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
gTensor . . . . . . .. .16
Comparison Between Ag1 and the
SpinDoubling 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 SECONDORDER
PERTURBATION THEORY . . . . . .
MATRIX ELEMENTS FOR THE SPIN
HAMILTONIAN OF Cl ......
2
LEASTSQUARES FIT FOR A LINEAR FUNCTION
MATRIX ELEMENTS AND PROGRAM FOR BENT
F NONCOLLINEAR A AND gTENSORS . .
MATRIX ELEMENTS AND PROGRAM FOR
LINEAR F COLLINEAR A AND gTENSORS
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 shortlived 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 poorbitals with very small sorbital 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
gtensor. It was found that a lowlying 2H state is mixed
u
with the ground state via spinorbit 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 alkalineearth 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 shortlived
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
420 K), these intermediates can now be isolated and studied
in a gaslike 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 gaslike 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 watercooled
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 singlecrystal 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
WATERCOOLED
ELECTRODES
TEMPERATURE
WINDOW
CAVITY
Figure 1. Dewar and Furnace Apparatus
ROTATABLE
FLAT
SAPPHIRE
ROD
BRIDGE
conductivity of singlecrystal 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 vacuumtight 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 105 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 106 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 1atm/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 codeposition 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 halflives 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 V4500 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 Xband 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 chromelgold
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 variabletemperature 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 gfactor (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 gvalue for the
molecule under study. In the present case, an Xband 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 (nonrotating in this
case) molecule in the absence of spinorbit
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 nuclearspin 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 (HI) 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 [LI + 3(Sr)(rI) SI
3 F ~
+ O SI(rJ (Ic)
where L, S, and I are the orbital, electronspin 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 gfactors, respec
tively. is the molecular spinorbit 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
LS 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 6function
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
scharacter 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 secondorder 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 offdiagonal elements can be made equal to zero
by a suitable rotation of the axes (see the discussion on
each tensor below). If the zaxis 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
scharacter of the wavefunction (the Fermi contact term) and
one due to the nonscharacter of the wavefunction (the mid
dle two terms). Calling these two types of interaction Ais
for the one dependent on the scharacter and Adip for the
dip
one dependent on the nonscharacter 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])
2K3X> 0 0
T g gnn 0 0
0r r5 )
02 323
and, therefore, it is a traceless tensor. It has been
assumed that the offdiagonal 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 zaxis, 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]).
gTensor
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)  LSI _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 socalled Kramer doublet representing degenerate wave
functions, which will, however, have different energies in
a magnetic field (see Carrington andMcLachlan [7]).
Now, LS can be written as
L*S = L S + L S + L S = L S + (L+S + LS)
~ ~ 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)
sl> = 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)
Inzero spin integrals are
BI sla> = 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 < L10 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 xdirection (if it acts in the ydirection
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 offdiagonal elements of the gtensor 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
SE E
n n 0
where the terms proportional to t2/(EnE )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 SpinDoubling 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 spindoubling constant and
has been shown by Van Vleck [8] to be given by
y = 4 (01o Lx n) (n BLxl0)/(EnEo)
n
where In) includes all excited 2H states, x is an axis per
pendicular to the symmetry axis, E is the spinorbit 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)/(EnEO) (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 = (Alg1 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 secondorder perturbation solution suffices.
The allowed transitions are observed when 6M=1 and
Am= 0, where M= S,Sl,...,S and m= I,Il,...,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 nons
where 0s and nons are the atomic orbitals representing an
stype orbital and the nons character is collected under
nons. In most cases these latter orbitals refer predomi
nons
nantly to the pcharacter, but since mixtures of dfunctions
are conceivable, particularly for the Cl case, it will be
left as nons. 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 spinorbital (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 spinorbital *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 "plusspin" 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 manyelectron 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 spindensity functionby
Q (r ) (P:'(r) ())
s 1 1 
since this measures the resultant zcomponent of spin (excess
of upspin over downspin 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 oneelectron 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 spindensity 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 gfactor 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 [1526].
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 gfactor 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
SI 0
c"00
'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 (IH type) has been omitted since it
is usually small. The nuclear quadrupole interaction has
also been omitted for the same reason. To firstorder 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,
McGrawHill, 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 shortlived, 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 [713].
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 ChromelAlumel 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 icewater bath.
The matrices formed were all opaque, greenishyellow 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 alkalineearth
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 35Cl35Cl sixteen lines for the
35C137Cl, and seven lines for the 37C137C1
(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_
 S00g
=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
r4
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 3535 case is located. In the
same region there are one 3737 and two 3537 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 alkalineearth 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 alkalineearth 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 secondorder 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 gvalue 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
 GI
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 gvalue 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 nriSrCI
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
gvalue 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 gvalue 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 variabletemperature
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 + SI+)
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 offdiagonal
+
terms are dependent upon X and Y. For the values we are
interested in, the offdiagonal 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 secondorder 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 pcharacter 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 pcharacter. 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
cos2el
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 + C2nons + C3s + C4nons
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 11 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(
41) 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%) scharacter and
a larger contribution (the order of 48%) for the pcharacter
for each Cl atom.
If the amount of s and nonscharacter 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 ionpair, 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
nonscharacter is plotted against the ionization potential
of the metal. It should be noted that the scale used for
the spindensity axis for the scharacter in Figure 21 is
larger than for nonscharacter 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
MOWAVE 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 leastsquare linear fitting program.
This program is listed in Appendix C. The lines obtained
were,
scharacter Y =2.4 x 102 X + 2.4 x 10'
1
nonscharacter 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 nonsspin density in
atomic units.
2. gTensor
The deviations from go = 2.0023 in the gvalues 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 spinorbit coupling. The changes in
g, were shown to be, according to secondorder 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
lowlying 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 alkalineearth 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
SPINDOUBLING 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 gtensor
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 alkalineearth 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 gtensor 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 alkalineearth
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 moleculeion in both the crystal and
the matrix.
Within the LCAOMO approximation, Knight and Weltner
[23] showed that the deviations from go of g, can be related
to the spindoubling constant y (see Eq. (11)) by
Y = 4 Z [(O[ Lx n) (nJBLxO)/(EnE0) 2 = 2BAg
n
where B is the rotational constant and E is the spinorbit
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 freerotating 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
