output was proportional to the absorption spectrum of the matrix

Figure 3.4. Schematic of absorption experiment.

MONOCHROMATOR
/\
STEPPI NG
MOTOR DRIVE
NTERFACE
bd
PHOT.
TRAN.
LED
LOCK-IN B
/\
SAMPLE
PM TUBE
-IMPEDANCE
ADAPTOR
U
Wl DE BAND
AMP
LOCK-IN A
GAI N
LEVEL
SHIFTER
LOG AMP
IMP.
ADAPT.
REF
AMP
MAN/FB.
SWITCH
SAM.
AMP
ERROR
AMP
PM
HV
VOLT.
SUPPLY
SCOPE

65
in addition to the factors mentioned above. Both outputs were connected
to a Log Amplifier which took the log of each signal and performed an
analog subtraction to give an output in the form of the ratio of sample
to reference intensities. This output was connected in parallel to a
Soltec 1242 series two channel strip-chart recorder and the computer
interface.
All MCD experiments were performed with the same light source and
monochromator. The light source and monochromator were rolled on case-
hardened steel rails into position for the MCD experiment without dis
turbing the chopper assembly (which is permanently fixed on the optical
bench to aid easy alignment). Figure 3.5 shows the optics for the MCD
experiment. The beam emerging from the monochromator is focused by the
same lens onto a Glan-Thomson prism oriented at an angle of 45 to the
D
modulation axis of a Morvue Electronic Systems PEM-3 photoelastic modu-
1ator.
With the cryostat situated in the light path and in the field of
an Alpha Model 4600 electromagnet, a single beam MCD experiment was
performed. The magnet had a 0.75 in hole coll inear with the magnetic
field in each of the adjustable-gap pole faces.
The MCD electronics are illustrated in Figure 3.6. The signal
from the photomultiplier tube was fed into an Ithaco Model 391 Lock-in
Amplifier which was locked to the 50 kHz photoelastic modulator fre
quency. The amplifier's bipolar output was level shifted to yield
only positive voltages which were suitable inputs for the computer
interface and chart recorder. The output from the Analog Devices 52 k
operational amplifier was fed into an error amplifier-feedback
circuit. The feedback circuit employs a Bertan PMT-20, option 3

Figure 3.
. Optics for MOD experiment.

Magnet

Figure 3.6. Schematic of MCD experiment.


70
programmable high voltage power supply. The gain of the photomultiplier
tube is controlled in an inverse relation to the dc output by the feed
back circuit. The photomultiplier tube signal consists of a relatively
small 50 kHz ac component riding on a larger dc component that is pro
portional to both the xenon lamp emission spectrum and the absorption
of the sample. Background effects in the MOD spectrum are automatically
corrected for by maintaining a constant dc level with the feedback cir
cuit. In later absorption experiments the feedback circuit was also
used. This was facilitated by passing the lock-in output through another
operational amplifier used as an impedance adaptor and then into the
feedback circuit.
Both the absorption and MCD experiments were controlled by a
Commodore CBM 8032 computer. The monochromator was driven by computer
pulsing a SLO-SYN^ Model M0GI-FD-301 stepper motor attached to the wave
length scan control. The motor was stepped 200 times per revolution.
This allowed 0.25 steps of the monochromator.
The data was digitized using a Datel Systems, Inc., ADC-EK8B
analog-to-digital converter of 8 bit resolution. The operating program
allowed data collection at 1, 0.5 or 0.25 & intervals. After collecting
a spectral scan, the data was stored on a floppy disk. The data collec
tion and storage program is listed in the appendix.
The computer was also used to control the photoelastic modulator
which was synchronized with the wavelength drive. The modulator's wave
length of quarter-wave retardation depended upon the amplitude of stress
applied to the quartz crystal which was linearly dependent upon the
modulator's input voltage. The program calculated the correct voltage
for the running wavelength after each 0.25 A step, and this output was

71
sent to the modulator through a Datel Systems, Inc., model DAC-IC8BC
digital-to-analog converter. This device was also used when another
program read data from a floppy disk for output to the chart recorder.
For matrix preparation a tantalum cell was filled with metal powder
as fully as possible, but some of the fine powder invariably blew out
of the effusion orifice into the vacuum chamber during pump down and
degassing of the furnace.
The Knudsen cell was mounted, in the tantalum straps, onto the
water-cooled electrodes making certain the effusion hole of the cell was
aligned with the collimating hole in the heat shield and the CaF2 target
window. This alignment could be checked by sighting the tantalum cell,
when mounted in the furnace, through a window on the outer vacuum shroud
of the cryostat into the furnace.
The furnace was rough pumped for a number of minutes (as long as
30 min for very finely divided powders) using a bypass line which iso
lated the diffusion pump and liquid nitrogen trap. The pumping was
continued until a pressure below 200 y was shown on the thermocouple
gauge at which time the gate valve to the diffusion pump was gradually
opened and the bypass closed. The system was then pumped to below
2><105 torr with the diffusion pump.
The tantalum cell was then gradually heated to the deposition
temperature while keeping the pressure below 2-4x10~5 torr. With rapid
heating, material blew out of the cell as a powder and resulted in weakly
absorbing matrices. The outgassing process took as long as 2 hr in some
R
cases. During this procedure the Displex was rotated so the CaF2 window
was shielded from the Knudsen cell to prevent metallic film deposition on
the target.

72
The CaF2 window had to be cleaned with acetone and ethanol (to
prevent residue from evaporated acetone) between subsequent experiments
in order to obtain transparent matrices. Simply allowing heating of the
window and loss of the matrix and then recooling for another deposition
resulted in cloudy matrices.
D
After the outgassing process, the Displex compressor was started
and the CaF2 window cooled to deposition temperature. In order to
achieve transparent matrices, the window was cooled to 14 K for argon
work and 20 K for krypton and xenon work. Depositions below these
temperatures resulted in cloudy matrices. After cooling to the proper
temperature, the window was rotated into deposition position and a flow
rate of rare gas was set to about 1-3 mmol/hr with the needle valve.
Gas was deposited for 10 min before heating the Knudsen cell to deposi
tion temperature. Initial estimates of the correct tantalum cell temper
ature were set as the temperature required to maintain a vapor pressure
of the sample at 'vlxlO-3 torr. Depositions continued anywhere from 5 to
120 min. At intervals during the deposition, the CaF2 window was rotated
through 90 so the absorption could be measured. Deposition continued
until the bands of interest showed absorption of 0.5 to 0.95 0D. Depo
sition temperatures for each metal can be found in the respective
sections discussing results.
Both MOD and absorption spectra were obtained on a matrix at 13 K
and 20 K. If temperature dependence was exhibited, three scans were
stored at each temperature from 13 K to the highest allowed by the
matrix gas in 1 K intervals. For argon spectra were observed to 25 K,
for krypton to 28 K, and for xenon to 32 K.

73
The monochromator was calibrated with He-Ne and argon ion lasers
and scans were always run from low to high energy to prevent stepping
motor assembly backlash and maximum photomultiplier tube sensitivity.
All MCD spectra were run at 0.55 Tesla as determined by an
F. W. Bell Model 640 Gaussmeter. Zero-field circular dichroism spectra
were recorded to determine the zero-field line in the MCD. With the
magnet power turned off, a residual field of ^60 Gauss was measured. A
test of the linear dependency of the MCD signal upon the magnetic field
yielded the expected result (see Figure 3.7).
The MCD apparatus was calibrated for each matrix using aqueous
solutions of [Co(en)3]Cl(d-tartrate) made such that the absorbance at
o
4690 A was near 1 0D as measured by a Cary 17 Spectrometer. The proce
ed
dure was similar to that of Tacn," and the circular dichroism of the
standard solution was measured at 4930 A. McCaffery and Mason^ measured
the ratio of AA max/A max = 0.0225. The same solution was used to cali
brate the absorption experiment. Digitized absorption data were cali
brated in optical density units through use of the relation
where is the number of 0D units per digital data unit, C is the
concentration of the standard solution in optical density, and 1^ is
the sample absorption band intensity in arbitrary units as stored on
the floppy disk. Calibration of digitized MCD data was done through
the relation
K (C)(0.0225) Ss
^M L. S

Figure 3.7. Magnetic field dependence of an MCD
signal.

MAGNETIC FIELD STRENGTH (KILOGAUSS)
MCD INTENSITY
(ARBITRARY UNITS)
o
i
OJ
-f*
cn
-^1
cn
CD
O

76
where is the number of OD units per digital data unit, C is the con
centration of the standard solution in optical density, 1^ is the sample
MCD band intensity in arbitrary units as stored on the floppy disk, and
Sg and Sc are the lock-in amplifier sensitivities for the sample and
standard solution scans, respectively.
The signature of bands was cross checked by measuring the MCD of a
solution of K3[Fe(CN)6] which was known to have a positive MCD band
centered at 4250 K. A check for any depolarization due to the matrix
was run by noting any difference in the intensity of the CD spectrum of
the spectrum of the standard solution placed before and after the
matrix. No measurable depolarization was noted in most experiments.

CHAPTER IV
RESULTS
Figure 4.1 shows the expected splitting pattern of the isolated 2S
and 2P states under the various perturbations one might expect in the
matrix environment. The left section of the diagram shows the effect
on the free atom states, first when placed in an octahedral field. The
state labels refer to the 0^ group. Operating on the basis set with the
spin orbit Hamiltonian causes a splitting in the 2TX state. This split
ting still cannot account for the observed triplet structure (vide infra)
of group lb metals in rare gas matrices. If, then, the effect of a
distorted octahedral field (possible trigonal D3 and tetragonal D4
reduced symmetries) is considered, a further splitting is induced.
Diagonalization of the trigonal field distortion matrix in equation (57)
holding the spin orbit coupling constant at the value obtained through a
moment analysis and varying the trigonal distortion parameter, A,
results in eigenvalues which can be plotted as functions of A. The top
panel in Figure 4.2 shows that there are no values of A (positive or
negative) which reproduce the observed peak positions given below (for
the Cu/Ar experiment). Even more decisive in excluding the trigonal
site model are the predicted C0/V0 values (see the bottom panel in
Figure 4.2). The value of Ca/V0 for the lowest energy peak (2A2E') is
positive only for A < -180 cm-1, but in this range the value for the
highest energy peak (2EE') is also positive, contrary to experiment
(refer, for example, to Figure 4.3). For no values of the trigonal
77

Figure 4.1. The splittings induced in free atom 2S and 2P
states. Note dependence upon the order of
application of various interactions in calcu
lation.

79
E" M
Id
u
Gl
OJ
M
V
/ \ 2 p
/
/ \ /
' /
\ -T i
' 11
'u
\
\ E'
w
M
Ifld
^j
/
/
/
H
2S
\
\ 2a
\ A'i E
h -
h -
H
2S
E' 2A1 /
Atom S.O. J.T. S.O. Atom

Figure 4.2. The eigenvalues and C0/V0 values predicted
for a reduction of pure 0^ site symmetry
to D3.

81

82
distortion is the observed combination of C0/£>0 signs found. Values for
C0/VQ viere also calculated as a function of X. For no value of X in the
range of 10 cm"1 to 500 cm'1 (for Cu in Ar) was the experimental MOD
sign combination found. Thus it can be unambiguously concluded on the
basis of energy level separations and MOD sign combinations that the
trigonally distorted site model is not a valid explanation of the
observed Cu/Ar absorption and MOD results. This conclusion prompted
calculations outlined as splittings shown in the right half of Figure 4.1.
This scheme is pursued here.
Included after a somewhat detailed treatment of Cu isolated in Ar
is included a concise presentation of results for Cu in Kr (including a
spectrum of the region from 340 nm to 210 nm) and Cu in Xe as well as
the results of a moment analysis for Au isolated in Ar, Kr and Xe.
Following these are the atomic spectra obtained for matrix isolated
silver and, finally, the results obtained for Pb and Pb2 isolated in Kr.
Copper in Argon
The absorption spectra of copper atoms isolated in rare gas matrices
have been studied extensively0' 5 1 and the triplet of bands at
310 nm attributed to a number of different causes. These include spin
50
orbit splitting and static axial site distortion, multiple matrix
c
sites, exciplex formation between the metal and a single matrix atom,
60
long-range metal-metal interactions, and a Jahn-Teller effect resulting
from matrix cage atom vibrations interacting with the excited state of
61 52
the metal. While this work was in progress, Armstrong et al. and
CO
Grinter et al. reported on the magnetic circular dichroism of Cu atoms
in Ne, Ar, Kr and Xe matrices and concluded that their results were

83
consistent with either the distorted site model or the Jahn-Teller
interpretation. One of the primary results of this work is that the
triplet of bands in matrix isolated Cu, Ag and Au arise from simulta
neous spin orbit and Jahn-Teller interactions in the 2P excited state.
The simple nature of the 2S ground state (no orbital moment) allows a
detailed interpretation of the experimental moments of absorption and
MOD bands. Excited state spin orbit coupling constants, orbital g
factors, and contributions to the band width from cubic and noncubic
matrix lattice modes can be deduced.
Copper metal (Spex) was vaporized at 1100C and codeposited with
matrix gas onto a CaF2 window typically cooled to 15 K for Ar and Kr
and 20 K for Xe. Typical absorption and MCD spectra are shown in
Figure 4.3. The spectra agree well with those reported by Grinter et
6 2
al. Spectra were run in triplicate at 1 K intervals from 13 K to 25 K
Each spectrum was digitized every 1.0 A, transferred to a Commodore CBM
8032, and recorded on a floppy disk for storage and calculations.
Figure 4.4 shows the temperature dependence of the Cu MCD band. A
detailed moment analysis was performed on the Cu C term. Figure 4.5
shows a plot of 0/
0 vs. 1/T from which the parameters AQ/Bo and
CQ/V0 were obtained (cf. Chapter II). The slope of the plot yields
CQ/V0 = -8(3)xl0-3, and the intercept yields A0/80 = 4(3)xl0-4. Both
these quantities are expected to be zero based on a consideration of
only first order intrastate (2P) interactions. There are several second
order spin orbit interactions which might account for the nonzero values
They include excited Cu atom states mixed into either the Cu 2P or 2S
states or excited matrix atom states mixed (via orbital overlap) with
the 2P or 2S states. It will be shown below that the former interaction

Figure 4.3. Absorption and MCD spectra observed for Cu
isolated in Ar.

85

Figure 4.4. Temperature dependence of the Cu atom C0 term
in an Ar matrix. The intensity decreases with
increased temperature.

87
290
300
310
320 X(nm)

Figure 4.5. Experimental plot of 0/
0 vs. 1/T for
Cu atoms in an Ar matrix.

89
!I I 1
0 0.02 0.04 0.06 0.08
I
0.10
l/T (KH)

90
is probably not operative in this case. Matrix atom excited state inter
action with the Cu ground state has been invoked by Kasai and McLeod^3
to explain the dependence of the Cu 2S g factor on matrix atom type.
64
Denning and Spencer have shown that second order effects contribute
in two ways to MOD C terms. Let |A&> = |A^>+y|B> where y is the extent
of mixing of the new state, B. Using the notation of Buckingham and
45
Stephens, the two additional C term contributions are
C
I
2
a,3,A
12} x 2y (70)
a1 +i A 1 a'z z1 3
The Cj contribution results from a modification of the ground state mag
netic moment while the electric dipole transition moments remain
unchanged. It is this modification in the magnetic moment which accounts
for the change in ground state g factors with matrix atom type. When
summed over all excited state spin orbit components this contribution is,
however, zero. It cannot therefore account for our nonzero C0/V0 value
since this result is based on moments calculated over the entire excited
2P state transition. The Cjj contribution, however, involves modifica
tions to the transition moment matrix elements which, when summed over
all the excited state spin orbit components, do not equal zero. It is
this contribution which is responsible for the observation of a nonzero
CQ/V0 value. Figure 4.6 shows a plot of -1/
0 vs. 1/T for Cu
isolated in Ar.

Figure 4.6. Experimental plot of i/
0 vs. 1/T for Cu
atoms in an Ar matrix. The spin orbit splitting,
A, is obtained from the slope, and the excited
state g k is obtained from the intercept.

-,/
0
92
l/KK'1)

93
The excited state spin orbit splitting, A, is obtained from the
slope:
i
n
(72)
slope = -3H j y
and the gorb is obtained from the intercept:
intercept = 2 gQrb 6H
The gQrb quantity is very sensitive to any random error in the plotted
moment or temperature values since it comes from the extrapolation to
infinite temperature (T_1 -* 0) of data gathered over a relatively small
temperature range (13 25 K). Theoretically gQrb = 1, but because of
the large uncertainty in the experimental result, it is not possible to
decide the influence of the matrix environment on this quantity. Alter
nately the spin orbit splitting, A, is obtained from the slope of the
linear plot and is therefore relatively insensitive to the errors arising
from the small temperature range sampled. Copper atoms in the gas phase
exhibit a 248 cm-1 splitting between the 2P3/ and 2PU components of the
65
excited state. The matrix value obtained from the plots shown in
Figure 4.6 is 185 cm-1 for Cu in Ar. The reduction in A (~25% for Ar)
in the matrix must arise from some out-of-state mixing since, as pointed
45
out by Buckingham and Stephens, both Cx and VQ (from which A is
obtained) are invariant to a unitary transformation within the excited
state basis set. Thus any first order interaction such as the
Jahn-Teller effect which vibronically mixes the 2P state components
cannot account for this reduction. Although second order spin orbit

94
interaction with other excited Cu state might account for this reduc
tion, the nearest states (2F and 2P) are 13,000 and 15,000 cm-1 away,
necessitating spin orbit mixing matrix elements of the order of
900 1000 cm-1. This is unrealistically large, particularly since
the first order splitting in the gaseous 2P state is only 248 cm"1.
It is therefore concluded that the observed reduction is the result of
mixing with the matrix atomic orbitals (a semi quantitative estimate of
this reduction appears below). This is consistent with the finding
that A decreases in going from Ar to Kr matrices and reverses sign in
c o
Xe matrices. This is also consistent with Kasai and McLeod's finding
that the Cu ground state g factors are also dependent on matrix type.
A plot of 3/
0 vs. 1/T is shown in Figure 4.7. The ratio
of the slope of this plot to the slope of the 1/
0 vs. 1/T plot
is
3[ + %( + )+ (A/3)2] (73)
and is also equal to the ratio of their intercepts. This is obvious if
one compares equations (67)/(65) with (68)/(66). Confirmation is by
experimental results. The experimental ratio of the slopes is
2.5x10s cm-2, and the ratio of intercepts is 2.51x10s cm-2, although
the close agreement is probably fortuitous considering the uncertainty
in the measurements. It is possible to extract the contributions from
noncubic and cubic lattice modes to the overall bandwidth through
equations (73) and (69). The quantity V2/V0 from equation (69) may be
obtained from a plot of
2/0 vs. T as shown in Figure 4.8. The
curve is of the form
2/0
A coth (E/2kT)

Figure 4.
Experimental plot of 3/
0 vs. 1/T for Cu
atoms in an Ar matrix.

96
l/T OC1)

Figure 4.8. Experimental plot of
2/0 vs. T for Cu atoms
in an Ar matrix.

-OI x / Z
98
T(K)

99
For Cu in Ar the best fit yields A = 2.01xl05 and E = 52 cm-1. Using
the value extrapolated to T = 0 yields V2/VQ = 2.0xio5. If we define
AR = 3[ + Jg( + ) + (A/3)2]
and
R = + ( + ) + 2(A/3)2
the cubic and noncubic contributions can be found as
A2 = = j AR R
ANC = + = 2[R - (A/3)2]
These expressions can be evaluated for Cu in each matrix. For Cu in
Ar A2 is found to be -0.3 0.4xl05 cm-2 and Aj^ is 2.3 0.6xl05 cm-2.
The negative sign in A2 is physically unreasonable and appears to result
from the general imprecision in the AR and R values, i.e., in the plot
of
2/0 vs. T and 3/0 vs. T. Mowery et al. discuss the
sensitivity of A2 and Aj^ to experimental errors in R and AR. Following
their discussion the quantity of physical significance in this analysis
is the ratio
The values of R and AR themselves are ratios of absorption and MCD
moments, respectively, and are therefore independent of multiplicative
errors in the measured absorption and MCD spectra. They point out the
main error arises in baseline uncertainties which become increasingly

1Q0
important as one calculates higher moments because the wings of the
band make an increasingly important contribution. Therefore AR is most
susceptible to error. It is interesting to consider two values of F,
namely 1 and 0. For F = 1 the ratio is very sensitive to experimental
uncertainties (AR varying as 3). If AR varies 15%, F will run from
2.9 to 0.5. Thus accurate values of F cannot be determined without
extraordinarily accurate measurements of R and particularly AR if cubic
and noncubic modes contribute comparable amounts. Fortunately the case
observed for matrix isolated Cu where F = 0 is much more favorable.
For F = 0 a 15% variation in AR yields F values from -0.09 to 0.11. From
these considerations it is difficult to say much about the cubic contri
bution although it does appear that it is nonexistent or quite small. It
is, however, possible to conclude that the noncubic contribution is
significant. This conclusion is central to the claim that the
Jahn-Teller effect is operative in this system since both the and
56
modes are Jahn-Teller active.
Having obtained evidence that the Jahn-Teller effect is operative
in this system it is interesting to determine the effect of different
lattice modes on the spectrum as well as the extent to which the excited
state components are mixed through spin orbit coupling. The Moran model
as previously discussed can be applied to the matrix isolated Cu atom
in Ar, Kr and Xe. The above analysis showed that both spin orbit inter
action and noncubic vibrational modes of the matrix cage are important
to the appearance of the 2P <- 2S transition in matrix isolated Cu. Three
components of the 2P state are apparent (see Figure 4.3) in the experi
mental absorption and MCD spectra. The observed C terms are positive,
negative and negative (increasing energy), and the separations between

101
the absorption maxima (in Ar) are 479 cm-1 and 402 cm-1 (increasing
energy, 12.9 K). These separations are more than a factor of two larger
than the spin orbit splitting (185 cm-1 for Cu in Ar) deduced from
the band moment analysis.
As mentioned previously the case of matrix isolated Cu, Ag and Au
exhibiting a 2P * 2S transition is very similar to the F center case, and
the results presented here can be compared to calculations done within
56
the framework of the adiabatic approximation as described by Moran
67
and Cho. Moran considered the effect on the splitting pattern and
band shapes of simultaneous first order spin order coupling and vibronic
54
interaction through the tetragonal e mode only. It has been shown
that consideration of the fourth moment and changes in it induced by
a magnetic field are necessary before the t2 mode interaction appears
in a manner other than simply additive. Thus the only effect of the T2
interaction is a modification of the existing band shapes but not the
triplet splitting pattern. Because of these facts the applicability of
the Moran model (with its restrictive use of only the ax and e vibronic
interactions) has been explored in order to determine whether it could
account for the experimental observations. The absorption band shape
is then compared to those calculated by Cho.^ Cho has performed a
multidimensional calculation of the absorption band shapes and included
spin orbit, e and t2 interactions.
Moran's 3x3 interaction matrix has been diagonalized varying t and
z displacements (as they represent the degenerate pair of lattice motions
in the e vibration) while holding X to the appropriate value for Cu in
Ar (124 cm-1) as obtained from the moment analysis. The degenerate t
and z components of the e vibration are sketched in Figure 4.9. Two

Figure 4.9. Diagram of the degenerate modes of the e lattice vibration.

e mode
(z)
o
CO
e mode
(t)

104
criteria were imposed on the solution: 1) that the interband spacings
match the experimental ones at 12.9 K, and 2) that the signs of the
C terms match the observed ones. The final computed results are shown
in Table 4.1 and show for Cu in Ar that the first order spin orbit
split states are thoroughly mixed by the vibronic interaction.
Figure 4.10 shows, for Cu in Ar, the variation of C0 with z mode
coordinate for a fixed t mode displacement. At z = 220 cm-1 and
t = 115 cm-1, one positive and two negative C0 terms are predicted for
transitions to states whose energy separations correspond closely to
the experimental intervals (calculated AE's are 476 cm-1 and 410 cm-1
as compared to the experimental 479 cm-1 and 402 cm-1). From the C0-z
space plot (see Figure 4.10) it is shown that only for z > 70 (at
t = 115) is the C0 of the lowest energy peak positive and the upper two
negative. From a similar C0-t space plot (shown in Figure 4.11), only
for 10 < |t| < 380 (at z = 220) can we obtain a similar combination of
C0 term signs. This plot also shows that the C0 term variation is
independent of the sign of the t mode displacement, whereas this is not
the case in z space. The ranges of allowed z and t displacements are
substantially narrowed to z = +2205 and t = 1155 when the criterion
of matching the observed band intervals is superimposed on the above
MCD sign criterion. A composite drawing for the transition energies vs.
t and z is shown in Figure 4.12. Thus it can be concluded that the
Moran model is applicable to the case of matrix isolated Cu atoms and
that the simultaneous spin orbit and vibronic interactions in the 2P
excited state can explain the observed C0 term signs and absorption band
separations. The initial limitations of this model do not, however,
yield any information about the respective influence of the e and tz

105
Table 4.1. Calculated eigenvalues, eigenfunctions and MCD C0 and V0
parameters for Cu atoms in Ar. E.'s are eigenvalues measured
from the excited state center of gravity; C-1s are coeffi
cients of the adiabatic wavefunctions [see equation (58)].
For Cu/Ar, X = 124 cm-1, t = 115 cm-1, and z = 220 cm-1
E,
1
s-
c,.
3i
Cj,
2
c0/?Q
-454
0.042
0.716
0.697
0.321
0.161
1.84
+ 22
-0.601
0.575
-0.555
-0.116
0.063
-1.84
+432
0.798
0.396
-0.455
-0.205
0.109
-1.88

Figure 4.10. Plot of calculated C0 term as a function of
lattice motion z holding lattice motion t = 115
and A constant (from moment plots) for Cu
atoms in an Ar matrix. Eigenvalues increase
energy from Ei to E2 to E3.

107
z

Figure 4.11. Plot of calculated C0 term as a function of
lattice motion t holding lattice motion z = 220
and X constant (from moment plots) for Cu
atoms in an Ar matrix. Eigenvalues increase
in energy from Ex to E2 to E3.

109

Figure 4.12. Composite drawing showing the effect of varying
contributions from lattice vibrational modes.

Energy/cm
in
Cu/Ar
-500

112
modes. That information can be obtained from the Monte Carlo integration
67
done by Cho. Cho calculates the expected band shapes using Moran's
model without limiting the degree of freedom of the lattice vibration to
ax and e modes. Because it is known from the moment analysis that in
matrix isolated Cu there is little or no coupling with the totally sym
metric mode, the experimental band shape can be compared to the results
67
of Cho's Figure 11, which is reproduced here as Figure 4.13. It is
clear that neither the e mode nor the t2 mode can be active alone. The
best agreement is reached when both the parameters which describe the
coupling with the e and t2 modes are roughly equal and furthermore of
the same order of magnitude as A.
63
Kasai and McLeod point out in their ESR study of Cu isolated in
Ar that each observed ESR signal is extremely sharp and isotropic
indicating little deviation, if any, of symmetry of the trapping site
from octahedral. They also indicate the variance of their results with
those of optical matrix isolation studies which reveal the triplet band
structure. The conclusion drawn in this research reconciles the finding
by Kasai and McLeod of an octahedral ground state symmetry with the
optical triplet as the triplet is shown to arise from an excited state
dynamical distortion resulting from nontotally symmetric cage vibrations.
The spin orbit interaction in the excited state also contributes to the
triplet structure. For Cu in Ar the matrix value for the spin orbit
coupling constant is 25% lower than the gas phase value. As mentioned
above this reduction cannot be accounted for by the intrastate vibronic
coupling. It is more likely a consequence of the interaction (i.e.,
overlap) of the Cu 4p orbital with the 3p Ar atom orbital. Ammeter and
68
Schlosnagle have done a careful and in-depth study of the ESR spectra

Figure 4.13. The effect of varying the magnitudes of the t2 and e
modes on absorption brofile. B represents the e mode
and C the t2 mode.

114

115
of matrix isolated A1 and Ga atoms (2P ground states). They orthogonal -
ized the metal orbitals with the rare gas cage atom orbitals by calcu
lating the a and it overlap integrals (S^ and S^) and evaluated a spin
orbit coupling constant reduction factor, k\ through the relation (for
nondistorted octahedral sites)
kA = 1 KAwA..-1 (2S S -S 2)
where K = 2 for an interstitial (MX6) site and K = 4 for a substitutional
(MX12) site, and A^ and A^ are the rare gas and metal spin orbit coupling
constants, respectively. Since Hartree-Fock calculations are not avail
able for the metal excited state configurations, the wavefunctions
were approximated from double zeta metal ground state functions. Using
= 941 cm-1 and A^ = 166 cm-1 (gas phase), the kAsub = 0.86 for the
substitutional octahedral site and kA-n^. = 0.59 for the interstitial
site. The observed kAQbs = 124 cm-1/166 cm-1 = 0.75. Both results
show that overlap of the matrix atom orbitals with Cu 4p orbitals can
reasonably explain the observed reduction in spin orbit in an Ar matrix.
Further support for this interpretation comes from the observation that
the A's for Cu in Kr and Xe are each further reduced, vide infra, with
the A in Xe actually becoming negative. This trend reversal can be
predicted from the above relation since the quantity A^/A^ increases
dramatically in going to Kr (20.96) and Xe (36.63).
Copper in Krypton
Figure 4.14 shows the absorption and MCD spectra for Cu atoms iso
lated in Kr. As for Ar experiments the Cu was vaporized from a cell
heated to ~1100C and codeposited with Kr at a pressure of 3-4xl0"5 torr

Figure 4.14. Absorption and MCD spectra for Cu atoms
isolated in a Kr matrix.

117
X(nm)

118
onto a CaF2 plate held at either 15 or 20 K. The Cu band in Kr has
generally the same appearance as in Ar.^
Figure 4.15 shows the temperature dependence of Cu in Kr, and
Figure 4.16 shows a plot of 1/
0 vs. 1/T for Cu in Kr. The
slope yields a spin orbit splitting, A = 143 cm"1 (A = 95 cm"1), and
a value of gQr,b = -0.17. The gQrb value is of little importance as
the uncertainty in the intercept of the 1/
0 vs. 1/T plot is quite
large. Of more interest is the further reduction of the spin orbit
splitting compared to Ar (185 cm"1) and the gas phase value (248 cm"1).
The spin orbit coupling constant reduction factor for Cu in Kr is calcu
lated as k^sub = 0.48 and k^-nt = -0.85. The observed k^Qbs =
95 cm_1/166 cm"1 = 0.57. As in the Cu/Ar case the spin orbit reduction
can be explained through an orbital overlap picture with the Cu residing
in a substitutional lattice site.
A plot of 3/
0 vs. 1/T is shown in Figure 4.17. From the
ratio of slopes, method A* and Ajj^ can be found: a£ = 1.9xl04 and
Aj^jc = 8.9xlO\ and therefore the ratio F = 0.21. The noncubic lattice
modes are, as expected from the Cu/Ar case, dominant.
As in the Cu/Ar case, the Moran model was applied to Cu isolated in
Kr. The values of t and z are 111 cm"1 and 152 cm-1, respectively, for
a A value of 95 cm"1, as determined from the moment analysis. As in
the Cu/Ar case, the coefficients listed in Table 4.2 indicate complete
mixing of the eigenfunctions through spin orbit/vibronic interaction so
that J is not a good quantum number.
Figure 4.18 shows the spectrum of Cu isolated in Kr in the range
200 nm to 540 nm. The triplet of bands centered near 245 nm is much
weaker than the set at 310 nm. In the gas phase, several spin-forbidden

Figure 4.15. Temperature dependence of the Cu atom C0 term
in a Kr matrix. The intensity decreases with
increased temperature.

120
~h
.A
300 315 330

Figure 4.16. Experimental plot of i/
0 vs. 1/T for
Cu atoms in a Kr matrix.

, /
,
122
l/T (KH)

Figure 4.17. Experimental plot of 3/
o vs. 1/T for
Cu atoms in a Kr matrix.

3 /
0 XIO
124
l/T (K'1)

125
Table 4.2. Calculated eigenvalues, eigenfunctions and MCD C0 and Vo
parameters for Cu atoms in Kr. E.s are eigenvalues meas
ured from the excited state center of gravity; c.'s are
coefficients of the adiabatic wavefunctions [see
equation
(58)].
For Cu/Kr X
= 95 cm-1,
t = 111 cm-i,
and
z = 152
cm-1.
E.
i
CH
C2i
CSi
C0
Po
C q/Vq
-317
0.070
0.691
0.719
0.323
0.163
1.98
- 36
0.621
-0.594
0.511
-0.127
0.065
-1.94
+353
-0.781
-0.411
0.471
-0.196
0.105
-1.86

Figure 4.18. Cu absorption and MCD bands in the range
220 nm to 340 nm.

127
WAVELENGTH (nm]

128
levels (^P3/ >4Pi) lie just above the 2P components. Again employing the
/2 "2
Wigner-Eckart theorem and tables of vector coupling coefficients, the
CJV0 values predicted for the atomic 4P3/ and 4Pt states are -1 and +2,
/2 -s
respectively. Since the bands at 240 nm and 245 nm display MCD C0
terms, they are assigned as transitions to the 4P state. There is no
indication at the resolution used (~0.6 nm) of a further splitting in
this state induced by Jahn-Teller-spin orbit interaction. Assuming
this to be the case, the 240 nm peak with its positive C0 term is
assigned as 2Pl 2Sj and the 245 nm peak (negative C0term) is assigned
-2 "
as 4P3^ 2S;^. The lowest energy 251 nm component of the triplet struc
ture displays only a weak MCD 8 term and thus cannot be a Cu atom band.
Further, it cannot be assigned to any species with a degeneracy in its
ground or excited state. It is therefore assigned to a Cu2 1^u +
transition.
In the gas phase the next three bands (with increasing energy) are
4D^, 2Pi) and 2P3^. In the region 200 nm to 230 nm, the MCD displays
two clear, positive C0 terms. The transition 4Dt - 2S, is predicted to
*2
be a positive C0 term. The band at 224 nm is assigned to this transi
tion. The band at 218 nm is assigned to one of the components of the
2P transition with the other presumably just outside the range of our
instrument. This accounts for all Cu atom transitions in the ultraviolet
region.
Figure 4.19 shows the spectrum obtained after further metal deposi
tion. New absorption bands appear at 271 nm and 236 nm. The 271 nm
band appears to have a triplet structure with associated weak 8 terms.
Note that although there is an apparent A term, this possibility is
eliminated through the observation that the three MCD peak maxima

Figure 4.19. Appearance of Cu/Kr spectrum after prolonged
deposition from 230 nm to 290 nm.

130
X(nm)

131
correspond in wavelength exactly with the absorption maxima. These
bands are therefore assigned to a Cu2 excited state, possibly exhibit
ing site effects. This is in agreement with the assignments of
60
Moskovits and Hulse. The lack of an MCD C0 term corresponding to the
236 nm absorption band also leads to assignment of this transition to
Cu2.
Figure 4.20 shows the region from 300 nm to 450 nm. Another
broad absorption feature due to continued deposition is seen centered
at 380 nm. Multiple trapping sites are again indicated. On the basis
of the lack of a corresponding MCD C0 term, this band is also assigned
to Cu2 consistent with the assignment given by Moskovits and Hulse.
All of these Cu2 bands grow in at the same rate with continued deposi
tion providing further evidence that all are due to the same species.
Copper in Xenon
Experimental spectra for the absorption and MCD of Cu isolated in
Xe are shown in Figure 4.21. For these experiments depositions were
made onto a CaF2 plate held at 20 K. The most striking feature of the
Cu in Xe spectrum is the reversal in sign of the MCD bands. Determina
tion of gQrb and A were made from the 1/
0 vs. 1/T plot shown in
Figure 4.22. From the slope A = -35 cm-1 (A = -23 cm"1)* and gQ^b is
calculated as 0.79. The spin orbit splitting constant for Cu is again
reduced from the Cu/Kr value and has actually gone negative indicating
a reversal in relative energy of excited state components. As in the
previous cases, the reduction factor k^ can be evaluated. The values
obtained are k^ = 0.08, k^. = -2.7, and k^ = -23 cm-1/166 cm-1
sub int obs
-0.14, again indicating isolation in a substitutional lattice site as
the k\ ^ is too large to match the experiment.

Figure 4.20. The Cu2 band in the range 330 nm to 450 nm.

I I I I I I I 1 1 1 1 I I I I I L
300 350 400 450
WAVELENGTH jnmj

Figure 4.21. Absorption and MCD bands for Cu in a Xe matrix.

135
290
300
310
320
330

Figure 4.22. Plot of i/
0 vs. 1/T for Cu in Xe.

O/WN / l/WV7\
137

138
From 3/
o vs. 1/T (Figure 4.23) and 2/o vs. 1/T
(Figure 4.24), = 3.3*104 and A^ = 5.4xl04 for a value of F = 0.61,
although the scatter in experimental points causes a large error in
this value. Again the noncubic lattic modes are dominant. Kasai and
6 3
McLeod0,3 also indicate Cu to reside in a pure octahedral site in Xe.
When applied to the Cu/Xe case, the Moran model yields values of
t = 86 cm-1 and z = -174 cm-1 for X = -23 cm-1. Again spin orbit/vibronic
interaction shows (see Table 4.3) all excited state components completely
mixed.
The observed decrease in the spin orbit constant of Cu isolated in
Ar, Kr and Xe can be discussed in terms of orbital overlap effects as
well as the effect of Jahn-Teller interactions. Overlap of the valence
metal orbitals with the outer p shells of the rare gases increases going
from Ar to Xe, thereby causing a reduction in spin orbit splitting. This
effect is somewhat counteracted by the Jahn-Teller interaction of non
cubic lattice vibrations coupling with the excited state of the metal
atom.
The absorption energy matrix shfts are shown, going from Ar to Xe,
a
in Figure 4.25 (gas phase = 326 nm).
Gold in Argon
Matrices of Ar, Kr and Xe containing Au atoms were prepared by
codeposition of Au from a Ta cell heated, typically, to 1125C under
the same conditions used in Cu work. The absorption spectra of Au
50 56
atoms in matrices have been reported previously. By measuring
the separation of the split component and the isolated component,
Gruen et al.^ arrived at values of 3215 cm-1, 2943 cm-1, and 2570 cm-1

Figure 4.23. Plot of 3/
0 vs. 1/T for Cu in Xe.

/ 140
T (K'1)

Figure 4.24. Plot of
2/o vs. 1/T for Cu in Xe.

/ 2
142
T (K)

143
Table 4.3. Calculated eigenvalues, eigenfunctions and MCD C0 and V0
parameters for Cu atoms in Xe. E.'s are eigenvalues meas-
ured
from
the excited state center of gravity
", c 1 s
are
coefficients of
the adiabatic
wave functions
[see
equation
(58)].
For Cu/Xe X :
= -23 cm-1, t =
86 cm'
-1, and
2 = -
-174
cm-1.
Ei
CH
C2i
C3i
^ 0
C0/VQ
-324
0.733
-0.406
0.545
-0.164
0.097
-1.69
- 25
-0.680
-0.449
0.580
-0.139
0.085
-1.64
346
-0.010
0.796
0.605
0.303
0.152
2.00

Figure 4.25. Relative positions of Cu MCD in Ar, Kr and Xe.
Note the reversal of MCD term sign in Xe.

145
300 310 320
n
290
X (nm)
~i
330
r~
340

146
for Ar, Kr and Xe, respectively. These are to be compared to the gas
phase value 2543 cm The moment analysis employed here yields values
50
comparable to those reported by Gruen et al As in Cu work Kasai and
63
McLeod indicate Au to be isolated in pure substitutional octahedral
matrix sites.
The absorption and MCD spectra of Au isolated in Ar are shown in
Figure 4.26. From the observed C term behavior, a plot of i/
o
vs. 1/T (see Figure 4.27) and a spin orbit constant of A = 316532 cm-1
are obtained. The intercept yields a gQr^ = 1.43, but due to the
experimental error and long extrapolation it is probably not very
accurate.
Following the precedure outlined for Cu/Ar, the spin orbit reduc
tion factor for Au in Ar is found to be k^ ^ = 0.988 and kV^ = 0.972
as compared to the experimental k^obs = 1.24. A plot of 0 vs.
1/T is shown in Figure 4.28. From the third moment plot, the AR value
(= 8xl06) can be compared to R (= 4.9xl06) and it is shown that noncubic
(Jahn-Teller-active) lattice modes are also important in understanding
Au/Ar spectra. Further indication of the role of Jahn-Teller interaction
between lattice vibrations and the Au excited state results from consid-
51
eration of data taken from work by Forstmann et al. where a detailed
study of the peak-maximum position in energy as a function of matrix
temperature was done. According to Englman^ the square of the peak
separation should follow 1/kT with a hyperbolic cotangent relation:
peak separation
Values of the energy differences of Au/Ar transitions at various
temperatures were measured directly from diagrams given in the paper

Figure 4.26. Absorption and MCD for Au in Ar.

148
\(nm)

Figure 4.27. Plot of i/
0 vs. 1/T for Au in Ar.

0
150
l/T (K*)

Figure 4.28. Plot of 3/
0 vs. 1/T for Au in Ar.

_0ix /£
152
l/T(K)

153
51
by Forstmann et al. (which had been photographically enlarged). A
typical plot is shown in Figure 4.29. The points plotted are the values
51
measured from work by Forstmann et al. while the line through the
points is a non-linear least-squares fit to the hyperbolic cotangent
relation. As discussed by Englman^ this behavior is indicative of
Jahn-Teller coupled transitions. The agreement of plotted data with
the coth fit as well as the indicated dominance of noncubic lattice
modes is strong justification for application of the Moran model to the
gold-matrix interaction analysis. Table 4.4 lists the results of the
Moran treatment for Au in Ar. The degenerate t and z modes were varied
with A held at 3165 cm-1. Inspection of the coefficients in the eigen
functions indicates little interaction between the high energy doublet
with the lower energy band. This situation is treated by Sturge.^
In such systems the spin orbit constant can be determined by measurement
of the energy separation of the center of gravity of the high energy
doublet and the position of the low energy band (3215 cm-1)- This is
50
the same measurement made by Gruen et al., but here it arises from a
50
different basis. Gruen et al. assumed a distorted octahedral D3 site
symmetry which is indicated in this work to be erroneous.
Gold in Krypton and Xenon
The absorption and MOD of Au isolated in Kr are shown in Figure 4.30.
There is perhaps some indication of a broad cluster band centered between
the atomic components. From the 1/
0 vs. 1/T plot in Figure 4.31,
a spin orbit constant of 316265 cm-1 is obtained. The intercept yields
gQrb ~ 7.710. The spin orbit reduction factor calculated for Au in Kr
is k^ = 0.953 and k^. ,
sub mt
= 0.869, compared to the experimental

Figure 4.29. Plot of best fit for Au in Kr of
= 4 hcoE
jyCOth
(peak separation)2

155
T(K)

156
Table 4.4. Calculated eigenvalues, eigenfunctions and MCD C0 and V0
parameters for Au atoms in Ar. E.'s are eigenvalues meas-
ured from the <
coefficients of
axcited state
the adiabatic
center of gravity; c.'s
wavefunctions [see
are
equation
z = 300
(58)].
cm-1.
For Au/Ar A
= 3165 cm-1, t
= 45 cm'
-1, and
Ei
CH
2i
C3i
c0
c0/p0
-3206
0.012
0.094
0.996
0.251
0.125
2.00
1318
0.089
-0.992
0.093
-0.080
0.042
-1.87
1888
-1.00
-0.088
0.020
-0.330
0.166
-2.00

Figure 4.30. Absorption and MOD for Au in Kr.

158
230 240 250 260 270
X(nm)

Figure 4.31. Plot of i/
0 1/T for Au in Kr.

, /
0
160
l/T (K-')

161
k^obs = 1-24. Figure 4.32 is a plot of 3/
o vs. 1/T. The spin
orbit value found here is somewhat larger than the value reported by
Gruen et al. (2943 cm-1). A possible explanation may be found in the
broad cluster band appearing under the atomic band. Data by Forstman
et al. as well as AR {- 6.3xl06) obtained from 3/
0 vs. 1/T (see
Figure 4.32) and R (= 4.6xl06) indicate Jahn-Teller interaction in this
system also.
Figure 4.33 shows absorption and MCD spectra obtained in a high
temperature vaporization (1340C) of Au into a Xe matrix. The bands at
246 nm, 249.5 nm, and 273.5 nm are assigned to Au atoms. The broad band
at 322 nm does not have an observable MCD band and is assigned to an Au2
transition. This is also true for the band at 228 nm, and it is assigned
to Au2. A broad temperature dependent band is observed at 282.5 nm.
63
Since Kasai and McLeod demonstrated Au to reside in a pure octahedral
site with no site splittings, this band is assigned to Au3. Figure 4.34
shows spectra obtained in a matrix deposited at 1300C. The expected
atomic triplet was not observed. Rather, two broad absorption features
were noted at 274 nm and 298 nm. The 274 nm has a corresponding C0 term
and matches the low energy Au atom transition seen in Figure 4.33. The
298 nm transition has a corresponding positive Aj term which is assigned
to an Au2 transition.
Matrices containing Ag were prepared by vaporization of Ag powder
(~900C) from a Knudsen cell and codeposition in Ar, Kr and Xe. The
absorption and MCD of Ag atoms in Ar are shown in Figure 4.35. As in
Cu and Au, the characteristic triplet structure is observed with (in
all three matrices) positive, negative, and negative (increasing energy)
MCD bands. Irradiation into the Ag/Ar absorption band by the scanning
monochromator provided enough light to cause the "cryophotoaggregation"

Figure 4.32. Plot 3/
0 vs. 1/T for Au in Kr.

0xicr
163
l/T (K-)

Figure 4.33. Absorption and MCD spectra for Au in Xe
after a high temperature metal vaporization.

165
ABS
220 260 3 00 X (nm) 340

Figure 4.34. Spectra obtained in a 1300C Au depositi
into Xe.

167
AA
ABS
X(nm)

Figure 4.35. Absorption and MCD for Ag in Ar.

169

170
72 73
observed by Mitchell and Ozin and Mitchell et al. With the appartus
utilized in these experiments it was therefore not possible to accurately
measure the MCD temperature dependence and obtain values for a moment
analysis. Even without this information it is possible to conclude,
from the triplet structure, that the same Jahn-Teller/spin orbit model is
effective in these systems. Orbital overlaps can be employed as in Cu
and Au matrices to estimate a spin orbit reduction factor and therefore
approximate the matrix spin orbit constants. The calculated spin orbit
reduction factors for Ag in Ar, Kr and Xe are listed in Table A.2 in
Appendix A.
Results for Lead Experiments
The matrix absorption spectra of Pb and Pb2 were first studied by
74
Brewer and Chang. Two bands were discovered for the dimer (508 nm
A X, and 244 nm E X). A band at 261.4 nm was assigned to the
3Pi - 3 P0 atomic transition in a Kr matrix. The Pb2 spectrum had been
75 76
studied previously in the gas phase by Shawhan' and then by Weniger.
The absorption and laser induced emission of Pb2 in solid Ne, Ar and Kr
77 78
was reported by Teichman and Nixon. Bondybey and English revised
Weniger's analysis of the 500 nm dimer band, determined a 112 cm-1
vibrational frequency in the ground state, and reported evidence for
six Pb2 states below 500 nm. They also suggested that transitions to
the 500 nm state be assigned as F0+ + X0+. This was the first symmetry
o g
assignment proposed for any Pb2 transition.
For preparation of Kr matrices containing Pb, a Ta Knudsen cell was
filled with Pb (Spex) powder and thoroughly outgassed at approximately
800C. Resistively heating the cell to 875C, a metal beam was produced
which was codeposited with Kr onto the CaF2 window at 20 K. For Pb

171
experiments it was possible to remove the internal heat shield of the
furnace, allowing greater flux of metal to enter the cryostat without
presenting an excessive heat load at the cold surface. Very clear
matrices were obtained in depositions of five to thirty minute duration.
Portions of the absorption and MCD spectra of lead in Kr are shown
in Figures 4.36 and 4.37. In the ultraviolet region two strong bands
(263.5 nm and 246.9 nm) and one weak band (232.7 nm) are observed. The
relative intensities of these three peaks were observed to change under
varied deposition conditions (Knudsen cell or cold window temperature).
Only the lowest energy band at 263.5 nm displays an MCD signal--a temper
ature independent, positive A term. In the visible range a highly
structured absorption band occurs at 508.2 nm. This band shows no MCD
signal. Four broad, higher energy bands (469 nm, 448 nm, 419 nm, and
400 nm) also show no MCD. With prolonged deposition these bands did
show some MCD signal attributable to very weak 8 terms. With deposition
conditions similar to those used to obtain the 508 nm band, a broad,
symmetrical band was observed at 612.9 nm with an intensity comparable
to the 508 nm band. The relative intensities of these two bands varied
somewhat with varied deposition conditions.
6 5
The ground state of atomic Pb is 3P0, 3 with the 3PX multiplet
component lying at 7819 cm-1. The first allowed gas phase transition
in the ultraviolet region occurs at 35.285 cm-1 (3Pj 6p7s 3P0 6p2).
For a AJ = +1 transition a positive Ax term is expected [A1/V0 =
-Jg^+(J+2)gg, where J is the ground state value],^ The 261.4 nm band,
assigned by Brewer and Chang to 3PX 3P0, is observed to have a posi
tive A term, thus confirming this assignment. A large gas-to-matrix
shift of 2957 cm-1 is observed in Kr.

Figure 4.36. Absorption and MOD for Pb in Kr between
220 nm and 280 nm.

173
220 250 280
X/nm

Figure 4.9. Diagram of the degenerate modes of the e lattice vibration.

WAVELENGTH/nm

176
For Pb2 the appearance of no observable MCD for the 508 nm band or
the 244 nm band is strong evidence for the assignment of the Pb2 ground
state to 0 Two ground state PQ atoms can combine to produce such a
y
80
state. Terms of C would have been expected for any other, degenerate
symmetries. The absence of A terms in these transitions leads to the
conclusion that both their excited states are nondegenerate 0*.
on
Recently Stranz and Khanna reported on the resonance Raman of
small Pb clusters in Xe matrices. Laser excitation into a band analogous
to the Pb/Kr band at 469 nm gave vibrational frequencies which were
interpreted as arising from a Pb3 species with D3^ symmetry. Such a
molecule could have an orbitally degenerate ground or excited state
which might give rise to C or A term MCD bands, although Jahn-Teller
distortions might be expected to reduce the degeneracy. The observa
tion of no MCD bands (or very weak 8 terms) provides no support for or
against a Pb3 species. However, if the 469 nm band does arise from a
Pb3 species, there is evidence that the ground and excited states of
Pb3 involved in this transition are orbitally and spin degenerate.
Further Studies
These experiments demonstrate the potential of the MCD technique,
both in the simple assignment of atomic and molecular states and in
the information attainable about excited states through the method of
moments.
There are a number of interesting extensions of this type of work.
It should be possible, with a faster data acquisition scheme, to arrive
at values for the spin orbit constant for Ag in various matrices. The
same improvement in data acquisition should facilitate measurements on

177
lifetimes of species such as the Pd matrix bands observed by Grinter and
81
Stern. An interesting extension would be measurement of ir and Raman
spectra of cluster species in order to gain insight into cluster size.
Another interesting area where matrix isolation MCD would be valuable
is in state assignments of diatomic metal hydrides. Molecules could be
prepared by codeposition of a metal vaporized from a standard Knudsen
cell with a beam of H atoms generated in a hot W cell (-2800 k) .82-84
This would require construction of a larger furnace and installing a
second power supply.
There has been an increasing application of heat pipes to the
41
study of optically pumped metal vapor lasers. This technique could
be adapted for gas phase study of many metal cluster species. The
necessary gas phase density could probably be attained by employing the
78
laser vaporization technique used by Bondybey and English. A crossed
arm heat pipe could be mounted vertically between the magnet pole faces,
and the vaporization beam might be introduced perpendicular to the mag
netic field. Standard heat pipes are generally constructed of stainless
steel. A Ta heat pipe enclosed in a vacuum shroud would enable studies
of much higher temperature species.

APPENDIX
ORBITAL OVERLAP CALCULATIONS
Atomic orbital overlaps were calculated using the Aarhus Diatomic
Properties Package. The quantity which enters into the Ammeter and
68 X
Schlosnagle spin orbit reduction factor, k is an overlap between
the host rare gas outer p shell with the excited state metal p orbital.
Hartree-Fock calculations are not available on the 2P states of Cu, Ag
and Au, so it was necessary to approximate wavefunctions. Slater's
rules^ for estimating electron screening constants include the
equivalence of electrons within an n level. Based on this the metal
atom ns exponents and coefficients are used with appropriate n, 1, and
m^ values to calculate p type overlaps. Double zeta Roothan-Hartree-Fock
86
atomic wavefunctions as given by Clementi and Roetti and by McLean
87
and McLean for Cu, Ag, Au, Ar, Kr and Xe were used. The basis sets
are shown in Figure A.l. The po and p^ type overlaps as well as the
calculated spin orbit reduction factors are listed in Table A.2. The
interatomic distances in atomic units were taken from rare gas lattice
parameters as given in Meyer's book.^
178

Table A.l. Data used in orbital overlap calculations.
Cu
i
I
2p
23.54780
-0.00941
2p
21.93670
2p
13.26670
0.05604
2p
21.32090
3p
11.52060
0.08953
3p
14.14920
3p
8.09772
-0.11580
3p
10.13800
3p
6.70827
-0.03951
4p
5.87182
4p
5.07948
-0.15751
4p
3.98770
4p
3.19095
0.17463
4p
1.53564
0.66426
5p
2.66401
4p
0.87051
0.34469
5p
1.65008
5p
1.04186
Au
a
0.31024
2p
38.341367
-0.066636
-0.37499
2p
35.121549
0.112650
-0.01483
3p
23.961490
0.052023
0.16544
3p
20.389333
-0.152927
-0.21760
4p
13.258438
0.056507
-0.05567
4p
10.132154
0.125050
0.25280
5p
6.484815
-0.262522
0.51023
5p
4.291229
0.010798
0.39485
6p
2.457881
0.535399
6p
1.330143
0.599705

Ar
I
ii
Kr
I
2p
9.05477
-0.17850
2p
17.03660
2p
26.04380
4p
15.54410
-0.00812
4p
12.39970
0.00520
3p
15.51000
4p
8.56120
-0.10986
3p
9.49403
4p
5.94658
0.10994
3p
6.57275
4p
3.42459
0.56149
4p
1.96709
0.46314
4p
5.38507
4p
1.06717
0.02951
4p
3.15603
4p
2.02966
4p
1.42733
C.
i
Xe
I
c.
0.08488
2p
34.88440
-0.00277
0.00571
2p
23.30470
-0.07054
0.04169
3p
12.54120
-0.18148
-0.07425
3p
12.02300
0.40692
-0.26866
4p
7.72390
-0.22741
0.01341
4p
5.40562
-0.21144
0.51241
0.42557
5p
3.32661
0.49354
0.18141
5p
2.09341
0.53529
5p
1.36686
0.13666

181
Table A.2. Orbital overlaps and predicted spin orbit reduction factors.
rab
Subst.
Site
System
S
IT
So
?X^M
7.098
CuAr
0.031677
0.106869
5.687
0.865
7.098
AgAr
0.036205
0.120881
1.564
0.953
7.098
AuAr
0.036791
0.127865
0.370
0.988
7.541
CuKr
0.031602
0.114655
20.96
0.476
7.541
AgKr
0.036040
0.130665
5.668
0.816
7.541
AuKr
0.036229
0.138423
1.368
0.953
3.193
CuXe
0.030587
0.118135
36.63
0.078
8.193
AgXe
0.034614
0.135470
9.902
0.676
8.193
AuXe
0.034145
0.142835
2.391
0.918
RAB
Interst.
Si te
System
IT
5.020
CuAr
0.111841
5.020
AgAr
0.122093
5.020
AuAr
0.124467
5.333
CuKr
0.118540
5.333
AgKr
0.130220
5.333
AuKr
0.132900
5.794
CuXe
0.122040
5.794
AgXe
0.134965
5.794
AuXe
0.137596
Sc
h'h
kX
0.218277
5.687
0.587
0.215312
1.564
0.882
0.213195
0.370
0.972
0.245030
20.96
-0.846
0.246968
5.668
0.463
0.247182
1.368
0.869
0.268690
36.63
-2.713
0.277948
9.902
-0.125
0.282058
2.391
0.719

APPENDIX B
PROGRAMS
The program used to control absorption and MOD measurements follows.
OO
The program is a modification of the version utilized by Powell for
use on the Commodore 8032 computer. Modifications were made by
Dr. Martin Vala, Dr. Jean-Claude Rivoal, Dr. Joseph Baiardo, and the
author.
The second program is used to calculate absorption and MCD moments.
The program is an expansion of the Simpson's rule integration algorithm
written by Dr. Marek Kreglewski.
182

183
1 Rr.ty***************rcn CONTROL PROGRAM*********"*******
10 PRINT" DO YOU WISH TO CHANGE THE MATRIX TEMPERATURE? (YES=1, NO=0)"
20 INPUT Z9
22 IF Z9=l THEN C-OSUB 38499
25 DIM A%(8000)
30 POKE 36865,0
31 POKE 36864,0
32 POKE 36865,4
34 POKE 36875,0
35 POKE 36874,255
36 POKE 36875,4
37 POKE 36867,0
38 POKE 36866,255
39 POKE 36867,4
40 POKE 36866,0
42 PRINT"INPUT INITIAL AND FINAL WAVELENGTHS(A)"
50 INPUT X,Y
52 WL=X
55 NT=(X~Y)*4
60 PRINT"NO. OF CYCLES FOR SIGNAL AVERAGING;NONE=l"
65 INPUT E
70 PRINT"CHAET RECORDER SPREAD:5A/MM(3),2.5A/MM(6),1.25A/MM(12),0.625A/MM(24)"
75 INPUT D
80 PRINT"COLLECT DATA EVERY 0.25A(1),0.5A(2),1.0A(4)?"
85 INPUT C
90 ON C GOTO 100,200,5000,300
95 GOSUB 32000
100 FOR 11=1 TO NT
105 GOSUB 36000
110 POKE 36866,24
115 WL=WL-.25
125 POKE 36866,25
130 GOSUB 34000
132 IP=11/200
135 IF IP =INT(IP) THEN 145
140 GOTO 150
145 GOSUB 38000
150 NEXT II
190 GO TO 4G0
2G0 N2=NT/2
202 FOR 11=1 TO N2
205 J2=0
210 GOSUB 36000
215 POKE 36866,24
220 WL=WL-.25
230 POKE 36866,25
235 GOSUB 34000
240 J2-J2+1
245 IF J2=4 GOTO 260

184
250 IF J2<>2 GCTO 215
255 IF J2=2 GOTO 210
258 IQ=I2/100
260 IF IQ =INT(IQ) THEN 270
265 GOTO 275
270 C-OSUB 38000
275 NEXT II
290 GOTO 400
300 N4=NT/4
302 FOR 11=1 TO N4
305 J3=0
310 GOSB 36000
315 POKE 36866,24
320 VJL=WL-.25
330 POKE 36866,25
335 GOSUB 34000
340 J3=J3+1
345 IF J3<>4 GOTO 315
350 IF (11/50) =1171(11/50) THEN 360
355 GOTO 365
360 GCSUB 38000
365 NEXT II
370 GOTO 400
400 PRINT"SAVE DATA? YES=1,N0=0
410 INPUT B
415 IF B=0 THEN 3072
1000 DATA "SAMPLE: ", "MATRIX: ", "DEPOS.TEMP. : ", "MATRIX TEMP.: ", "INITIAL WVL.
1002 DATA "FINAL WVL:","RESOLUTION:","CYCLES FOR SIG. AVG.:"
1003 DATA "PTE. PER ANG. AND GAIN"DATE:"
1004 PRINT"INPUT FILE NAME"
1006 INPUT A6$
1010 DOPEN#8,(A6$) ,W
1020 IF DSO0 THEN PRINT DS$:STOP
1030 PRINT ENTER DATA INFORMATION"
1040 FOR 1=1 TO 10
1050 READ F$
1060 PRINTF?;:INPUT DA$(I)
1070 NEXT I
1080 RESTORE
1090 PRINT"ENTER Y TO RECORD, N TO RE-ENTER";
1100 GET Y$: IF Y$<>"Y" AND Y$<>"N" THEN 1100
1110 PRINTY$
1120 IF Y$="N" THEN 1030
2000 FOR 1=1 TO 8
2010 PRINTtr8 ,DA$(I)
2020 NEXT I
2030 IF DSO0 THEN PRINT DS$:STOP
3010 N=4*(X-Y)/C

185
3030 X%=A%(I)
3040 PRINT#8,X%
3050 IF DSO0 THEN PRINT DS$:STOP
3060 NEXT I
3070 DCL0SE#8
3071 PRINT" DO YOU WISH TO CHANGE THE MATRIX TEMPERATURE?(YES=1,NO=0)"
3072 INPUT Z8
3073 IF Z8=l THEN GCSUB 38499
3074 FOR 11=1 TO NT
3075 POKE 36866,10
3076 POKE 36866,11
3078 NEXT II
3090 PRINT "FINISHED"
5000 END
32000 V=0.105E-03*(WL/2)*255+0.5: REM MODULATOR VOLTAGE
32500 Dl=INT(V)
33000 POKE 36874,Dl
33500 RETURN
34000 FOR Kl=l TO D:REH CHART RECORDER STEPPER MCTOR
34100 POKE 36866,9
34200 POKE 36866,25:GOSUB 38499
34300 NEXT Kl
34400 RETURN
36000 X1=0:REM SIGNAL AVERAGING
36100 FOR KS=1 TO E
36200 Xl=Xl+PEEK(36864)
36300 NEXT KS
36400 A%(II)=INT(Xl/E)
36500 RETURN
38000 POKE 36866,57:REM CHART RECORDER EVENT MARKER
381C0 FOR 19=1 TO 50
38200 NEXT 19
38300 POKE 36866,25
38350 GOSUB 32000
38400 RETURN
38499 PRINT:PRINT:PRINT:PRINT
38500 PRINT "TO SET TEMP., ENTER A#lB#2CA WHERE #1 IS THE DESIRED t (A 3-DIGIT"
38501 PRINT "NUMBER) AIT) #2 IS A SINGLE DIGIT FROM 1 TO 9. iF THE t-CONTROLLER"
38502 PRINT"IF THE t CONTROLLER IS NOT UNDER COMPUTER CONTROL"
38503 PRINT"ENTER A#lB#2CAD TO SWITCH CONTROL "
38504 PRINT"OVER TO THE pet. aNOTHER D ENTERED IN THE SUBROUTINE WILL SWITCH"
38505 PRINT"CONTROL BACK TO THE FRONT PANEL."
38506 PRINT:PRINT:PRINT:PRINT
38510 INPUT"ENTER t CHANGE ";A$
38515 OPENl,6

186
38520 PRINTS,A$CHR$(13)
38530 CLOSEl
38540 0PEN2,6
38550 INFUT#2,G$,R$,P$,S$,T$
38560 CL0SE2
38570 PRINT:PRINT
38580 PRINT"gain ";G$
38590 PRINT"reset ";R$
38600 PRINT"panel ";P$
38610 PRlNT"set point ";S$
38620 PRINT"teinper£ture ";T$
38625 PRINT:PRINT:PRINT:PRINT
38630 RETURN
38700 END

187
1000
1100
1110
1150
1200
1400
1410
1420
1430
1440
1450
1460
1470
1472
1474
1476
1478
1480
1482
1484
1486
1488
1490
1500
1505
1510
1550
1560
1570
1580
1590
1595
2000
2100
2150
2160
2170
DIM A%(2000)
PRINT" LOAD DATA DISK INTO DRIVE 0."
PRINT" ":PRINT" "
PRINT" ABS OR MCD?":INPUT A3$
PRINT" INPUT FILE NAME. INPUT A$
PRINT" ENTER NUMBER OF BANDSINPUT NB
PRINT" ":PRINT" ":PRINT" "
PRINT" FILE ;A$
PRINT" ":PRINT" ":PRINT" "
DOPEN#l, (A$)
FOR 1=1 TO 8: REM TRANSFER OF FILE INFORMATION TO MEMORY
INPUT#l,flD$(I)
NEXT I
PRINT" sample ";AD$(1)
PRINT" matrix ";AD$(2)
PRINT" deposition cell temperature ";AD$(3)
PRINT" thermocouple range ";AD$(4)
PRINT" initial wavelength ";AD$(5)
PRINT" final wavelength ";AD$(6)
PRINT" resolution ";AD$(7)
PRINT" date ;AD$(8)
PRINT" ":PRINT" ":PRINT" "
NA=VAL (AD$ (5)) -VAL (AD$ (6))
PRINT" # OF POINTS IN SCAN IS ";NA
X=VAL(AD$(5))
PRINr"ENTER MATRIX TEMPERATURE":INPUT TP
FOR 11=0 TO NA-1
INPUTfl,A%(II)
AY=X-(II)
PRINT AY;A%(II)
NEXT II
CLOSEl
FOR K=1 TO NB
PRINT" DATA FOR BAND #";K
PRINT" DO YOU WANT THE MOMENTS OUTPUT TO PRINTER? Y OR N":INPUT
PRINT" ENTER LONG WAVELENGTH LIMIT OF BAND.":INPUTXL
PRINT "ENTER LCW WAVELENGTH LIMIT OF BAND.":INFUTXS
2500 KI=X-XL
2520 ZL=((A%(KI-2)+A%(KI-1)+A%(KI)+A%(KI+1)+A%(KI+2))/5)
2530 ZS=((A%(X-XS-2)+A%(X-XS-1)+A%(X-XS)+A%(X-XS+1)+A% (X-XS+2))/5)
3100 PRINT" ENTER CALIBRATION FACTOR.":INPUT CERT
3200 PRINT" ENTER APPROXIMATE BAND CENTER.":INPUT P
3210 CR=P
3700 P=2/P
3800 A=(ZS-ZL)/(XL-XS)
3900 Xl=l/XL
4000 Z3=A%(KI)-ZL
Z$

188
4050 Zl=Z3*XL
4100 S=0
4150 AREA=0
4200 T=0
4210 U=0
4220 V=0
4225 W=0
4230 J=KI+1
4300 FOR I=XL-1 TO XS STEP -1
4400 X2=l/l
4700 Z4=A%(J)-A*(XL-I)-ZL
4750 Z2=Z4*I
4800 R=(X2-Xl)*(Zl+Z2)
4850 Q=(X2-Xl)*(Z3+Z4)
4860 AREA=AREA+Q
4900 S=S+R
5000 T=TH-R*(X2+Xl-P)
5010 U=U+R*(X2+X1-P)~2
5020 V=V+R*(X2+X1-P)~3
5030 W=W+R*(X2+X1-P)"4
5100 Xl=X2
5200 Zl=Z2
5210 Z3=Z4
5220 J=J+1
5300 NEXT I
5310 MA=.5 *AREA*CBRT
5320 M0=.5*S*CBRT
5321 IF A3 $="MOD" THEN GO TO 5330
5323 PE=2*MA/M0
5324 IF ABS(PE-P)<1E-12 THEN GO TO 5330
5325 P=N0/MA
5328 GO TO 3700
5330 Ml=.25E08*T*CBRT
5340 M2=.125E16*U*CBRT
5345 M3=.0625E24*V*CBRT
5350 M4=.03125E32 *W*CBRT
5400 PRINT" FILE ";A$,A3$
5420 PRIi7T"THERKCCOUPLE READS ";AD$(4)FOR A MATRIX TEMP. OF ";TP;"k"
5430 PRINT"AREA= ";MA*lE08
5440 PRINT"0TH Ma4ENT=";M0,"LONG WAVE LIMIT=";XL
5450 PRINT "1ST M0-1ENT=" ;Ml, "LCW WAVE LIMITO" ;XS
5460 PRINT "2ND MOMENTO";M2,"CEUTTER OF BAND=";CR
5470 PRINT"3RD MOMENTO";M3,"ZL=";ZL;"ZS=";ZS
5475 PRINT"4TH MOi'lENTO" ;M4
5480 PRINT"AVG. ENERGY AT ";M0/MA
5490 PRI1T"CALIBRATION FACTOR= ";CBRT
5495 IF Z$="N" THEN GO TO 5800
5500 OPEN5,4,0

189
8510 PRINTS
5520 PRINTS
5530 PRINT#5
5540 PRINTS
5550 PRINT#5
5560 PRINTS
5570 PRINTS
5575 PRINT#5
5580 PRINTS
5590 PRINTS
5595 PRINTS
58G0 NEXT K
FILE ";A$,A3$,CHR$(10)
,"T.C. READS ";AD$(4);" FOR A MATRIX TEMP. OF ";TP;"k",CHR$(10)
,"AREA "MA*1E08, CHR?(10)
,"0TH MOMENT";H0,"LONG WAVE LIMIT";XL,CHR?(10)
, "1ST MOMENT ";Ml, "LOW WAVE LIMIT";XS,CHR$(10)
, "2ND MOMENT";M2, "CENTER OF BAND" ;CR,CHR$(10)
f "3RD MOMENT" ;M3, "ZL= ";ZL; "ZS= ";ZS,CHR?(10)
, "4TH MOMENT ";M4,CHR$(10)
r"AVG. ENERGY AT ";M0/MA;" ANGSTROMS",CHR$(10)
,"CALIBRATION FACTOR";CBRT,CHR?(10)
,CHR$(10),CHR$(10),CHR?(10)
9999 END
6300B PRINT"TYPE ANY KEY WHEN READY"
63010 GET B6?:IF B6"" THEN 63010
63020 RETURN

APPENDIX C
TEMPERATURE CALIBRATION
As mentioned in the text, temperature measurements are very
critical to the moment analysis employed here. Accurate matrix temper
ature measurement has been a problem for matrix isolation spectroscopists
for many years. Often a hole is drilled in the spectroscopic plate or
its metal frame and a thermocouple inserted. The matrix is then assumed
to be at the same temperature. An alternate method is outlined here
which relies on the temperature dependence of the moment ratio 0/
0
of a paramagnetic matrix isolated sample and a temperature difference as
measured by a thermocouple. For a paramagnetic substance the tempera
ture dependence of the ratio of its MCD/absorption signals may be
expressed as
p Co yBB
<^>o | For two temperatures (T2 >Ti)
T2 = Tj + AT
If x represents the moment ratio, one can consider the ratio of x2 (at
T2) to xx (at TJ:
Ti
1
\
The specification of the low(est) temperature, Tx, is thus dependent
only on the determination of the moment ratio X1/X2 anc* the temperature
190

191
interval AT. To find xjxl an argon isolated Au band was chosen since
Au has one component of its 2P - 2S transition completely resolved from
the other two (see Figure C.l). The quantity AT is simply found by
noting the difference in thermocouple readings (in yV) at the two
temperatures and dividing by the thermocouple sensitivity (in yV/K).
This procedure is dependent on the similarity in time response of
the thermocouple and the MCD signal of the sample. This was measured
by plotting the thermocouple output and the MCD signal (of Fe atoms in
an Ar matrix, A = 266.2 nm) simultaneously on a dual-pen strip chart
recorder as the temperature was cyclically raised and lowered. The
result is shown in Figure C.2. It is clear that both signals tracked
the temperature variation together and with a time lag less than one
second. The lowest temperature on the apparatus was found to be 10.2 K
by this method.

Figure C.l. The Au/Ar band and equations used to calibrate
the lowest T attained on the Displex.

193
y = ( AA)q i Go, yB_ const.
; V
0 "W^T, I
For T2 >T, : T2 = I, +AT
T =AT(XT/XT)(1-XT/XTr1
1 12 *1 f >1
Au/Ar
+
AA

Figure C.2. Plot of MCD and thermocouple tracking of
temperature fluctuations. Note lag less
than one second. The arrows indicate
times at which the temperature cycling
period was changed. The right most por
tion shows the temperature stability at
the lowest temperature.

195
low T
high T
t t
THERMOCOUPLE
highT
low T

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BIOGRAPHICAL SKETCH
Kyle J. Zeringue was born in Thibodaux, Louisiana, on
February 13, 1954. He graduated from Thibodaux High School in 1972 and
attended Nicholls State University, Thibodaux, Louisiana, where he
worked on a degree in chemistry with physics and applied mathematics
minors through 1975. Since January 1976 he has pursued a circuitous
course of study leading to the Doctor of Philosophy degree in chemistry
at the University of Florida in Gainesville, Florida. He is married to
Jan Ellin Olson. They are the reluctant owners of two parasitic cats
from the Louisiana swamps named Theophile and PI acide.
201

I certify that I have read this study and that in my opinion it conforms
to acceptable standards of scholarly presentation and is fully adequate,
in scope and quality, as a dissertation for the degree of Doctor of
Philosophy.
Dr. Martin T. Val a, Chairman
Professor of Chemistry
I certify that I have read this study and that in my opinion it conforms
to acceptable standards of scholarly presentation and is fully adequate,
in scope and quality, as a dissertation for the degree of Doctor of
Philosophy.
Dr. Willis B. Person
Professor of Chemistry
I certify that I have read this study and that in my opinion it conforms
to acceptable standards of scholarly presentation and is fully adequate,
in scope and quality, as a dissertation for the degree of Doctor of
Philosophy.
(\( 9 ro
Dr. John R. Eyler (J
Professor of Chemistry

I certify that I have read this study and that in my opinion it conforms
to acceptable standards of scholarly presentation and is fully adequate,
in scope and quality, as a dissertation for the degree of Doctor of
Philosophy.
Dr. Gerhard M. Schmid
Professor of Chemistry
I certify that I have read this study and that in my opinion it conforms
to acceptable standards of scholarly presentation and is fully adequate,
in scope and quality, as a dissertation for the degree of Doctor of
Philosophy.
Dr. Thomas L. Bailey
Professor of Physics
This dissertation was submitted to the Graduate Faculty of the Department
of Chemistry in the College of Liberal Arts and Sciences and to the
Graduate Council, and was accepted as partial fulfillment of the require
ments for the degree of Doctor of Philosophy.
April 1983
Dean for Graduate Studies and Research



Figure 4.18. Cu absorption and MCD bands in the range
220 nm to 340 nm.


127
WAVELENGTH (nm]


Figure 4.1. The splittings induced in free atom 2S and 2P
states. Note dependence upon the order of
application of various interactions in calcu
lation.


197
18. L. Andrews, Vib. Spectra Struct., 4_, 1 (1975).
19. G. C. Pimentel, New Synth. Methods, 3_, 21 (1975).
20. R. J. Van Zee, C. M. Brown, K. J. Zeringue, and W. Weltner, Jr.,
Acc. Chem. Res., 13_, 237 (1980).
21. D. Milligan and M. E. Jacox, "MTP International Review of Science,
Physical Chemistry, Series I," Vol. 3 (D. A. Ramsay, ed.),
Butterworth, London, 1972, p. 1.
22. I. Douglas, R. Grinter, and A. J. Thomson, Dalton Division
Symposium, Chemical Society, Autumn Meeting, University of East
Anglia, 1973.
23. S. F. Mason, Quart. Rev., 17_, 20 (1963).
24. J. A. Spencer, J. Chem. Phys., 54, 5139 (1971).
25. G. Barth, R. Records, E. Bannenberg, and C. Djerassi, J. Am. Chem.
Soc., 93, 2545 (1971).
26. G. Barth, W. Voelter, E. Bunnenberg, and C. Djerassi, J. Am. Chem.
Soc., 94, 1293 (1972).
27. J. LoMenzo, B. D. Bird, G. A. Osborne, and P. J. Stephens, Chem.
Phys. Lett., 9, 332 (1971).
28. M. J. Harding and B. Briat, Mol. Phys., 25, 745 (1973).
29. I. N. Douglas, R. Grinter, and A. J. Thomson, Chem. Phys. Lett.,
28, 192 (1974).
30. J. C. Miller, R. L. Mowery, E. R. Krausz, S. M. Jacobs, H. W. Kim,
P. N. Schatz, and L. Andrews, J. Chem. Phys., 74., 6349 (1981).
31. M. Kreglewski and M. Vala, Chem. Phys., 56_, 381 (1981).
32. E. R. Krausz, R. L. Mowery, and P. N. Schatz, Ber. Bun. Phys. Chem.,
82, 134 (1978).
33. M. A. Goetschlackx, R. L. Mowery, E. R. Krausz, W. C. Yeakel,
P. N. Schatz, B. S. Ault, and L. Andrews, Chem. Phys. Lett., 47,
23 (1977).
34. R. D. Brittain, PhD Dissertation, University of Florida, 1979.
35. T. J. Barton, I. N. Douglas, R. Grinter, and A. J. Thomson, Mol.
Phys., 30, 1677 (1975).
36. T. J. Barton, R. Grinter, and A. J. Thomson, Chem. Phys. Lett., 40,
399 (1976).
37. G. A. Osborne, J. Mol. Spectrosc., 49_, 48 (1974).


188
4050 Zl=Z3*XL
4100 S=0
4150 AREA=0
4200 T=0
4210 U=0
4220 V=0
4225 W=0
4230 J=KI+1
4300 FOR I=XL-1 TO XS STEP -1
4400 X2=l/l
4700 Z4=A%(J)-A*(XL-I)-ZL
4750 Z2=Z4*I
4800 R=(X2-Xl)*(Zl+Z2)
4850 Q=(X2-Xl)*(Z3+Z4)
4860 AREA=AREA+Q
4900 S=S+R
5000 T=TH-R*(X2+Xl-P)
5010 U=U+R*(X2+X1-P)~2
5020 V=V+R*(X2+X1-P)~3
5030 W=W+R*(X2+X1-P)"4
5100 Xl=X2
5200 Zl=Z2
5210 Z3=Z4
5220 J=J+1
5300 NEXT I
5310 MA=.5 *AREA*CBRT
5320 M0=.5*S*CBRT
5321 IF A3 $="MOD" THEN GO TO 5330
5323 PE=2*MA/M0
5324 IF ABS(PE-P)<1E-12 THEN GO TO 5330
5325 P=N0/MA
5328 GO TO 3700
5330 Ml=.25E08*T*CBRT
5340 M2=.125E16*U*CBRT
5345 M3=.0625E24*V*CBRT
5350 M4=.03125E32 *W*CBRT
5400 PRINT" FILE ";A$,A3$
5420 PRIi7T"THERKCCOUPLE READS ";AD$(4)FOR A MATRIX TEMP. OF ";TP;"k"
5430 PRINT"AREA= ";MA*lE08
5440 PRINT"0TH Ma4ENT=";M0,"LONG WAVE LIMIT=";XL
5450 PRINT "1ST M0-1ENT=" ;Ml, "LCW WAVE LIMITO" ;XS
5460 PRINT "2ND MOMENTO";M2,"CEUTTER OF BAND=";CR
5470 PRINT"3RD MOMENTO";M3,"ZL=";ZL;"ZS=";ZS
5475 PRINT"4TH MOi'lENTO" ;M4
5480 PRINT"AVG. ENERGY AT ";M0/MA
5490 PRI1T"CALIBRATION FACTOR= ";CBRT
5495 IF Z$="N" THEN GO TO 5800
5500 OPEN5,4,0


158
230 240 250 260 270
X(nm)


50
breaks down, and it is no longer possible to associate a vibronic state
with only one electronic state. The calculation of zero field absorption
and MOD becomes very much more difficult. The diagonality of H1 in
eouation (26) is not maintained, and the magnetic field perturbation
scrambles different vibronic levels of the same electronic state. The
calculation of the Zeeman effect within an electronic state is then
dependent on the details of the Jahn-Teller phenomenon. In such situa
tions where the absorption and MCD are evaluated with difficulty, it is
of interest to look at alternative methods of analysis that enable more
complex models to be treated without dispersion calculations. The method
of moments is such an approach. The method of moments was developed by
54
Henry et al. in work formulating the theoretical framework for the
relationship between the moments of F center bands and the changes in
these moments with applied perturbations to the interactions (spin orbit,
55
vibronic) within an excited 2TX state. Osborne and Stephens modified
this work for treatment of F centers in LiF. The moment analysis per
formed here follows closely the equations as developed by Osborne and
Stephens. The various absorption and MCD moments are obtained from
(62)
where A and AA are the optical absorbance and differential absorbance,
A^-AR, resPec't've^y ar|d the average frequency of the zero field absorp
tion is given by
v


Figure C.2. Plot of MCD and thermocouple tracking of
temperature fluctuations. Note lag less
than one second. The arrows indicate
times at which the temperature cycling
period was changed. The right most por
tion shows the temperature stability at
the lowest temperature.


96
l/T OC1)


19
so that
Aaa exp(-ea/kT) 1
N X exp(-ea/kT) dA
(34)
N
Since under Zeeman splittings the center of gravity is retained,
(35)
This shows that the fractional change of population in |A^a> is not
dependent upon vibrational level and is the same as obtained in a purely
electronic system at RQ.
With these effects of the magnetic field on transition energies and
moments and on ground state populations, the circularly polarized absorp
tion MCD can be derived.
From equation (9),
A
Y
(36)
X,j
Y
X
+ 'H f1 (e) cz
a1 ' X a1 1 A aA '
Here,
f


Figure 4.19. Appearance of Cu/Kr spectrum after prolonged
deposition from 230 nm to 290 nm.


MONOCHROMATOR
/\
STEPPI NG
MOTOR DRIVE
NTERFACE
bd
PHOT.
TRAN.
LED
LOCK-IN B
/\
SAMPLE
PM TUBE
-IMPEDANCE
ADAPTOR
U
Wl DE BAND
AMP
LOCK-IN A
GAI N
LEVEL
SHIFTER
LOG AMP
IMP.
ADAPT.
REF
AMP
MAN/FB.
SWITCH
SAM.
AMP
ERROR
AMP
PM
HV
VOLT.
SUPPLY
SCOPE


118
onto a CaF2 plate held at either 15 or 20 K. The Cu band in Kr has
generally the same appearance as in Ar.^
Figure 4.15 shows the temperature dependence of Cu in Kr, and
Figure 4.16 shows a plot of 1/
0 vs. 1/T for Cu in Kr. The
slope yields a spin orbit splitting, A = 143 cm"1 (A = 95 cm"1), and
a value of gQr,b = -0.17. The gQrb value is of little importance as
the uncertainty in the intercept of the 1/
0 vs. 1/T plot is quite
large. Of more interest is the further reduction of the spin orbit
splitting compared to Ar (185 cm"1) and the gas phase value (248 cm"1).
The spin orbit coupling constant reduction factor for Cu in Kr is calcu
lated as k^sub = 0.48 and k^-nt = -0.85. The observed k^Qbs =
95 cm_1/166 cm"1 = 0.57. As in the Cu/Ar case the spin orbit reduction
can be explained through an orbital overlap picture with the Cu residing
in a substitutional lattice site.
A plot of 3/
0 vs. 1/T is shown in Figure 4.17. From the
ratio of slopes, method A* and Ajj^ can be found: a£ = 1.9xl04 and
Aj^jc = 8.9xlO\ and therefore the ratio F = 0.21. The noncubic lattice
modes are, as expected from the Cu/Ar case, dominant.
As in the Cu/Ar case, the Moran model was applied to Cu isolated in
Kr. The values of t and z are 111 cm"1 and 152 cm-1, respectively, for
a A value of 95 cm"1, as determined from the moment analysis. As in
the Cu/Ar case, the coefficients listed in Table 4.2 indicate complete
mixing of the eigenfunctions through spin orbit/vibronic interaction so
that J is not a good quantum number.
Figure 4.18 shows the spectrum of Cu isolated in Kr in the range
200 nm to 540 nm. The triplet of bands centered near 245 nm is much
weaker than the set at 310 nm. In the gas phase, several spin-forbidden


199
59. L. Brewer and B. King, J. Chem. Phys., 53_, 3981 (1970).
60. M. Moskovits and J. Hulse, J. Chem. Phys., 67_, 4271 (1977).
61. L. Andrews and G. C. Pimentel, J. Chem. Phys., 47, 2905 (1967).
62. R. Grinter, S. Armstrong, U. Jayasooriya, J. McCombie, D. Norris,
and J. Springall, Fara. Symp. Chem. Soc., 14, 94 (1980).
63. P. H. Kasai and D. McLeod, Jr., J. Chem. Phys., 55, 1566 (1971).
64. R. G. Denning and J. A. Spencer, Symp. Fara. Soc., No. 3, 84 (1969).
65. C. E. Moore, Atomic Energy Levels, Nat'l Bureau Standards (UCS)
Circ. 467, Vol. I, 1949; Vol. II, 1952; Vol. Ill, 1958.
66. R. L. Mowery, J. C. Miller, E. R. Krausz, P. N. Schatz,
S. M. Jacobs, and L. Andrews, J. Chem. Phys., 70_, 3920 (1979).
67. K. Cho, J. Phys. Soc. Jap., 23, 1372 (1968).
68. J. H. Ammeter and D. C. Schlosnagle, J. Chem. Phys., 59_, 4784
(1973).
69. K. J. Zeringue, J. ShakhsEmampour, and M. Vala, "Metal Bonding and
Interactions in High Temperature Systems with Emphasis on Alkali
Metals," ACS Symposium Series No. 179 (J. L. Gole and
W. C. Stwalley, eds.), 1981, p. 229.
70. R. Englman, "The Jahn-Teller Effect in Molecules and Crystals,"
Wiley Interscience, New York, 1972.
71. M. D. Sturge, "Solid State Physics," Vol. 20 (F. Seitz, D. Turnbull,
and H. Ehrenreich, eds.), Academic Press, New York, 1967, p. 92.
72. S. A. Mitchell and G. A. Ozin, J. Am. Chem. Soc., 100, 6776 (1978).
73. S. A. Mitchell, G. Kenney-Wallace, and G. A. Ozin, J. Am. Chem.
Soc., 103, 6030 (1981).
74. L. Brewer and C. Chang, J. Chem. Phys., 56_, 1728 (1972).
75. E. N. Shawhan, Phys. Rev., 48_, 343 (1935).
76. S. Weniger, J. Phys. (Paris), Z8_, 595 (1967).
77. R. Teichman and E. R. Nixon, J. Mol. Spec., 59_, 299 (1976).
78. V. E. Bondybey and J. H. English, J. Chem. Phys., 67_, 3405 (1977).
79. M. Kreglewski and M. Vala, J. Chem. Phys., 7Q_, 5411 (1981).
80. D. D. Stranz and R. K. Khanna, J. Chem. Phys., 74^ 2116 (1981).


Figure 4.3. Absorption and MCD spectra observed for Cu
isolated in Ar.


6
If in some medium the indices of refraction for RCP and LCP light are
different, optical rotation occurs. If the absorption coefficients for
some transition differ for RCP and LCP light, circular dichroism (CD) is
said to be present.
There are two sources for these inequality. Natural optical
activity arises in a molecule of low symmetry or unit cell in the case
of crystals, and its wavelength dependence is known as optical rotary
dispersion (ORD). The quantum mechanical theory ascribes the ORD of a
molecule to electronic transitions which have parallel or antiparallel
23
electric and magnetic transition moments. The second source of inqual-
/\
ity is application of an external magnetic field, H, in the direction of
light propagation. In this magnetic optical rotation, the right- and
left-handed circular motions around A do not interact equivalently with
the medium, and the absorption coefficients of RCP and LCP light in
regions of absorption differ in the presence of the magnetic field. This
gives rise to magnetic circular dichroism (MCD) which is the differential
absorbance of RCP and LCP light. The increase in information content
offered by polarization-dependent selection rules for optical absorptions
makes MCD a very powerful complement to conventional spectroscopic meth
ods in electronic structure determination.
Magnetic circular dichroism can provide information on the ground
states of atoms and molecules although the prime utility of MCD has been
in extracting excited state information otherwise unavailable. Excited
state magnetic moments and g values are attainable as well as spin-orbit
coupling constants and information on static and dynamic Jahn-Teller
24
interactions.
The same information is available from Zeeman spectra if all Zeeman
components are resolved. This resolution is often difficult, requiring


62
frequencies of 150 Hz and 270 Hz. These frequencies were selected to
minimize ac powerline pick-up since they were not integral multiples
of ac line frequency, 60 Hz.
The beam chopped at 270 Hz traversed the matrix and arrived at the
photocathode of an EMI 9683 QB photomultiplier tube. The beam chopped
at 150 Hz was reflected around the cryostat by two Edmund Scientific
aluminized front-surface mirrors and onto the same photomultiplier tube.
An iris allowed attenuation of the reference beam.
The chopping wheel assembly was equipped with two light emitting
diodes and two phototransistors located on opposite sides of the chopping
wheel from the LEDs so the signals from the phototransistors were used as
reference signals for the two chopping frequencies. The LEDs were
powered by a 15 V supply. Both signals were amplifed by RCA 3140 opera
tional amplifiers. A diagram of the absorption electronics is shown in
Figure 3.4.
The current output of the photomultiplier tube (^lO-7 amp) was con
verted to a voltage by a 15 to resistor connected to the ground. Part
of the signal was amplified by a factor of 100 using an Analog Devices
52 k low-drift operational amplifier and sent to an oscilloscope for
monitoring the wave form during the experiment. The rest of the signal
was introduced in parallel to two lock-in amplifiers--an Ithaco Dynatrac
391A Lock-in Amplifier and an Ithaco Model 353 Phase-lock Amplifier.
The Ithaco 353 was locked to the 150 Hz reference frequency from the
chopper, and its output was proportional to the lamp emission spectrum,
monochromator dispersion characteristics, and the photomultiplier tube
spectral response. The Ithaco 391A was locked to the 270 Hz reference,
and its output was proportional to the absorption spectrum of the matrix


187
1000
1100
1110
1150
1200
1400
1410
1420
1430
1440
1450
1460
1470
1472
1474
1476
1478
1480
1482
1484
1486
1488
1490
1500
1505
1510
1550
1560
1570
1580
1590
1595
2000
2100
2150
2160
2170
DIM A%(2000)
PRINT" LOAD DATA DISK INTO DRIVE 0."
PRINT" ":PRINT" "
PRINT" ABS OR MCD?":INPUT A3$
PRINT" INPUT FILE NAME. INPUT A$
PRINT" ENTER NUMBER OF BANDSINPUT NB
PRINT" ":PRINT" ":PRINT" "
PRINT" FILE ;A$
PRINT" ":PRINT" ":PRINT" "
DOPEN#l, (A$)
FOR 1=1 TO 8: REM TRANSFER OF FILE INFORMATION TO MEMORY
INPUT#l,flD$(I)
NEXT I
PRINT" sample ";AD$(1)
PRINT" matrix ";AD$(2)
PRINT" deposition cell temperature ";AD$(3)
PRINT" thermocouple range ";AD$(4)
PRINT" initial wavelength ";AD$(5)
PRINT" final wavelength ";AD$(6)
PRINT" resolution ";AD$(7)
PRINT" date ;AD$(8)
PRINT" ":PRINT" ":PRINT" "
NA=VAL (AD$ (5)) -VAL (AD$ (6))
PRINT" # OF POINTS IN SCAN IS ";NA
X=VAL(AD$(5))
PRINr"ENTER MATRIX TEMPERATURE":INPUT TP
FOR 11=0 TO NA-1
INPUTfl,A%(II)
AY=X-(II)
PRINT AY;A%(II)
NEXT II
CLOSEl
FOR K=1 TO NB
PRINT" DATA FOR BAND #";K
PRINT" DO YOU WANT THE MOMENTS OUTPUT TO PRINTER? Y OR N":INPUT
PRINT" ENTER LONG WAVELENGTH LIMIT OF BAND.":INPUTXL
PRINT "ENTER LCW WAVELENGTH LIMIT OF BAND.":INFUTXS
2500 KI=X-XL
2520 ZL=((A%(KI-2)+A%(KI-1)+A%(KI)+A%(KI+1)+A%(KI+2))/5)
2530 ZS=((A%(X-XS-2)+A%(X-XS-1)+A%(X-XS)+A%(X-XS+1)+A% (X-XS+2))/5)
3100 PRINT" ENTER CALIBRATION FACTOR.":INPUT CERT
3200 PRINT" ENTER APPROXIMATE BAND CENTER.":INPUT P
3210 CR=P
3700 P=2/P
3800 A=(ZS-ZL)/(XL-XS)
3900 Xl=l/XL
4000 Z3=A%(KI)-ZL
Z$


I certify that I have read this study and that in my opinion it conforms
to acceptable standards of scholarly presentation and is fully adequate,
in scope and quality, as a dissertation for the degree of Doctor of
Philosophy.
Dr. Gerhard M. Schmid
Professor of Chemistry
I certify that I have read this study and that in my opinion it conforms
to acceptable standards of scholarly presentation and is fully adequate,
in scope and quality, as a dissertation for the degree of Doctor of
Philosophy.
Dr. Thomas L. Bailey
Professor of Physics
This dissertation was submitted to the Graduate Faculty of the Department
of Chemistry in the College of Liberal Arts and Sciences and to the
Graduate Council, and was accepted as partial fulfillment of the require
ments for the degree of Doctor of Philosophy.
April 1983
Dean for Graduate Studies and Research


38
<2A1E'3Im¡2T1E1S' > =
<2A1E'a|m_|2T1U1k'> =
<2A1E18iIm|2TU1k1> =
<2A1Elal|m|2T1U,vl> =
<2A1E'3 Im+pTjU'v^ =
<2A1E'a1|m|2T1U1A1> =
<2A1E'3iIm_|2T!UX'> =
<2A1E,a |m+|2T1UV> =
<2A1E,3|m|2TXU'y'> =
Note that the bra is the ground state and the ket the excited state.
The energy level diagram in Figure 2.4 can be redrawn including the
sign of light polarity of each transition and the square of transition
probabilities as in Figure 2.5. It is interesting to note that the
polarity of a transition will be a+ for the m+ step-up operator and o_
step-down operator.
Having determined the integrals above and the transition probabil
ities, the C0 and V0 expressions in equations (21) and (41) can now be
evaluated. Recall equation (41):
Cn = -i- [I
[2 II2]
0 dn ; L| a1 -1 A 1 1 a1 Tl X 1 J a1 z z1 a
A a,A
and equation (21):
= 37 2 l A a,A
+ /3<2A1| |m_Ti| |2V
+ 7=<2A1||m+Ti||2T1>
+ ¡r<2A, I Im Ti| I2
3 I 1 1 T1>
+ ^-<2A1||m+TM|2T1>
2


176
For Pb2 the appearance of no observable MCD for the 508 nm band or
the 244 nm band is strong evidence for the assignment of the Pb2 ground
state to 0 Two ground state PQ atoms can combine to produce such a
y
80
state. Terms of C would have been expected for any other, degenerate
symmetries. The absence of A terms in these transitions leads to the
conclusion that both their excited states are nondegenerate 0*.
on
Recently Stranz and Khanna reported on the resonance Raman of
small Pb clusters in Xe matrices. Laser excitation into a band analogous
to the Pb/Kr band at 469 nm gave vibrational frequencies which were
interpreted as arising from a Pb3 species with D3^ symmetry. Such a
molecule could have an orbitally degenerate ground or excited state
which might give rise to C or A term MCD bands, although Jahn-Teller
distortions might be expected to reduce the degeneracy. The observa
tion of no MCD bands (or very weak 8 terms) provides no support for or
against a Pb3 species. However, if the 469 nm band does arise from a
Pb3 species, there is evidence that the ground and excited states of
Pb3 involved in this transition are orbitally and spin degenerate.
Further Studies
These experiments demonstrate the potential of the MCD technique,
both in the simple assignment of atomic and molecular states and in
the information attainable about excited states through the method of
moments.
There are a number of interesting extensions of this type of work.
It should be possible, with a faster data acquisition scheme, to arrive
at values for the spin orbit constant for Ag in various matrices. The
same improvement in data acquisition should facilitate measurements on


WAVELENGTH/nm


22
MCD and CP absorption. Other contributions to Zeeman splitting or
intensity changes due to either ground state redistribution or inter
mixing of electronic states are physically separable through their
dependence on e or T. The relative magnitudes of the A, 8 and C terms
determine the overall MCD. The A terms require either ground or excited
state degeneracy; 8 terms can exist under any condition of ground and
excited state degeneracy; and C terms require the ground state A to be
degenerate. Calculation of these terms can be used to predict the sign
and shape of the MCD dispersion. The maximum contribution to the MCD
of the three terms are related as
A i 8 o: C q
zz_z_
T'AW'kT
(42)
where T is the bandwidth of an electronic transition, AW is the order of
magnitude of an electronic energy gap, k is the Boltzmann constant, Z is
the Zeeman energy, and T is the temperature.
The experimental form of Aj 80 and C0 terms is illustrated in
Figure 2.1. The A: terms occur if there is a degeneracy in either the
ground or excited state. In positively signed Aj terms, the high energy
lobe is of positive sign and the low energy lobe of negative sign. In
Aj terms the two lobes are always oppositely signed and of equal magni
tude. Since the two lobes are separated by a small Zeeman splitting of
the degenerate level involved, the derivative-shaped term arises. The
intensity of allowed Aj terms is influenced by the sharpness of the
absorption band as indicated by the 3f/9c factor. The Ax term size is
also affected by the difference in magnetic moments for the ground and
excited states. If these are equal, no A1 term is observed.


44


APPENDIX
ORBITAL OVERLAP CALCULATIONS
Atomic orbital overlaps were calculated using the Aarhus Diatomic
Properties Package. The quantity which enters into the Ammeter and
68 X
Schlosnagle spin orbit reduction factor, k is an overlap between
the host rare gas outer p shell with the excited state metal p orbital.
Hartree-Fock calculations are not available on the 2P states of Cu, Ag
and Au, so it was necessary to approximate wavefunctions. Slater's
rules^ for estimating electron screening constants include the
equivalence of electrons within an n level. Based on this the metal
atom ns exponents and coefficients are used with appropriate n, 1, and
m^ values to calculate p type overlaps. Double zeta Roothan-Hartree-Fock
86
atomic wavefunctions as given by Clementi and Roetti and by McLean
87
and McLean for Cu, Ag, Au, Ar, Kr and Xe were used. The basis sets
are shown in Figure A.l. The po and p^ type overlaps as well as the
calculated spin orbit reduction factors are listed in Table A.2. The
interatomic distances in atomic units were taken from rare gas lattice
parameters as given in Meyer's book.^
178


36
FREE
ATOM
Oh
SPIN
ORBIT
ZEEMAN
SPLITTING
(units of ¡3)


, /
0
160
l/T (K-')


189
8510 PRINTS
5520 PRINTS
5530 PRINT#5
5540 PRINTS
5550 PRINT#5
5560 PRINTS
5570 PRINTS
5575 PRINT#5
5580 PRINTS
5590 PRINTS
5595 PRINTS
58G0 NEXT K
FILE ";A$,A3$,CHR$(10)
,"T.C. READS ";AD$(4);" FOR A MATRIX TEMP. OF ";TP;"k",CHR$(10)
,"AREA "MA*1E08, CHR?(10)
,"0TH MOMENT";H0,"LONG WAVE LIMIT";XL,CHR?(10)
, "1ST MOMENT ";Ml, "LOW WAVE LIMIT";XS,CHR$(10)
, "2ND MOMENT";M2, "CENTER OF BAND" ;CR,CHR$(10)
f "3RD MOMENT" ;M3, "ZL= ";ZL; "ZS= ";ZS,CHR?(10)
, "4TH MOMENT ";M4,CHR$(10)
r"AVG. ENERGY AT ";M0/MA;" ANGSTROMS",CHR$(10)
,"CALIBRATION FACTOR";CBRT,CHR?(10)
,CHR$(10),CHR$(10),CHR?(10)
9999 END
6300B PRINT"TYPE ANY KEY WHEN READY"
63010 GET B6?:IF B6"" THEN 63010
63020 RETURN


Figure 4.35. Absorption and MCD for Ag in Ar.


138
From 3/
o vs. 1/T (Figure 4.23) and 2/o vs. 1/T
(Figure 4.24), = 3.3*104 and A^ = 5.4xl04 for a value of F = 0.61,
although the scatter in experimental points causes a large error in
this value. Again the noncubic lattic modes are dominant. Kasai and
6 3
McLeod0,3 also indicate Cu to reside in a pure octahedral site in Xe.
When applied to the Cu/Xe case, the Moran model yields values of
t = 86 cm-1 and z = -174 cm-1 for X = -23 cm-1. Again spin orbit/vibronic
interaction shows (see Table 4.3) all excited state components completely
mixed.
The observed decrease in the spin orbit constant of Cu isolated in
Ar, Kr and Xe can be discussed in terms of orbital overlap effects as
well as the effect of Jahn-Teller interactions. Overlap of the valence
metal orbitals with the outer p shells of the rare gases increases going
from Ar to Xe, thereby causing a reduction in spin orbit splitting. This
effect is somewhat counteracted by the Jahn-Teller interaction of non
cubic lattice vibrations coupling with the excited state of the metal
atom.
The absorption energy matrix shfts are shown, going from Ar to Xe,
a
in Figure 4.25 (gas phase = 326 nm).
Gold in Argon
Matrices of Ar, Kr and Xe containing Au atoms were prepared by
codeposition of Au from a Ta cell heated, typically, to 1125C under
the same conditions used in Cu work. The absorption spectra of Au
50 56
atoms in matrices have been reported previously. By measuring
the separation of the split component and the isolated component,
Gruen et al.^ arrived at values of 3215 cm-1, 2943 cm-1, and 2570 cm-1


Figure 2.5. The state splittings and allowed transitions for
an atom in an octahedral field showing the effect
of spin orbit and Zeeman splitting.


Figure 4.25. Relative positions of Cu MCD in Ar, Kr and Xe.
Note the reversal of MCD term sign in Xe.


18
equation (28) becomes
>1
H
I Jxj> Z, |K J> 4
KZJ W W
(30)
[ A a>'
1 a
, , H
A a> Zj K a>
Ot iTZn K 1,0 ,0
kk/a Wa WK
To first order in H there is no energy contribution from these wavefunc-
tion perturbations. The transition moments become
'

a1 1 X
(31)
. K /J
1 K

a1 ¡ k k1 z1 X
"k
\
rv 1 + 1 iz~ \r 1 ^ 7 1 rv
K fk
K
a1 1 k k 1 z a
WK V

= [ + ']H a1 1 X
Ground state Zeeman splitting also leads to population changes,
A a
a
exp(-c'A a/kT)
a
I exp(-e'fl a/kT)
a ,a a
(32)
exp(-ea/kT) exp( H/kT)
^ exp(-ea/kT) exp(H/kT)
a, a
At large T where Zeeman energies are small relative to kT,
exp( H/kT) ^ 1 +
H
rv I rv
kT
(33)


Figure 4.9. Diagram of the degenerate modes of the e lattice vibration.


0
150
l/T (K*)


183
1 Rr.ty***************rcn CONTROL PROGRAM*********"*******
10 PRINT" DO YOU WISH TO CHANGE THE MATRIX TEMPERATURE? (YES=1, NO=0)"
20 INPUT Z9
22 IF Z9=l THEN C-OSUB 38499
25 DIM A%(8000)
30 POKE 36865,0
31 POKE 36864,0
32 POKE 36865,4
34 POKE 36875,0
35 POKE 36874,255
36 POKE 36875,4
37 POKE 36867,0
38 POKE 36866,255
39 POKE 36867,4
40 POKE 36866,0
42 PRINT"INPUT INITIAL AND FINAL WAVELENGTHS(A)"
50 INPUT X,Y
52 WL=X
55 NT=(X~Y)*4
60 PRINT"NO. OF CYCLES FOR SIGNAL AVERAGING;NONE=l"
65 INPUT E
70 PRINT"CHAET RECORDER SPREAD:5A/MM(3),2.5A/MM(6),1.25A/MM(12),0.625A/MM(24)"
75 INPUT D
80 PRINT"COLLECT DATA EVERY 0.25A(1),0.5A(2),1.0A(4)?"
85 INPUT C
90 ON C GOTO 100,200,5000,300
95 GOSUB 32000
100 FOR 11=1 TO NT
105 GOSUB 36000
110 POKE 36866,24
115 WL=WL-.25
125 POKE 36866,25
130 GOSUB 34000
132 IP=11/200
135 IF IP =INT(IP) THEN 145
140 GOTO 150
145 GOSUB 38000
150 NEXT II
190 GO TO 4G0
2G0 N2=NT/2
202 FOR 11=1 TO N2
205 J2=0
210 GOSUB 36000
215 POKE 36866,24
220 WL=WL-.25
230 POKE 36866,25
235 GOSUB 34000
240 J2-J2+1
245 IF J2=4 GOTO 260


33
matrix where all off-diagonal terms are zero for the Zeeman Hamiltonian.
This facilitates determination of Zeeman energies. Such a basis set is
49
obtained by reference to Griffith's book. The spin orbit basis can be
expressed in the form |rryn >.
Ground
state:
|2AX E1
ia
3'
>
= |o h>
l ,
2 .
Excited
States:
iv
'a'
>
= /y |0 +Js> "
1
1
-h>
Sz ,
1
1 2txe
'3'
'>
= ^ ll +%> -
SZ 1
0
-h>
I2TiU
V
'>
= 1 +Jg>
SZ ,
1
1 2T i U
'X
'>
- /y |0 -h> +
S3 1
1
-h>
1
SZ
l^u
V
'>
= /3 1-1 +Js>
+ S3
|0
-h>
|2TlU
V
>
= | -1 -%>
The wavefunctions in equation (45) are found by taking cross products of
orbital and spin representations in group 0^ such as r4r6 Tj @E for
the excited state, so the appropriate table (A20 for T^E) is consulted
49
in Griffiths book.
The Zeeman operator is Lz+2Sz, so matrix elements of the form
<2T1E'al|Lz+2Sz|2T1Ea'>
are calculated.
. JL
The results
of applying these operators are
S I
m >
= m,.
m >
if = 1
z1
s
s1
s
L I
z1
lv
if - = 1
(46)


128
levels (^P3/ >4Pi) lie just above the 2P components. Again employing the
/2 "2
Wigner-Eckart theorem and tables of vector coupling coefficients, the
CJV0 values predicted for the atomic 4P3/ and 4Pt states are -1 and +2,
/2 -s
respectively. Since the bands at 240 nm and 245 nm display MCD C0
terms, they are assigned as transitions to the 4P state. There is no
indication at the resolution used (~0.6 nm) of a further splitting in
this state induced by Jahn-Teller-spin orbit interaction. Assuming
this to be the case, the 240 nm peak with its positive C0 term is
assigned as 2Pl 2Sj and the 245 nm peak (negative C0term) is assigned
-2 "
as 4P3^ 2S;^. The lowest energy 251 nm component of the triplet struc
ture displays only a weak MCD 8 term and thus cannot be a Cu atom band.
Further, it cannot be assigned to any species with a degeneracy in its
ground or excited state. It is therefore assigned to a Cu2 1^u +
transition.
In the gas phase the next three bands (with increasing energy) are
4D^, 2Pi) and 2P3^. In the region 200 nm to 230 nm, the MCD displays
two clear, positive C0 terms. The transition 4Dt - 2S, is predicted to
*2
be a positive C0 term. The band at 224 nm is assigned to this transi
tion. The band at 218 nm is assigned to one of the components of the
2P transition with the other presumably just outside the range of our
instrument. This accounts for all Cu atom transitions in the ultraviolet
region.
Figure 4.19 shows the spectrum obtained after further metal deposi
tion. New absorption bands appear at 271 nm and 236 nm. The 271 nm
band appears to have a triplet structure with associated weak 8 terms.
Note that although there is an apparent A term, this possibility is
eliminated through the observation that the three MCD peak maxima


TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS iii
LIST OF TABLES vi
LIST OF FIGURES vii
ABSTRACT xi
CHAPTER I INTRODUCTION 1
CHAPTER II THEORY OF MAGNETIC CIRCULAR DICHROISM 9
Basic Equations 10
Magnetic Circular Dichroism Calculation for Atoms... 25
Effect of Reduced Site Symmetry 42
The Adiabatic Model 46
Band Moment Analysis 49
CHAPTER III EXPERIMENTAL 52
Sample Preparation 52
Spectroscopic Apparatus 59
CHAPTER IV RESULTS 77
Copper in Argon 82
Copper in Krypton 115
Copper in Xenon 131
Gold in Argon 138
Gold in Krypton and Xenon 153
Results for Lead Experiments 170
Further Studies 176
APPENDIX A ORBITAL OVERLAP CALCULATIONS 178
APPENDIX B PROGRAMS 182
i v


ABSORPTION AND MAGNETIC CIRCULAR DICHROISM
OF MATRIX ISOLATED METAL ATOMS AND
SMALL CLUSTERS: A STUDY OF ATOM-MATRIX INTERACTIONS
BY
KYLE J. ZERINGUE
A DISSERTATION PRESENTED TO THE GRADUATE
COUNCIL OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
1983


167
AA
ABS
X(nm)


99
For Cu in Ar the best fit yields A = 2.01xl05 and E = 52 cm-1. Using
the value extrapolated to T = 0 yields V2/VQ = 2.0xio5. If we define
AR = 3[ + Jg( + ) + (A/3)2]
and
R = + ( + ) + 2(A/3)2
the cubic and noncubic contributions can be found as
A2 = = j AR R
ANC = + = 2[R - (A/3)2]
These expressions can be evaluated for Cu in each matrix. For Cu in
Ar A2 is found to be -0.3 0.4xl05 cm-2 and Aj^ is 2.3 0.6xl05 cm-2.
The negative sign in A2 is physically unreasonable and appears to result
from the general imprecision in the AR and R values, i.e., in the plot
of
2/0 vs. T and 3/0 vs. T. Mowery et al. discuss the
sensitivity of A2 and Aj^ to experimental errors in R and AR. Following
their discussion the quantity of physical significance in this analysis
is the ratio
The values of R and AR themselves are ratios of absorption and MCD
moments, respectively, and are therefore independent of multiplicative
errors in the measured absorption and MCD spectra. They point out the
main error arises in baseline uncertainties which become increasingly


171
experiments it was possible to remove the internal heat shield of the
furnace, allowing greater flux of metal to enter the cryostat without
presenting an excessive heat load at the cold surface. Very clear
matrices were obtained in depositions of five to thirty minute duration.
Portions of the absorption and MCD spectra of lead in Kr are shown
in Figures 4.36 and 4.37. In the ultraviolet region two strong bands
(263.5 nm and 246.9 nm) and one weak band (232.7 nm) are observed. The
relative intensities of these three peaks were observed to change under
varied deposition conditions (Knudsen cell or cold window temperature).
Only the lowest energy band at 263.5 nm displays an MCD signal--a temper
ature independent, positive A term. In the visible range a highly
structured absorption band occurs at 508.2 nm. This band shows no MCD
signal. Four broad, higher energy bands (469 nm, 448 nm, 419 nm, and
400 nm) also show no MCD. With prolonged deposition these bands did
show some MCD signal attributable to very weak 8 terms. With deposition
conditions similar to those used to obtain the 508 nm band, a broad,
symmetrical band was observed at 612.9 nm with an intensity comparable
to the 508 nm band. The relative intensities of these two bands varied
somewhat with varied deposition conditions.
6 5
The ground state of atomic Pb is 3P0, 3 with the 3PX multiplet
component lying at 7819 cm-1. The first allowed gas phase transition
in the ultraviolet region occurs at 35.285 cm-1 (3Pj 6p7s 3P0 6p2).
For a AJ = +1 transition a positive Ax term is expected [A1/V0 =
-Jg^+(J+2)gg, where J is the ground state value],^ The 261.4 nm band,
assigned by Brewer and Chang to 3PX 3P0, is observed to have a posi
tive A term, thus confirming this assignment. A large gas-to-matrix
shift of 2957 cm-1 is observed in Kr.


Figure 4.30. Absorption and MOD for Au in Kr.


Figure 4.33. Absorption and MCD spectra for Au in Xe
after a high temperature metal vaporization.


Figure 4.5. Experimental plot of 0/
0 vs. 1/T for
Cu atoms in an Ar matrix.


65
in addition to the factors mentioned above. Both outputs were connected
to a Log Amplifier which took the log of each signal and performed an
analog subtraction to give an output in the form of the ratio of sample
to reference intensities. This output was connected in parallel to a
Soltec 1242 series two channel strip-chart recorder and the computer
interface.
All MCD experiments were performed with the same light source and
monochromator. The light source and monochromator were rolled on case-
hardened steel rails into position for the MCD experiment without dis
turbing the chopper assembly (which is permanently fixed on the optical
bench to aid easy alignment). Figure 3.5 shows the optics for the MCD
experiment. The beam emerging from the monochromator is focused by the
same lens onto a Glan-Thomson prism oriented at an angle of 45 to the
D
modulation axis of a Morvue Electronic Systems PEM-3 photoelastic modu-
1ator.
With the cryostat situated in the light path and in the field of
an Alpha Model 4600 electromagnet, a single beam MCD experiment was
performed. The magnet had a 0.75 in hole coll inear with the magnetic
field in each of the adjustable-gap pole faces.
The MCD electronics are illustrated in Figure 3.6. The signal
from the photomultiplier tube was fed into an Ithaco Model 391 Lock-in
Amplifier which was locked to the 50 kHz photoelastic modulator fre
quency. The amplifier's bipolar output was level shifted to yield
only positive voltages which were suitable inputs for the computer
interface and chart recorder. The output from the Analog Devices 52 k
operational amplifier was fed into an error amplifier-feedback
circuit. The feedback circuit employs a Bertan PMT-20, option 3


27
J
O
o
H = O
H/0


94
interaction with other excited Cu state might account for this reduc
tion, the nearest states (2F and 2P) are 13,000 and 15,000 cm-1 away,
necessitating spin orbit mixing matrix elements of the order of
900 1000 cm-1. This is unrealistically large, particularly since
the first order splitting in the gaseous 2P state is only 248 cm"1.
It is therefore concluded that the observed reduction is the result of
mixing with the matrix atomic orbitals (a semi quantitative estimate of
this reduction appears below). This is consistent with the finding
that A decreases in going from Ar to Kr matrices and reverses sign in
c o
Xe matrices. This is also consistent with Kasai and McLeod's finding
that the Cu ground state g factors are also dependent on matrix type.
A plot of 3/
0 vs. 1/T is shown in Figure 4.7. The ratio
of the slope of this plot to the slope of the 1/
0 vs. 1/T plot
is
3[ + %( + )+ (A/3)2] (73)
and is also equal to the ratio of their intercepts. This is obvious if
one compares equations (67)/(65) with (68)/(66). Confirmation is by
experimental results. The experimental ratio of the slopes is
2.5x10s cm-2, and the ratio of intercepts is 2.51x10s cm-2, although
the close agreement is probably fortuitous considering the uncertainty
in the measurements. It is possible to extract the contributions from
noncubic and cubic lattice modes to the overall bandwidth through
equations (73) and (69). The quantity V2/V0 from equation (69) may be
obtained from a plot of
2/0 vs. T as shown in Figure 4.8. The
curve is of the form
2/0
A coth (E/2kT)


Ar
I
ii
Kr
I
2p
9.05477
-0.17850
2p
17.03660
2p
26.04380
4p
15.54410
-0.00812
4p
12.39970
0.00520
3p
15.51000
4p
8.56120
-0.10986
3p
9.49403
4p
5.94658
0.10994
3p
6.57275
4p
3.42459
0.56149
4p
1.96709
0.46314
4p
5.38507
4p
1.06717
0.02951
4p
3.15603
4p
2.02966
4p
1.42733
C.
i
Xe
I
c.
0.08488
2p
34.88440
-0.00277
0.00571
2p
23.30470
-0.07054
0.04169
3p
12.54120
-0.18148
-0.07425
3p
12.02300
0.40692
-0.26866
4p
7.72390
-0.22741
0.01341
4p
5.40562
-0.21144
0.51241
0.42557
5p
3.32661
0.49354
0.18141
5p
2.09341
0.53529
5p
1.36686
0.13666


Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of
the Requirements for the Degree of Doctor of Philosophy
ABSORPTION AND MAGNETIC CIRCULAR DICHROISM
OF MATRIX ISOLATED METAL ATOMS AND
SMALL CLUSTERS: A STUDY OF ATOM-MATRIX INTERACTIONS
By
Kyle J. Zeringue
April 1983
Chairman: Dr. Martin T. Vala
Major Department: Chemistry
Copper, silver, gold and lead have been vaporized and codeposited
with argon, krypton and xenon on a cold surface. Magnetic circular
dichroism and zero field absorption spectra are presented. Data are
digitized and stored on a microcomputer for analysis.
A brief introduction to matrix isolation and the magnetic circular
dichroism (MCD) technique is given. The theoretical background for the
MCD experiment is outlined. Calculations of predicted absorption and
MCD spectra for copper atoms trapped in rare gas lattices are presented
for various site symmetries and interactions with the surrounding matrix
cage.
The cause of the triplet structure of the 2P - 2S transition for
group IB metals is discussed in terms of 0^ symmetry, D3 symmetry,
spin orbit coupling, Zeeman splitting, and ultimately, a model involv
ing simultaneous spin orbit and Jahn-Teller interaction of the
xi




105
Table 4.1. Calculated eigenvalues, eigenfunctions and MCD C0 and V0
parameters for Cu atoms in Ar. E.'s are eigenvalues measured
from the excited state center of gravity; C-1s are coeffi
cients of the adiabatic wavefunctions [see equation (58)].
For Cu/Ar, X = 124 cm-1, t = 115 cm-1, and z = 220 cm-1
E,
1
s-
c,.
3i
Cj,
2
c0/?Q
-454
0.042
0.716
0.697
0.321
0.161
1.84
+ 22
-0.601
0.575
-0.555
-0.116
0.063
-1.84
+432
0.798
0.396
-0.455
-0.205
0.109
-1.88


37
a g y
[-l]a+a I |gbl lovf
a c
i t t
\-a y
where a and c are the ground and excited states, g represents the mj1
dipole moment operator, and V is a vector coupling coefficient found in
49
Griffith's tables. These integrals are calculated over the wavefunc-
tions given in equations (45) above. In order to have a non-zero matrix
element the spin must be the same in each wavefunction in the integral.
The m operators of interest for MCD transitions are step-up and step-
down operators m+ and m_. It is possible to consider all possible tran
sitions from the ground state to each excited state function and deter
mine which are a+ and o .
<2A1E'al|m|2T1E'a'>
1 /2~
| 2T10+h> yf <2A104is|m_|2T1l-J$> (50)
1
= <2A, 01 m_ | 2Tj 0>
= [-l]TlV
Ai h Ti'
0 0 -1.
<2A1E'B'Im|2T1E'a>
<2A1E'a'[m+12Tj E'G1>
1 /2 .
7f |2T10+%> yf <2A10-%|m_|2T1l-%>
- tI <2A10|m_|2Tx1>
C-i]Tl v|Al Tl Tl|
L -T,
" /3 m
- 4
+
/2
3
%>


Figure 4.29. Plot of best fit for Au in Kr of
= 4 hcoE
jyCOth
(peak separation)2


CHAPTER II
THEORY OF MAGNETIC CIRCULAR DICHROISM
The theoretical treatment and pertinent equations as developed by
42-44 45
Stephens and Buckingham and Stephens are outlined. The treatment
has gained wide acceptance and is employed in this work. It is conven
ient to begin with consideration of circularly polarized light. Various
suggestions have arisen recently to explain the anomalous structure of
the 2P - 2S transitions of matrix isolated atoms. The quantum mechanical
equations necessary for evaluation of these theories are also developed
here.
Unpolarized light consists of an electric field vector, , and a
/\
magnetic field vector, H, both with random direction and both varying
sinusoidally with the direction of propagation. In plane polarized light
the vectors E and H vary in magnitude but are constant in direction. If
now plane polarized light traverses a transparent birefringent medium
where the speed of light depends upon the direction of light polariza
tion, then part of the beam will be delayed with respect to the other,
depending upon the thickness of the medium and the difference in the
indices of refraction. If the plane-polarized beam enters the bire
fringent medium oriented at 45 relative to two perpendicular axes of
/s i ^
different refractive index, components of the projection of the E and H
vectors of equal magnitude will be phase shifted relative to each other.
If this phase shift is equal to the light wavelength, X, the emergent
beam is restored to plane polarization. If, however, the phase shift
9


Figure 4.4. Temperature dependence of the Cu atom C0 term
in an Ar matrix. The intensity decreases with
increased temperature.


Figure 4.17. Experimental plot of 3/
o vs. 1/T for
Cu atoms in a Kr matrix.


Figure 4.28. Plot of 3/
0 vs. 1/T for Au in Ar.


I certify that I have read this study and that in my opinion it conforms
to acceptable standards of scholarly presentation and is fully adequate,
in scope and quality, as a dissertation for the degree of Doctor of
Philosophy.
Dr. Martin T. Val a, Chairman
Professor of Chemistry
I certify that I have read this study and that in my opinion it conforms
to acceptable standards of scholarly presentation and is fully adequate,
in scope and quality, as a dissertation for the degree of Doctor of
Philosophy.
Dr. Willis B. Person
Professor of Chemistry
I certify that I have read this study and that in my opinion it conforms
to acceptable standards of scholarly presentation and is fully adequate,
in scope and quality, as a dissertation for the degree of Doctor of
Philosophy.
(\( 9 ro
Dr. John R. Eyler (J
Professor of Chemistry


Figure 3.6. Schematic of MCD experiment.


Figure 4.26. Absorption and MCD for Au in Ar.


Figure 4.20. The Cu2 band in the range 330 nm to 450 nm.


83
consistent with either the distorted site model or the Jahn-Teller
interpretation. One of the primary results of this work is that the
triplet of bands in matrix isolated Cu, Ag and Au arise from simulta
neous spin orbit and Jahn-Teller interactions in the 2P excited state.
The simple nature of the 2S ground state (no orbital moment) allows a
detailed interpretation of the experimental moments of absorption and
MOD bands. Excited state spin orbit coupling constants, orbital g
factors, and contributions to the band width from cubic and noncubic
matrix lattice modes can be deduced.
Copper metal (Spex) was vaporized at 1100C and codeposited with
matrix gas onto a CaF2 window typically cooled to 15 K for Ar and Kr
and 20 K for Xe. Typical absorption and MCD spectra are shown in
Figure 4.3. The spectra agree well with those reported by Grinter et
6 2
al. Spectra were run in triplicate at 1 K intervals from 13 K to 25 K
Each spectrum was digitized every 1.0 A, transferred to a Commodore CBM
8032, and recorded on a floppy disk for storage and calculations.
Figure 4.4 shows the temperature dependence of the Cu MCD band. A
detailed moment analysis was performed on the Cu C term. Figure 4.5
shows a plot of 0/
0 vs. 1/T from which the parameters AQ/Bo and
CQ/V0 were obtained (cf. Chapter II). The slope of the plot yields
CQ/V0 = -8(3)xl0-3, and the intercept yields A0/80 = 4(3)xl0-4. Both
these quantities are expected to be zero based on a consideration of
only first order intrastate (2P) interactions. There are several second
order spin orbit interactions which might account for the nonzero values
They include excited Cu atom states mixed into either the Cu 2P or 2S
states or excited matrix atom states mixed (via orbital overlap) with
the 2P or 2S states. It will be shown below that the former interaction


Figure 4.
Experimental plot of 3/
0 vs. 1/T for Cu
atoms in an Ar matrix.


Figure 3.
. Optics for MOD experiment.


APPENDIX C
TEMPERATURE CALIBRATION
As mentioned in the text, temperature measurements are very
critical to the moment analysis employed here. Accurate matrix temper
ature measurement has been a problem for matrix isolation spectroscopists
for many years. Often a hole is drilled in the spectroscopic plate or
its metal frame and a thermocouple inserted. The matrix is then assumed
to be at the same temperature. An alternate method is outlined here
which relies on the temperature dependence of the moment ratio 0/
0
of a paramagnetic matrix isolated sample and a temperature difference as
measured by a thermocouple. For a paramagnetic substance the tempera
ture dependence of the ratio of its MCD/absorption signals may be
expressed as
p Co yBB
<^>o | For two temperatures (T2 >Ti)
T2 = Tj + AT
If x represents the moment ratio, one can consider the ratio of x2 (at
T2) to xx (at TJ:
Ti
1
\
The specification of the low(est) temperature, Tx, is thus dependent
only on the determination of the moment ratio X1/X2 anc* the temperature
190


21
where
The effect of an applied magnetic field on the circularly polarized
absorption is shown in equation (36). Each of the component transitions
contributes absorption identical in shape to that at zero field.
The intensity is modified by the ground state Zeeman effect and inter
mixing of the zern-field electronic wavefunctions, and the energy of the
band is changed by the Zeeman shift. Each of these changes is the same
as that obtained with nuclei located at R0 configuration. The term
"rigid shift" is used because the absorptions shift in an applied mag
netic field without change in shape.
The total MCD and CP absorption is the sum of contributions from
all Zeeman components -* J^. On inspection equations (39) and (41)
show that at high temperature and large band width the intensity and
energy changes of the Zeeman components of the transition due to the
magnetic field contribute additively and linearly in H to the change in


169


BIOGRAPHICAL SKETCH
Kyle J. Zeringue was born in Thibodaux, Louisiana, on
February 13, 1954. He graduated from Thibodaux High School in 1972 and
attended Nicholls State University, Thibodaux, Louisiana, where he
worked on a degree in chemistry with physics and applied mathematics
minors through 1975. Since January 1976 he has pursued a circuitous
course of study leading to the Doctor of Philosophy degree in chemistry
at the University of Florida in Gainesville, Florida. He is married to
Jan Ellin Olson. They are the reluctant owners of two parasitic cats
from the Louisiana swamps named Theophile and PI acide.
201


59
removed and rolled along rails into an electromagnet for MCD measure
ments. When joined to the furnace assembly, the entire assembly is
pumped by a 2 in oil diffusion pump backed by a mechanical forepump and
equipped with a liquid N2 cold trap. Pressures below lxlO-6 torr are
attainable. Pressures are monitored by thermocouple and ionization
gauges connected to a Granville-Phi11ips Series 270 gauge controller.
Spectroscopic Apparatus
A diagram of the optics used in absorption measurements is shown in
Figure 3.3. The apparatus operates as a "pseudo double beam" spectrom
eter. The reference beam was not passed through a matched cell but
rather reflected around the cryostat onto the photomultiplier tube.
Light scattering from matrices caused some drift in the baseline at
higher energy wavelengths, but the Xe lamp emission spectrum was quite
effectively nulled over most of the spectral range. Spectra were
obtainable over the range of 8500 to 2200 A. The lamp was a 300 W
D
Eimac xenon lamp made by Varian Associates and operated at a pressure
of 115 atm and had a built-in parabolic reflector and a sapphire window
yielding an intense, wel1-col 1imated beam. The lamp was enclosed in a
small hood for removal of the ozone generated during operation. The
lamp housing was attached to a Spex 0.75 m Czerny-Turner Spectrometer
with a grating blazed at (1200 lines/mm) 3000 and an f-number of 6.8.
The slits were set for a spectral band pass of less than 6 A.
The beam emerging from the monochromator slit was spread by a 3 in
quartz lens (f/3) and then passed through two sets of slots on a spin
ning wheel. The wheel was driven by a hysteresis-synchronous motor at
1800 rpm. Five outer and nine inner slots in the wheel gave chopping


165
ABS
220 260 3 00 X (nm) 340


101
the absorption maxima (in Ar) are 479 cm-1 and 402 cm-1 (increasing
energy, 12.9 K). These separations are more than a factor of two larger
than the spin orbit splitting (185 cm-1 for Cu in Ar) deduced from
the band moment analysis.
As mentioned previously the case of matrix isolated Cu, Ag and Au
exhibiting a 2P * 2S transition is very similar to the F center case, and
the results presented here can be compared to calculations done within
56
the framework of the adiabatic approximation as described by Moran
67
and Cho. Moran considered the effect on the splitting pattern and
band shapes of simultaneous first order spin order coupling and vibronic
54
interaction through the tetragonal e mode only. It has been shown
that consideration of the fourth moment and changes in it induced by
a magnetic field are necessary before the t2 mode interaction appears
in a manner other than simply additive. Thus the only effect of the T2
interaction is a modification of the existing band shapes but not the
triplet splitting pattern. Because of these facts the applicability of
the Moran model (with its restrictive use of only the ax and e vibronic
interactions) has been explored in order to determine whether it could
account for the experimental observations. The absorption band shape
is then compared to those calculated by Cho.^ Cho has performed a
multidimensional calculation of the absorption band shapes and included
spin orbit, e and t2 interactions.
Moran's 3x3 interaction matrix has been diagonalized varying t and
z displacements (as they represent the degenerate pair of lattice motions
in the e vibration) while holding X to the appropriate value for Cu in
Ar (124 cm-1) as obtained from the moment analysis. The degenerate t
and z components of the e vibration are sketched in Figure 4.9. Two


31
ground state split. At low temperature the population of the lowest
magnetic sublevel is much greater than that of the higher sublevels, and
the observed MCD will be similar to that at the right of the figure.
Increasing the temperature depopulates the lowest state thus decreasing
the MCD at the higher energy transition and increasing the MCD transi
tion at lower energy (dashed curve higher T). If all the sublevels are
equally populated the MCD will be as in the middle spectrum. The
populations are governed by Boltzmann statistics. A CQ term such as the
middle spectrum appears to have the A: term derivative shape and is
sometimes referred to as a "pseudo A term."
Consider the transition of an electron in a free atom of 2S ground
state to a 2P excited state. If the atom is placed in an octahedral
field, the representation of these states must be determined in group 0. .
Full Rotation Group ^h
Note that for group 0 the r representations are rx = A1, T2 = A2, F3 = E,
r4 = ri5 r5 = T2, r6 = E', r7 = E", and r8 = U'.47 Thus, in 0^ the 2S
state representation is A,, and the 2P state representation is Tx.
47
Using Koster's table of compatibility for orbital angular momentum,
the representations for 0 and 1 are D0 and D1S respectively. Both states
are spin %, and again from Koster's tables Dt r.(E'). The spin-orbit
-i
coupling effect in these states can be determined taking cross products
of the spin and orbital representations. For 2S,
r. rK = r = e1
lb b


, /
,
122
l/T (KH)


76
where is the number of OD units per digital data unit, C is the con
centration of the standard solution in optical density, 1^ is the sample
MCD band intensity in arbitrary units as stored on the floppy disk, and
Sg and Sc are the lock-in amplifier sensitivities for the sample and
standard solution scans, respectively.
The signature of bands was cross checked by measuring the MCD of a
solution of K3[Fe(CN)6] which was known to have a positive MCD band
centered at 4250 K. A check for any depolarization due to the matrix
was run by noting any difference in the intensity of the CD spectrum of
the spectrum of the standard solution placed before and after the
matrix. No measurable depolarization was noted in most experiments.


131
correspond in wavelength exactly with the absorption maxima. These
bands are therefore assigned to a Cu2 excited state, possibly exhibit
ing site effects. This is in agreement with the assignments of
60
Moskovits and Hulse. The lack of an MCD C0 term corresponding to the
236 nm absorption band also leads to assignment of this transition to
Cu2.
Figure 4.20 shows the region from 300 nm to 450 nm. Another
broad absorption feature due to continued deposition is seen centered
at 380 nm. Multiple trapping sites are again indicated. On the basis
of the lack of a corresponding MCD C0 term, this band is also assigned
to Cu2 consistent with the assignment given by Moskovits and Hulse.
All of these Cu2 bands grow in at the same rate with continued deposi
tion providing further evidence that all are due to the same species.
Copper in Xenon
Experimental spectra for the absorption and MCD of Cu isolated in
Xe are shown in Figure 4.21. For these experiments depositions were
made onto a CaF2 plate held at 20 K. The most striking feature of the
Cu in Xe spectrum is the reversal in sign of the MCD bands. Determina
tion of gQrb and A were made from the 1/
0 vs. 1/T plot shown in
Figure 4.22. From the slope A = -35 cm-1 (A = -23 cm"1)* and gQ^b is
calculated as 0.79. The spin orbit splitting constant for Cu is again
reduced from the Cu/Kr value and has actually gone negative indicating
a reversal in relative energy of excited state components. As in the
previous cases, the reduction factor k^ can be evaluated. The values
obtained are k^ = 0.08, k^. = -2.7, and k^ = -23 cm-1/166 cm-1
sub int obs
-0.14, again indicating isolation in a substitutional lattice site as
the k\ ^ is too large to match the experiment.


93
The excited state spin orbit splitting, A, is obtained from the
slope:
i
n
(72)
slope = -3H j y
and the gorb is obtained from the intercept:
intercept = 2 gQrb 6H
The gQrb quantity is very sensitive to any random error in the plotted
moment or temperature values since it comes from the extrapolation to
infinite temperature (T_1 -* 0) of data gathered over a relatively small
temperature range (13 25 K). Theoretically gQrb = 1, but because of
the large uncertainty in the experimental result, it is not possible to
decide the influence of the matrix environment on this quantity. Alter
nately the spin orbit splitting, A, is obtained from the slope of the
linear plot and is therefore relatively insensitive to the errors arising
from the small temperature range sampled. Copper atoms in the gas phase
exhibit a 248 cm-1 splitting between the 2P3/ and 2PU components of the
65
excited state. The matrix value obtained from the plots shown in
Figure 4.6 is 185 cm-1 for Cu in Ar. The reduction in A (~25% for Ar)
in the matrix must arise from some out-of-state mixing since, as pointed
45
out by Buckingham and Stephens, both Cx and VQ (from which A is
obtained) are invariant to a unitary transformation within the excited
state basis set. Thus any first order interaction such as the
Jahn-Teller effect which vibronically mixes the 2P state components
cannot account for this reduction. Although second order spin orbit


146
for Ar, Kr and Xe, respectively. These are to be compared to the gas
phase value 2543 cm The moment analysis employed here yields values
50
comparable to those reported by Gruen et al As in Cu work Kasai and
63
McLeod indicate Au to be isolated in pure substitutional octahedral
matrix sites.
The absorption and MCD spectra of Au isolated in Ar are shown in
Figure 4.26. From the observed C term behavior, a plot of i/
o
vs. 1/T (see Figure 4.27) and a spin orbit constant of A = 316532 cm-1
are obtained. The intercept yields a gQr^ = 1.43, but due to the
experimental error and long extrapolation it is probably not very
accurate.
Following the precedure outlined for Cu/Ar, the spin orbit reduc
tion factor for Au in Ar is found to be k^ ^ = 0.988 and kV^ = 0.972
as compared to the experimental k^obs = 1.24. A plot of 0 vs.
1/T is shown in Figure 4.28. From the third moment plot, the AR value
(= 8xl06) can be compared to R (= 4.9xl06) and it is shown that noncubic
(Jahn-Teller-active) lattice modes are also important in understanding
Au/Ar spectra. Further indication of the role of Jahn-Teller interaction
between lattice vibrations and the Au excited state results from consid-
51
eration of data taken from work by Forstmann et al. where a detailed
study of the peak-maximum position in energy as a function of matrix
temperature was done. According to Englman^ the square of the peak
separation should follow 1/kT with a hyperbolic cotangent relation:
peak separation
Values of the energy differences of Au/Ar transitions at various
temperatures were measured directly from diagrams given in the paper


85


Figure 2.6. The predicted MCD and absorption patterns for
the 2P 2S transition in an octahedral field.


15
Equation (18) now can be written
A+
= yDnf(e)cz
(20)
where
D
1
o h
>
0 dn c 1 a1 1 X
A a,A
nI 2
__1
2d
A a,A
I2 + |I2
a' 1 X 1 1 a1 1 A 1
(21)
and
f(e)
I
Na,
a,j
12S(c. -e)
Jd
(22)
with
r<
f(e)de = 1
The ZFA as given in equation (20) has a shape originating in the ground
and excited state vibrational wavefunctions and an integrated intensity
dependent only upon the electronic wavefunctions, evaluated at equilib
rium position R0. The line shape is temperature dependent due to the
Boltzmann term Na/N, but the integrated intensity is temperature inde
pendent.
If a magnetic field is applied, the absorption coefficients, k+,
display a field dependence. The eigenfunction and eigenvalues of the
system's Hamiltonian must now be obtained as explicit functions of the
magnetic field. This is only feasible in an analytical form when per
turbation theory may be employed to treat field-dependent terms.


Figure 4.27. Plot of i/
0 vs. 1/T for Au in Ar.


Figure 3.4. Schematic of absorption experiment.


CHAPTER I
INTRODUCTION
Molecular spectroscopy, the primary tool utilized to study details
of molecular geometry and electronic structure, has been applied rou
tinely to many stable chemical species in the solid, liquid and gaseous
phases. The study of short-lived or unstable species has been aided
greatly by high-speed electronic instrumentation. There are, however,
many species yet very difficult or impossible to observe due to reactiv
ity, short lifetime, or method of preparation. Among these are high
temperature atoms or molecules that exist only in extreme conditions
such as stellar atmospheres or in arcs and radicals or fragments with
such high reactivity that production of quantities sufficient for normal
analyses is difficult or impossible. Even when high temperature species
are observed, analysis of their spectra is difficult due to their popu
lation distribution in various electronic, vibrational and rotational
states. This is often the case in laboratory generation of such frag
ments via flash photolysis, plasmas, arcs, etc. Employment of the
matrix-isolation technique can circumvent many of these difficulties.
1 2
Norman and Porter and Whittle et al. independently proposed the
technique of matrix-isolation spectroscopy in 1954. Since that time a
vast literature has evolved which includes excellent reviews by
3 4 5 6
Chadwick, Downs and Peake, and Jacox, as well as books by Meyer,
7 8
Ozin and Moskovits, and more recently by Barnes et al. Matrix-isolated
samples are prepared by codeposition of "guest radical fragments,
1


e mode
(z)
o
CO
e mode
(t)


Figure 2.3. Magnetic field splitting in
degenerate ground and excited
states illustrating the origin
of A0 and C0 terms.


Figure 4.24. Plot of
2/o vs. 1/T for Cu in Xe.


2
reactive molecules, or high temperature species in inert, transparent
solids (matrices) at cryogenic temperatures.
A basic assumption in matrix isolation is that there is little or
no interaction between the matrix and the isolated species, and essen
tially gas-like species is obtained. Though this assumption is valid
as a first approximation, matrix interactions do occur which cause
shifts in the energies of spectra. The sample can also be trapped in
multiple sites in the crystalline lattice (examples are substitutional
or interstitial sites) which lead to band broadening and multiplets
due to differing energies of the various sites. These site effects
can often be removed by warming the matrix to allow controlled diffu
sion and thus permit the sample species to settle into the more stable
sites resulting in more simplified spectra. Lattice modes and Jahn-
Teller distortions due to matrix-sample interactions have also been
g
observed. Mowery et al. have observed Jahn-Teller distortions in the
magnetic circular dichroism spectra of matrix isolated magnesium atoms.
The matrix material can be any non-reactive gas which can be rigidly
solidified. Many substances have been used for this purpose including
N2, CH4, CO, the freons, SF6, CS2, and 02, as well as large organic mole
cules. More often, though, the solid rare gases Ne, Ar, Kr and Xe are
used as these elements are relatively chemically inert and transparent
over a broad spectrum, and provide a rather broad selection of melting
points and atomic sizes. Neon is expected to perturb a guest specimen
least, as it is least polarizable. However, neon requires temperatures
below 10 K and has a lower trapping efficiency compared to other rare
gases. It is usually easier to trap samples in Ar, and it is most
widely used as a host gas. Krypton and Xe are found to perturb trapped


81


28
It is possible to calculate the probability for the absorption of
a photon for a transition from states a to j. The probability is pro
portional to the square of the transition dipole moment matrix element
along the direction of the photon polarization,
(tf-i. ) = (-
) (43)
ja
where "u is the unit vector determining light polarization and rfi- is
\J u
the electric dipole moment. Selection rules for the transitions in
Figure 2.2 can be derived considering the three possible light polariza
tions (x, y and z) in equation (43) and the properties of the wavefunc-
46
tions as described by spherical harmonics.
First, considering polarization in the z direction (parallel to the
applied magnetic field), equation (43) is non-zero if AJ = 1 and
Amj = 0. Since this is the direction of light propagation in the MCD
experiment, it is not available. The two possible polarizations u and
uy for light propagating along z are more conveniently examined in the
linear combinations ftxiu corresponding to circular polarizations. The
sum is RCP and the difference LCP. For RCP equation (43) is non-zero if
Anij = = -1 and the non-zero LCP values arise for Arrij = +1. For
both cases AJ = 1. Transition b in Figure 2.2 is thus not observed.
Transition a corresponds to RCP and c to LCP. In this case circularly
polarized light corresponds to electric dipole photons of J = 1 and
mj = -1 for RCP and +1 for LCP. Similar selection rules apply for any
system due to conservation of angular momentum.
To illustrate how the various magnetic field splittings give rise
to the MCD Ax and C0 terms, Figure 2.3 shows MCD transitions with either
ground or excited state degenerate. Two cases are shown with only the


-OI x / Z
98
T(K)


130
X(nm)


Table A.l. Data used in orbital overlap calculations.
Cu
i
I
2p
23.54780
-0.00941
2p
21.93670
2p
13.26670
0.05604
2p
21.32090
3p
11.52060
0.08953
3p
14.14920
3p
8.09772
-0.11580
3p
10.13800
3p
6.70827
-0.03951
4p
5.87182
4p
5.07948
-0.15751
4p
3.98770
4p
3.19095
0.17463
4p
1.53564
0.66426
5p
2.66401
4p
0.87051
0.34469
5p
1.65008
5p
1.04186
Au
a
0.31024
2p
38.341367
-0.066636
-0.37499
2p
35.121549
0.112650
-0.01483
3p
23.961490
0.052023
0.16544
3p
20.389333
-0.152927
-0.21760
4p
13.258438
0.056507
-0.05567
4p
10.132154
0.125050
0.25280
5p
6.484815
-0.262522
0.51023
5p
4.291229
0.010798
0.39485
6p
2.457881
0.535399
6p
1.330143
0.599705


117
X(nm)


70
programmable high voltage power supply. The gain of the photomultiplier
tube is controlled in an inverse relation to the dc output by the feed
back circuit. The photomultiplier tube signal consists of a relatively
small 50 kHz ac component riding on a larger dc component that is pro
portional to both the xenon lamp emission spectrum and the absorption
of the sample. Background effects in the MOD spectrum are automatically
corrected for by maintaining a constant dc level with the feedback cir
cuit. In later absorption experiments the feedback circuit was also
used. This was facilitated by passing the lock-in output through another
operational amplifier used as an impedance adaptor and then into the
feedback circuit.
Both the absorption and MCD experiments were controlled by a
Commodore CBM 8032 computer. The monochromator was driven by computer
pulsing a SLO-SYN^ Model M0GI-FD-301 stepper motor attached to the wave
length scan control. The motor was stepped 200 times per revolution.
This allowed 0.25 steps of the monochromator.
The data was digitized using a Datel Systems, Inc., ADC-EK8B
analog-to-digital converter of 8 bit resolution. The operating program
allowed data collection at 1, 0.5 or 0.25 & intervals. After collecting
a spectral scan, the data was stored on a floppy disk. The data collec
tion and storage program is listed in the appendix.
The computer was also used to control the photoelastic modulator
which was synchronized with the wavelength drive. The modulator's wave
length of quarter-wave retardation depended upon the amplitude of stress
applied to the quartz crystal which was linearly dependent upon the
modulator's input voltage. The program calculated the correct voltage
for the running wavelength after each 0.25 A step, and this output was


Figure 4.15. Temperature dependence of the Cu atom C0 term
in a Kr matrix. The intensity decreases with
increased temperature.


161
k^obs = 1-24. Figure 4.32 is a plot of 3/
o vs. 1/T. The spin
orbit value found here is somewhat larger than the value reported by
Gruen et al. (2943 cm-1). A possible explanation may be found in the
broad cluster band appearing under the atomic band. Data by Forstman
et al. as well as AR {- 6.3xl06) obtained from 3/
0 vs. 1/T (see
Figure 4.32) and R (= 4.6xl06) indicate Jahn-Teller interaction in this
system also.
Figure 4.33 shows absorption and MCD spectra obtained in a high
temperature vaporization (1340C) of Au into a Xe matrix. The bands at
246 nm, 249.5 nm, and 273.5 nm are assigned to Au atoms. The broad band
at 322 nm does not have an observable MCD band and is assigned to an Au2
transition. This is also true for the band at 228 nm, and it is assigned
to Au2. A broad temperature dependent band is observed at 282.5 nm.
63
Since Kasai and McLeod demonstrated Au to reside in a pure octahedral
site with no site splittings, this band is assigned to Au3. Figure 4.34
shows spectra obtained in a matrix deposited at 1300C. The expected
atomic triplet was not observed. Rather, two broad absorption features
were noted at 274 nm and 298 nm. The 274 nm has a corresponding C0 term
and matches the low energy Au atom transition seen in Figure 4.33. The
298 nm transition has a corresponding positive Aj term which is assigned
to an Au2 transition.
Matrices containing Ag were prepared by vaporization of Ag powder
(~900C) from a Knudsen cell and codeposition in Ar, Kr and Xe. The
absorption and MCD of Ag atoms in Ar are shown in Figure 4.35. As in
Cu and Au, the characteristic triplet structure is observed with (in
all three matrices) positive, negative, and negative (increasing energy)
MCD bands. Irradiation into the Ag/Ar absorption band by the scanning
monochromator provided enough light to cause the "cryophotoaggregation"


3
molecules to a greater extent but provide a broader temperature range for
matrix isolation than do Ne and Ar.
Temperatures sufficiently low to condense matrix gases can be
achieved by mechanical closed-cycle refrigerators utilizing Joule-Thomp
son expansion of high pressure hydrogen or helium gas. Alternatively
physical refrigerants such as liquified nitrogen, hydrogen or helium may
be employed. Liquid nitrogen (boiling point 77.4 K) is plentiful and
inexpensive. Although it is adequate for the more stable matrix mate
rials, much lower temperatures are necessary for the better rare gas
matrices. Liquid H2 (boiling point 20.4 K) has been used, but it entails
a fire hazard in addition to the normal dangers associated with cryogenic
fluids. The most useful refrigerant is liquid He (boiling point 4.2 K).
It is also the only refrigerant useful for condensation of Ne which melts
at 24 K and allows solid state diffusion at less than half that tempera
ture (which is a general rule by which the temperature required for
controlled diffusion may be apprixmated). Closed-cycle refrigerators
which can attain temperatures near the liquid He boiling point are avail
able commercially.
The main advantages of the refrigerators include convenience, low
operating cost after the initial investment, and relief of the require
ment to replenish cryogenic fluids during experiments.
A deposition substrate is chosen that is transparent in the spectral
range of interest. Some common materials are CaF2, quartz and sapphire
for the visible and ultraviolet regions; Csl, NaCl and KBr for the
infrared region; and some nonconducting material such as sapphire for
microwave spectroscopy. A polished crystal plate is mounted on a
cold block (often copper) which makes good thermal contact with the


34
Since there is some reduction in angular momentum if the
a free atom, integrals of the form
system is not
<1[LZ|1>
= y
rather than 1. To facilitate approximation of MCD and absorption inten
sities, the y can be approximated as 1. The integrals in equation (46)
for the excited state are
<2T1Eal|
Lz+2Sz|2T1E'a'> = ^+§(y-l)
(47)
<2T1EI6'|
Lz+2Sz|2T1E'6'> = 4-|(y-l)
<2T1U,ki1
LZ+2SZ|2T1UV> = y + 1
<2T1U1v1|
Lz+2Sz|2T1U'v'> = -y 1
<2T1U'A'1
LZ+2SZ|2T1U'A,> = j + j (y-i)
<2T1U'y'|
Lz+2Sz|2T1U'y'> = -|-|(y-l)
and for the ground
state
<2A1E'al|
L z+2S z|2Aj Ea1> = +1
(48)
<2A1E'8i1
|Lz+2Sz|2A1E'3'> = -1
The energy level diagram in Figure 2.4 can now be drawn.
In order to predict MCD and absorption spectra it is
to calculate electric dipole transition moment integrals.
hedral point group the dipole moment operator transforms
also necessary
In the octa-
as the Tx
symmetry representation. The integrals are of the form in equation (48)


Figure 4.32. Plot 3/
0 vs. 1/T for Au in Kr.


198
38. E. Draugliss and R. I. Jaffee, eds., "The Physical Basis of
Heterogeneous Catalysis," Plenum, New York, 1975.
39. F. F. Abraham, "Homogeneous Nucleation Theory," Academic Press,
New York, 1974.
40. J. F. Hamilton and P. C. Logel, Photo. Sci. Eng., 18_, 507 (1974).
41. B. Wellegehausen, IEEE J. Quantum Electron., QE-15, 1108 (1979).
42. P. J. Stephens, PhD Dissertation, Oxford University, 1964.
43. P. J. Stephens, J. Chem. Phys., 52_, 3489 (1970).
44. P. J. Stephens, "Advances in Chemical Physics," Vol. 35
(I. Prigogine and S. A. Rice, eds.), Wiley, New York, 1976, p. 197.
45. A. D. Buckingham and P. J. Stephens, Ann. Rev. Phys. Chem., 17, 399
(1966).
46. A. S. Davydov, "Quantum Mechanics," Addison-Wesley, Reading, Mass.,
1961, p. 302.
47. G. F. Koster, J. 0. Dimmock, R. G. Wheeler, and H. Statz, "Proper
ties of the Thirty-Two Point Groups," M.I.T. Press, Cambridge, 1963.
48. J. S. Griffith, "The Irreducible Tensor Method for Molecular
Symmetry Groups," Prentice-Hall, Englewood Cliffs, New Jersey, 1962.
49. J. S. Griffith, "The Theory of Transition Metal Ions," Cambridge
Press, Cambridge, 1961.
50. D. Gruen, S. Gaudioso, R. McBeth, and J. Lerner, J. Chem. Phys., 60^,
89 (1974).
51. F. Forstmann, D. Kolb, D. Leutloff, and W. Schulze, J. Chem. Phys.,
66, 2806 (1977).
52. S. Armstrong, R. Grinter, and J. McCombie, J. Chem. Soc., Faraday
Trans. 2, 77, 123 (1981).
53. S. Piepho, "Recent Advances in Group Theory and Their Application to
Spectroscopy" (J. C. Donini, ed.), Plenum, New York, 1979, p. 405.
54. C. H. Henry, S. E. Schnatterly, and C. P. Slichter, Phys. Rev.,
A137, 583 (1965).
55. G. A. Osborne and P. J. Stephens, J. Chem. Phys., 56_, 609 (1972).
56. P. R. Moran, Phys. Rev., 137, A1016 (1965).
57. R. J. Tacn, PhD Dissertation, Oxford University, 1977.
58. A. J. McCaffery and S. F. Mason, Mol. Phys., 6, 359 (1963).


CHAPTER III
EXPERIMENTAL
Sample Preparation
Detailed descriptions of the furnace assembly as well as the absorp
tion and MCD apparatus are outlined. Figure 3.1a shows the furnace
assembly used in these experiments.
Metal beams were generated from a resistively heated Knudsen cell
which is shown in Figure 3.1b. The cell was constructed of 0.15-0.020
in wall thickness, 0.25 in outer diameter tantalum tubing. The cell
was closed on either end by solid tantalum endcaps and strapped to two
water cooled copper electrodes. One of the electrodes was electrically
isolated from the furnace while the other was in contact with the fur
nace assembly. Alternating current as high as 300 amp, 60 Hz could be
run through the cell allowing temperatures in excess of 2300C. The fur
nace was cooled by water flowing through 0.25 in diameter copper tubing
soldered onto the exterior surface of the furnace. A Leeds and Northrup
optical pyrometer was used to measure the cell's surface temperature by
sighting the cell via a magnetic shutter on the furnace. The magnetic
shutter prevented metallic depositions on the surface of the viewing
window and associated inaccuracies in temperature measurement.
In order to prevent heating of the cryogenic window by heat radiat
ing from the Knudsen cell, a water cooled shield was installed in the
furnace. It is worth noting that this radiation shield could be removed
when generating vapors at temperatures below 1000C allowing a greater
52


8
reveal a triplet structure while the corresponding gas phase spectra
display only doublet structure. The on-going controversy as to the
origin of the matrix triplet structure can be resolved by a moment
analysis of the MCD spectra as is shown later.


177
lifetimes of species such as the Pd matrix bands observed by Grinter and
81
Stern. An interesting extension would be measurement of ir and Raman
spectra of cluster species in order to gain insight into cluster size.
Another interesting area where matrix isolation MCD would be valuable
is in state assignments of diatomic metal hydrides. Molecules could be
prepared by codeposition of a metal vaporized from a standard Knudsen
cell with a beam of H atoms generated in a hot W cell (-2800 k) .82-84
This would require construction of a larger furnace and installing a
second power supply.
There has been an increasing application of heat pipes to the
41
study of optically pumped metal vapor lasers. This technique could
be adapted for gas phase study of many metal cluster species. The
necessary gas phase density could probably be attained by employing the
78
laser vaporization technique used by Bondybey and English. A crossed
arm heat pipe could be mounted vertically between the magnet pole faces,
and the vaporization beam might be introduced perpendicular to the mag
netic field. Standard heat pipes are generally constructed of stainless
steel. A Ta heat pipe enclosed in a vacuum shroud would enable studies
of much higher temperature species.


42
Thus,
C0/P0 = -1 (56)
The predicted MCD and absorption transitions of 2P 2S in an octahedral
field can be diagrammed as in Figure 2.6.
Effect of Reduced Site Symmetry
Another possible cause of MCD C terms which must be explored arises
through a reduction of the octahedral site symmetry described above.
The most likely reduced symmetries are due to displacement of the copper
from the center of the surrounding octahedral rare gas atoms resulting
in a D3 symmetry and a change in the distance of the "axial" octahedral
distance resulting in a D4 symmetry. Either of these distorted matrix
sites yields a further splitting in the 2TiU'(2P3/z) octahedral state.
The predicted MCD term signs can then be compared with experimental
results. The distorted symmetry approach can be illustrated by consid
ering a static trigonal distortion (D3) and calculation of the eigen
values, eigenfunctions and CQ/VQ values. The 3x3 energy matrix for the
cnco
D3* case is given asJ
2E,1,%>
0
0
2 E,1,h>
0
_x
/2
-a2,o,%>
0
_X
/?
-A-ei
(57)
where A denotes the trigonal field distortion parameter. The matrix
consists of lxl (2EE" state) and 2x2 (the 2A2E and 2EE1 states)


Figure 4.23. Plot of 3/
0 vs. 1/T for Cu in Xe.


46
where d is the ground state degeneracy; 3 is the Bohr magneton; and p+,
do m+, and m_ represent integrals between states (for example, the
2 Aa E1 2 A i E' transition):
d+ =
<2AiE
/2
'a'|i3(L++2S+)|2AiE'3'>
0 =
<2A1E'a'
|-i3(Lz+2Sz)|2A1E'a,>
m0 =
<2A1Ea'
|m01 2A2E1 a.'>
m+ =
<2A1E'al
|m+|2A2E13>
m_ =
<2A1E'3i
|m_|2A2E'a>
In the case of trigonal distortion
(C2^r] 2C2C3mA rcv
C = 3
(C2mE)2 + (C3mA )2
Vq = 1
6
where m^ = and m^ = are reduced matrix ele
ments for the electric dipole transition moment. Possible eigenvalues
and values of C0/V0 could be estimated if a value for the spin orbit
constant, A, was chosen (see, for example, the discussion of the method
of moments for Cu in an Ar matrix) and the trigonal field distortion
parameter, A, was varied (vide infra). A similar treatment can be
followed for a Di+ distorted octahedral site.
The Adiabatic Model
From the band moment analysis it was shown that both spin orbit
interaction and noncubic vibrational modes of the matrix cage are


Figure 3.2. Detail of furnace-cryostat assembly used in
matrix isolation experiments.


90
is probably not operative in this case. Matrix atom excited state inter
action with the Cu ground state has been invoked by Kasai and McLeod^3
to explain the dependence of the Cu 2S g factor on matrix atom type.
64
Denning and Spencer have shown that second order effects contribute
in two ways to MOD C terms. Let |A&> = |A^>+y|B> where y is the extent
of mixing of the new state, B. Using the notation of Buckingham and
45
Stephens, the two additional C term contributions are
C
I
2
a,3,A
12} x 2y (70)
a1 +i A 1 a'z z1 3
The Cj contribution results from a modification of the ground state mag
netic moment while the electric dipole transition moments remain
unchanged. It is this modification in the magnetic moment which accounts
for the change in ground state g factors with matrix atom type. When
summed over all excited state spin orbit components this contribution is,
however, zero. It cannot therefore account for our nonzero C0/V0 value
since this result is based on moments calculated over the entire excited
2P state transition. The Cjj contribution, however, involves modifica
tions to the transition moment matrix elements which, when summed over
all the excited state spin orbit components, do not equal zero. It is
this contribution which is responsible for the observation of a nonzero
CQ/V0 value. Figure 4.6 shows a plot of -1/
0 vs. 1/T for Cu
isolated in Ar.


47
important to the spectroscopic appearance of the 2P - 2S transition in
matrix isolated Cu, Ag and Au. Three components of the 2P state are
apparent in the experimental MCD and absorption spectra. The observed
C terms are positive, negative, and negative (with the exception of Cu
isolated in Xe) as energy increases. The band separations in all three
metals are much larger than the spin orbit splitting deduced from band
54
moments. Because of similarities of these systems to the much studied
F center case (although in several F center crystals the triplet is not
55
resolved ), it is possible to compare these results with theoretical
calculations done within the framework of the adiabatic approximation.
In particular the effect of the two degenerate components of the noncubic
e mode on the MCD C terms and band separations are considered.
Because of the noncubic vibrational activity which mixes the first-
order spin orbit split states, it is not possible to describe the compo
nent states by a simple J,Mj (or other) description. The first-order
states become coupled by vibronic interaction. Any calculation of the
sign and magnitude of the C terms of the transitions to each component
56
of the 2P state must account for this coupling. To do this Moran's
adiabatic model of vibronic and spin orbit interactions in an excited
2Ti(2P) state is examined. Moran considered the effect of simultaneous
first-order spin orbit coupling and vibronic interaction via the tetrag
onal e mode only. The effect of the t mode will be to modify the exist
ing band shapes but not the splitting pattern (i.e., the triplet of
56
bands). In the Moran model the wavefunctions are
Â¥i
= C
11
+ + c3j l2T,E
i p
}>
(58)
where i runs from 1 to 3 and the coefficients are given by


114


200
81. R. Grinter and D. Stern, J. Chem. Soc., Chem. Commun., 40 (1982).
82. L. B. Knight and W. Weltner, Jr., J. Chem. Phys., 54, 3875 (1971).
83. L. B. Knight and W. Weltner, Jr., J. Chem Phys., 55_, 2061 (1971).
84. R. E. Smith, Proc. Royal Soc. London, A332, 113 (1973).
85. I. N. Levine, "Quantum Chemistry," Allyn and Bacon, Boston, 1974.
86. E. Clementi and C. Roetti, Atomic Data and Nuclear Data Tables,
14, 183 (1974).
87. A. D. McLean and R. S. McLean, Atomic Data and Nuclear Data Tables,
26, 315 (1981).
88. D. H. Powell, PhD Dissertation, University of Florida, 1979.


48
(59)
and
pn- -/2[z(A/2 + z ei) t2]
(60)
-/2[t(A/2 z e.) tz]
psi = 26z + + £i}
In equation (60) t and z represent the degenerate pair of lattice coor
dinate displacements belonging to the e vibration, and X is the experi
mentally determined 2P spin orbit coupling constant. Using these expres
sions and the Wigner-Eckart theorem for the transition probabilities in
the 0* group as in previous cases, an expression for C0/P0 can be found.
(61)
C0'/V
The influence of the e mode components on the spectral splitting
pattern and MOD sign behavior can be determined by diagonalization of
Moran's 3x3 interaction varying the t and z displacements while keeping
X constant (and equal to the experimental value). For the case of large
spin orbit coupling, the effective Hamiltonian is given by:


45
submatrices. The eigenvalues and eigenfunctions in the m,ms basis are
wi th
where
2EE"{^}> = |2E,1,%> with E]
A+A
and
!A2E{,}> = C2 | 2E ,1 ,%> C 31 2 A2,0, Jg>
!2E E1{gi}>
= C2|2E,1,%> + C3|2A2>0,>5>
'2,3
(A+A) +
4 '
(A2
2AA + A2j%
2
_x
/2
r 2 +
U 2
2 \ 2
A2/2 + C4:
A A
2 £i
for i = 1,2,3
In the limit where the trigonal field distortion parameter, A, is
zero, the functions reduce to those obtained above for octahedral sym
metry.
53
Using these eigenfunctions and Piepho's tables for the D3* group
53
the C0 and V0 terms may be calculated from the standard formulae for
randomly distributed anisotropic centers:
C0 = 3f yo Im+l2 + 2y+m0m_}
V0 = i Im+12 + |m_|2 + |m012)


12
where are electric dipole transition moments, E. = E.-E a is
1 ja J a
a Lorentz effective field correction factor which relates the electric
field due to the light at the absorption center to the macroscopic elec
tric field, m+ is the transition dipole moment operator for LCP and RCP
transitions, and 5 is the Kronecker operator which arises because tran
sition lifetimes are neglected. The absorption coefficients can now be
expressed as
2tt a
2,2
a ,j
Na||26(Eja-E)
(7)
This equation can be expressed in terms of absorbance
exp
-2ekz
-tic
= 10
-A IU1
1
10
-e cz
(8)
where A = absorbance, e' is the molar extinction coefficient, and c is
now the concentration of absorbing species. The absorbance is
A
£ '
Y+
Z_i j-pl
¡ 2a(£ja-e)cz
(9)
where
NniT2ct2loqi 0e
250 ficn
(10)
N0 is Avogadro's number, Na/N is the relative population of ground state
a, and e is the Naperian log base. This equation assumes Beer's law is
obeyed and does not apply for the non-linear effects present for intense
light. The difference in LCP and RCP light dichroism, AA, is expressed
= A_ A+
AA
(11)


Figure 2.2. Polarized transition to an atomic P state and
magnetic field splittings. Transition a is
right circularly polarized, transition c is
left circularly polarized, and transition b
is polarized parallel to the magnetic field.


13
Substituting into equation (9)
= Y+ X {r I|2 ||2 fi(e-a-e)cz (12)
^ 5 j
The summations are over all sublevels a and j of the ground and excited
states, and the integrals are electric dipole transition moments.
Equation (12) is general and applies to natural CD as seen in optically
active media. Magnetic circular dichroism is not a perturbation of
natural optical activity but rather arises from different polarizabili
ties which are zero when no external magnetic field is present. The
natural and magnetically induced phenomena are additive. In a system
possessing no natural optical activity in a region absent of a magnetic
field,AA = 0 and ||2 = ||2. In this case the zero-field
absorption, ZFA, is defined as
A = A+ = A = Jg(A+ + A.) (13)
At this point it is convenient to introduce the rigid shift model
in order to modify these results to reflect the actual bandwidths in the
presence of a magnetic field. The rigid shift model requires adherence
to the Born-Oppenheimer approximation in the ground and excited states.
Separation of electronic wave functions under the Born-Oppenheimer
approximation into nuclear and electronic terms may be denoted by a
product of wave functions
|Aaa> = Ta (r,R)x (R) a = 1 to dft (14)
a
|JXJ> = Tj (r,R)x-(R) A = 1 to dj (15)
X
where ip indicates electronic wavefunctions with dependence upon the


Figure 3.
(a) Diagram of the furnace assembly.
(b) Diagram of Knudsen cell used for metal
vaporization.


-,/
0
92
l/KK'1)


Figure 4.22. Plot of i/
0 vs. 1/T for Cu in Xe.


11
electric field at z = 0, n+ are the complex refractive indices for LCP
and RCP light, and 1 is the incident light intensity. Differentiating
and solving for k+>
h "6I(z)
k ne|E(z)|2 <5z
where
n /-2ek z\
|E(2}|2 = (E¡)2 oxp' ^--J (3)
The quantity ^ ' expresses the energy absorbed per unit time at z
which is dependent upon the number of sample species, Na, the photon
energy e, and the transition probability Pa -> j.
-<5I(z)
5z
Na Pa-\j
(z) e
(4)
If electric quadrupole and magnetic dipole interactions are ignored
and we consider only electric dipole transitions, the above probabilities
can be related to the electric dipole transition matrix elements through
time-dependent perturbation theory if the assumption that the effective
Hamiltonian H0 is a sum of independent components is embraced.
H0 = H0 + V (5)
where is the Hamiltonian for the system with no light, and H0 1 is the
Hamiltonian for the perturbation due to a radiation field. The subscripts
denote the absence of an external magnetic field.
= ^IL!E(z)|2||26(Eja-E)
Pa-j (z)
(6)


25
Terms of B0 are a general property of all MCD spectra and arise
from magnetic field mixing of neighboring electronic states with
either the ground or excited state of a transition. These terms have
the same shape as the absorption spectrum and can be positively or
negatively signed. It is generally difficult to calculate 80 terms as
knowledge of multiplicities and energies of all states near A and J
must be known.
Only when the ground state is degenerate can C0 terms exist.
Population changes induced by magnetic field splitting are demonstrated
by the inverse temperature dependence of the parametric equation. The
C0 terms may have either sign and have the same shape as the absorption
band.
Magnetic Circular Dichroism Calculation for Atoms
Photons possess well-defined values of angular momentum and are
absorbed or emitted by systems which are characterized by well-defined
values of their angular momenta.^6 The selection rules characterizing
transitions involving photons with angular momenta must account for the
conservation of angular momentum.
Consider transitions occurring in an isolated atom with total angu
lar momentum J. The degeneracy of the state is given by 2J+1, corre
sponding to the number of distinct eigenvalues rrij. The field around
an atom is spherically symmetric so there is no preferential direction
ality of the angular momentum. Under an external magnetic field this
degeneracy is lifted via the space quantization imposed by the direction
of the magnetic field. Figure 2.2 shows the Zeeman splitting of the
eigenstates of atoms with total angular momentum J = 0 and J = 1 in a
magnetic field and the possible transitions.


Page
Figure 4.14 Absorption and MCD spectra for Cu atoms isolated 117
in a Kr matrix.
Figure 4.15 Temperature dependence of the Cu atom Co term in 120
a Kr matrix. The intensity decreases with
increased temperature.
Figure 4.16 Experimental plot of i/
0 vs. 1/T for Cu 122
atoms in a Kr matrix.
Figure 4.17 Experimental plot of 3/
0 vs. 1/T for Cu 124
atoms in a Kr matrix.
Figure 4.18 Cu absorption and MCD bands in the range 220 nm to 127
340 nm.
Figure 4.19 Appearance of Cu/Kr spectrum after prolonged depo- 130
sition from 230 nm to 290 nm.
Figure 4.20 The Cu2 band in the range 330 nm to 450 nm. 133
Figure 4.21 Absorption and MCD bands for Cu in a Xe matrix. 135
Figure 4.22 Plot of i/
0 vs. 1/T for Cu in Xe. 137
Figure 4.23 Plot of 3/
0 vs. 1/T for Cu in Xe. 140
Figure 4.24 Plot of
2/0 vs. 1/T for Cu in Xe. 142
Figure 4.25 Relative positions of Cu MCD in Ar, Kr and Xe. 145
Note the reversal of MCD term sign in Xe.
Figure 4.26 Absorption and MCD for Au in Ar. 148
Figure 4.27 Plot of i/
0 vs. 1/T for Au in Ar. 150
Figure 4.28 Plot of 3/
0 vs. 1/T for Au in Ar. 152
Figure 4.29 Plot of best fit for Au in Kr of (peak separation)2 = 155
4 hwEJTcoth^2j-y)
Figure 4.30 Absorption and MCD for Au in Kr. 158
Figure 4.31 Plot of i/
0 vs. 1/T for Au in Kr. 160
Figure 4.32 Plot of 3/
0 vs. 1/T for Au in Kr. 163
Figure 4.33 Absorption and MCD spectra for Au in Xe after a 165
high temperature metal vaporization.
Figure 4.34 Spectra obtained in a 1300C Au deposition into Xe. 167
ix


4
cryogenic fluid reservoir or the expansion chamber of the Joule-Thompson
refrigerator.
Several methods have been employed for generation of guest species.
The simplest method involves a gas phase sample mixed with the matrix
gas at the desired guest-host ratio in an external container and subse
quent introduction of the mixture into the vacuum chamber, condensing the
mixture onto the cooled substrate. This, of course, is not useful in the
study of high temperature samples. The vaporization of nonvolatile sub
stances has been approached in different ways. One interesting method
recently employed by Bondybey and English^ involves irradiation of the
sample with a powerful laser, thus introducing the necessary energy for
vaporization. A more widely employed method is vaporization from a high
temperature Knudsen cell in a vacuum furnace. These cells can be con
structed of carbon, or a refractory metal such as Ta, W or Mo. In some
cases it is necessary to prevent cell degradation by including a liner,
usually of C, BN or AI2O3. The cells are heated either by induction or
resistance to temperatures as high as 2900 K. The vapor effuses in a
crude molecular beam through a small orifice in the cell and is intro
duced simultaneously with isolant gas onto the target. Molar ratios of
matrix gas to sample used are anywhere from 100:1 to 10,000:1. Another
technique used to introduce gas samples involves passing the sample
through a heated inlet tube, the resulting thermolysis products then
being matrix isolated. Unstable species and fragments are generated by
exposing a parent molecule to photolysis with ultraviolet lamps, electron
bombardment, gamma rays, or plasmas, again cocondensing the products with
matrix gas.


ACKNOWLEDGEMENTS
The author would like to thank Dr. Martin Vala for his guidance
in this research. A great debt is owed to Dr. Robert Ferrante for the
training he provided in high vacuum technology and matrix isolation.
The invaluable assistance of Dr. Jean-Claude Rivoal in calibration
and design and construction of electronics is greatly appreciated.
Thanks are also due to Dr. Joseph Baiardo for many helpful discussions
and his computer interfacing expertise. Thanks are also extended to
Dr. Richard Van Zee, Dr. Marek Kreglewski, and Dr. Robert Pyzalski for
helpful and informative discussions. For assistance in data collection
the author thanks Mr. Bill Copeland.
The author greatly appreciates the craftsmanship of Mr. Art Grant,
Mr. Rudy Strohschein, and Mr. Chester Eastman,shown in the fabrication
of the apparatus.
The author thanks Mrs. Laura Griggs for her diligence and attention
to detail in preparing this dissertation.
The seemingly unending patience, understanding, and assistance of
Jan Olson-Zeringue are most deeply appreciated.
Funding for this research has been provided by the National Science
Foundation and the Graduate School. Partial support by the Division of
Sponsored Research is also appreciated.


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LIST OF FIGURES
Figure 2.1
Figure 2.2
Figure 2.3
Figure 2.4
Figure 2.5
Figure 2.6
Figure 3.1
Figure 3.2
Page
The appearance of terms predicted by MOD theory 24
(a) The zero field absorption and MOD for a
transition with a positive Ai term. The
positive lobe lies at higher energy.
(b) A So term may be positive or negative, the
maximum coinicident with the absorption
maximum.
(c) A negative C0 term at two temperatures, Thigh
and T-]ow, may be positive or negative with
its maximum coincident with the absorption
maximum.
Polarized transition to an atomic P state and mag- 27
netic field splittings. Transition a is right cir
cularly polarized, transition c is left circularly
polarized, and transition b is polarized parallel
to the magnetic field.
Magnetic field splitting in degenerate ground and 30
excited states illustrating the origin of A0 and C0
terms.
Splittings in free atom 2S and 2P orbitals for 36
(a) an octahedral site
(b) spin orbit interaction
(c) Zeeman splitting.
The state splittings and allowed transitions for an 40
atom in an octahedral field showing the effect of
spin orbit and Zeeman splitting.
The predicted MOD and absorption patterns for the 44
2P 2S transition in an octahedral field.
(a) Diagram of the furnace assembly. 54
(b) Diagram of Knudsen cell used for metal vapori-
zation.
Detail of furnace-cryostat assembly used in matrix 58
isolation experiments.
Optics for absorption experiment
vi i
Figure 3.3
61


193
y = ( AA)q i Go, yB_ const.
; V
0 "W^T, I
For T2 >T, : T2 = I, +AT
T =AT(XT/XT)(1-XT/XTr1
1 12 *1 f >1
Au/Ar
+
AA


16
The assumption here is that the magnetic field energy is small compared
to the zero field separation of the states. A perturbation term is added
to the system Hamiltonian [equation (5)]:
H = Hq + H (23)
Considering only electronic contributions to the first order mag
netic field perturbation,
' = -I +2s )H (24)
i i S'
where the summation runs over all electrons, i of mass m and charge e.
The magnitude of the magnetic field is given by H and is directed along
+ h
the z axis. The projection of the angular momentum of the i electron
onto the z axis is given by and the projection of the spin onto the
i
z axis is given by szi. Summation over all electrons yields
H = -uzH=e(Lz + 2Sz)H (25)
where 3 is the electronic Bohr magneton (= 4.6681xl0_1cm_1/gauss), and
yz is the electronic magnetic moment along z. The corresponding orbital
and spin angular momenta along z are given by l_z and Sz- Equation (25)
ignores interaction with the nuclei since nuclear magnetons are at least
three orders of magnitude smaller than electronic magnetons. Within the
ground and excited state manifolds, H' is diagonal in the Franck-Condon
approximation:
| H1
\ A ,
i a' > =
- u
A >H6
a
1 a
a
1 HZ
' a aa
| H'
i-V
.j> =
- lyZ
IV"H5aa
(26)


Figure 4.14. Absorption and MCD spectra for Cu atoms
isolated in a Kr matrix.


55
flux of metal toward the cryostat. The heat shield is a 0.25 in diameter
copper tube spiral between two 0.125 in copper plates. A 0.125 in diam
eter hole drilled at the center of the shield also served to collimate
the metal beam. This provided the added benefit of reducing the thermal
load of hot metal striking parts of the cryostat other than the cold win
dow. Careful alignment of the Knudsen cell effusion orifice with the
heat shield hole was necessary to ensure that the metal beam was directed
properly toward the cold window.
The metal beam was codeposited with an inert gas onto one face of
the cold CaF2 plate. The temperature of the cold window was maintained
by an Air Products Displex Model CS 202 closed-cycle helium refrigerator
capable of cooling to approximately 13 K. The temperature of the window
was set using an Air Products APD-B temperature controller and monitored
by use of a chromel-Au, 0.07% Fe thermocouple mounted near the middle of
the copper window frame and referenced to liquid nitrogen. The stability
of the temperature controller was rated at better than 2 K at the set
point but at times performed to better than 1 K from 13 K to 40 K. In
later experiments a Lakeshore Cryotronics Model DRC-80C Digital Cryogenic
Thermometer/Controller utilizing silicon diode detectors with a rated
stability of 0.1 K was employed. The detectors were mounted in holes
drilled into the copper window frame. The window frame assembly was
made from high purity oxygen-free copper and had a V'-28 thread stud for
mounting to the second stage of the refrigerator. The entire piece was
machined from a single block of copper and indium gaskets smeared with
Cry-con grease were used between all metal junctions on the copper
window assembly to ensure good thermal contact.
The cold window was a one inch diameter, 4 mm thick CaF2 plate. It
proved necessary to use an ultraviolet grade window since the lower


148
\(nm)