Magnetic circular dichroism of matrix-isolated metal oxides


Material Information

Magnetic circular dichroism of matrix-isolated metal oxides
Physical Description:
xii, 173 leaves : ill. ; 28 cm.
Brittain, Robert Dameron, 1949-
Publication Date:


Subjects / Keywords:
Metallic oxides -- Spectra   ( lcsh )
Spectrum analysis   ( lcsh )
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )


Thesis--University of Florida.
Includes bibliographical references (leaves 169-172).
Statement of Responsibility:
by Robert Dameron Brittain.
General Note:
General Note:

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Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 000098004
notis - AAL3447
oclc - 06655481
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Full Text









The author would like to thank Dr. Martin Vala for

conceiving this project and supporting the conclusion of the

research. Thanks are also due to Dr. Willis Person and

Dr. William Weltner, Jr., for many helpful discussions

regarding the design of experiments and interpretation of


The completion of the apparatus has been made possible

by the patience and craftsmanship of Mr. Art Grant,

Mr. DaileyBurch, Mr. Chester Eastman, Mr. Rudy Strohschein,

and Mr. Edwin Whitehead.

The author greatly appreciates the training in design

and fabrication of materials provided by Dr. Samuel Colgate

and Mr. Edwin Whitehead.

The loan of various components of the experimental

apparatus by the following persons is appreciated:

Dr. Samuel Colgate, Dr. John Eyler, Dr..Earle Muschlitz,

Dr. Harry Sisler and Dr. William Weltner, Jr.

The friendship and assistance of other research group

members Joe Baiardo, Edward Voigtman, and David Powell will

always be valued by the author. Joe and Ed have made

valuable contributions to the implementation of the digital

signal acquisition system. David's ability to design and

build portions of the apparatus and electronic accessories

has been admirable.

The author thanks Ms. Laura Wagner for her diligence

and attention to detail in preparing this dissertation.

The patience and understanding of Cynthia Brittain are

beyond acknowledgement.

Funding for this project has been provided by the

National Science Foundation and the Graduate School.



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

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

LIST OF FIGURES ..............................viii

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

TEMPERATURE MOLECULES ........................ 1

Introduction................................... 1
The Matrix Isolation Technique................ 2
The MCD Technique.............................. 4
Aims of This Investigation.................... 5


Introduction.................................. 7
Basic Theory.................................. 8
MCD Calculations for Atoms.................... 23
MCD Calculations for Diatomic Molecules........ 26
Derivation of MCD Values from ExperimentalData 36

III APPARATUS ... ..... .......... ... ....... ........ 38

Introduction.................. ............... 38
Matrix Isolation Apparatus.................... 38
Spectroscopic Apparatus....................... 49

IV EXPERIMENTAL PROCEDURE....................... 59

Introduction............................ ....... 59
Matrix Isolation Procedure................... 59
Spectroscopic Analysis........................ 61
Calibration Procedures........................ 63


Introduction................................... 70
Predicted MCD of TiO, ZrO and HfO... .......... 72
Observed Spectra of TiO...................... 73
Observed Spectra of ZrO....................... 81
Observed Spectra of HfO....................... 86


VI MCD OF VANADIUM MONOXIDE....................... 89

Introduction.......................... ........ 89
Experimental Procedure......................... 92
Predicted MCD of VO............................ 93
Observed Spectra of VO......................... 97
Discussion...................................... 103
Conclusions...................................... 115

VII MCD OF NIOBIUM MONOXIDES.......................117

Experimental Procedure......................... 121
Predicted MCD of NbO...........................124
Observed Spectra of NbO........................124
Conclusions....................................... 142

VIII MCD OF TANTALUM MONOXIDE.......................143

Introduction................ .......... ........ 143
Experimental Procedure..........................147
Predicted MCD of TaO...........................147
Observed Spectra of TaO.......................152
Discussion .....................................162
Conclusions...................................... 163

IX CONCLUSION.................... ... ........ ......164

Suggested Apparatus Modifications...............164
Concluding Remarks .............................167

BIBLIOGRAPHY.. .. ...............................169

BIOGRAPHICAL SKETCH..........................173



1 Excited States of TiO, ZrO and HfO 74

2 Observed Band Systems of VO 90

3 Observed MCD Bands of VO in Ar 104

4 Peak Positions of Positive and Negative Lobes
of the B 4H-X 4X Transition 105

5 Integrated Areas of MCD Peaks in the B System 110

6 Relative Populations of X 4E- Multiplets 113

7 Relative Magnitudes of B 4H X 4- Transitions
Including Population Factors 113

8 Assignments of Electronic Transitions in NbO 118

9 Observed Absorption Bands of NbO in Ne and Ar
Matrices 122

10 Sharp Peaks Observed in MCD Spectrum of NbO
in Ar 131

11 Broad Bands Observed in MCD Spectra of NbO in
Argon and Krypton Matrices 132

12 Matrix Site Bands of the A+ and A'+ Systems 135

13 Excited States of TaO 146

14 Comparison of Gas Phase and Neon Matrix
Spectra of TaO 148

15 Absorption Spectrum of TaO in Ne at 40K 149

16 Absorption Spectrum of TaO in Ar at 40K 151

17 Assignment of State Symmetries for TaO in Ar 160

18 Observed MCD and ZFA of TaO Between 3000 A
and 2500 A 161




1 The Behavior of Circularly Polarized Light 11

2 Schematic Diagram of the MCD Experiment 14

3 Appearance of Terms Predicted by MCD Theory 21

4 Case(a) Coupling of L and S 29

5 Spin-orbit Splitting and Magnetic Field
Splitting of 3H Multiplets 31
6 Allowed MCD Transitions for a 3]T 3 System 33

7 Diagram of Furnace and Cryostat 41

8 Diagram of Knudsen Cell Assembly 42

9 Vacuum System for the Matrix Isolation
Apparatus 45

10 Rare Gas Inlet System 48

11 Optical Train for Absorption Experiments 51

12 Optical Train for MCD Experiments 52

13 Schematic Diagram of Absorption Electronics 55

14 Schematic Diagram of MCD Electronics 57

15 Calibration Curve for Magnetic Field Strength 65

16 Approximate Molecular Orbital Diagram for TiO 71

17 Allowed MCD Transitions of TiO 76

18 Allowed MCD Transitions of ZrO and HfO 78

19 ZFA and MCD Spectra of TiO Isolated in Argon 80

20 ZFA Spectrum of ZrO Isolated in Argon 83

21 MCD Spectrum of ZrO Isolated in Argon 85

22 ZFA and MCD Spectra of HfO Isolated in Argon 88

23 MCD Transitions Allowed for VO and NbO 95


24 ZFA Spectrum of VO Isolated in Argon in the
Region of the C 4EZ X4E- Transition 99

25 ZFA Spectrum of VO Isolated in Argon in the
Region of the B 4HTIX4Z- Transition 100

26 MCD Spectrum of VO Isolated in Argon in the
Region of the C 4E--X4E- Transition 101

27 MCD Spectrum of VO Isolated in Argon in the
Region of the B 4 X 4E- Transition 102

28 Temperature Dependence of Co Terms of VO 109

29 Approximate Molecular Orbital Diagram for NbO 125

30 ZFA Spectra of NbO Isolated in Argon 126

31 MCD Spectrum of NbO Isolated in Argon 127

32 MCD Spectrum of NbO Isolated in Krypton 128

33 Approximate Molecular Orbital Diagram for TaO 144

34 MCD Transitions Allowed for TaO 154

35 ZFA Spectrum of TaO Isolated in Argon 155

36 MCD Spectrum of TaO Isolated in Argon
(3000 X 5000 A) 156

37 Temperature Dependence of the MCD of TaO 157

38 MCD Spectrum of TaO Isolated in Argon
(4700 X 8000 A) 158

39 MCD Spectrum of TaO Isolated in Argon
(2500 X 3000 A) 159

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



Robert Dameron Brittain

August 1979

Chairman: Martin Vala
Major Department: Chemistry

The diatomic oxides of Group IVB and Group VB have been

prepared by vaporization of higher oxides from Knudsen cells

and condensation in argon or krypton matrices at 140K.

Magnetic circular dichroism (MCD) and zero field absorbance

(ZFA) spectra of all six molecules are presented. A detailed

analysis of results for VO, NbO and TaO is given.

An apparatus for the deposition of metal oxide molecules

has been constructed. The sDectra have been obtained under

microprocessor control and stored on tape cassette in digital

form. It has been shown that a low field electromagnet

(-5500 gauss) can induce MCD transitions of sufficient

intensity fcr qualitative analysis of high-temperature

molecules isolated in rare gas matrices.

The ground state of VO is 4- MCD transitions to B 4I
multiplets are observed to have alternating Co terms. The

effect of spin-spin splitting of 4 3 and 4Z sublevels
/2 a 1/2
upon the temperature dependence of Co terms in the B 4I X 4E

transition is discussed. A broad negative Co term is

observed for the C 4E- X 4E transition. The appearance of

this term in the MCD spectrum indicates that spin-orbit

mixing between the B H state and either or both 4Z states

The NbO molecule also has a Z- ground state. The ZFA

spectrum consists of a series of sharp and broad peaks which

have similar progressions. The MCD spectrum proves that both

broad and sharp peaks arise from isolated NbO molecules

because of the characteristic alternately-signed C, terms

observed for transitions from the 47- ground state to multi-

plets of two 4H excited states. The broad and sharp peaks

are assigned to electronic transitions of NbO from two

different matrix environments. Based upon trends observed

for spin-orbit splitting and vibrational frequencies for the

two types of bands, the broad peaks are related to NbO in

substitutional sites in the lattices while sharp peaks

observed in neon and argon matrices are proposed to correlate

with distorted lattice sites. In contrast with the spectrum

of VO, no Co term is observed for the A 4 X4 transition.

The ground state of TaC is 2 Negative MCD CO
2 22
terms are observed for 24-- A transitions while positive
2 /2
Co terms are observed for 2 12 A/ systems. Transitions


between states with 0 =- are observed in ZFA but not MCD.

Based on this simple model, state symmetries of 21 excited

states are tentatively assigned; seven new systems are
o 0
reported in the region 2500 A 3000 A. It is suggested

that the technique of matrix isolation MCD be extended to

the study of other high-temperature molecules.





The technique of magnetic circular dichroism (MCD) has

generated considerable interest among molecular spectro-

scopists since the theoretical development introduced by

Buckingham and Stephens1 in 1966. MCD is the measurement of

the differential absorbance of left circularly-polarized

light (LCPL) and right circularly-polarized light (RCPL)

over a range of the electromagnetic spectrum by a sample

subjected to a magnetic field parallel to the incident

light. The increased information content afforded by polar-

ization-dependent selection rules for optical absorption

makes MCD a potentially powerful partner of conventional

spectroscopic methods in the elucidation of molecular struc-


Early MCD studies were focused on species in single

crystals and on room temperature solutions, as shown in
reviews by Buckingham and Stephens,2 and Schatz and

McCaffery. Low temperature experiments on glasses, polymer

films and uniaxial crystals have since demonstrated that

valuable additional information is obtained from the temper-

ature dependence of MCD for a species with a degenerate



ground state. The species most commonly exhibiting ground

state degeneracy, however, are open shell systems which are

unstable in ordinary chemical environments. The development

of the matrix isolation MCD technique by Andrew Thomson and

coworkers at the University of East Anglia has opened a

pathway to the convenient observation of these and a variety

of other interesting chemical species. Matrix isolation

systems studied by MCD to date have included mercury4 and

magnesium atoms and the diatomic molecules oxygen,
7 8
chlorine, and xenon halides.

The Matrix Isolation Technique

Matrix isolation was introduced in 1954 by Whittle,

Dows,and Pimentel9 as a means of studying stabilized free

radicals which were candidates for use as rocket fuels. The

subsequent development of commercial cryostats has stimu-

lated applications of matrix isolation methods in many areas

of spectroscopy and has established a growing field of cryo-

chemical synthesis.0 A detailed introduction to methods of

matrix isolation, including an extensive review of the early

literature, has been published by Beat Meyer.11

Matrix-isolated samples are prepared by codepositing a

molecular beam of the analyte (guest) species in a great

excess of nonreactive host gas on a cooled sample window.

Host-guest ratios of 103:1 to 10s:1 are commonly employed to

ensure isolation of the guest species. The apparatus must

be evacuated to a pressure of less than 10-s torr by a

suitable pumping system. The sample window must be chosen


to provide transparency in the range of spectral interest

while also being sufficiently conductive to allow rapid

thermal quenching of the host and guest species. Temperature

requirements are met by the thermal contact of the window

with either a closed-cycle refrigeration system operating by

Joule-Thomson expansion of helium or by a reservoir of a

refrigerant which maintains the window at 40K (liquid He),

200K (liquid H2), or 770K (liquid N2). The choice of host

gases which may be used in an apparatus is limited by the

choice of refrigerant, which must cool the sample to a Kelvin

temperature below forty percent of the melting point of the

host gas to prevent thermal diffusion and clustering of the

guest species. Matrices of stable molecules with vapor

pressures above 1 torr at room temperature may be prepared

by the simple mixing of guest and host in the gas inlet

line. Reactive or low vapor pressure systems may be gener-

ated in molecular beams by the inductive or resistive heating

of refractory Knudsen cells containing the species of

interest or by discharge in a hollow cathode lamp or micro-

wave cavity.

Spectroscopic techniques applied to matrix-isolated

samples include optical, ultraviolet (UV), infrared (IR) and

Raman spectrophotometry, nuclear (NMR) and electron spin (ESR)

resonance, and laser-induced luminescence. The optical

spectra of molecular species normally observable only at high

temperatures are greatly simplified because rotational

structure is eliminated,and absorption occurs only from the

lowest vibrational level of the ground electronic state.


Isotopic substitution studies in IR allow the determination of

vibrational bandheads of electronic states,and optical, IR and

ESR spectra can often be employed to establish the symmetry of

the ground state. The energies of excited states are shifted

by small magnitudes from gas phase values, generally allowing

confident assignment of systems previously assigned by gas

phase analysis. Due to the loss of rotational structure upon

isolation, however, the symmetries of excited states of

matrix-isolated molecules have not been susceptible to analy-

sis by spectroscopic techniques usually employed to study

matrix samples. The development of the matrix isolation MCD

technique has made the determination of excited state symme-

tries possible for matrix-isolated species.

The MCD Technique

The measurement of MCD requires the passage of a beam of

alternating LCPL and RCPL along the axis of a magnetic field

within which is placed a sample of interest. The differen-

tial absorption signal is detected by a photomultiplier tube,

the output of which is fed to a phase sensitive detector.

The MCD spectrum is displayed as a wavelength function of

differential absorbance. The only additional requirements in

the study of matrix-isolated samples are that the sample and be nonbirefringent, and that the depolariza-

tion of CPL by matrix scattering be minimized. The experi-

mental advantages of MCD over conventional zero field absor-

bance (ZFA) reside primarily in the bipolar resultant signal,

differential detection technique, and temperature dependence

of spectra for molecules with degenerate ground states. The

selection rules giving rise to differential absorbance bring

additional theoretical power to the analysis of experimental


The applications of matrix isolation MCD have been

limited to a very few molecular species to this date. In

particular, no investigation of the highly promising area of

high temperature molecules has yet been undertaken. Refrac-

tory diatomic oxides are among the most stable molecular

species known, as evidenced by their appearance in stellar

atmospheres and as ablation products of jet exhaust and
atmospheric reentry processes.12-14 These molecules gener-

ally have challenging molecular electronic structures which

have not been thoroughly analyzed by either gas phase or

matrix techniques. The contributions of conventional matrix

spectroscopic techniques and theoretical studies5 to the

elucidation of these systems create a favorable situation for

the investigation of the same molecules by MCD.

Aims of This Investigation

The present research consists of the analysis of MCD and

ZFA spectra of matrix-isolated Group IVB and Group VB

diatomic oxides. The primary analysis tests the validity of

present ground state assignments for the six molecules by the

signs and temperature dependence of the observed MCD spectral

bands. The correlation of matrix and gas phase assignments

of excited electronic states of the molecules is then checked

by comparison with the signs of MCD peaks for allowed tran-

sitions. In addition to its role in confirming previous

assignments, the analysis enables the identification of bands

arising from impurity species trapped with the diatomic

oxides during isolation. Recent photoluminescence

studies617 on TiO and ZrO have suggested values for the

separation of singlet and triplet state manifolds in these

molecules. The MCD spectra are checked for confirmation of

these assignments by the appearance of transitions between

singlet and triplet states, and similar forbidden transi-

tions are searched for in the other molecules studied. The

determination of manifold separation energies is of great

value in development of chemiluminescent laser systems and

in calculation of dissociation energies by the third law
method. The magnetic field or spin-orbit coupling induced

mixing of low-lying states with ground states of these

oxides is also susceptible to analysis by the observation of

MCD transitions forbidden by electric dipole selection rules.

In summary the investigation of these refractory oxides

is an appropriate test of the power of MCD applied to high

temperature species. The success of these studies in eluci-

dating the electronic structure of the molecules studied

justifies the extension of the matrix MCD technique to the

study of less well-defined systems.




More than a century passed between the first observa-

tions of magnetic optical rotation by Faradayl9'20 and the

development of a quantum mechanical model explaining the

behavior of the complex refractive index of materials in

regions of absorption. As might be expected in the develop-

ment of a theoretical model, choices of symbols and conven-

tions by different theorists have given rise to difficulties

in interpretation of the mathematical formulas derived for
MCD. The recent revised treatment by Stephens21 has received

wide acceptance and will be employed in this work. A

condensed version of Stephens' approach will be presented so

that the assumptions required by the parametric equation for

MCD may be emphasized. Subsequent discussion will concern

the calculation of parameters for electronic transitions in

atoms and diatomic molecules isolated in rare gas matrices.

It will be shown that calculations for these systems are

relatively simple compared to those for polyatomic molecules.

Basic Theory

The general form of the Faraday effect may be expressed


S= (P i9 = VH (1)

where 0 is the complex rotation of a plane-polarized light

beam propagating through a sample of thickness Z parallel to

a magnetic field H, ( is the angle of rotation of plane-

polarized light by the sample, and e is the ellipticity

occurring in regions of absorption. The Verdet constant V

is dependent upon the concentration and temperature of the

sample as well as the frequency of the light. An alternative

form of equation (1) is

D = (n_ n+) (2)

where X is the light wavelength and n_ are the complex
refractive indices for LCPL and RCPL, respectively. Inspec-

tion of the differential form of the complex refractive index

shows that the angle of rotation ( results from behavior of

the real refractive indices n_ while the ellipticity 6 arises

from differences in sample absorption indices k.,

An_ = An iAk. (3)
+ + *

( = (n_ n +) (4)

6 = i(k k+) (5)

Plane-polarized light may be considered to be composed

of equal components of LCPL and RCPL as shown in Figure 1(a).

The electric vector for RCPL appears to rotate clockwise to

an observer looking toward the polarizer and light source,

while the electric vector for LCPL rotates in a counterclock-

wise manner. A difference in the real refractive indices n_

and n+ of a sample results in a rotation of the unresolved

electric vector by an angle p as shown in Figure 1(b). The

analog of this effect at a single wavelength in the absence

of magnetic field is the subject of polarimetry, while the

dispersion of with wavelength is the subject of optical

rotatory dispersion (ORD). The obvious name for ( of a

sample in a magnetic field is then magnetic optical rotatory

dispersion (MORD). Differences in absorption indices k

result in varying amplitudes of the electric vectors for RCPL

and LCPL which are reflected in the ellipticity e as indica-

ted in Figure l(c). The ratio of the electric vectors of the

two components is in proportion to the difference of absorp-

tion indices. The wavelength dispersion of 6 in the absence

of an external field is called circular dichroism (CD)

leading to the obvious acronym MCD for samples studied in a

magnetic field.

This work will be confined to the study of MCD of

matrix-isolated samples, for which the behavior in absorption

regions is subject to easier calculation than MORD. It

should be noted that, due to the functional form of the

complex refractive index, the MCD of a system may be explic-

itly derived from the MORD if data are available over the

"4 0
0 U >
(1 00

,.-t C

O U)


0 c -L-
H, a

0 r
0 -4 0

U) Hn
a) )
= r4 U


4 -H

0 z

0 0

,- -H
0 04
r-4 44

O 0

r-, U
U 0

H -H
*i- C
U 0
r -


-: '-*




-4 0

0 r.


rd 0)

*l *H

C*H o

ro( au
Z -

rdA 0


amlb m

entire frequency range. The relationship of the real and

imaginary terms of the complex refractive index is given by

the Kramers-Kronig transforms.22

The MCD spectrum of a sample system is directly related

to the difference in absorption indices k_, but is usually
measured as a difference in absorbance A of LCPL and RCPL.
The values of A_ may be calculated by time-dependent pertur-
bation theory, given certain assumptions about the separabil-

ity of the components of ground and excited state wavefunc-

tions involved in a transition.

Consider a light beam parallel to a magnetic field H

passing through a sample with ground state A and excited

states J and K as indicated in Figure 2. The intensity of

the light at point z is given by the Poynting vector,

I2. (Ekz)
I_(z) = ()n (E') exp -
+ = TC

S2Ek z
= I ()exp 7f (6)
+ I fic

where E = hv is the photon energy and I (o) is the incident
light intensity. Solving for k by differentiation,

h ~- (Sl (z)
k= h +Tz (7)
+ nEIE_(z)2 L 5z
+ +


+E_(z) 2 = (E ) exp (8)
+ 0fie

c S>

S t>i C
+ p s 44-1 4-) >4

M M( O( -10

C) (1) i c() 0

a) 54 0 O- ao
r- o X l i4 ) 0 C) 0

4 Z4- UJC 04 0
+J 1 c 0 n 7

Sr- 0 U W4

0 Qr:; 0 f : r-
Ori e O 3 | -
-) C( Z (1) *) 0 U) 4-I-
a) afa C-n I 4c ()j q
4i) Q.)% 3 (

4 C 0 c0 i) W
4l XN rO 44-H *

d cd rd-1 0 4 1e c>)
,C: (1) U243 0WC- M
*H(d H ~ *H ~ U t t 4J
E-4 e 4J 04 E S



< H
_ 1* --

The quantity -6I(z) is the energy absorbed per unit time at

z, which is dependent on the photon energy E, the number of

sample species Na and the probability of transition Pa-j'

I(z) N P (z)E (9)
6z a,j a aj

Time-dependent perturbation techniques are applied to

the solution of transition probabilities Pa-j. Only electric

dipole allowed transitions are considered in this treatment,

where it is assumed that Beer's Law is obeyed and radiative

lifetimes are not included, so that predicted absorption

bands are Dirac 6 functions of the absorption energy. The

resulting equations for zero field absorbance (ZFA) and MCD


A E Na
S= a,j N j26(Ej E)}cz (10)

N221log 0e
S= (11)

A = Y. ( 12 |1
+ a, j
X 6(E. E)cz (12)

where the sums are over all sublevels a and j of the ground

and excited states, ( NJ is the relative population of the

ground state level a, and are electric dipole
transition moments.

The modification of these results to reflect the actual

linewidth requires the assumption that the ZFA band shifts


rigidly upon introduction of a magnetic field perturbation.

The rigid shift model requires that the Born-Oppenheimer

approximation be valid for both ground and excited states.

Within the Born-Oppenheimer approximation,electronic wave-

functions are separable into nuclear and electronic terms.

The separation may be denoted by

IAaa> = A (r,R)Xa(R) (a = 1 to dA) (13)

IJij> = p (r,R)X.(R) (A = 1 to d ) (14)

where r is the electronic coordinate, R is the nuclear

coordinate, dA and d are degeneracies of the two states,

and X and X. are vibrational wavefunctions. Further
a 3
assuming by the Franck-Condon approximation that most elec-

tronic transitions occur when R is close to the equilibrium

internuclear distance R0, the vibronic contributions to

electronic transitions may be separated into Franck-Condon

factors . Summation over all vibronic bands results in

a ZFA equation dependent only on the electronic transition

. The form for ZFA derived with the

approximations of the rigid shift model is given by

T- = Y-,f(E)cz (15)

where c is the concentration, z is the pathlength, and the

superscript o indicates evaluation at Ro by the Franck-Condon

approximation. Vibrational overlap factors are included

explicitly in the line shape factor f(E). The parameter VD

is the weighted sum of the transition moments,

o = 21 { 12 + l
2 (16)
S 2d c,A ia. + + (16)

where a and X are electronic sublevels and dA is the degen-

eracy of the ground state. The factor of 2 enters the Do

equation because, in the absence of field perturbation,

absorbance is equal for light of either polarization,

= (17)

It is now possible to apply the rigid shift model to

molecules in the presence of a magnetic field. The applied

field introduces a perturbation term in the molecular

Hamiltonian of the form

Ho = -uzH E (Lz + 2Sz)H (18)

where Pz is the z component of the electronic magnetic moment

operator, Sz and Lz are z components of the total spin and

orbital angular momentum operators, and 6 is the electronic

Bohr magneton. H. is diagonal in the Franck-Condon approxi-


= -HH ,6 (19)
a 0 1 C a aaa

H6 (20)

Stephens includes the additional mixing by the magnetic

field of different excited states K with states A and J,which

results in a better approximation of the transition moment,

= [

+{ i
o e o
+ K J< }H]

Note that the magnetic field mixing is inversely proportional

to the separation of the mixing states and is linear with

field strength H. There is also a complex dependence on

electric and magnetic dipole transition moments relating the

electronic states, and Stephens has implicitly assumed that

only vibronic levels of the same vibrational symmetry partic-

ipate in mixing.

One other effect which must be taken into account is the

difference in population of ground state sublevels due to

magnetic field splitting. Stephens assumes that for split-

ting much smaller than kT the exponential Boltzmann popula-

tion factors for ground state levels may be approximated by a

Taylor series expansion.

The combination of all assumptions in the rigid shift

model applied to equation (12) gives a parametric form for

the MCD of the transition A-J,

=YA f(-) + (B, + C}f(BHcz (22)

where all symbols are as previously defined except for the

parameters A B and C which are given by
1 0 0


A1 = [I
d aX C- + X

X [ ] (23)

S= 2 Re{ [
Bo dA X, KJ > K I+ cA

] X 0------
a' + I K J
+ KJ [
K#J X X + K t +'X K

X (24)

C0 = X [I K A

1 0
X (25)

The MCD of any electronic transition may be described by

contributions from one or more of these parameters.

Before applying the parametric equation to the analysis

of MCD spectra of atoms and molecules, it is worthwhile to

examine the experimental form of the Al, 8B and Co terms, the

appearance of which is illustrated in Figure 3. Al terms

occur when there is a degeneracy in either the ground or

excited state. The selection rules for the electric dipole

transition moment are,

L (J) L (A) = AL = +1 LCPL
z z z
L (J) L (A) = AL = -1 RCPL
z z z
AS = 0 (26)

a 44

>1 r
o- E ) a)c

Ok 4Ca)xC
4-4a a)r a)m (4-


So unoa

,C ; t~
-4~4 a)ra~-i
(1 3 M ::I Q

a 0:- U2 OW
V 4 4
44 O 4-44 -

a 4) 1 MQ a) 4
>~ r4 E 4 (a

.-o Cd-
0 0) 41 a)

E-H -H41
C) MO U]a)U -

0 ol z0C
4-) Q) ) (

4-,J aL)
MO >C(n
a) -H- a1)

-i E-4 -r -H4

41 J 0

0- 0
C.)-4 pu
E-4 a)

-Hi c'~H

a) N-'Q E
9 E -1 >1 W 4

Or( 45

WE-4 c C4-

a) a)0
a)J 4Jr ,d
~CO4- CO~rd

4 4 O>
Ca) na)E

~ 4-)
04 ( 44 O

.U a) -
04 40 ) 0 -)
as () Q)O
04 Z$:
(d 4 rl
r-f 4J D)







r4 0


(a r
4 (






+ <


In Hund's case (a) only transitions allowed by these selection

rules give Al terms, which always consist of overlapping

bands of opposite sign but equal magnitude. Since the two

bands are separated by the small Zeeman splitting of degener-

ate state sublevels, a derivative-shaped term results. In Al

terms of positive sign, the positive lobe appears at higher

energy. The magnitude of allowed Al terms is influenced by

the sharpness of the absorption band, as indicated by the
factor -E in the parametric equation. Another factor affec-

ting the size of A terms is the difference of magnetic

moments for the ground and excited substates of the transi-

tion. If these moments are equal, an Al term will not be


Bo terms are a general property of all MCD spectra

caused by the magnetic field-induced mixing of neighboring

electronic states with either the ground or excited state in

the transition. These terms have the same shape as the

absorption band and may be of either sign. The calculation

of 8 terms is difficult, however, because it demands know-

ledge of the energies and multiplicities of all states near

A and J.

C0 terms are possible only when the ground state is

degenerate. Population changes induced by magnetic field

splitting are reflected by the inverse temperature dependence

of the parametric equation. Like B terms, Co terms may be of

either sign and will follow the shape of the ZFA.

The relative magnitudes of the three terms may be

approximated by the relation


BO0 : A-W: k* (27)
A1 ::Co I'AW'kT (27)

where F is the full width at half maximum of the ZFA band,

AW is the separation of state K from A or J, and kT is the

thermal energy of the system. For matrix-isolated diatomic

molecules we may assume F 200 cm1, AW v 2000 cm",

kT % 10 cm-', whence,

A :So:Co 10:1:200

It is obvious that Co terms will dominate other features of

the MCD when the ground state of a species is degenerate.

When a species having only A1 and 8, terms is studied, CO

terms due to impurity species present in much smaller concen-

tration may still contribute to the observed MCD.

MCD Calculations for Atoms

Consider the simplest atomic transition in which MCD

may be observed, the P 1 S case,


+1 0

p 0 0

-1 0

+ -
s 0 0

H ---

where o_ and + indicate the transitions allowed for LCPL and

RCPL, respectively. Since only the excited state is

degenerate and no neighboring states are shown, only an A1

term need be calculated for this transition. Applying equa-

tions (23) and (16) to the allowed transitions shown above,

Ai = lI }

I! P _11-iP_> } (28)


= +
= -

= 0

= =

by the rigid shift approximation, so that,

Al = + B (29)

Do = 1{ + }

= (30)

Dividing (29) by (30),

= +2B (31)

we see that the MCD Al term provides the magnitude of the

magnetic moment for the iP excited state, which will have a

Zeeman splitting of 2BH.

The MCD spectrum of the P S transition of Mg atoms

isolated in various rare gas matrices has been reported by

Mowery et al. The MCD spectrum of Mg in Ne shows the

predicted Al term dispersion, but the MCD spectra of Mg in

Ar, Kr and Xe are dominated by Bo terms induced by Jahn-Teller

distortion of the Mg atom in the octahedral sites of the

heavier inert gases. The interaction of the 1P excited state

with the surrounding lattice also results in quenching of the

angular momentum. This is evidenced by the values of A-
calculated from experimental results, which are all lower

than the expected value of 2.0 a. Possible excimer formation

by the P excited state of Mg atoms with the matrix lattice

has been suggested by the observation of non-resonant fluo-

rescence of Mg in Ar and Ne matrices.23 The magnitude of

may then be a measure of the extent of bonding in this case.

It should be noted that Jahn-Teller distortions are not

expected for diatomic molecules in matrices unless there is

strong interaction with the matrix. The reason is that such

effects require the interference of a non-symmetric vibra-

tional mode which lifts the degeneracy of a ground or an
excited state;24 the spectra of diatomic molecules in

matrices are dominated by well-defined progressions of the

symmetric vibrational mode of the molecule.

Consider now the simplest atomic transition in which a

C, term may be observed, the case 1S i P.


I 0 0

+1 0
ip 0 0
1 0

H ---


Applying equations (16), (23) and (25),

A = -{
{ )

= + PB (32)

Co = {


3 T+
= + 8


o = 1 (34)
D 6

1O = (35)

= (36)

The Al and C, values calculated have the same value, but as

already noted, the C, term will dominate the spectrum for

broad transitions in low-temperature matrices. It is inter-

esting to note that in this case one may simply sum the
values calculated for the a- transitions and double the

result to obtain Al and CO term magnitudes, due to the

symmetry properties of the transitions.

MCD Calculations for Diatomic Molecules

The values of L and S are no longer good quantum numbers
in the axially symmetric field of a diatomic molecule. The

projections A and E of L and S, respectively, on the


internuclear axis are good quantum numbers in Hund's coupling
case (a),24 otherwise known as L-S coupling. In Hund's

case (c), or j-j coupling, the projection of the total

angular momentum J, designated Q, is the only good quantum

number. We need not be concerned with the coupling of rota-

tion and angular momentum because rotation of matrix-isolated

species has been observed only for a few molecules containing
hydrogen.2 The MCD selection rules for case (a) are

AMA = 1 and AME = 0, where MA and ME signify the values of A

and I for particular substates. In case (c) coupling MCD is

observed if AM = 1. A diagram illustrating the coupling of

L and S and resultant values for A, Z and 2 is given for

case (a) in Figure 4. Case (a) states are designated
2S+1 24
2S+A, as usual,24 where each multiple has a particular

value of Q. The A values of 0, 1, 2, etc. are designated as

E, i and A states, respectively. In the case of a 3H state,

for example, there are three pairs of doubly-degenerate

multiple states equally separated in energy by the spin-

orbit coupling energy A as shown in Figure 5. The inter-
action of each of these multiplets with an applied magnetic

field depends on the magnitude of p~ for each multiple.

Except for the case of spin degenerate, non-orbitally degen-

erate ground states, discussed later in the text, the calcu-

lation of Al and CO terms is quite simple for matrix-isolated

diatomic molecules in both Hund's case (a) and (c).

Consider the electronic transition 3 3A which is

observed in spectra of TiO. The relevant details of the

transition are diagrammed in Figure 6. The MCD spectrum is

(D r
Cd O3

Zd Cd 4)

oa l EH

aI' ) 0 (1)

Cd4 0

04 0>

0 QQ r-4 a)
>CdWU4 (
"Ar r-i4 ,

Zd 4-4'
- Cd- 04 fd
a) U)-i I

-4 (d Z

.4 p- 0-1
E-4 0 (n 4-) 4-)


4 C

U) ~-
4-)4.4 +
a) Mn.
-4 -

44 r U)

0 +

0 N

U r-4 Ul




ro a) (1)
i-I H

a) a, ,q u
44 r-l rl 4.) r-I
W 1I r-4,4J N
0 0Z 44J (1)
-rH= a) E a

4QJen -4 m N
rd E 0Q-H O

04-) 4J4-()4J d -

-rir ~r- Nr U

z -ri m = (a ~
r-q -i 44 W m >,

0 N 4(
o wo ow

4-hJ -4 Z rq
4-) (0 4-) 0 -r-
-1 r4-) -HMU-H
m ( 3) 0r
0 -)0 4 M 4J
o 41 U (Q > z z4i

i z r q L) (2) (3)
-Hl rE-I 0 ( V W 4 E
04 C1 4 r-q44 0
Ern 4J E-4 M W M




0 0


0 a E
< 4-4 p p (a
0 0 )4 U
rO 4 4-1 4
+ A '0 -

r-i -4 (d
, rd t| 0
.4 0 4a)
4m o aj 4 J 4j

0 0 0) 0
-rI -iH Q ) C
ri -H H M (

CQ C+ l +En 4 0 0 (

0 IE- -H -
3 l +1 (
4J 4E M MM
U 0 ad0 rca

-i 4C *0 m

















greatly simplified by the fact that only the lowest vibra-

tional state of the 3A1 multiple will be populated if the

constant A (3A) is >> kT, which is the case for TiO. None
of the allowed transitions from the A and A multiplets

will then be seen. Considering only the allowed transitions

from Al to 3I0, one may further simplify the calculation of

MCD terms by considering only the a_ components and doubling

the result. This simplification may always be used in MCD

calculations within the rigid shift approximation,

1 = [ ] (37)

o ]B (38)

Thus, for the transition 3IT + A ,

= +B (39)

O = 0 (40)

It is interesting that, although the A1 state is doubly-

degenerate, no Co term is predicted because the magnetic

moment iz = MA + 2M is zero. This effect is also observed

for 2H and 4 states.
/2 /2

Calculation of A and Co terms for molecules exhibiting

Hund's case (c) coupling is not so rigorous because the

magnetic moment is no longer equal to MA + 2M,, but includes


a factor dependent on the magnitude of spin-orbit coupling.

Observation of a temperature-dependent MCD for TiO, as well

as the loss of equal multiple spacings, would indicate a

coupling case intermediate between (a) and (c). Spectra

observed in this study can generally be explained by case (a)

even though the spin-orbit coupling is large for some of the

molecules studied.

In later application of the formulas derived for MCD

terms it should be remembered that this treatment has assumed

pure electronic states which are not influenced by any per-

turbation except the magnetic field. Steinfeld has made a

comment which seems appropriate to this situation:

Since one particular state usually makes
the dominant contribution to a real system,
it is convenient to think of one idealized
state. One should never forget, however,
that in every case the molecule has solved
its own Schr6dinger equation exactly, and is
probably laughing at our attempts at attain-
ing some approximate solution.25

For the molecules investigated in this study, the interfer-

ence of spin-orbit coupling may influence the observed MCD

spectra by the mixing of neighboring states with either the

ground or excited states of an electronic transition. As a

result of spin-orbit mixing of states, one may be forced to

revise the state description by explicitly including the

mixing states in the electronic transitions. Such an

approximation has been used to explain the MCD spectra of

xenon halides.

Derivation of MCD Values from Experimental Data

Experimental values for Al, Bo and CO terms may be
derived from MCD spectra by the method of moments.2 The

nth moments of ZFA and MCD bands are defined by,

E = (E EO )dE (41)

A =f (E E) ndE (42)

where E is the center about which bands are integrated. The

subscripts of Al, Bo and Co terms are related to the moment

integrated for AA. VD is derived from the zeroth moment of

the absorption spectrum. If H is expressed in 104 gauss, c

is the sample concentration, and z is the pathlength, the

theoretical parameters are derived from experimental data by

the formulas,21

= 326.6Docz (43)

o = 152.5([B + L]Hcz (44)

= 152.5A Hcz (45)

from which, if 8B = 0 and H = 5500 gauss,

1 1
= 0.257- (46)

C < A> ( 1
Co = 0.372 1---- (47)
Do 0 +

In order to apply these equations, one must integrate over

the entire vibrational progression of a transition. The

integration of first moments to obtain Al terms requires the

inclusion of the factor (E EO) for each data point, which

can be handled easily only by computer treatment. After

appropriate scale adjustments to convert from chart inches

to wavenumbers and from AuV to AA, planimeter integration

may be used to derive CO terms.

The use of the method of moments has been severely

limited in this study by the complex overlap of vibrational

bands of different electronic states for all molecules. The

analysis of most bands systems is therefore qualitative in

nature. The signs of predicted transitions will be calcu-

lated and compared with experimental MCD results. Forbidden

transitions will be explained on the basis of mixing by the

magnetic field or by spin-orbit coupling of neighboring





The description of the apparatus employed in the meas-

urement of MCD and absorption spectra for this study can be

conveniently divided into two parts. The hardware necessary

for preparation of a matrix sample will be treated first,

followed by a discussion of data acquisition and signal

handling in the two spectroscopic experiments.

Matrix Isolation Apparatus

The preparation of a matrix-isolated sample of high-tem-

perature molecules required the construction of a high-vacuum

system containing a furnace for sample vaporization and a cold

surface on which the sample could be cocondensed with a large

excess of host atoms or molecules. Provision was made for tem-

perature measurements on the Knudsen cell and sample window,

and for monitoring system pressure and host deposition rate.

The vacuum furnace originally constructed for this

experiment was a 6" diameter brass cylinder connected by a

double gate valve assembly to a closed-cycle helium expan-

sion cryostat. The furnace was detachable from the cryostat

after deposition to allow cleanup during spectroscopic

analysis, affording a more rapid turn-around time between


experiments. Attempts to isolate samples using the first

furnace were unsuccessful because of a relatively long

deposition distance of ten inches between the Knudsen cell

and sample window, and because radiative heat flux from the

Knudsen cell allowed aggregation of sample molecules during

isolation. Both problems were resolved by construction of

the more compact system illustrated in Figure 7. The cell

assembly consisted of 1.00" tungsten or tantalum Knudsen

cells mounted by tantalum straps and copper screws on two

water-cooled copper electrodes, as shown in Figure 8. A

heat shield constructed by soldering copper plates to either

side of a spiral of water-cooled copper tubing was placed

immediately in front of the Knudsen cell. While sample

molecules could pass through the 1/8" holes in the heat

shield to strike any area of the sample window, the shield

intercepted most of the radiative heat flux from the cell.

The distance between the Knudsen cell and the sample window

was only 3.5" for the second furnace. The disadvantage of

the compact furnace was that the furnace was no longer

isolable from the sample window during the experiment.

The Knudsen cell was heated resistively by passing up

to 300 A of current at 10 V through the copper electrodes.

Significant heating occurred only in the thin-walled Knudsen

cell due to the inverse dependence of resistance on the

cross-sectional area of the conductor system. Cell-surface

temperature measurements were accomplished by raising the

magnetic shutter collinear with the viewport window and

Knudsen cell. A Leeds-and-Northrup optical pyrometer was


rl O

0) 0
an (

d u









0 r-4

0 0








t4 J

m 0

S --
kc -

r t 0


r d

0 )


0 -1
rn r

t I7 1-4


i I .





0 "
O 0O


oCX a
T z 7
-J I >1

OO < .


U n

o 0I C

(n1 m
-I I -,
0 C

< --

kel Q
(-> ,_ i --- __ ______ce n

S i j ;~? I4

employed in all cell temperature measurements, which were

subsequently corrected for emissivity of the Knudsen cell.

The furnace and cryostat were pumped through a 2"

vacuum part by a 2" Consolidated Vacuum Corporation diffu-

sion pump charged with Dow Corning 704 silicone diffusion

pump oil. Vacuum components are diagrammed in Figure 9.

A stainless steel vacuum trap between the furnace and diffu-

sion pump allowed maintenance of a system pressure at or

below 10-" torr for 20 hr with the addition of 3 1 of

liquid nitrogen. A 2" CVC gate valve isolated the diffusion

pump and cold trap from the furnace during cleanup and

rough pumping. Rough pumping to a pressure of less than

200 j was performed by bypassing the diffusion pump with a

1/4" copper line to the fore pump of the system. A 1/4"

control valve in the roughing line allowed slow initial

pumpdown in order to avoid blowout of the sample from the

Knudsen cell. A single thermocouple gauge at the intersec-

tion of the roughing line and the high-pressure port of the

diffusion pump was used to monitor the progress of rough

pumping, or to ensure that back pressure was less than 20 p

when the diffusion pump was open to the furnace. An ioni-

zation gauge mounted between the furnace and gate valve

monitored system pressure between 10-3 and 10-7 torr while

the diffusion pump. was in operation. Both the ionization

and thermocouple gauges were operated by a Granville-Phillips

Series 270 Gauge Controller. The ultimate pressure of the

vacuum system was 4 X 10-7 torr with the liquid nitrogen

trap filled and the furnace off.


-0 >
04Mr-I -
0 4 0) 0

00 0Q-

+} (U

EO Oa 0

pj i o 0
c0 4 .l 4 Mu 4

r4 4 (



- oi a) o

2 -H >, 0

0 0
01 = r --

>C 4 --
.U 4 -1
O l 7



Sample molecules effusing from the Knudsen cell passed

through the furnace heat shield and impinged on the sample

window with an excess of molecules from the matrix gas inlet.

The sample window was a 1" diameter, 1/4" thick CaF2 window

tightly sealed by indium gaskets within an oxygen-free

copper window-holder. The window-holder was connected by a

1/4"-28 screw and an indium gasket to the second stage of a

Displex R CS 202 Closed-Cycle Helium Cryostat which had a

temperature range of 100K to 3000K. The temperature was

controlled by a 10 W, variable duty cycle heater attached to

the cold tip. The sample window was surrounded by a heat

shield maintained at 770K to reduce radiative heat reaching

the window. Three holes in the heat shield allowed sample

deposition and spectroscopic access. Suprasil-1 quartz

windows (2" diameter) were attached to three sides of the

cryostat shroud by O-ring seals. The remaining side of the

shroud was connected by a stainless steel flange and O-ring

seal to the evaporation furnace. A Kp/Au -0.07 at. % Fe

thermocouple was mounted at the bottom of the sample window-

holder to provide an upper-limit measurement of the sample

temperature. A temperature gradient of 20K was observed

between the top and bottom of the window-holder. The cryo-

stat was mounted to allow rotation by 900 in either direc-

tion after sample deposition in order to perform spectro-

scopic experiments on the sample.

The rare gas inlet system is shown in Figure 10. Ace

Glass Company Teflon R valves with O-ring seals were

employed in the glass line. A Hoke 1/4" stainless steel

0) Cr-
*H N
-l 0 *N
>i 0 r.
U 41i r -H

(0 ) r )

q-I C EC
0 *H 0 rd

C 0 0O


0 p
S-*I 41 z rd
0) En -*4 P 0 g

H -H N I

14 C* C N 3







C~ ~"~'~;"~i~~"E~;1-"i~i~

needle valve controlled rare gas loading into the system. A

Nupro 1/4" Extra Fine Metering Valve controlled gas flow to

the inlet nozzle. The three-liter reservoir bulbs made it

possible to store two different matrix gases at once,

increasing efficiency of gas-loading procedures. Gas flow

rates were measured by pressure changes observed in a

mercury sidearm manometer. Before gas loading, the system

was baked at about 600C under high vacuum for several days

until a pressure below 1 X 10-6 torr was observed on the

attached ion gauge. Gas flowing from the manifold was

passed through a liquid nitrogen trap and into the sample

system through stainless steel tubing.

The primary consideration in operation of the matrix-

isolation apparatus was the prevention of atmospheric or

water leaks into the system. During construction, component

parts were separately checked for leaks with a CVC MS-9

Helium Leak Detector. The entire system was examined with

the leak detector after major modifications. The only

recurrent leaks encountered after cleanup and reassembly

were in the Suprasil window O-ring seals and the flange seal

at the rear of the furnace. These leaks were generally

detected by spraying acetone on the suspect seal and noting

pressure drops in the ionization gauge signal.

Spectroscopic Apparatus

Components comprising a double-beam absorption spec-

trometer or, with minor modifications, a magnetic circular

dichroism spectrometer were mounted on a pair of 3' X 4'


aluminum tables constructed so that power supplies and pumps

could be easily mounted beneath. the work surface. Pump

vibration was reduced by foam rubber and styrofoam insula-


Optical Train for Absorption Experiments

Optical elements were positioned so that the sample

light beam travelled a path collinear with the sample window

and parallel to, but 15 1/4" above, the work surface.

Figure 11 is a diagram of the optical train for the absorp-

tion experiment. The source employed in most MCD and

absorption experiments was a Varian Associates 300-watt
Eimac high-pressure xenon lamp. This lamp was chosen

because of the high radiant flux and the well-collimated

beam provided by a parabolic reflector built into the lamp

housing. Ozone generated by the ultraviolet output of the

lamp was removed from the laboratory by a fan and duct

system mounted above the enclosed source area. The output

of the lamp was adequate for spectroscopy between 2500 and

8500 A, but xenon emission lines caused some signal-handling

problems, especially between 7500 and 8500 A. In some

experiments an Osram 55 W tungsten lamp was used to measure

spectra in the region above 7000 A.
The unfocused output of the Eimac Rlamp entered a

Spex 3/4 m Czerny-Turner Spectrometer with a 1200 line/mm
grating blazed at 3000 A and an aperture of f/6.8. The

spectrometer was generally operated with a band pass of 1.5

to 3.0 X since Ar and Kr matrices rarely had spectral fine


,D j1









U 0


. S


1 9 C

c 4I






structure resolvable below 2 A. Output from the monochro-

mator was collimated by a quartz lens and divided by a

double chopping wheel into a sample and reference beam. The

reference beam was reflected by two Edmund Scientific alumi-

nized front-surface mirrors around the cryostat and into the

detector. The sample beam passed directly through the

cryostat and sample to the detector.

The detector used in all experiments was an EMI 9683QB

photomultiplier tube enclosed in a FACT-50 R cooled housing.

The response curve of the tube followed the extended S-20

range so that the tube was adequate for detection of signals

over a spectral range of 2000-8500 X. The signal was

preamplified to give a voltage output for the reference and

sample signals in the absorption experiment.

Optical Train for MCD Experiments

The optical train for the MCD experiment is shown in

Figure 12. Light from the monochromator was collimated by

an f/7 quartz cylindrical lens positioned 7" from the exit

slit of the monochromator. The beam was then polarized by a

Glan-Thomson prism oriented at 450 to the optic axes of a
PEM-3 photoelastic modulator manufactured by Morvue Elec-

tronic Systems. The resultant beam from the operating

modulator was a 50 HKz signal alternating between LCPL and

RCPL. The circularly polarized light passed down the axis

of an Alpha Model 4600 electromagnet which had a 4" adjust-

able pole force gap. The magnet was mounted by open ball

bushings on case-hardened steel tracks so that it could be


moved easily into a position collinear with the center of the

sample window for MCD experiments. The absorption reference

beam mirrors and chopping wheel were removed for the MCD

experiments. Components in the MCD optical train were

aligned so that no signal was detected by the lock-in ampli-

fier without a matrix sample present.

Absorption Signal Handling

A diagram of the signal-handling electronics for

absorption experiments is given in Figure 13. The preampli-

fied voltage output of the photomultiplier tube was fed to

two phase-sensitive detectors. An Ithaco Model 353 Phase-

Lock Amplifier detected the reference signal at 150 Hz while

an Ithaco Dynatrac 391A Lock-In Amplifier detected the

270 Hz sample signal. Both amplifiers were supplied with

appropriate reference signals from the chopping wheel. The

outputs of the phase-sensitive detectors were converted to

log form and subtracted by a Semiconductor Circuits Inc. Log

Amplifier giving an absorbance output in the range 0.0 to

1.0. A Texas Instruments potentiometric recorder and a

microcomputer interface recorded the output from the Log

Amplifier. The computer interface contained a Datel EK8B

analog-to-digital converter set to digitize the absorbance

signal for storage on cassette tape by a Commodore PET-2001

microprocessor. The interface also allowed computer control

of the monochromator stepping motor so that the entire

spectrum of a sample could be obtained under program control.











." 0



,-} I

03 ^-


f i
Cd 0
1x W






MCD Signal Handling

Signal-handling electronics for the MCD experiment are

diagrammed in Figure 14. The non-amplified voltage output

of the photomultiplier tube consisted of a 50 KHz AC compo-

nent superimposed on a DC level proportional to the source

intensity and the sample absorbance. The DC component was

maintained at a constant value by passing the DC level to a

feedback loop. An error amplifier read the difference

between the desired DC level set by the operator and the

actual DC output of the PM tube. This difference voltage

was used to control the output from a Bertan PMT-20

programmable high-voltage power supply to the PM tube. The

resultant constant-voltage DC signal level compensated for

variations in lamp intensity and sample absorbance.

The MCD signal was detected by the Ithaco Model 353

Phase-Lock Amplifier which was locked into a 50 KHz refer-

ence signal from the PEM-3 modulator power supply. The

bipolar output of the phase-sensitive detector was shifted

by a constant positive voltage level to allow sample digiti-

zation by the computer interface and output by the potentio-

metric recorder. The computer controlled the monochromator

stepping motor as in the absorption experiment, but in the

MCD experiments the computer also provided the appropriate

voltage level to the modulator for quarter-wave retardation

at each wavelength during the scan. The maximum storage

capability of the computer was 2,000 data points for both

MCD and absorption scans. Since the points were taken at

r----------- --T


each integral wavelength, the MCD or absorption spectrum of

a sample from 2500 A to 8500 K required three tape cassette

data files. The reader is referred to the Ph.D. disserta-

tion of Powell26 for a thorough treatment of computer

programs for data collection and analysis.




In this section the general experimental procedure

followed in obtaining a matrix-isolated sample and per-

forming spectroscopic analysis on the sample will be

presented. Calibration experiments performed on the appa-

ratus also will be discussed. Specific experimental details

for particular molecular species studied will be presented

with the discussion of those systems.

Matrix Isolation Procedure

Fresh tungsten or tantalum Knudsen cells were outgassed

at 22000C for 1/2 hr to release interstitial hydrogen trapped

in the metal lattice during reductive extrusion. The outgas-

sing was accompanied by a considerable pressure rise in the

system. The outgassed cell was loaded through the cell effu-

sion hole with the chosen metal oxide. During attachment of

the cell assembly, the effusion hole of the cell was aligned

with the 1/8" holes in the furnace heat shield. Cleaning

procedures during cell loading included washing all windows

in the vacuum system and removal of dust and films from metal

surfaces in the system with tissues soaked in acetone.

Whenever O-ring seals were uncoupled during loading, the

0-rings were regreased with Apiezon NR vacuum grease. Fol-

lowing reassembly of the vacuum system, the diffusion pump

was isolated by closing the valve on the high pressure port,

and the bypass line valve was opened far enough to make pump

gurgling audible. Very little sample escaped from the Knud-

sen cell if rough pumping was carried out over a period of 5

to 10 min. After the system pressure was below 200 p, the

high pressure port valve of the diffusion pump was reopened.

The bypass valve was then closed,and the CVC gate valve was

opened gradually so that the thermocouple gauge pressure on

the high pressure side of the diffusion pump did not exceed

200 j. With the gate valve fully open, system pressure was

observed on the ion gauge controller. When the pressure

dropped below 3 X10-5 torr, the liquid nitrogen trap was

filled. After ensuring that water was flowing in all system

cooling lines and that the cryostat sample window was not

turned toward the furnace, the operator gradually increased

the temperature of the Knudsen cell, ensuring that the system

pressure did not rise above 2 X10-5 torr. This gradual pre-

heating of the Knudsen cell prevented the loss of sample

which had been observed in early experiments.

Preheating of the Knudsen cell to operating temperature

eliminated adsorbed species in the sample, allowed reduction

of the sample to a thermodynamically stable form, and served

to clean furnace surfaces exposed to radiation from the cell.

The cell was then cooled to 8000C and left at that tempera-

ture overnight. The sample window was turned to allow the


observation of the Knudsen cell. Alignment was considered

satisfactory if the effusion hole of the cell could be seen

along the entire circumference of the sample window.

On the morning of the experimental run, the Knudsen

cell temperature was gradually increased to within 2000C of

the deposition temperature. The Displex R compressor was

then turned on, and the Knudsen cell temperature was

increased to operating temperature while the cryostat cooled

to deposition temperature in a period of 1 hr. The Knudsen

cell temperature was decreased by 1000C, and the sample

window was rotated to the deposition position. The host gas

line vacuum trap was filled with liquid nitrogen, and the

host gas was deposited for 10 min before the Knudsen cell

temperature was once again increased to the desired operating

temperature. Knudsen cell operating temperatures were

employed which allowed deposition of a suitable sample

matrix in a period of 1 hr or less. Rare gas flow rates

were generally in the range of 1 to 3 mmol/hr. Higher flow

rates resulted in considerable polarization scrambling in

MCD experiments and scattering losses in absorption experi-

ments, which decreased observable signals. The host:guest

ratios in all matrices were estimated to be above 1000:1.

Spectroscopic Analysis

After deposition was complete the sample window was

rotated by 900, and sample and reference beams were aligned

for absorption spectroscopy. The sample beam was adjusted so

that the light did not pass through the area of the matrix

where the host gas nozzle blocked sample deposition. The

PET computer operating program was loaded, and an absorption

spectrum was run over the spectral region of interest. If

necessary, a subsequent deposition was performed to give

maximum absorbance bands in the range of 0.5 to 0.95. The

spectroscopic apparatus was then modified so that a prelimi-

nary MCD spectrum could be taken. The optical components

were adjusted so that a maximum DC output level could be

obtained. The spectrum was then scanned manually, and the

lock-in amplifier sensitivity and feedback voltage level were

adjusted so that the largest MCD peak was near full-scale on

the chart-recorder. The MCD spectrum was then recorded

under computer control. All MCD and absorption spectra

taken with aid of the computer were stored on cassette tapes

for later analysis.

Subsequent to preliminary experiments the Ar matrix

samples were annealed at 30-330K for at least 1/2 hr. Post-

annealing MCD spectra were taken at 140K and 240K for mole-

cules with no temperature dependent bands and at intervals

of 2-30K between 140K and 250K for molecules in which Co

terms were observed. The zero-field spectrum and calibra-

tion factors were obtained to complete the MCD analysis.

Post-annealing absorption spectra at 140K and 240K were then

recorded and stored. While recording of spectra was

generally not completed until 18-20 hr after completion of

the deposit, no impurity bands were ever observed to develop

in MCD or absorption spectra after the initial deposition.

Calibration Procedures


Before experimental study of any systems was commenced,

the calibration of the monochromator was checked by obser-

ving the wavelength of lines from a 4 W Spectra-Physics

Argon Ion Laser. The wavelengths for all lines observed

were within 0.5 A of known values. In a separate experiment

it was noted that wavelengths measured for absorption peaks

depended on the direction of scan, even at slow scan rates.

The variation was caused by backlash in the stepping gear

assembly leading to deviations of up to 1 A in observed peak

positions. The backlash error was systematized by always

recording spectra while scanning from long to short wave-



The magnetic field of the electromagnet was calibrated

with a F. W. Bell Model 640 Gaussmeter. Field measurements

were made with a pole face gap of 2.5" which was maintained

in all MCD experiments. A plot of field intensity vs. power

supply current is given in Figure 15. MCD spectra were

recorded at the maximum field of 5.5 kG. The residual field

observed between the pole faces with the magnet power supply

off was 62 G. "Zero-field" baseline values were thus actu-

ally taken under the slight residual field. In some experi-

ments the strongest MCD peaks could be observed during the

"zero-field" scan if the lock-in amplifier was placed on a


O rd


0 -

3 t

41 m
l <

Car n
w ec









(ssntef)OTTY) Hi
q48u24S ~a~ OT4uBP


high sensitivity scale. There was some concern that photo-

multiplier efficiency would be affected by the magnetic

field at the end of the magnet during MCD runs. At full

power the field was observed to vary from 150 G at 0.5" from

the magnet to 19 G, 6" away. The face of the detector was

placed 4" from the end of the magnet where the field

strength was 38 G. The DC component of the photomultiplier

output with field on was less than 5% lower than with the

field off; the detector performance was considered adequate

without further modification.

Calibration of MCD Data

In order to calibrate the intensity of MCD transitions

the complex salt [Co(en) 3]Cl*(d-tartrate) was chosen as a

standard. The salt was synthesized according to the proce-
dure of Broomhead et al. The measured specific rotation

a D] was 1030 as reported by Broomhead. The circular

dichroism and absorption spectra were measured by McCaffery

and Mason.28 For the prominent band with absorption maximum
at 4690 A and CD maximum at 4930 A, the value of AA /A
max max
was found to be 0.0225. Following the procedure of Tacon29

a solution of the standard was prepared that had a measured

absorbance of 1.00 at 4690 A. Each time a matrix sample was

studied by MCD, the AA/pV was applicable to all spectra

taken at the same DC feedback voltage as the calibration

solution. During early experiments it was verified that

changes of sensitivity between the scales 10, 30, 100, and


300 pV of the Ithaco lock-in amplifier did not introduce

significant error in the measurements.

The final factor necessary in measurement of the MCD

spectra was the determination of the zero-field line for the

spectrum. Ideally, under zero-field conditions all differ-

ential absorbance should disappear. Deviation from AA = 0

could be caused by birefringence in optical components

between the modulator. and the photocathode of the detector

or by the presence of an optically active sample such as the

calibration solution. Considerable birefringence was

observed in the zero-field spectra of matrices prepared in

early experiments. A procedure was devised whereby the

origin of the birefringence problem could be traced. An

analyzing polarizer was placed immediately before the

detector and oriented at 900 to the polarizer. With the

optical components of the MCD experiment in place, the maxi-

mum birefringence signal was 3pV at 3800 A. The magnitude

of the signal was continually measured as the quartz sample

window was cooled to operating temperature; the amplitude

increased to 160 iV at 14K. Therefore, the birefringence

arose from strain developing in the quartz sample window

upon cooling. When a CaF2 sample window was used instead of

quartz, the maximum birefringence observable at 14K

decreased by 97% to 5 pV. The small strain birefringence of

CaF2 was surprising since both CaF2 and quartz are employed

as modulator materials. The development of strain bire-

fringence in quartz at low temperatures also has been noted

by Denning.3

With the CaF2 window MCD spectra showed no birefringent

interference. Digitized zero-field values varied by less

than 1% over the spectral range studied for most systems.

In calibration of digitized MCD spectra it proved convenient

to simply subtract a single digital zero field value from

all.stored MCD data values to obtain bipolar digital inten-

sity values. The conversion of stored digital values to

units of AA was then straightforward.

S= 022 S(s) I(s) I (z) (48)
AA = 0.0225S-5 iA() z) (48)
[S(c) I X (c) 1I (z)


S(s) = amplifier sensitivity scale of sample

S(c) = amplifier sensitivity scale of calibration

I (s) = digital MCD value of sample at wavelength X

I (z) = digital MCD value of zero-field at wave-
length X

I (c) = digital MCD value of calibration solution
at 4930 A.

Calibration of Absorption Data

The log amplifier was adjusted in a region of no sample

absorption to give an output of 0.0 on the chart recorder.

The output voltage was then set to give a full scale reading

for a matrix absorbance of 1.0. A solution sample of

[Co(en) ] *C(d-tartrate) with a known absorbance of 1.0 at

4690 A verified the calibration of the log amplifier.

Actual absorbance values for the sample were affected by the


amount of scattering by the matrix, which increased with

photon energy as expected.




The diatomic oxides of Group IV B are among the most

thoroughly studied of all transition metal molecules. While

the thermochemical and spectroscopic behavior of TiO has re-

ceived the most attention, ZrO and HfO are well-characterized

considering the difficulties involved in their production.

An approximate molecular orbital (MO) diagram for TiO based

on the ligand field approach is shown in Figure 16. Ab initio

calculations by Carlson and Moser31 and Carlson and Nesbit32

have indicated that valence electrons adopt a 6a configura-

tion because large 6 repulsion energy prevents electron

pairing. The 6 electron is localized on the Ti atom while

the a electron density is predominantly on the 0 atom, as

shown in a later study by Carlson and Moser on the isoelec-

tronic molecule ScF. The electronic ground state must be

either A or 1A based on the calculated electron configuration.

Matrix isolation experiments on TiO, ZrO and HfO by Weltner
34 3
and McLeod34 confirm the ground state assignment as A based
on the comparison of the ground state vibrational frequency

with the value for the 3A state observed in the gas phase and

on the observed energies of excited 3, 3 and I states.
and II states.



Figure 16. Approximate molecular orbital
diagram for TiO.




In the cases of ZrO and HfO, however, similar comparisons

lead to the assignment of 1I+ as the ground state of both

molecules. In the heavier oxides it appears that electron

correlation effects cause a reversal in the positions of the

valence 6 and a orbitals with a resulting ground state elec-

tron configuration of a for ZrO and HfO.

Brewer and Green summarized the early work on the isoe-

lectronic series ScF, TiO and ZrO35 in 1969. Their analysis

correlates the known experimental band positions with those
calculated by Carlson et al. 3 The transitions in the

three molecules are shown to occur with approximately the same

energy ordering. Matrix isolation has been very useful in

establishing the relative ordering of the states because the

inversion of ground states allows the observation of both

singlet and triplet manifolds in the isoelectronic series.

Photoluminescence studies on TiO6 and ZrO have proposed

values for the separation energies of the singlet and triplet

manifolds in these molecules. The 1A state of TiO is proposed

to be 3500 cm-1 above the A state based on an observed tran-
sition from the b I state to the X 3 state. The A state
of ZrO is proposed to be 1650 cm-1 above the 1 + ground state.

Predicted MCD of TiO, ZrO and HfO

The observation of forbidden transitions in absorption

by the MCD technique would serve to confirm the proposals of

Brom and Broida16 and greatly aid in the calculation of sta-

tistical weights of various states in high temperature

studies. Predicted excited states resulting from electronic

excitation for TiO, ZrO and HfO are shown in order of in-

creasing energy in Table 1.34 One may easily calculate the

MCD terms for allowed transitions to the various excited

states. Assuming case(a) coupling for all three oxides,

transitions allowed for TiO are shown in Figure 17, and those

allowed for ZrO and HfO are shown in Figure 18. In TiO pos-

itive A terms are calculated for both the 30 + 31 and

3 2 31 transitions, while the 31 3 transition is

allowed in ZFA but not MCD. In ZrO and HfO i1 1 + bands

are allowed in MCD. Transitions to other states are not

allowed in case(a) coupling but 31 1 transitions may

occur in MCD if coupling approaches case(c) for the heavier

oxides since the ZE =Al selection rule would be obeyed. The

spectra of the major band systems for the Group IVB oxides

are presented here to demonstrate the validity of the predic-

tions and to enlighten later discussion of the Group VB

oxides. A detailed analysis of the experimental conditions,

peak positions, and fine details of observed spectra is

given by Powell.26

Observed Spectra of TiO

The ZFA and MCD spectra of TiO isolated in Ar at 14K

are shown in Figure 19. The assigned transitions indicated

follow those of Weltner and McLeod.34 The appearance of

positive A terms for transitions to IT and 3 excited

states confirms the previous assignments. The weak bands

seen to the red of all vibrational bands for TiO are appar-

ently due to another species since they are


Excited States of TiO, ZrO and HfOa


Excited States

TiO [ground state A (so)]



'A (low-lying)

3 1
1 + (low-lying)

3I, -II
3 1 3 1
3 I1 3T, I I

3 1
3 + 1+





2 3,- 1C+ 1
# L F

ZrO and HfO [ground state 1 +(o2)]

6 A 1r A (low-lying)

4al 3 'I 1,

32* 1ll
400 3 + 1 +

3 2I*2 3a, 1i 3 H, 1K+ 1 1 1

3 2 3 ., 1

a W. Weltner, Jr.

and D. McLeod, Jr.34
and D. McLeod, Jr.

Figure 17. Allowed MCD transitions of
TiO in case (a). For both
the 31o 3A and 3 1
transitions, the calculated
value of Al/.o is +a.

+3 -i +2
-3 +1 -2

+1 -I 0
--1 +1 0


__2 1 -1




Figure 18. Allowed MCD transitions of
ZrO and HfO in case (a).
The calculated value of
A,/Do is +.












> r
4 r









+ :< I







temperature-dependent C terms. The strength of the subsidi-

ary bands is proportional to the magnitude of Ti atom peaks

observed in the UV. Powell26 investigates the possibility that

the subsidiary peaks may be assigned to either TiO2, (TiO)2

or Ti.**TiO. It is of particular interest that a close

examination of the spectra taken by Weltner and McLeod

reveals the presence of the same peaks.36

The absence of any MCD bands for the a system indicates

that TiO is best described by a case(a) coupling scheme.

The appearance of Al terms is expected if the coupling of

angular moment is intermediate between case(a) and case(c).

Observed Spectra of ZrO

The ZFA and MCD spectra of ZrO isolated in Ar at 140K

are shown in Figure 20 and Figure 21, respectively. The
band system starting at 3578 A was identified by Weltner as

the A + X E+ system while the systems at 6633 A and

6024 X were tentatively assigned to 1I 1 + transitions.3

Balfour and Tatum37 have since confirmed the existence of a
1 o
H gas phase system with a (0,0) band head at 6495 A while
Phillips and Davis have identified a new gas phase singlet

system at 5860 A. The matrix MCD results confirm the

assignment of Phillips and Davis for the system at 6024 A,

and those of Weltner for the other two systems. A B term

is observed for the lower energy 1 + excited state which

probably arises from field-induced mixing with the nearby I1

state. The MCD transitions in the region 3500-4000 A are

CO terms resulting from transitions in Zr atoms.









N 4r1



83 0

0 LO

+ 0



M -C

-- f -

,-.___________ ,, !








u z













Observed Spectra of HfO

The ZFA and MCD spectra of HfO isolated in Ar at 14K

are shown in Figure 22. The band systems assignments follow

those of Weltner and McLeod34 and Edvinsson and Nylen.39

The MCD spectra confirm the previous assignments by the

appearance of Al terms for the D and E bonds and the absence

of MCD for the F and G systems. The A term of the E system

is much broader and weaker than that of the D system because

the absorption bands are so broad. The derivative of the

absorption line shape changes slowly with wavelength. When
this factor ofj
this factor of equation (22), is included, the resultant

A. term is expected to be weak. The broad negative C term

observed at 3400 A is possibly a transition of HfO2.

Figure 22. ZFA and MCD spectra of
HfO isolated in Ar at 140K.




abs. AJ

mcd .

I I I |