Title: Electron spin resonance of collision complexes
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Title: Electron spin resonance of collision complexes
Physical Description: viii, 258 leaves. : illus. ; 28 cm.
Language: English
Creator: Martinez de Pinillos, Joaquin Victor, 1941-
Publication Date: 1974
Copyright Date: 1974
 Subjects
Subject: Electron paramagnetic resonance   ( lcsh )
Collisions (Nuclear physics)   ( lcsh )
Chemistry thesis Ph. D
Dissertations, Academic -- Chemistry -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
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Thesis: Thesis--University of Florida.
Bibliography: Bibliography: at end of each chapter.
Additional Physical Form: Also available on World Wide Web
General Note: Typescript.
General Note: Vita.
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Bibliographic ID: UF00097552
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
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Resource Identifier: alephbibnum - 000585171
oclc - 14198398
notis - ADB3803

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ELECTRON SPIN RESONANCE OF COLLISION COMPLEXES


BY

JOAQUIN VICTORMARTINEZ de PINILLOS




















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


UNIVERSITY OF FLORIDA
1974


























TO

JOAQUIN JAVIER

AND

VICTOR IGNACIO











ACKNOWLEDGMENTS


The author wishes to acknowledge Dr. William Weltner,

Jr., for his support and encouragement. He also wishes to

recognize the special help received from Dr. Weltner's entire

research group, primarily from Dr. W. R. M. Graham for his

help in running the MAGNSPEC 3 program and his very lucid

discussions about ESR; Mr. Clifton H. Durham, Jr., for his

help in proofreading and editing the manuscript; and Mr.

Warren D. Hewett for very helpful discussions.

A very special word of thanks is due to the author's

wife, Carmen, whose help was deeply appreciated, mainly,

during the periods of anxiety and depression when her words

of reassurance made the outlook a bit brighter. A special

recognition is due to the author's mother for all she has

done for him and whose help was indispensable during these

last few years.

The author also wishes to acknowledge the National

Science Foundation (NSF) for support during the period of

this research.











TABLE OF CONTENTS

Page

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

ABSTRACT . . . . . . .. . . vii

CHAPTER
I INTRODUCTION . . . . . . . .
Experimental . . . . . . . . 2
Apparatus . . . . . . . . 2
References . . . . . . . . 9

II ESR THEORY . . . . . . . .. 10
Introduction . . . . . . ... 10
Diatomic Molecules . . . . . .. 11
Phenomenological Hamiltonian . . .. 13
Hyperfine Tensor . . . . . . 14
g-Tensor . . . . . . .. .16
Comparison Between Ag1 and the
Spin-Doubling Constant . . . .. 21
Angular Dependence of the Spectrum . .. 22
Molecular Interpretation of ESR
Parameters ............. .24
Spin Density Functions . . . .. 25
Details of the Spectra . . . .. 30
References . . . . . . . .. 37

III M+CI; . . . . . . . . .. .39

Introduction . . . . . ... .39
Experimental . . . . . . . .. 40
Method of Preparation of the M+ Cl 40
Observed Spectrum of M+C12 ....... 42
Mg+C12 . . . . 49
+-2
Ca C12 . . . . . . ... .53

SrC12 . . . . . . ... .58

Ba+Cl2 . . . . . . . . 62






TABLE OF CONTENTS (Continued)

CHAPTER Page

III (Continued)
Li+Cl2 ................ 66

Na'Cl . . . . . . . .. 72

K+C12 . . . . . . . ... 76
Discussion . . . . . . ... .80
Linewidths . . . . . . ... .93
CNDO Calculation ........... 96
Temperature Variation Experiments . 97
Optical Experiments . . . ... 98

M+Cl- . . . . . . . ... .99
M and M . . . . .... .. . 100
Summary . . . . . . ... 103

References . . . . . . . ... 104

IV M+FF 106
IV M+F2 . . . . . . . . . .. 106

Introduction . . . . . ... 106
Experimental . . . . . . . . 110
Method of Preparation of M F2 . 110

Observed Spectra of M F2 ....... 111

K F2 . . . . . . . ... .121

Ca +F 125
Ca .F2 . . . . . . . .. 125

Mg+F2 ................. 128

Ba+F . . . . . . . .. 132

Discussion . . . . . . ... 132
Linewidths . . . . . . ... 146
INDO Calculation . . . . . .. 149
M+ Ions . . . . . . ... 150
Summary . . . . . . ... 150

References . . . . . . . ... 152







TABLE OF CONTENTS (Continued)


Page


APPENDIX A -



APPENDIX B -


APPENDIX

APPENDIX


APPENDIX E -


PROGRAM TO SIMULATE THE ESR SPECTRUM
OF 2Z MOLECULES TO SECOND-ORDER
PERTURBATION THEORY . . . . . .

MATRIX ELEMENTS FOR THE SPIN
HAMILTONIAN OF Cl ......
2
LEAST-SQUARES FIT FOR A LINEAR FUNCTION

MATRIX ELEMENTS AND PROGRAM FOR BENT
F- NON-COLLINEAR A- AND g-TENSORS . .

MATRIX ELEMENTS AND PROGRAM FOR
LINEAR F COLLINEAR A- AND g-TENSORS
2


BIOGRAPHICAL SKETCH . . . . . . . . .




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

ELECTRON SPIN RESONANCE OF COLLISION COMPLEXES

By

Joaquin Victor Martinez de Pinillos

August, 1974

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

Reaction complexes formed when alkali and alkaline-

earth atoms are allowed to react with either Cl2 or F2

were isolated in argon matrices at 4 K. Ionic complexes are

formed where the halogen occurs as essentially X2, which is

observable via electron spin resonance (ESR) spectroscopy.

The metals used in the case of Cl2 were Li, Na, K, Mg, Ca,

Sr, and Ba; for F2, Na, K, Cs, Mg, and Ba were used. In

all cases, except for Cs, the atoms were produced by heating

the metal to a temperature where its vapor pressure was of
-l
the order of 101 torr in a Knudsen cell. Cs metal atoms were

prepared by reaction of Cs2CrO4 with Si in a Knudsen cell.

The complexes produced are too short-lived in the gas phase

to be studied by conventional spectroscopic techniques.

The hyperfine interaction observed shows that the inter-

mediate trapped was primarily M X2. This ion pair is very

loosely coupled and the ions can be treated independently of

one another. The presence of the metal can be detected, in

the cases where it has a magnetic moment, by the broadening





it produces on the X2 lines. It also indicates that the

electron is in a 2Eu state with a wavefunction composed mainly

of po-orbitals with very small s-orbital contribution. The

increase in the hyperfine splitting with decreasing ioniza-

tion potential of the metal indicates that the electron

resides mostly on the X2 species as expected.

The properties of some of the excited states were

studied by the variations observed in the components of the

g-tensor. It was found that a low-lying 2H state is mixed
u
with the ground state via spin-orbit coupling for the case

of Cl2 and that this state is inverted (since the observed

shift from g is positive). On the other hand, it was found

that in the case of F2 the presence of the metal ion per-

turbed the system enough to cause a splitting of the linear

molecule states and mix in an excited 2A1 state with the

resulting 2B1 ground state.

It was interesting that the presence of the M ion was

detected when the alkaline-earth metals were used in the C12

but not in the F2 experiments. This was interpreted as

another indication of the degree of interaction between the

metal ion and X2. In Cl2 the interaction was "loose" and

allowed for observation ot essentially independent ions;

in F2, the coupling was "tighter" and this broadened the M

line, making it unobservable.

The presence of the MC1 molecules, where M was Mg, Ca,

and Sr, was also detected. In the experiments with F2,

only MgF was detected.

viii










CHAPTER I


INTRODUCTION



The technique of electron spin resonance (ESR) has been

widely used to study molecules and ions with unpaired elec-

trons. In many instances, the intermediates in some chemical

reactions are paramagnetic, which renders them very attractive

to the ESR spectroscopist. The major problem he confronts is

that many of these intermediates are extremely short-lived

and, therefore, their study via conventional methods is, at

best, difficult.

With the advent of matrix isolation techniques in which

species can be trapped at very low temperatures (usually

4-20 K), these intermediates can now be isolated and studied

in a gas-like environment. Some recent studies have been

carried out on transition metal ions [1] and of some molecules

formed as intermediates in chemical reactions [2,3]. The main

advantage of this technique is that the molecular information

obtained is gas-like within a few percent. Extensive details

and reviews of the matrix isolation technique as applied to

atomic and molecular studies have been given by Bass and

Broida [4], Jacox and Milligan [5,6] and Weltner [71.








Experimental


Apparatus

The apparatus used to study the reaction intermediates

described here will be discussed in this general section.

Details of the preparation of different molecules as well as

variations from the main structure of the apparatus will be

discussed under each specific heading.

The Dewar was adapted from a design of Jen, Foner,

Cochran and Bowers [8]. Some of the important features of

the apparatus are shown in Figure 1. The sample in the fur-

nace was always placed in a tantalum cell (1" long by 0.25"

I.D., 0.025" wall) and firmly attached to two water-cooled

electrodes. The electrodes were then connected to a power

supply and the cell was heated in a resistance fashion.

The "inert solids" were research grade argon and neon

gases (purity 99.999%) obtained from commercial sources and

used without further purification. The trapping surface con-

sists of a flat single-crystal sapphire rod (13 long, 1/8"

wide, 3/64" thick). The rod is securely embedded in the inner

Dewar where it is cooled to approximately 4 K by contact with

liquid He. In some cases, the temperature of the rod was

monitored by a chromel vs. gold plus 0.07at%-iron thermocouple.

This was done when the temperature of the rod was allowed to

change in order to anneal the matrix and observe the appear-

ance or disappearance of some features. The thermal



































WATER-COOLED
ELECTRODES
TEMPERATURE


WINDOW


CAVITY


Figure 1. Dewar and Furnace Apparatus


ROTATABLE
FLAT
SAPPHIRE
ROD


BRIDGE









conductivity of single-crystal sapphire is very high so that the

rod was an excellent substrate for condensation of the inert gas

matrix.

The sapphire rod could be lowered into a microwave cavity

by a vacuum-tight bellows assembly located at the top of the

Dewar, and it could also be rotated 3600 inside or outside the

cavity. The front of the cavity is slotted so that photolysis

or specialized irradiation can be conducted while scanning the

ESR spectrum. The outer Dewar wall is equipped with a quartz

window to allow a wide range of photolytic light to be trans-

mitted to the matrix. When needed, for extreme ultraviolet

photolysis, LiF could be used for this window.

When the rod is outside the cavity, it is directly in

front of the nozzle that carries the gas mixture and in front

of the furnace window through which the vaporized metal comes

into the reaction chamber. The distance between the Knudsen

cell and the sapphire rod is approximately twelve centimeters.

The furnace is mounted on a movable table and attached to the

Dewar by a double gate valve which allows decoupling of these

two systems without breaking the vacuum in either. The Dewar

can then be rolled on fixed tracks between the pole faces of

the ESR magnet.

The Dewar and the furnace are individually pumped by

mechanical and 2" silicone oil diffusion pumps. The pressures

obtained before any cryogenic liquids are placed in the Dewar

are of the order of 2 x 10-5 torr. When all the traps are
are of the order of 2 x 10 torr. When all the traps are









filled with liquid nitrogen and the main Dewar filled with liquid
-8
helium, the pressure obtained is of the order of 5 x 10 torr.

The pressure in the furnace with its trap filled with liquid

nitrogen is of the order of 6 x 10-6 torr with the connecting

valve to the Dewar closed.

The inert gas was allowed to deposit for 5 minutes on

each side of the rod before the gate valve was opened to allow

materials vaporized in the furnace to come into the Dewar.

While the gas mixture was being deposited, the metal was being

warmed up to a temperature at which its vapor pressure was of
-l
the order of 101 torr. The gas was allowed to deposit at a

rate of about 0.6 1-atm/hr. This was accomplished by maintain-
-5
ing a pressure of about 3 x 10 torr in the Dewar as measured

by an ion gauge. The co-deposition of the metal and the gas

mixture or inert gas, depending on the nature of the experiment,

lasted approximately 30 minutes. The rod was turned 1800 every

five minutes in order to obtain an even surface distribution of

matrix material.

To observe ESR spectra of acceptable intensity, a ratio

of rare gas molecules to species under study of approximately

1000:1 is required. In the present case, much higher concentra-

tion of the X2 gases was required initially, perhaps because the

short half-lives of the intermediates made their trapping very

difficult. The concentration ratio was determined by trying dif-

ferent mixtures until sufficiently intense ESR signals were

obtained.








The instrument used to record the spectrum was the

Varian V-4500 Electron Spin Resonance Spectrometer employing

superheterodyne detection. The magnetic field was measured

with an NMR fluxmeter, whose frequency was determined with a

Beckman 6121 counter. The X-band microwave cavity frequency

was determined with a high Q wavemeter.

When annealing was considered necessary, the Dewar was

changed to one in which the amount of liquid helium in contact

with the rod could be varied. This consisted of a copper cyl-

inder connected to the main reservoir and to the outside via

another tube. The latter was fitted with a needle value (see

Figure 2). The liquid helium in the main reservoir would be

forced down by pressure and cooled the rod to 4 K. When an

increase in temperature was desired, the flow of liquid helium

into the lower copper chamber could be either reduced or com-

pletely stopped by closing the needle valve. This allowed the

temperature to rise while being monitored by the chromel-gold

thermocouple. When the desired level was achieved, the needle

valve was opened and the flow of liquid helium brought the

temperature down to 4 K again. The major disadvantage encoun-

tered with the variable-temperature Dewar was that the evapora-

tion rate of the liquid helium was much larger than for the

fixed temperature one. This made its utilization on a permanent

basis impractical when the matrix was to be studied for a long

period. Long studies could only be achieved by refilling the




















S ( .. .uL... 0

0


%S=-=j .4-





/ 0
0 -








Dewar with liquid helium, which was difficult when neon matrices

were used because they are very unstable and any small perturba-

tion can cause them to evaporate.

The annealing process was used when the presence of

different sites in the matrix was suspected or when the progress

of the reaction was to be followed over a temperature range.

Sites tend to obscure some features of the ESR spectrum and in

order to understand all the details, their removal may become

mandatory.

When the matrix was warmed in order to follow the reac-

tion, an expected observation was the disappearance of some of

the spectral features and the appearance of others. In most of

the systems studied, annealing had to be done very carefully

since the reactions involved were extremely exothermic and,

occasionally, the matrix was lost since the heat generated vapor-

ized the inert gas solid, destroying the vacuum and vaporizing

the liquid helium in the reservoir.












References


[1] Ozin, G. A., and Vander Voet, A., Acc. Chem. Res., 6,
313 (1973).

[2] Noble, P. N., and Pimentel, G. C., J. Chem. Phys., 49,
3165 (1968).

[3] Milligan, D. E., and Jacox, M. E., J. Chem. Phys., 53,
2034 (1968).

[4] Bass, A. M., and Broida, H. P., Formation and Trapping
of Free Radicals, Academic Press, New York (1960).

[5] Jacox, M. E., and Milligan, D. E., Appl. Opt., 3, 873
(1964).

[6] Milligan, D. E., and Jacox, M. E., MTP International
Review of Science, University Park Press (1972),
Vol. 3, p. 1.

[7] Weltner, W., Advances in High Temperature Chemistry,
Academic Press, New York (1970), Vol. 2, p. 85.

[8] Jen, C. K., Foner, S. N., Cochran, E. L., and Bowers,
V. A., Phys. Rev., 112, 1169 (1958).












CHAPTER II


ESR THEORY



Introduction

The systems of interest in this work consist of 2E

molecules in all cases; therefore, the description of the

theory will be restricted to these types of molecules.

A 2Z molecule consists of a linear molecule with an

unpaired electron and no angular momentum. When these mole-

cules are placed in a magnetic field, the degenerate spin

levels are split and a transition between them can be

induced. The energy difference between these levels is

approximately equal to g o H = hvo, where go is the free

electron g-factor (2.0023), Bo is the Bohr magneton
-21
(9.2732 x 102 erg/G), H is the magnetic field, h is Planck's

constant (6.6256 x 1027 erg sec) and v is the frequency of

the transition inducing radiation. It is then expected that

an absorption line at a given H value for the v of the

instrument will occur at the position of the g-value for the

molecule under study. In the present case, an X-band instru-

ment with v = 9400 MHz was used.

The Hamiltonian describing the interaction under study

was introduced by Dirac [1].







It can be shown (see McWeeny [2] and McWeeny and

Sutcliffe [3]) that Dirac's Hamiltonian can be broken down

into a sum of terms representing the different interactions

present in a molecule placed in a magnetic field.


Diatomic Molecules

The Hamiltonian V for a diatomic molecule with one un-

paired electron in an external magnetic field is given by


V= F + VLS +Z hf

where

yF = Hamiltonian of the free (non-rotating in this
case) molecule in the absence of spin-orbit

coupling and an external magnetic field.


5LS = Hamiltonian for the coupling of spin and orbital

angular moment of the electrons.


yZ = Zeeman energy arising from the interaction between

the electron spin, orbital and nuclear-spin mag-

netic moments and an externally applied magnetic

field.


Vhf = Hyperfine interaction arising from the electron-

spin magnetic moment interacting with any nuclear

moment present in the molecule.








The nuclear Zeeman term (H-I) and other types of inter-

actions will be neglected here since, in general, they are

very small, and in the cases of interest here, they are par-

ticularly small.

Since wT is much larger than any of the other terms,

A(S' ~ and 2hf can be treated as perturbations. The dif-
ferent perturbing terms are given by (for a detailed discus-

sion of these terms, see McWeeny [2], McWeeny and Sutcliffe

[3], and Hameka [4]).


ALS = EL*S (la)

WZ = H*(L + g S) (lb)

Whf = n o [L-I + 3(S-r)(r-I) SI



3 F ~
+ O S-I(rJ (Ic)


where L, S, and I are the orbital, electron-spin and nuclear-

spin angular momentum operators, H is the magnetic field,

Bo and Bn are the Bohr and nuclear magnetons, respectively,
g and g are the electronic and nuclear g-factors, respec-

tively. is the molecular spin-orbit coupling constant.

Shf, the hyperfine Hamiltonian of Eq. (Ic), consists of
three parts. The first term in square brackets involves

the interaction between the magnetic field produced by the

orbital momentum and the nuclear moment. This term will

necessarily be zero for a 2E molecule since L = 0, except








for any small orbital angular momentum entering through the

L-S interaction. The next two terms are related to the

interaction of two magnetic dipoles, the spin of the electron

and the nuclear magnetic dipole. The third part of Whf is

the isotropic Fermi or contact term and depends on the elec-

tron spin density at the nucleus since the Dirac 6-function

indicates that its value is zero unless r= 0. Within a simple

linear combination of atomic orbitals (LCAO) treatment it

can be seen that this term is a measure of the amount of

s-character of the wavefunction for the odd electron.


Phenomenological Hamiltonian

The spin Hamiltonian can be represented in a phenome-

nological manner by


spin = o H'g.S + I.A.S (2)

as has been shown in several texts (e.g., see McWeeny [2]).

In this expression, g and A are second-order tensors, where

all the interactions that may affect the Zeeman and hyper-

fine terms, respectively, are presented in a compact form.

For a diatomic molecule, it can easily be seen that

these tensors can be written as


x 0 0 gx 0 0
A = Ay 0 g = 0 gy 0

0 0 A 0 0 g








where the off-diagonal elements can be made equal to zero

by a suitable rotation of the axes (see the discussion on

each tensor below). If the z-axis is taken as parallel to

the magnetic field, Az and gz will then be called Al and g

respectively, while the x and y axes are perpendicular to

the parallel axis and therefore A and A and g and g will

be called A and g respectively. For a linear molecule,

gx and gy will be equal, as will be A and A since the two
directions are equivalent.


Hyperfine Tensor

As was seen in Eq. (Ic), the hyperfine tensor A will

comprise two types of interactions, one due to the amount of

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

one due to the non-s-character of the wavefunction (the mid-

dle two terms). Calling these two types of interaction Ais

for the one dependent on the s-character and Adip for the
dip
one dependent on the non-s-character of the wavefunction,

Eq. (Ic) can then be written


hf = iso + Adip] S- (3)

where Ai = g n (6(r)) = Trg2nn (o)
-ig 3 gnBng 0 rsngoso(o) 1 2

and Adip = nn 0 3 cos -)
2r3

The brackets indicate the average of the expressed operator

over the wave function i In tensor form, Eq. (3) can then

be written









Ahf = I (Aiso + T)* (4)

where T and Adip are related in a manner to be discussed.
dip
Equating the hyperfine tensor in Eq. (2) with the one in

Eq. (4) it is found that



0 A 0 = 0 Ai 0 + 0 T .
O AA. 00 s o

T can be shown to be (see Wertz and Bolton [5])T
T can be shown to be (see Wertz and Bolton [5])


2K--3X> 0 0


T -g gnn 0 0


0r r5 )
0-2 3-2-3




and, therefore, it is a traceless tensor. It has been

assumed that the off-diagonal elements are small and there-

fore have been equated to zero. From this fact, it can then

be seen that

Aiso (All + 2A )/3 .(5)

The relationship between T and Adip can be seen, for

some special cases. Referring to Eq. (3), it can also be

written

hf +ychf = [Ais + Adip] S I
so dip ~ ~








Therefore,


hfdip= (Adip) .I. (6)
dip


Since both S and I are quantized along H, taken as the

direction of the z-axis, the x and y components of S and I

may be neglected in Eq. (6). With the substitution z = rcos 6,

and for the special case of a p orbital centered on the

interacting nucleus, it can be seen (Wertz and Bolton [5])

that

Adip g 3 cos2 1 Al
=dip nn 2 > 2r (7)

(For more details see Frosch and Foley [6]).


g-Tensor

Let us assume that the solution to k gave us a wave-

function for the ground state of our molecule 10) and a

series of excited states In). If yLS is now applied as a

perturbation, to first order we get

(nI< S -s |0>
y = o0> + n In)
E E
n n 0

where yLS was defined in Eq. (la). (This is for a non-

rotating molecule.) If the spin is taken into consider-

ation, and in view of the fact that only one unpaired spin

is present, we can write two different wave functions








+) = O0a) -- L-SI _Oa In)
n E0
n

(n L *S 0)
I-) = lo0 n | O n)
n 0


where a and g refer to spin up or down as usual. This is

the so-called Kramer doublet representing degenerate wave-

functions, which will, however, have different energies in

a magnetic field (see Carrington andMcLachlan [7]).

Now, L-S can be written as

L*S = L S + L S + L S = L S + (L+S + L-S)
~ ~ xx y y zz zz

where L and S+ are the raising operators and L and S

are the lowering operators defined by

L =L i L
x y


S = S i S
x y

Since S acts only on

can be seen that


SzIa) = 1>a)

S+I) = 1a)

s-|l> = 0

Therefore, the nc

(a S+lB> =(

(a| Szl> =


the spin part of the wavefunction it


sl 10 =- o 1s)

S+la) = 0


S I ) = I)

In-zero spin integrals are

BI s-la> = 1

-,







and for a molecule where 10) is a E state,

( 0 Lz 10) = (n Lj 0) = (0[ LZ n) = 0.

Then Eq. (8) becomes


+>) = IOn (nlj E L 10) jng)
E -E
n n 0-


I-) = 10o I < L-10 na>
n E E

The Zeeman term of the phenomenological Hamiltonian

(Eq. (2)) was given by


S= 8 H.gS



S= B H. 0 gx 0 *S

0 0 1

but, from Eq. (lb), the Zeeman term is

v' = H. (L + g S)
S oa-
where the prime is introduced to differentiate it from the

phenomenological one.

From these equations, assuming that the magnetic field

is acting in the x-direction (if it acts in the y-direction

a similar result is obtained), it can be seen that


W z= H(g, S + g S + g S ) = o Hg S
Z o H'g x + xy y gzy z o x








since all the off-diagonal elements of the g-tensor can be

made equal to zero. But, from W we get the following
matrix

0 <-Lx + g S +

0H +ILx + goSx -) 0


while from the phenomenological Hamiltonian we get

1+> I-)

<(- 0 g ioH)
(<-l\gloH 0

Solving these two systems, we obtain

g = (+L + gS I-) + (-IL + gS +)
Sox ox x ox
+ + -
If we let L + g S = {L+ + L + g (S + S )}
x ox o

substituting the values of +) and I-) and carrying out the

operations involving S and S-, we obtain

<+IL, + gSj) = o nE -LEO0) 0oL+n)
n

+ <(0L-]n] j ILLI) +o
S-E E
n n 0

where the terms proportional to t2/(En-E )2 have been neg-

lected. If L and L are replaced by their L and L
x y
counterparts, we obtain








(+IL + gS x-> = (g ( L L (OIL xn)
x o x 9o L En E 0 x
n
(01 < Li n)
-En E0
n

and similarly for (-IL + goS x+). Therefore,


g9 = g 2 E (n Lx I) (OL- E xn (9a)
SEn 0
n

For g a similar treatment can be carried out and

S (01Lz n)
g =go 2 E (9b)
n o
n

but (for a Z molecule) this reduces to

g = go

Thus, any changes on g can only be attributed to matrix

effects to this order of approximation.








Comparison Between Ag1 and
the Spin-Doubling Constant

It has just been shown, Eq. (9a), that Ag1 is given by

S<(nlS Lxl0) (<0L ln
Ag, = g, go = -2- E E (10)
n 0
n

On the other hand, 2Z molecules exhibit a splitting of their

rotational levels given by y(K+), where y is very small com-

pared with the rotational constant, B, and K is the rotational

quantum number. y is called the spin-doubling constant and

has been shown by Van Vleck [8] to be given by

y = 4 (01o Lx n) (n BLxl0)/(En-Eo)
n

where In) includes all excited 2H states, x is an axis per-

pendicular to the symmetry axis, E is the spin-orbit operator

and B is the rotational operator h2/(8I2 pr2). If B is

assumed to be constant, it can be taken out of the integral

and y reduces to

Y = 4BZ (<01 LxIn) (nlLx 0)/(En-EO) (11)
n

Then, from Eqs. (10) and (11), we obtain

y = -2B AgI

for a molecule in a 2E state. This relation was derived by

Knight and Weltner [9].








Angular Dependence of the Spectrum

So far we have not discussed the behavior of the spectrum

when the angle between the molecular axis and the magnetic

field varies. The Hamiltonian for a linear molecule can be

written

W = g H S z + g o(HSx + HS) + AIS
II o xx yy z z

+ A(fxSx+ IyS) (12)


by simply expanding Eq. (2) and substituting the values of

g and A for a linear molecule. The problem then consists of

finding a relationship between these quantities and the angle

between the magnetic field and the molecular axis.

Let us consider the Zeeman term first. It is desirable

to write this term in the form

Z = 9gVHSz'

where x', y' and z' are a new set of axes and z' is parallel

to H. Let x, y and z be the coordinate axes of the molecule,

where z is along the molecular axis. For a linear molecule

the direction of H can be taken as the polar axis and e the

angle between z and H (or z'). The y axis can be arbitrarily

chosen as perpendicular to H so that y=y' and therefore

H =0. Since H =H sin 6 and H =H cos 8,
y x z

Z = Bo II[ cos e z + g sin B xJH.








If new direction cosines are chosen such that

1 = (g cos 6)/g and lx = (gI sin 6)/g

where g2 = g2 cos2 + g2 sin2e, (13a)

we get

V = gioHSz' (13b)

where


S = 1 S + (14)
z Z Z Xx

S = -lS + z S (14)

S = S
y y

For the hyperfine term, a similar transformation can be

used. If Eq. (14) is inverted and new direction cosines are

chosen for the nuclear coordinate system relative to the

electronic coordinate such that

in = (A|lg1 cos 8)/Kg

n = (Ag., sin 8)/Kg

where K2g2 = Ag29 cos2e + A2q2 sin28, then Eq. (12) becomes


S= g HS + KI ,S + (AIIA/K)Ix,Sx,

(A A2)
+ _K g11 g sin 0 cos 9 I ,Sx'

+ A Iy,Sy,. (15)

If we now introduce the raising and lowering operators
+ +
S- = S iS and I = I + iI the Hamiltonian (Eq. (15))

becomes







A2 A2 g g +
y= gB BS + KSz z K 9 cos e sin 8 Iz


+ A- SI +SI + + I + SI I (16)


When a matrix is written using this Hamiltonian, the eigen-

values, as well as the corresponding eigenvectors, can be

found. This can be a laborious exercise; however, in most

cases, a second-order perturbation solution suffices.

The allowed transitions are observed when 6M=-1 and

Am= 0, where M= S,S-l,...,-S and m= I,I-l,...,-I. The second-

order solution gives (see Abragam and Bleaney [10]),

A2 A2 + K2



2 2
hv = gfoH + Km + AI [l (I+1) m-



2gHo \ K2 g2


for a 2Z molecule, where Ho = (hv)/(go ).



Molecular Interpretation of ESR Parameters

In Eq. (3), it was shown that the observed ESR param-

eters A and Al can be related to fundamental molecular param-

eters in terms of Aiso and Adip. If we now write the molecular

wavefunction i as a linear combination of atomic orbitals, we get

l = C d + C d
I= Cs + C2 non-s

where 0s and non-s are the atomic orbitals representing an

s-type orbital and the non-s character is collected under








non-s. In most cases these latter orbitals refer predomi-
non-s
nantly to the p-character, but since mixtures of d-functions

are conceivable, particularly for the Cl case, it will be

left as non-s. If it is assumed that this wavefunction is

normalized and that the cross terms are small, integration

and evaluation yields

i(0) |2 = C2l (0)5 2

It can be seen that A. for the molecule is proportional to

the term on the left, while ()(0) 2 is approximately propor-

tional to A! for the atom. Therefore
1SO
A.
C2 iSO
l A! (18)


Similarly,

A
C di
d ip


where A' is the value of the anisotropic hyperfine split-
dip
ting constant for the atom (see Ayscough [11]).


Spin Density Functions

In chemistry, one is usually interested in orbital

yavefunctions; i.e., electrons are allocated to orbitals

A,B,...,R,..., with spin factor a or B, and antisymmetrical

functions are formed from them in accordance with the Pauli

principle (Slater determinants). Each orbital with its spin

factor is a spin-orbital (Aa, AB), and any specification of








spin orbitals for all the electrons concerned is a spin-

orbital configuration associated with one Slater determinant.

An orbital is a function of position in space (position

vector r) and its value squared at r, IA(r) 2 = IA*(r)-A(r) ,

indicates the probability of finding the electron there.

Space and spin variables (r,s) will be denoted collectively

by x and the spin-orbital *A(x) = A(r)a(s) describes an elec-

tron in orbital A with spin +%. The probability of finding

the electron in volume element dr and with spin between s

and s+ds, is given by a density function p(x) such that



Probability of finding the electron in dx = p(x)dx

= IA(x)12 dx


= IA(r) 121a(s)2 dr ds

and is zero unless s is in the vicinity of +% since this

is a "plus-spin" electron.

If the position is of particular interest at a given

time regardless of spin, a sum over all possible spins can

be carried out, and then the probability of the electron

being found in dr can be written as

P(r)dr = (p(x) ds) dr = IA(r)12 dr

just as if the electron had no spin and was simply put into

orbital A.








For a many-electron system, the wavefunction can be

written as

(X ,x,2 .... Nx )

and has the interpretation

(xl'X2'"..' N) *(xx ...,)dxldX2,...,dxN =


SProbability of electron 1 in dx1,2 simultaneously in

dx ..

The probability of 1 in dxl and the other electrons

anywhere is thus

dxl f i N) *(l'2 .... N) d 2 'd 3,''... dxN


and the probability of finding any of the N electrons in dx1

is N times this. This is now written as pl(x1), defined as

l (l) =-Ndxlf(xl',2 ..... "'"N) (xl'2""'x N) dx2'dx3 '""... dXN

It should be noted that this statement implies a slight

change in the interpretation of x as an argument in the

density function; it no longer denotes exclusively the

variables of particle 1 but rather a point of configuration

space at which any particle may be found (with equal prob-

ability due to indistinguishability). Thus, p1(xl)dx1 is

the probability of finding any electron (1,2,...,N) in

volume element dx at x

As in the case of one electron, the probability of find-

ing an electron in a volume element drl in ordinary three-








dimensional space with any spin can be found by

P1(r ) = f PI(xI) dsl.


If this integral is to be carried over the electrons

with spin a and over those with spin 8 separately, we can

write

P(r = P (r + P(r


where the superscript indicates over which spin the summa-

tion is taken. Now, let us define a spin-density functionby

Q (r ) (P:'(r) ())
s 1 1 -


since this measures the resultant z-component of spin (excess

of up-spin over down-spin density multiplied by the spin mag-

nitude k).

Let us introduce a slightly different notation.

Let pl(X1) = P1 (x1,x). This change is introduced so that

when dealing with operators we can write the expectation

value of the one-electron operator F as

= f I*(x ) Fi(x ) dxl = Fi(x1) p*(x1) dx

f= Fp1(x1,xl) dxl


since the order of the factors does not matter. The expec-

tation value is obtained simply by averaging F=F(x ) over

the electron density pl(xl). In order to avoid confusion,

the density matrix is written as pl(xl,xl) to indicate that








the operator acts on xl first, then x! is made equal to x,

and the integral is taken. Therefore, this is simply a

clarification, or change in notation.

Applying this to the case of the Sz operator, we have

(S ) = Sz(1) P (x,1'x) dx


= f Sz(1) PC(rl,r')a(Sla*(Sl


+ P1 (rl,r)B (Sl) *(Sl) dxl


and carrying out the summation over spins after operating

with S (1) we get

(S f = Qs(rl) drl = M


Therefore, Qs could be normalized. So, the function

-1
D (rI) = M1 Q (r )


is the normalized spin-density function.

It can be proved that


iso 3 n n s -

and


Adip = 3q onn (xn/r )Ds(r) dr (19b)

where R is the radial distance to nucleus n, usually
-n
represented as D (0), and r is the distance of the field
s ~n
point (r) from nucleus n and has Cartesian coordinates x ,

yn, and zn (see McWeeny [3] and McWeeny and Sutcliffe [4]).









It can be seen then, that the magnetic parameters

provide a direct relationship to the density matrix. There-

fore, Aiso gives a probe into the nature of the density

matrix at each nucleus and Adip measures the magnetic dipole-

dipole interaction in a distribution of spins of density

Ds(rl).


Details of the Spectra

It has been shown (see Eq. (13a)) that the angular depen-

dence of the g-factor can be written as

2 = 2 os28 + 2 sin 2
g= g coS

where 8 was the angle between the molecular axis and the

magnetic field. Then, as far as the Zeeman term is concerned,

two absorptions will be observed, one at the field position

corresponding to g and another one at the field position

corresponding to g Let us call these corresponding field
O O
positions H and H respectively, and define them by

hv hv
0O 0 0 0
H H
II 11 Bo and g Bo


It is assumed that the molecules are randomly oriented

in the matrix, but rigidly held by it. Under these condi-

tions, the spectrum will be independent of the angle the

magnetic field makes with the sample. Experimentally, the

random orientation of the molecules may be established by

rotating the sample with respect to the magnetic field and








recording the spectrum. If no changes are detected, the

molecules are assumed to be randomly oriented. The spectrum

expected for randomly oriented molecules was first analyzed

by Bleaney [12,13] and by Sands [14]. Later treatments can

be found in the literature [15-26].

If a sample contains No randomly oriented molecules,

the number of them within an increment of angle de, where 6

is the angle measured from the field direction, is given by
N
dN = sin 6 dO (20)

Therefore, dN is proportional to the area of the surface of

a sphere included within de. The factor is introduced

since it is only necessary to include a hemisphere.

The intensity of the ESR absorption is proportional to

the number dN of molecules between 9 and 8 + de, if it is

assumed that the transition probability is independent of

orientation.

The field position at which a transition will be observed

can be written as

hv
H (g2 cos28 + g2 sin2e) (21)
H = osin ) (21)


where the angular dependence of the g-factor has been intro-

duced. Differentiating Eq. (21) and letting H = hv /g'B,

and g' = (g + 2g )/3, it is found that

g'22 H -
sin 0 dO = 2 g2) (g'Ho/H) ga dH (22)
H 3 g11l








The intensity of absorption in range of magnetic field

dH is proportional to

IdN/dHj = jdN/dOj I* (d/dHI

Manipulation of Eqs. (20) and (22) and solving Eq. (21) for

6 = 00 and for 6 = 90 yields

ldN/dH| = N og/2g'H (g2- g) at = 0

and that

dN/dH = = at 6 = 900.

Therefore, if the natural width of the line is considered,

the extreme points of the absorption become rounded and in

Figure 3a a plot of this absorption versus the field inten-

sity for the case of g > g is shown. When the first deriva-

tive of this curve is obtained, Figure 3b results under the

same conditions. The line that occurs at 6 = 00 is called

a parallel line and the one that occurs at 8 = 90 is called

a perpendicular line.

In almost every molecule that is studied, at least one

nucleus possessing a magnetic moment is encountered. Hyper-

fine (Hf) interaction can occur and each line will be split

into 21+ 1 lines (where I is the nuclear spin), if only one

nucleus of spin I is present. In Figure 3c the spectrum

obtained when the molecule has one unpaired electron and a

nucleus with I = has been plotted. It is further assumed

that gll g and that A > A The distance between the two



































S--I -0


c"0-0


'-4








parallel lines is called A and the distance between the two

perpendicular lines is called A .

The spin Hamiltonian for an axially symmetric molecule,

including Hf interaction, was given in Eq. (12). In it,

the nuclear Zeeman term (I-H type) has been omitted since it

is usually small. The nuclear quadrupole interaction has

also been omitted for the same reason. To first-order per-

turbation theory, the field position at which absorption will

occur is given by (Eq. (17))

hv
o K
H =g g mI (23)
gB gB I

where all symbols have been already defined.

The absorption intensity (dN/dHJ can be written


dN o cos [(g ) O g2A2 ( 2 2)
dH 2 2 2g o 2K g '

(24)
The solution to Eq. (24) is much more complicated than that

for Eq. (21), since there is no explicit form for sin 9, so

that jdN/dHJ cannot be written as a function of only the

magnetic parameters. One must solve Eq. (23) and (24) for

a series of values of 6 to obtain the resonant fields and

intensities as a function of orientation. For the cases

9 = 0 and 6 = 900, we have








H = (g'Ho/g) (mAl /g i o) at e = 0

and

H = (g'Ho/g1) (mAL/g1 B0) at 6 = 90;


therefore, IdN/dHI goes to as 6 900 (see Low [27]).

It is then concluded that the absorption pattern will

consist of 21+1 superimposed patterns of the type in

Figure la. Therefore, we get 21+ 1 parallel lines and

21+1 perpendicular lines.

When several nuclei in the molecule possess magnetic

moments, each nucleus will split the line into 21. + 1 lines,
th
where I. is the nuclear spin of the i nucleus. In Fig-

ure 4a, this is illustrated for a molecule containing two

magnetic nuclei; the first one has I1 = 3/2 and the second

one has 12 = . It is further assumed that the hyperfine

splitting produced by the first nucleus is larger than that

produced by the second one. Each one of these absorption

lines gives rise to one parallel and one perpendicular com-

ponent as depicted in Figure 4b. In this case, it is assumed

that Al > A and that gl g. In Figure 4c, the first deriv-

ative spectrum obtained when this kind of a system is simu-

lated is recorded. The values used for the simulation were

g = g = 2.0023, A' = 40.0 G, A' = 20.0 G, A2 = 10.0 G,

and A2 = 5.0 G.
I










POWDER PATTERN
TWO MAGNETIC NUCLEI

a)


c)


3270 V3350 3430
Figure Powder Pattern
Figure A. Powder Pattern












References


[1] Dirac, P. A. M., Proc. Roy. Soc. (London) Ser. A 117.
610 (1928).

[2] McWeeny, R., Spins in Chemistry, Academic Press, New
York (1970).

[3] McWeeny, R., and Sutcliffe, B. T., Methods of Molecular
Quantum Mechanics, Academic Press, New York (1969).

[4] Hameka, H. F., Advanced Quantum Chemistry, Addison and
Wesley, Massachusetts (1965).

[5] Wertz, J. E., and Bolton, J. R., Electron Spin Resonance,
McGraw-Hill, New York (1972).

[6] Frosch, R. A., and Foley, H. M., Phys. Rev. 88, 1337
(1952).

[7] Carrington, A., and McLachlan, A. D., Introduction to
Magnetic Resonance, Harper & Row, New York (1967).

[8] Van Vleck, J. H., Phys. Rev., 33, 467 (1929).

[9] Knight, L. B., and Weltner, Jr., W., J. Chem. Phys.,
53, 4111 (1970).

[10] Abragam, A., and Bleaney, B., Electron Paramagnetic
Resonance of Transition Ions, Clarendon, Osford (1970).

[11] Ayscough, P. B., Electron Spin Resonance in Chemistry,
Methuen, London (1967).

[12] Bleaney, B., Proc. Phys. Soc. (London), A63, 407 (1950).

[13] Bleaney, B., Phil. Mag., 42, 441 (1951).

[14] Sands, R. H., Phys. Rev., 99, 1222 (1955).

[15] Searl, J. W., Smith, R. C., and Wyard, S. J., Proc.
Phys. Soc., 74, 491 (1959).

[16] Bleaney, B., Proc. Phys. Soc., A75, 621 (1960).








[17] Roberts, E. M., and Koski, W. S., J. Am. Chem. Soc.,
82 (1960).

[18] O'Reilly, D. E., J. Chem. Phys., 29, 1188 (1958).

[19] Kneubuhl, F. K., J. Chem. Phys., 33, 1074 (1960).

[20] Neiman, R., and Kivelson, D., J. Chem. Phys., 35, 156
(1961).

[21] Ibers, J. A., and Swalen, J. D., Phys. Rev., 127, 1914
(1962).

[22] Gersmann, H. R. and Swalen, J. D., J. Chem. Phys., 36,
3221 (1962).

[23] Swalen, J. D., and Gladney, H. M., IBM J. Res. and
Develop., 8, 515 (1964).

[24] Johnston, T. S., and Hecht, H. G., J. Mol. Spectr.,
17, 98 (1965).

[25] Malley, M. M., Mol. Spectr., 17, 210 (1965).

[26] Kasai, P. H., Whipple, E. B., and Weltner, Jr., W.,
J. Chem. Phys., 44, 2581 (1966).

[27] Low, W., Paramagnetic Resonance in Solids, Academic
Press, New York (1960).












CHAPTER III


M Cl2



Introduction

The Cl2 molecule ion has received very intense study

in the last few years. Since Castner and Kanzig [1] dis-

cussed the nature of the Vk color centers in crystalline

solids, this species has been investigated in several environ-

ments. The Vk center is a trapped electronic hole between

two Cl ions in alkali halide crystals. It is formed upon

the irradiation of these crystals.

This molecule has been postulated as a possible

intermediate in the general reaction M + Cl2 MCI + Cl.

This intermediate must be very short-lived, since the

molecular beam data fail to show its presence. This reac-

tion apparently proceeds via the spectator stripping model

[2], implying that the metal atom collides with the Cl2

molecule and that the reaction product, MC1, proceeds with

very little angular variation from the original path.

The data indicate that the reaction cross section is very

large. Some luminescence experiments[3,4]detected a short-

lived intermediate formed when an electron leaves the metal

atom and goes on the C12 molecule forming the M Cl2 specie.
2peie








The study of the M Cl2 specie was decided via the ESR

method since the ground state of Cl- is 2E, which makes them

observable trapped in matrices at 4 K. C12 has been studied

trapped in other matrices [5,6]. It has also been studied

in different types of irradiated crystals [7-13].



Experimental


Method of Preparation of the M+ Cl


A problem in the production of the M Cl2 species is the

trapping of a large enough amount in order to obtain a suf-

ficiently intense signal. Several mole ratios of C12 to

argon were tried: 1:1000, 1:200, 1:100 and 1:20. The 1:20

produced the most intense ESR signal, although this is a

higher concentration than is usually used in matrix isola-

tion studies.

The metals were deposited at different temperatures, and

measured with a Chromel-Alumel thermocouple attached to the

Knudsen cell. It was found that the best temperatures were

those that provided a metal vapor pressure of the order of
-l
10- torr (see Table I). The temperature was recorded by

using a Leeds and Northrup potentiometer, with a cold junc-

tion immersed in an ice-water bath.

The matrices formed were all opaque, greenish-yellow in

color and icy in appearance. When either too large a con-

centration of the metal or too low a concentration of C12















TABLE I

METALS, SOURCES AND TEMPERATURES USED


Metal Source and Purity T (K) to Obtain
a Vapor Pressure of
-1
About 10- Torr


Mg J. T. Baker (99.9%) 782

Ca Fisher (99.9%) 962

Sr Alpha Inorganics (99.9%) 900

Ba Alpha Inorganics (99.999%) 984

Li MC & B (99.9%) 900

Na J. T. Baker (99.9%) 630

K Mallickrodt (99.9%) 540








is present in the matrix, the color was red to orange, which

is the typical color that the alkali and alkaline-earth

metals exhibit when isolated in inert gases by themselves.

The Cl2 used was obtained from research grade (99.9%)

chlorine provided by Air Products Company without further puri-

fication. The gas mixture was prepared in a glass vacuum

line that was evacuated to pressures of the order of 2 x 10 j

as read on an ion gauge. C12 was allowed to enter the bulb

until a pressure of 36 torr was achieved. Then, Ar was

passed into the bulb until the pressure was 760 torr. The

metals were obtained from commercial sources with purity as

specified in Table I.

All these experiments were done in argon since several

trials in neon were unsuccessful. This appears to be due to

the fact that quenching in a neon matrix is slower than that

in an argon matrix, since its solidification point is con-

siderably lower (24 K) than that of argon (84 K).


Observed Spectrum of M Cl2


The observed spectra correspond to the C12 ion.

Figures 7, 9, 11, 13, 15, 17, and 19 show the spectra

recorded when Mg, Ca, Sr, Ba, Li, Na, and K, respectively,

were used as electron donors. In all cases the parallel

features of the C12 ion could be observed, consisting of

seven lines for the 35Cl-35Cl sixteen lines for the

35C1-37Cl, and seven lines for the 37C1-37C1








(see Fig. 5). These lines should have intensities propor-

tional to their relative abundances, i.e.,

35C135Cl 3/4 x 3/4 = 9/16

35C137Cl 3/4 x 1/4 = 3/16
6/16
37C135Cl 1/4 x 3/4 = 3/16J

37C137C1 1/4 x 1/4 = 1/16

This is observed in the spectra, although some of the

37C137C1 signals are very weak at certain points.

Each C1 nucleus has a spin of 3/2 and therefore splits

the signal into 2(3/2) + 1 = 4 lines. In the homonuclear

cases some of them overlap, increasing their intensities,

but in the heteronuclear case they do not. This yields

a total of seven lines in an intensity ratio of 1:2:3:4:3:2:1

for the homonuclear case and sixteen equally intense lines

for the heteronuclear case. In Figure 1, the different par-

allel lines for these molecules are identified with a bar

whose height is proportional to the relative intensity and

abundance of the given species. The perpendicular lines could

not be individually identified since they overlap to a

great extent.

The values of A for the different molecules are larger

than the corresponding values for A The ratio of the

corresponding A values for the two isotopes is in very close

agreement with the ratio of their magnetic moments 35/37 =

1.201, as expected. Values of Al and A for each molecule

studied are given in Table II.




















0
0
LD




















oo
0n




- -







in 0









C 0r







c74.
t n


N


'I
~0
0


z ,










E D

L-)
c>
b


ii


CO '


Cr
LJ















0
N


0
mi


Nr
02l


I N\
u

Cr
0
LL
o







f-



F-



U


0
0


Cn


0


______ ______ _______ ~ ______ _______ 1. _______


) Q6 Q Q
oJ C CJ-


0N 0 I


E N_ N 0 -

=, LO r,-
r-


ro 8 8 ro
C\ o U cJ oN oj c N_
-- -S00--g--
=0 8 8 0
NQ ) N C\J CN C\j Cj_

7 In 0 0 0


C C) a) 0 0



ro co co o3 O OD cOD
r co oQ d u 0
(9 ro d d- rN- Lt


Ocd n 0 0) o Cj
__ro n a G) Q ) 0 0


+1
o


rl
+l







- 4







a
CC










r O
-H



r-4




ia,
MJ 0


a)


x m




w (1







In all of these cases, the values of A1 and of g, had

to be determined through computer simulation of the spectrum

(see Appendix A). A is small and g is located close to

where a parallel line for the 35-35 case is located. In the

same region there are one 37-37 and two 35-37 parallel lines.

To add to the complexity, it should be realized that all the

perpendicular lines for all three molecules reside within

the same region of the spectrum.

The procedure used to determine the value of Al and g1

consisted of feeding to a computer the values of A l, A, g ,

g, the spectrometer frequency, and the estimated linewidth.

By careful comparison of the simulated spectra with the expr-

mentally obtained one, a final value for the A, and g, param-

eters could be obtained. In Figure 6, the chosen spectrum

for the Ba Cl2 case, as a typical example, is displayed com-

pared with other small variations in the parameters in order

to indicate the sensitivity of this method to the different

parameters and their variations. The parameters used for

Figure 2a are those listed in Table II for Ba+Cl2. Figure 2b

is drawn by using the same parameters except that g was

changed to a value of 2.0420 rather than 2.0393. Figure 2c

shows the results of changing the A, values from 8.0 G and

6.7 G to 10.0 G and 8.0 G for the 35 and 37 nuclei, respec-

tively. Figure 2d shows the result of changing the linewidth

from 4.0 G to 8.0 G.

The sensitivity of the spectrum in this region to the

different parameters allowed the determination of their

experimental values to the accuracy stated in Table II.









Ba + Cl- Bd6C
g.I.


H-


Figure 6


a)




b)





c)




d)








In all of these experiments there was no way to deter-

mine the sign of the A values since they all enter the math-

ematical formulation as the square root of the square of the

given value. Therefore, they will all be reported as the

absolute value throughout this paper.

No angular variation was detected when the rod was turned

to different positions with respect to the applied magnetic

field. This is taken as evidence that there is a completely

random distribution of the species under study in the matrix.

No variation of the spectra was encountered when the

metal was deposited at different rates. It is assumed, then,

that all the spectra were essentially recorded at infinite

dilution as far as these experiments can distinguish. This

may appear as a rather strong assumption since a mole ratio

of C12 to Ar of 1:20 was used. However, it should be real-

ized that although the initial concentration of Cl2 is high

the actual amount of trapped M+Cl1 may be small.

In the spectra in which the alkaline-earth metals were

used as electron donors, the presence of the corresponding

MC1 specie could be tentatively assigned, except in the case

of BaC1. The perpendicular lines of these molecules occur

close to go = 2.0023. Parallel lines were not assigned since

they are small and appear to be covered by the Cl2 signals.

In all the alkaline-earth spectra, the presence of the

M ion could be observed at g = 2.0023. In the Mg case,

even the lines corresponding to 2SMg+ (abundance 10.13%)

could be observed.








Mg+ C2


In Figure 7, the spectrum obtained when Mg atoms were

deposited with the C12 and Ar mixture is shown. The salient

features observed are those of the Cl2 ion.

The values of A and of g1 were obtained directly from

the spectrum by measuring the separation of the parallel

lines. Since A. is small, the second-order correction

(see Low [15]) is of the order of 0.05 G, and therefore will

not affect the accuracy of A and g within the accuracy of

the experimentally measurable value. In Table III a list

of the parallel line positions, both as observed and as cal-

culated, is included using the previously determined paral-

lel parameters. The perpendicular parameters were obtained

by computer simulation. The assigned values for this mole-

cule are: A = 95.4 1.0 G, A = 7.5 2.0 G, for the

3 Clnucleus and A = 78.8 1.0 G, A = 6.2 2.0 G for the

Clnucleus; g = 2.0030 0.001, g = 2.0342 0.001.

In Figure 8, a comparison between the computer simulated

spectrum (Fig. 8a) and the experimentally determined one

(Fig. 8b) in the region around g and gI is plotted.

It is believed that the MgCl spectrum is also observed

in this system. In Table XVIII the Al value for this mole-

cule is listed. The parallel lines could not be identified

since they probably lie under some of the Cl, lines.
2








MG +CL.2-- MGCTL- -MGCL + CL.

,11
II i











i-----------
IOO G \ I II


Figure 7







Mg+CI2-- M2\II
*^ d ^ c l -


9I,


a)






b)


H


25g-
Mgt


91 40


MgCi


Figure 8








TABLE III

PARALLEL LINE POSITIONS FOR THE Mg+Cl2


3sCC 1C "C13lCl 35C13Cl
m m exp. calc. exp. calc. exp. calc.


3/2 3/2 3066.9 3066.4 3116.1 3116.0 3092.5 3091.1

3/2 i3169.9 3169.9
1/2 3/2J 3161.7 3161.7 3194.8 3194.8 3195.9 3169.9
1/2 3/2)3185.9 3186.5
3/2 -1/2 3249.0 3248.7
1/2 1/2 3256.0 3257.0* 3273.6 3262.6* 3265.3
-1/2 3/2J 3281.3 3281.9
3/2 -3/2 3329.5
1/2 -1/2 3352.4 3352.4 3352.4 3352.4 3344.1


3352.4 3352.4 3352.4 3352.4
-1/2 1/2 3360.7
-3/2 3/2 3377.7 3377.3
1/2 -3/2T 3422.1 3422.9
-1/2 -1/2 3447.4 3447.4 3431.6 3431.2 3439.1 3439.5
-3/2 1/2) 3455.9 3456.1
-1/2 -3/2 ** 3518.3
-3/2 -1/2) 3542.5 3543.1 3510.9 3510.0 3534.9 3534.1
-3/2 -3/2 3638.8 3638.5 3588.8 3612.7 3613.7


* Denotes heavy overlap of lines.
** Denotes the fact that the line is weak, therefore
difficult to evaluate.

SDenotes overlap in homonuclear molecules.

All values in G.








The analysis of this spectrum also shows evidence of

the presence of the Mg ion. This ion is believed to

accompany the formation of C12, forming an ion pair system

(see discussion). The natMg+ signal appears at 3364.6 0.5 G

which yields a g-value of 1.9940. The lines for 25Mg+

(10.13%) natural abundance, I = 5/2) were also observed.

In this case, it is assumed that A A A and therefore
iso i A
Adip = 0.0 (for a treatment of these parameters see the dis-

cussion). The A. value for this ion is found to be 130.3 G.
iso
This value compares favorably with the one obtained by Brom

and Weltner [16] for MgOH.

The values of the line positions as observed experi-

mentally and those calculated (see Low [15, p. 60 ff]) are

listed in Table IV.


Ca C1l


In Figure 9, the spectrum obtained when Ca atoms were

deposited simultaneously with the C12 and Ar mixture is

shown. The salient features of it are those of the Cl2 ion.

The values of Al and g were directly obtained from the spec-

trum by measuring the difference between the parallel lines

as in the case of Mg C12. The values of A and of g,

however, had to be obtained by computer simulation. In Fig-

ure 10, the computer simulated spectrum (Fig. 10a) is compared

with the experimentally observed one (Fig. 1Ob) for the region

close to g and g .



















TABLE IV

25Mg+ Lines


m Experimental (G) Calculated (G)


5/2 3059.5 3059.4

3/2 3187.8 3188.9

1/2 3318.8 3318.8

-1/2 3447.8 3447.8

-3/2 3566.2 3577.2

-5/2 3706.6


* Indicates the line is too weak to be
measured correctly.










CA + CL2,- C CL2 --CACL+CL


9II
I I I I


-~I


ARGON, 40 K


- G---I
100 G


Figure 9


I


1 1 1








Ca + C!2-- Ca Ci


40 G
I----


a)




b)


H-


Figure 10








TABLE V

PARALLEL LINE POSITIONS FOR THE Ca Cl1


5C135 ci 3"C17Cl 3 5C37C1

m m exp. calc. exp. calc. exp. calc.


3057.5 3057.1 3103.7 3102.3 3079.4

3163.6
3155.8 3155.8 3187.0 3186.1
3179.2


3079.8

3163.6

3178.6


-1/2V

1/2 3253.4

3/2,

-3/2

-1/2
S3353.7
1/2

3/2

-3/2

-1/2 3451.8

1/29

-3/2
S3550.8
-1/2

-3/2 3650.0


3254.5* *


3353.7 3353.7


3452.1 3437.5




3551.1 3521.5


3649.9 3606.7


3247.4

3269.9 3262.4

3277.4

3330.3 3331.2

3346.2
3353.7
3361.2

3376.2

** 3430.0

3437.5 3447.0 3445.0

3459.1 3460.0

3525.3 3528.8
3521.3
3544.6 3543.8

3605.1 ** 36.27.6


* Denotes heavy overlap.

** Denotes the fact that the line is weak, therefore difficult
to evaluate.

SDenotes overlap in homonuclear molecules.

All values in G.


3/2

1/2

3/2 J


3/2

1/2

-1/2

3/2

1/2

-1/2

-3/2

1/2

-1/2

-3/2

-1/2

-3/2

-3/2


3649.93606.








In Table V, the field positions of the parallel lines

as observed and as calculated are listed. The magnetic

parameters used are: A = 98.8 1.0 G, A = 7.8 2.0 G

for the 35 nucleus, A = 83.8 1.0 G, A = 6.2 2.0 G for
II
the 37 nucleus; g = 2.0020 0.001 and g = 2.0353 0.001.

It is believed that the presence of the CaCI molecule

can be positively identified. In Table XVIII, the A value

for it is listed. As in the case of MgCl, only the perpen-

dicular lines are observed.

Ca is also observed in this spectrum at 3364.6 G for

a g-value of 1.9957. 3Ca+ (I= 7/2) is only present to the

extent of 0.145% so that no Hf splitting due to interaction

with the metal nucleus could be observed.


Sr C1l


In Figure 11, the spectrum observed when Sr atoms were

deposited with the C12 and Ar mixture is reproduced. The

salient features are again those of the Cl2 ion. The

values of A and of g were directly obtained from the line

positions as before. The values of A and of g had to be

obtained by computer simulation. Tn.Figure 12,, the computer

simulated spectrum is compared with the experimentally observed

one (Fig. 12b) for the region close to g11 and to g .

In Table VI, the field positions of the parallel lines

as observed and as calculated are listed. The magnetic

parameters used are: A = 99.4 1.0 G, A = 7.8 2.0 G




59



















o
OO









O F "




0ro
o -




-0-








Sr C12- Sr Cl



I% 19'
40 G

a)


b) Sr+
n nr-iSrCI


Figure 12


H-









TABLE VI

PARALLEL LINE POSITIONS FOR THE Sr Cl


3sCl3sCl 3"C1 Cl 35C137C1
m mI exp. calc. exp. calc. exp. calc.


3054.0 4053.6 *


3153.3 3152.9 3182.9


3250.6


3252.3* *


3097.8 3075.2 3075.6

3160.2 3160.2
3182.4
3176.7 3175.0

3244.8

3267.0 3259.6

3274.4


3/2

3/2

1/2

3/2

1/2

-1/2

3/2

1/2

-1/2

-3/2

1/2

-1/2

-3/2

-1/2

-3/2

=3/2


3/2

1/2

3/2

-1/2

1/2

3/2J

-3/2

-1/2

1/2

3/29

-3/2

-1/2

1/2

-3/2

-1/2

-3/2


* Denotes heavy overlap.

Denotes overlap in homonuclear molecules.

All values in G.


3330.4

3344.4
3351.6 3351.6 3351.6 3351.6
3359.1

3373.8

3429.4

3451.5 3451.0 3436.7 3436.2 3443.0

3458.5

3527.7
3551.1 3550.3 3519.2 3520.8
3542.2

3649.7 3649.7 3605.4 3627.4


3329.4

3344.2

3359.0

3373.8

3428.8

3443.6

3458.4

3528.2

3543.0

3627.6









for the 35 nucleus and A = 84.6 1.0 G, A = 6.5 2.0 G
II
for the 37 nucleus; g = 2.0030 0.001 and g = 2.0364 0.001.

It is believed that the presence of the SrCl molecule

can be detected. In Table XVIII the A value for it is

listed. As in the case of MgCl, only the perpendicular lines

are observed.

Sr is detected at a field position of 3359.1 G for a

g-value of 1.9991. 87Sr+ (I =9/2) is only present to the

extent of 7.02% and no Hf splitting due to the interaction

with the metal nucleus could be observed.


Ba Cl


In Figure 13, the spectrum recorded when Ba atoms were

allowed to react with the Cl2 and Ar mixture is shown.

In it, again, the salient features are those of the Cl2 ion.

The magnetic parameters were obtained as in the previous

cases; the parallel parameters by direct measurement of the

line positions, and the perpendicular parameters by computer

simulation. In Figure 14, the computer simulated spectrum

(Fig. 14a) is compared with the experimentally obtained one

(Fig. 14b) for the region close to gll and g .

In Table VII, the field positions of the parallel lines

as observed and as calculated are listed. The magnetic

parameters used are: A = 100.7 1.0 G, A1 = 8.0 2.0 G

for the 35 nucleus, A = 84.8 1.0 G, A1 = 6.7 2.0 G for

the 37 nucleus: g11 = 2.0020 0.001 and g, = 2.0393 0.001.
























I


Cd

t
_J

J-


----


--


oo
CO
C!)
D
<,
Z
T:




















-II *




0
CD


0









TABLE VII

PARALLEL LINE POSITIONS FOR THE Ba Cl2


35Cl35Cl 37C137Cl 3SC13C1

mI mI exp. calc. exp. calc. exp. calc.


3/2

1/2

3/21

-1/2

1/2

3/2)

-3/2

-1/2

1/2

3/2J

-3/2

-1/2

1/2)

-3/2

-1/2)

-3/2


3057.4 3057.4 3107.3 3107.3 30

31
3158.2 3158.1 3192.1 3195.5
31


3256.6


3258.8* 3275.5


84.1

.67.7

84.3

*

*

*

*


3/2

3/2

1/2

3/2

1/2

-1/2

3/2

1/2

-1/2

-3/2

1/2

-1/2

-3/2

-1/2

-3/2

-3/2


3083.5

3167.5

3184.2

3251.5

3268.2

3284.9

3335.5

3352.2

3368.9

3384.4

3436.2

3452.9

3469.2

3536.9

3553.6

3637.6


* Denotes heavy overlap.

Denotes overlap in homonuclear molecules.

All values in G.


3351.3
3360.5 3359.5 3360.5 3359.5
3367.4

3384.0

3436.8

3460.1 3460.2 3444.0 3443.5 3452.4

3468.9

3536.7
3560.4 3560.9 3528.0 3527.5
3552.9

3661.9 3661.6 3612.1 3611.5 3637.0









The presence of the BaCl molecule is not detected in

this case.

Ba is detected at a field position of 3360.5 G for

a g-value of 2.0020. 137Ba+ (I= 3/2) is only present to the

extent of 11.32% and no Hf splitting due to the interaction

with the metal nucleus could be observed.

The Ba C12 case was also run in the variable-temperature

Dewar in order to observe, if possible, whether BaCl would

form as the temperature was being increased. When the temper-

ature was raised to about 15 K, a sudden change in the spec-

trum was detected. The Ba+ line increased significantly,

while the C12 pattern decreased a small amount. No lines

that could be attributed to BaC1 appeared.


Li C12


In Figure 15, the spectrum obtained when Li atoms were

deposited with the C12 and Ar mixture is shown. In it, again,

the salient features are those of the C12 ion. The magnetic

parameters for this species were determined as before, the

parallel ones by direct measurement of the line positions

and the perpendicular ones by computer simulation. It is

interesting to notice that this is the only case in which

the alkali metals were used in which the unreacted atoms

appear in the spectrum. The 7Li lines are indicated in








Figure 15. It appears that since Li has the highest ioniza-

tion potential of the alkaline metals, the reaction is not

as efficient.

In Table VIII the field positions of the parallel

lines as observed and as calculated are listed. The mag-

netic parameters used are: A = 99.4 1.0 G, A = 7.9 2.0 G

for the 35 nucleus, A = 83.91.0 G, A, = 6.6 2.0 G for

the 37 nucleus; gl = 2.0004 0.001 and g, = 2.0328 0.001.

In Figure 16, the computed spectrum (Fig. 16a) is com-

pared with the experimentally obtained one (Fig. 16b) for

the area close to gl and gi.

No lines corresponding to either Li or to LiCI are

observed or expected in this spectrum since they have 'S and

'Z ground states, respectively.

In this spectrum, the presence of HCO and CH3 is

detected in fairly large amounts. This is probably due to

the fact that Li is kept under a generous amount of petroleum

jelly. It was thoroughly washed in benzene before introduc-

tion into the furnace, but in spite of this, it is believed

that some hydrocarbons stay with it, producing the radicals

HCO and CH3 due to either thermal decomposition or reaction

with the C12.











Li+ Cl,--. LiLC;


31001 3300 e 3s 3700
H (Gauss)-


Figure 15








L CLj Li C l
2 2


a) 19i




b)


H--


Figure 16


1g91
|40G,









TABLE VIII
+IO -
PARALLEL LINE POSITIONS FOR THE Li+ClI
2


35Cl 3sCl 37"C37Cl 35cl37C

mI m exp. calc. exp. calc. exp. calc.


3053.0


3151.6


3251.8*


*


3/2

3/2

1/2

3/2

1/2

-1/2

3/2

1/2

-1/2

-3/2

1/2

-1/2

-3/2

-1/2

-3/2

-3/2


3052.2 ** 3098.7 3075.4

3159.5 3159.3
3151.6 3182.4 3182.5
3174.8 3174.8

3243.2

3250.9 3266.4 3258.7

3274.2

3327.1

3342.6
3350.3 3350.3
3358.0

3373.5

3426.6 3426.4

3449.7 3433.9 3434.2 3442.1 3441.9

3457.3 3457.4

3525.0 3525.8
3549.0 3517.7 3518.1
3451.5 3541.3

3648.4 3601.9 3601.9 3524.9 3625.2


*Denotes heavy overlap.
**Denotes weak lines.
***Denotes overlap with the 7Li lines.

SDenotes overlap in homonuclear molecules.

All values in G.


3/2

1/2

3/2

-1/2

1/2

3/2

-3/2

-1/2

1/2

3/2)

-3/2

-1/2

1/2J

-3/2

01/2

-3/2


3449.7




***


3648.0









In Table IX, the value of the parallel and the perpen-

dicular lines for 7Li (I= 3/2) are listed. The magnetic

parameters determined for this atom are A = 149.5 1.0 G,

A = 141.2 1.0 G, l = 2.0008 0.001 and g = 2.0011 0.001,

which compare favorably with the values of A = 143.4 G and

g = 2.0023 determined by Jen, Bowers, Cochran and Foner [17].





TABLE IX

PARALLEL AND PERPENDICULAR LINES FOR
'Li ATOMS IN ARGON


mI Parallel Lines Perpendicular Lines
exp. calc. exp. calc.

3/2 3120.9 3120.9 3132.6 3132.6

1/2 3264.5 3267.4

-1/2 3414.6 3414.0 3408.6 3407.1

-3/2 3569.4 3569.4 3556.0 3555.5


Indicates that the line could not be measured
accurately due to overlap.

Note: All line positions are estimated to be
correct to 0.5 G.









Na Cl_
2

In Figure 17, the spectrum obtained when Na atoms were

deposited with the C12 and Ar mixture is shown. The salient

features of it are those of the Cl2 ion. The magnetic param-

eters for this species were obtained as in the previous cases,

the parameters by actual measurement of the line positions

and the perpendicular parameters by computer simulation.

In Figure 18, the computed spectrum (Fig. 18a) is compared

with the experimentally obtained one (Fig. 18b), for the

area close to g and gl.

In Table X, the parallel line positions, both calculated

and experimental, are listed. The magnetic parameters used

are: A = 100.7 1.0 G, A = 8.0 2.0 G for the 35 nucleus,

A = 83.4 1.0 G, A = 6.5 2.0 G for the 37 nucleus;

g = 2.006 0.001 and g1 = 2.0371 0.001.

As in all the other alkali metals, neither the metal

ion nor the monochloride is observable via ESR.

No Na lines were observed in this spectrum, indicating

that Na has essentially reacted completely.

HCO and CH3 are present in this case, as they were in

the Li Cl2 case. Again, Na is kept under kerosene and,

in spite of being washed with benzene, it is believed that it

will generate the radicals upon thermal decomposition or

reaction with C12.











Na+I CL- NaCI;









L LI
CHs
H H


IOOG


3100i 330 .s 3s 5 3700
H (Gauss)-


Figure 17







Na + ClI- NcClI

a)




b) / iii


H-


4AQ


Figure 18









TABLE X

PARALLEL LINE POSITIONS FOR THE Na Cl
2


35Cl35Cll


"3C1 7C1


m mI exp. calc. exp. calc. exp. calc.


3/2

1/2

3/2

-1/2

1/2

3/2

-3/2)

-1/2

1/2

3/2J

-3/2

-1/21

1/2J

-3/2'

-1/2J

-3/2


3054.1 3053.7 3101.7


3154.1 3154.4 3187.2




3256.3 3255.1* *


3355.8 3355.8 3355.8


3102.9 ** 3078.3

3162.9 3162.6
3187.2
3180.1 3179.0

3246.9

3271.5 3279.1 3279.7

3331.2

3347.6

3364.0
3355.8
3379.6 3380.4


3/2

3/2

1/2

3/2

1/2

-1/2

3/2

1/2

-1/2

-3/2

1/2

-1/2

-3/2

-1/2

-3/2

-3/2


* Denotes heavy overlap.

** Denotes very weak lines.

SDenotes overlap for homonuclear molecules.

All values in G.


5Cl 37Cl


3431.9

3449.0 3448.3

3456.7 3456.5 3440.1 3440.1 3465.0 3464.7

3465.0 3464.7

3533.2 3532.6
3556.1 3557.2 ** 3524.4
3550.8 3549.0

3657.3 3657.9 ** 3608.7 3633.3








K Cl1
2

In Figure 19, the spectrum obtained when K atoms are

deposited with the C12 and Ar mixture is shown. The salient

features are those of the Cl2 ion. The magnetic parameters

for this specie were obtained in the same fashion as before,

parallel parameters by direct measurement of the line posi-

tions and the perpendicular ones by computer simulation.

In Figure 20, the computed spectrum (Fig. 20a) is compared

with the experimentally obtained one (Fig. 20b) for the region

close to g and g.

In Table XI, the parallel line positions as obtained both

from calculation and experiment are listed. The parameters

used are: A = 102.5 1.0 G, A = 8.1 2.0 G for the 35

nucleus, All = 85.6 1.0 G, A = 6.8 2.0 G for the 37 nucleus;

g = 2.0009 0.001 and g1 = 2.0370 0.001.

As in all other alkali metals, neither the metal ion

nor the monochloride is observable via ESR since they are

IS and 'I, respectively.

No K lines were observed in this spectrum, indicating

that K has essentially reacted completely.

HCO and CH3 are again present in this spectrum. K is

kept under kerosene and, although it was thoroughly washed

with benzene before insertion in the furnace, it is believed

that the kerosene generated the radicals by either thermal

decomposition or reaction with C12.












K+C1,-- K'CIl


LOOG


3100 3300 1 35001 37CO
H (Gauss)-


Figure 19










K+ C2--- -KC!;



a)












C HV
I


H-


HCO


40 G


'a


Figure 20


l I


I









TABLE XI

PARALLEL LINE POSITION FOR THE K+Cl-
2


35ClCl "3C137Cl 35C1l3Cl

m m exp. calc. exp. calc. exp. calc.


3048.4 3047.7 3100.9 3098.5 3C

31
3150.0 3150.2 3186.4 3184.1
31


3251.5


3252.7* 3269.4


3269.6


3355.2 3355.2 3355.2 3355.2


)74.0

.58.5

.74.7

*

*

*

*

*

*


3/2

3/2

1/2

3/2

1/2

-3/2

3/2

1/2

-1/2

-3/2

1/2

-1/2

-3/2

-1/2

-3/2

-3/2


3073.1

3158.7

3175.6

3244.3

3261.2

3278.1

3329.8

3346.8

3363.7

3380.6

3432.3

3449.3

3466.2

3534.9

3551.8

3637.4


3/2

1/2

3/2J

-1/2

1/2

1/2J

-3/2

-1/2

1/2

3/29

-3/2

-1/2

1/2j

-3/2

-1/2J

-3/2


3379.7

3432.8

3458.3 3457.7 3441.0 3440.8 3450.1

3465.9

3534.5
3559.6 3560.2 3524.8 3526.4
3551.9

3663.4 3662.8 3614.6 3612.0 3637.0


* Denotes heavy overlap.

SDenotes overlap for homonuclear molecules.

All values in G.









Discussion

In the following discussion of the obtained spectra,

the main assumption made is that the experimental results

can be explained by treating the complex as two loosely bound

entities, M and Cl2, and that they can be treated indepen-

dently of one another.

1. Hyperfine Tensor

The spin Hamiltonian used to describe the behavior of

a molecule in a magnetic field can be written (Eq. (16))

V = gg HS + KS I + Y(S+ +S-)I + X-(S+I++S I)
o z z z z

+ X+(S+I- + S-I+)
where
+ AAA2 A2
X= -2 and Y = -cosesin .
4K 4 2K g

In Appendix B, the matrix elements and the Hamiltonian

matrix are derived for basis eigenvectors of the type

IS,M)II,m) where S,M,I, and m have their usual meaning.

The diagonal elements of the largest magnitude involve terms

of the type F 3K, where F = gH/2g ; and the off-diagonal
+
terms are dependent upon X and Y. For the values we are

interested in, the off-diagonal elements are very small,

e.g., in the case of Mg +C2, for a typical field of about

3000.0 G, F = 1500.5 G for the parallel lines, while

X = 3.8, X = 0, and Y = 0; for the perpendicular lines,

F = 1515.7 G, while X = 25.7 g, X = 22.0 G and Y = 0.









These two particular orientations were chosen since they are

the ones of greatest interest here; in any event, all other

orientations will give values lying between these two extemes.

Therefore, a second-order perturbation theory solution can

be used in this case. This is given by Eq. (17) as

2
A A2 + K2
hv = gBoH + Km + K [1(1+1) m2]
4gHo K


for the parallel and perpendicular positions since in this

case, either sin 8 or cos 6 equals zero, making the last term

of Eq. (17) equal to zero.

From the values of A and A thus determined, the

values of A. and of Adip can be obtained from Eqs. (3 & 7)

by

Ais = (A + 2A )/3 and Aip = (A A )/3

A. is correlated with the Fermi contact term. It measures
ISO
the spin density at the nucleus. Adip, on the other hand,

is a measure of the anisotropy of the ion. It is usually

correlated with the amount of p-character of the wavefunction

describing the system. The values obtained for Aiso and Adip

from the experimentally determined hyperfine splitting are

listed in Table XIV for all the different complexes studied.

As will be seen, the value of Adip is relatively large

in all cases and substantiates the idea that the electron

goes into an orbital with distinctive p-character. This is

to be expected if the electronic configuration of the Cl2

ion is

















TABLE XIV

MAGNETIC PARAMETERS FOR Cl2
2


Metal


35C1 37C1
A. (iMHz)* Adip(MHz)** A. (MHz)* A dip(MHz)**
iso dip iso dip


Mg 104.0 82.8 85.9 68.4

Ca 107.6 85.5 91.2 72.5

Sr 108.9 86.5 92.2 73.7

Ba 110.3 87.6 92.7 70.9

Li 108.9 86.5 91.8 73.1

Na 110.3 87.6 91.3 72.6

K 112.2 89.3 93.8 74.5


these values

these values


are within 4.0 MHz.

are within 2.0 MHz.


All
A*
All









(a 35) 2(0 35)2(0 3p)'(H 3p)4(Hg 3p) ( 3p) ,

in agreement with past work [14].

The values of A. and Adip can be correlated with funda-
iso dip
mental properties of the molecule via the Dirac equation, as

discussed in detail in Chapter II. As was shown there

(Eqs. (3 & 7))


iso 3 g n n (0))12
and

cos2e-l
Adip = onn 0 cs 2r3



The values of (o) 2 and < cs2e derived from the

values of A. and Adp found in Table XIV are listed in
iso dip
Table XV.

If the wavefunction p for the C12 ion is assumed to be

expandable by an LCAO in terms of the atomic orbitals p of

the Cl atoms, it can be seen that

(1) (1) (+ 2) (3)
SC1s + C2non-s + C3s + C4non-s

where the superscripts identify the atomic center involved

and the subscripts identify the character of the atomic

orbital. The Cs are the weighting coefficients. If the two

Cl atoms are identical, then C = C3 and C = C If the
2
wavefunction is normalized, E C. = 1 and the cross terms,
i
C. (i j), are small. It can be seen, following the
i]
















Cd
















-I







Cd






0














OCN
U











Cd




0


o "T Co r- 0
SWm CN r- o


a. i.0 C LO r4 C
0 <7> o o 10 (















M m rlM 1-1 o r-
S Ln Ln LA LA LO
(N (N (N (N (N (N (N

o 0 0 0 0 0 0














m LDn I LA LO I 7Y r
Co n n rA In rN C


H H H H H- H H













N LO LO r- Ln H L-
r o Ln co 1- co .
-V T LA L) LA


0 0 0 a 0 C C








C Cd Cd -rH C(
s U cA oa -i m


O *
O C
0 0

0 0

+1 +1


'lH -H(

4-1) 4)
-H -






H H

3 3

rfl 12


-9' a

0() a







*









procedure outlined in Eq. (18) that

A. A
C2 = C2 A_ o and C2 C2 A dip
C1 3 A atom 2 4 Aatom
iso dip


The values of these coefficients were obtained utilizing the

atomic values given by Ayscough [17] and are tabulated in

Table XVI. From the nature of the wavefunction, its coef-

ficients can be interpreted as the percent character of its

given parts. It is easy to see, then, that the wavefunction

consists of very small (the order of 2%) s-character and

a larger contribution (the order of 48%) for the p-character

for each Cl atom.

If the amount of s- and non-s-character is plotted

against the ionization potential for the donor metal, two

straight lines are obtained. This indicates that as the

ionization potential of the metal decreases, the amount of

electronic density lying on the Cl2 increases. This indi-

cates that an ion-pair, MCl.2, is formed; although its

presence is felt only to a small degree, the metal does

influence the spin density and bonding of the halogen

anion. In Figure 21, the spin density both for s- and

non-s-character is plotted against the ionization potential

of the metal. It should be noted that the scale used for

the spin-density axis for the s-character in Figure 21 is

larger than for non-s-character in order to show the small

variations.














--
W


U)
o




Ic
0-
0

0 0
o .


Lr


_J





-->

o
0 >-
n3 L


. 0 0C 0D
o oy
. C)
0 0


co r- co U -)

(^A)-VIiN 3 Od


NO IVZIZNOI


0o 0
m nz


>-



Lo


00







-0
5C
o
0
r0
















TABLE XVI

MO-WAVE FUNCTION COEFFICIENTS FOR


Ionization **
Metal Potential (eV) C2 C2


Mg 7.61 0.0182 0.467

Ca 6.09 0.018S 0.483

Sr 5.67 0.0190 0.486

Ba 5.19 0.0193 0.492

Li 5.36 0.0190 0.486

Na 5.12 0.0193 0.492

K 4.32 0.0196 0.501


(All these values are per Cl atom).

Atomic values used (Ayscough [18]).


atom
iso


= 5650 MHz.


atom
Adip = 176 MHz.

All these values are within 0.0007.
All these values are within 0.01.
All these values are within 0.01.








The lines going through the experimental points can

be determined by a least-square linear fitting program.

This program is listed in Appendix C. The lines obtained

were,

s-character Y =-2.4 x 102 X + 2.4 x 10-'
-1
non-s-character Y =-8.4 X + 5.2 x 10

where Y is the ionization potential in eV of the metal atom

and X is the corresponding s- or non-s-spin density in

atomic units.


2. g-Tensor

The deviations from go = 2.0023 in the g-values for the

molecules studied can be accounted for by mixing of 2H states

with the 2Z ground state. As was discussed in the deriva-

tion of Eq.(9a & b), this mixing of excited states enters

the wavefunction via spin-orbit coupling. The changes in

g, were shown to be, according to second-order perturbation

theory (for a general treatment, see Stone [19])

S= <(nj Lx ic (<0L xn)
g go = -2L x x 0 In
n 0
n

On the other hand, the mixing of excited states affects g

only in higher order so that the changes in g are believed

to be due to matrix effects. If it is assumed that the

matrix effects will be the same for both gl and g then it

might be more meaningful to study g, g rather than g, g ,

but since the value of Ag is very small the conventional

way of treating the problem will be used here.









The experimentally determined values of both gl and gL

are listed in Table II. In Table XVII, the values for Ag1

and ag, are listed. It can be seen there that the deriva-

tions from go of g1 are indeed very small. On the other

hand, the deviations from go of g, are approximately two

orders of magnitude larger and indicate that there are some

low-lying 2n states mixed with the ground state. It can

also be seen in Table XVII that as the atom becomes larger

within a given group of the Periodic Table, the mixing of

the excited states increases. This is very apparent, pri-

marily in the alkaline-earth metals. In the alkali metals,

on the contrary, the changes are fairly constant.

In Gilbert and Wahl's [20] calculation, they found two
2H excited states. The lowest one, 21g, lies about 2 eV

above the 2Eu ground state, a higher one, 2u lies about

3.5 eV above the ground state. These two 2H states are

assumed to have the MO configuration

2 : (Og3s)2 (0 3s) 2(a 3p)2( u3P) 3 (Ig3p) (u3P)2

2Hg: (ag3s)2(ag 3s)2(a 3p)2( 3p)4 3p)3 p)2

(See Slichter [21].) As has been discussed by Herzberg [22],

in order to have coupling between states, the parity must be

the same; i.e., since the ground state of the C12 molecule-

ion is 2 u, it can only mix with the 2fH excited state.

The sign of Ag can be correlated with the nature of

the mixed 2H state as shown by Knight and Weltner [23].

















TABLE XVII

SPIN-DOUBLING CONSTANT AND Ag FOR Cl1



Metal Ag Ag y(cm )


Mg 0.0007 0.0319 -0.0087

Ca -0.0003 0.0330 -0.0090

Sr 0.0007 0.0341 -0.0093

Ba -0.0003 0.0370 -0.0101

Li -0.0019 0.0344 -0.0094

Na -0.0017 0.0348 -0.0095

K -0.0014 0.0347 -0.0094


B = 0.136 cm -1
B=0.136 cm


these values

these values


are within

are within


All
All
All


0.001.

0.0005.








If the excited state is regular, the value of Ag1 will be

negative, whereas if the excited state is inverted, it will

be positive. In the present case, since all the values of

Ag1 are positive, it is concluded that the state that is

mixed with the ground state is inverted. Both excited

states described previously are inverted, but, for symmetry

considerations, it is concluded that the 2H1 is the one that

contributes most to the mixing. This is in agreement with

Schoemaker [14] and Slichter's [21] study of the g-tensor

for the Vk center, and also with Castner and Kanzig's [1]

experimental results.

As far as the effects encountered in moving down a

given group in the Periodic Table, it can be seen that the

effect is most noticeable in the alkaline-earth metals.

The alkali metals have an ns0 configuration,while the alkaline-

earth ones have an ns configuration after losing one

electron. If the effect encountered in the g-tensor were to

be ascribed to changes in size of the monovalent ion as one

moves down the Periodic Table, the alkali metals should dis-

play an effect similar to the one found for the alkaline-

earth metals. This is not observed and it is believed that

the differences in Ag are due to the presence of the outer-

most, supposedly very loose, electron in the alkaline-earth

ones. This electron will interact with C12 to a greater

extent as the ionic radius for the metal increases, causing

a larger perturbation on its ground state.








The values of both g, and of g, are in good agreement,

as stated before, with those determined experimentally by

Castner and Kanzig [1] and those theoretically calculated

by Schoemaker [14] for C12 in the crystal. This is inter-

preted to mean that the field exerts very little or a

similar effect on the molecule-ion in both the crystal and

the matrix.

Within the LCAO-MO approximation, Knight and Weltner

[23] showed that the deviations from go of g, can be related

to the spin-doubling constant y (see Eq. (11)) by

Y = 4 Z [(O[ Lx n) (nJBLxO)/(En-E0) 2 = -2BAg
n

where B is the rotational constant and E is the spin-orbit

operator for the molecule. Using the value of B = 0.136
-l
cm calculated by Gilbert and Wahl [20], values for y were

calculated and are included in Table XVII. This is a mea-

sure of the value expected for a free-rotating Cl2 ion in

the gas phase, if it is assumed that the metal donor con-

tributes a negligible amount. It can be seen that y does

not change its value to a large extent with the different

metals. Therefore, it is assumed chat the value of y for

a free rotating Cl2 in the gas phase, is of the order of
-0.009 cm
-0.009 cm




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