NUCLEAR QUADRUPGLE RESGNAN‘CE STUDY
OF CHARGE-TRANSFER COMPLEXES

Thesis for flu Degree of DE. D.
MICHEGAN STATE UNEVERSITY

James Austin Ryan
1967

 

 

TH ‘u L
a” 'J LIBRA 12 Y

Michigan State
University

    
   

This is to certify that the

thesis entitled

Nuclear Quadrupole Resonance Study of Charge-Transfer
Complexes

presented by

James Austin Ryan

has been accepted towards fulfillment
of the requirements for

fliL—degree mghs'm—iflx

Wfizw
;' ( finial-wt;

Date December 16, 1966

0-169

 

ABSTRACT

NUCLEAR QUADRUPOLE RESONANCE STUDY
OF CHARGE-TRANSFER COMPLEXES

by James Austin Ryan

A nuclear quadrupole resonance Spectrometer of the
Dean type has been constructed both for frequency and field
modulation and for display of the signal either on an
oscillosc0pe screen or, by use of a lock-in amplifier. on
a recorder.

New chlorine quadrupole resonances have been found in
the following charge-transfer complexes, SbCls-POC13,
Fec13-Poc13, TiCl4-2POC13 and (TiCl4-POC13)2. These reso-
nances were observed both at liquid nitrogen temperature and
at room temperature, although in all cases the resonances
due to the chlorine nuclei of POC13 in the complex molecule
disappear below room temperature. A study of the temperature
dependence of the resonance due to the "axial" chlorines of
the SbCls part of SbCls'POC13 has been made. This study indi—
cates a possible phase transition between 770K and 1650K.

An estimate of the contribution of the solid-state
effect to the observed resonance frequencies has been made
assuming that the partially charged atomic sites in the

lattice may be replaced by point charges and that this lattice

James Austin Ryan

of point charges makes the dominant contribution to the
measured field gradients. A comparison of the calculated
contributions of the lattice charges with the measured contribu-
tions indicated that the Sternheimer antishielding factor
for chlorine is much smaller than the value previously used
by other workers.

The shift in the absorption frequency of the chlorine
atoms of POC13 in the complex, compared to their frequency
in solid POCls itself, was used to estimate the relative
amounts of charge shifted from donor to acceptor on complex
formation for the complexes studied.

The absorption frequencies due to chlorine atoms of
SbCls and SnCl4 in SbCls-POC13 and SnCl4°2POC13 were used both
to indicate the existence of nonequivalent bonding orbitals
on the central metal atom and to estimate the total charge
shifted to the central atom upon complex formation. The
problems associated with the interpretation of NOR data for

donor-acceptor complexes have been discussed in detail.

NUCLEAR QUADRUPOLE RESONANCE STUDY

OF CHARGE-TRANSFER COMPLEXES

BY

James Austin Ryan

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Chemistry

1967

ACKNOWLEDGMENTS

The author is deeply indebted to Professor M. T. Rogers
for his guidance and encouragement during the course of this
work.

He would also like to give special thanks to Dr. V.
Nagarajan for his valuable advice and assistance in the con-
struction of the NQR Spectrometer and Professor R. Schwendeman
for several stimulating discussions.

The experimental assistance of Mr. Michael Buckley,
Mr. Russel Geyer and Mr. James Grumblatt is gratefully
acknowledged.

Finally the author would like to thank the Atomic Energy
Commission and the Dow Chemical Company for financial support
during a part of this work.

ii

TABLE OF CONTENTS

Page
.INTRODUCTION . . . . . . . . . . . . . . . . 1
I. THEORY AND BACKGROUND. . . . . . . . . . . . . . 4
Physical Theory. . . . . . . . . . . . . . . . . 4
A. Absorption Frequencies . . . . . . . . . 4
1) Basic Equations . . . . . . . 4
2) Absorbtion Frequencies and U .
Selection Rules . . . . . . . . . 12

B. Zeeman Splitting of Quadrupole Spectra . 18
C. The Effect of an Electric Field on an

NQR Absorption Line. . . . . . . . . . 21
D. The Effect of Temperature on the NQR

Absorption Frequency . . . . . . . . 26
E. The Effect of Internal Electric Fields
on the NQR Frequencies . . . . . . . . . 52
Chemical Interpretation of NOR Data. . . . . . . 40
A. Atomic Field Gradients . . . . . . . . 40
B. The Townes and Dailey Theory of Mole-
cular Field Gradients. . . . . . . . . 44
C. Evaluation of the Parameters of the
Townes and Dailey Equation . . . . . . . 57
Previous NQR Studies of Charge Transfer Com—"
plexes. . . . . . . . . . . . . . . . . . . 63
II. EXPERIMENTAL . . . . . . . . . . . . . . . . . . . 70
A. The Nuclear Quadrupole Resonance Spec-
trometer . . . . . . . . . . . . . . . . 7O
1) Introduction. . . . . . . . . . . . 7O
2) Superregenerative Oscillators . . . 75
5) Modulation and the Lock—in Ampli- '
fier. . . . . . . . . . . . . . . . 82
4) Frequency Measurement . . . . . . . 89
5) Spectrometer Operation and Problems
in Detecting Resonances . . . . . 95

6) Temperature Dependence of the 27. 512
MHz Resonance in SbCls POClg. . . . 101
B. Chemical Synthesis . . . . . . . . . . . 101
1) Trans-dichlorobisethylenediamine
Cobalt(III) Chloride-HCl'ngo . . . 101

iii

TABLE OF CONTENTS - Continued Page

2) The Cu(I) Complexes of Some Thio-
semicarbazones. . . . . . . . . . . 105
5) Mercuric Chloride Complexes . . . . 104
4) The Complexes of ICl with Pyridine
and Its Derivatives . . . . . . . . 106
5) Binary Complexes of POC13 . . . . . 106
6) Ternary Complexes of POCla. . . . . 112

III. CALCULATION OF THE CONTRIBUTION TO THE MEASURED
FIELD GRADIENT FROM CHARGES SITUATED IN THE
LATTICE. . . . . . . . . . . . . . . . . . . . . 114

A. Introduction . . . . . . . . . . . . . . 114
B. Theory . . . . . . . . . . . . . . . . 118
C. Some Details of the Modification and Use
of LATSUM. . . . . . . . . . . . . . . . 125
D. A Test of LATSUM . . . . . . . . . 125
E. The Crystal Lattice Field Gradient Model
and Programs ROTATE and DIAG
1) The First Model . . . . . . . . . . 126

2) An Improved Model . . . . . . . . . 128
5) ROTATE. . . . . . . . . . . . . . . 151
4) PROGRAM DIAG. . . . . . . . . . . . 154
IV. RESULTS. . . . . . . . . . . . . . . . . . . . . 158

A. Assignment of Absorption Frequencies to
Specific Atoms in the Complexes. . . . . 158

1) SbC15°POC13 . . . . . . . . . . . . 158
2) SDC14'2POC13. . . . . . . . . . . . 143
5) (Tic14 POC13)2. . . . . . . . . . . 144
4) Pure SbC15.. . . . . . . . . . . 144
B. New Resonance Frequencies and Their
Temperature Dependence . . . . . . . . . 146

C. Compounds in Which No Resonances were
Found. . . . . . . . . . . . . . . . . . 152
D. LATSUM, ROTATE, and DIAG Results . . . . 156
1) Tabulated Results of LATSUM and
ROTATE. . . . . . . . . . . . . . . 156
2) Comparison of the Lattice Sum Re-
sults Using Both the First Model
and the Revised Model . . . . . . . 180
5) DIAG Results. . . . . . . . . . . . 180

iv

TABLE OF CONTENTS - Continued Page

V. DISCUSSION. . . . . . . . . . . . . . . . . . . . 187

A. Temperature Dependence of the Absorption
Frequencies and Phase Transitions . . . . 187
B. Calculation of the Point-Charge Field
Gradient. . . . . . . . . . . . . . . . . 195
C. Frequency Shifts in the Complexed POC13
Chlorine Atoms. . . . . . . . . . . . . . 200
D. Shifts in the NQR Spectra of SnC14 and
SbCls Upon Complex Formation. . . . . . . 204
1) General Comments . . . . . . . . . . 204
2) SnCl4-2POC13 . . . . . . . . . . . . 206
5) Sbc15-Poc13. . . . . . . . . . . . . 211

SUMMARY. . . . . . . . . . . . . . . . . . . . . . . . 215
REFERENCES . . . . . . . . . . . . . . . . . . . . . . 216

APPENDIX . . . . . . . . . . . . . . . . . . . . . . . 225

TABLE

10.

11.

12.

15.

14.

LIST OF TABLES

Secular Equations for Nuclei with Half—
Integral Spin. . . . . . . . . . . . . . . . .

Formulas for the Nuclear Quadrupole Resonance
Frequencies. . . . . . . . . . . . . . . . . .

Quadrupole Coupling Constants of Halogen Con-
taining Molecules Which Have Been Measured
Both in the Solid and in the Gaseous State .

NQR Data Indicating Hydrogen Bonding . . . . .

2
Values of anO = gig for Various Atomic States

Frequency Shifts Upon Complex Formation Be-
tween Brg and Some Substituted Benzenes. . . .

NQR Resonance Frequencies in Charge Transfer
Complexes Compared to the Resonance Frequenc-
ies in the Pure Compounds. . . . . . . . . . .

Physical Dimensions of the Coils Used With the

High Range Oscillator. . . . . . . . . . . . .
Comparison of q and n as Calculated Both by
LATSUM and by Other Authors. . . . . . . . .
Charges Used in LATSUM . . . . . . . . . . .

Resonance Frequencies for the Compounds
Studied in This Work . . . . . . . . . . . .

Temperature Dependence of the Most Intense
Line of SbCls'POC13 . . . . . . . . . . . .

Coupling Constants and Field Gradients for the
Compounds Studied in This Work . . . . . . . .

Temperature Coefficients for the Chlorine
Resonances of Complexed SbCls and SnCl4. . . .

vi

Page

16

17

58

59
42

64

67

99

126
151

148

149

150

152

LIST OF TABLES - Continued

15. Compounds in which NQR Absorptions were
Missed. . . . . . . . . . . . . . . . . . . .

16-572 LATSUM and ROTATE Results for the Complexes
Studied in This Work. . . . . . . . . . . .

58. Comparison of LATSUM Results Using the New
Charges to LATSUM Results Using the Old
Charges . . . . . . . . . . . . . .

59. Line SplittingslAql and "Experimental" Values
of y . . . . . . . . . . . . . . . .
oo

40. DIAG Results. . . . . . . . . . . . . . .

41. Temperature Factors for SnCl4°2POC13. . .

42. Bond Angles (in Degrees) and Bond Lengths (in
ngstroms) of POCl3 in Various Complexes From

X-ray Investigations. . . . . . . . . . .

45. Electronic Charge Lost by the POC13 Chlorine

Atoms Estimated from NQR Data . . . . . .
44. Charge Transfer in Complexed SnCl4. . . .
45. Charge Transfer in Complexed SbCls. . . .

vii

Page

154

158-179

181

182
. 184
192

. 201

205
210

215

FIGURE

1.

2.

10.

11.

12.

15.
14.
15.

16.

LIST OF FIGURES

Pictorial representation of the various
vectors and volume elements. . . . . . .

Splitting of the quadrupolar levels by a mag-

netic field.

Assumed electric field direction

Line width

change with temperature for

a) Hexachlorobenzene, b) 1, 2, 5- Trichloro-

benzene. .

A plot of the Sternheimer factor (7

) versus

ionic charge for helium-like ions. . . . . . .

Ionicity versus electronegativity difference
according to the approximations of Pauling

(80).

High Range

Gordy (60).

and Townes and Dailey (44)

(15-55 MHz) Oscillator. . . . . . .

Low Range (2-20(MHz) Oscillator) . . . .

Modulation

unit for the NQR Spectrometer

Block diagram of the NQR spectrometer. . . . .

The partial Spectrum of SbCls'POCls showing

the 50.560
also shown
line . . .

Definition
ROTATE . .

A molecule
A molecule

A molecule

and the 50.616 MHz absorption lines;

are the quench Sidebands from each

of the angles a and 8 as used by

Of SbCls'POCls. . . . . . . . . . .
Of SDC14'2POC13 . . . . . . .

Of the dimer [TiCl4'2POC13]2. . . .

Temperature variation of the most intense
SbCls resonance of SbC15°POC13 . . . . . . .

viii

Page

19

24

28

56

62
74
75
85

90

91

155
159
140

141

151

INTRODUCTION

Although the first pure quadrupole resonance was ob-
served in 1950 (1), as yet no extensive application of this
technique has been made to chemical problems. This is not
due to a lack of potential applications but rather to experi-
mental difficulties and the fact that the theory which con—
nects experimental results to molecular structure is not,
as yet, well deve10ped. Since the absorption frequencies
measured by nuclear quadrupole resonance (NQR) spectroscopy
may be interpreted in terms of migration of charge away
from or toward, the resonant nucleus, this method is ideally
suited to the study of charge-transfer complexes.

At the beginning of this work there had been several
NQR investigations (2-9) of charge-transfer complexes
reported in the literature, but the results of these investi-
gations seemed somewhat chaotic. In some cases they indicate
no charge transfer while in other cases possible Shifts are
obscured by solid-state effects on the resonance frequency.
Finally, in the cases where an unambiguous charge-transfer
effect is seen in the NQR absorption frequencies, no attempt
has been made to study the size of this effect in a series
of charge-transfer complexes. The solid-state effects,

which result in a Splitting of NQR lines, have been known

since the beginning of NQR Spectroscopy but they have never
been studied in detail. The usual method for taking them
into account is to take an average of the measured fre—
quencies. Unfortunately for the study of charge-transfer
complexes, this method is unsatisfactory because the split-
tings may be of the same order of magnitude as the charge-
transfer effects.

In this work an NQR Spectrometer was constructed and
used to study charge-transfer complexes. The complexes
studied were chosen because chemical and X-ray data indicated
that strong charge transfer takes place and because they
represent a chemically related series. The adducts studied
are formed by a transfer of electrons from the Lewis base
POC13 to a Lewis acid. They include [TiCl4'POC13]2, SbC15°
POC13 and FeCla‘POCla which, together with the previously
investigated SnCl4°2POC13 (9), form a series whose charge
transfer Should be related to the strength of the Lewis acid
involved. Furthermore, since complete X-ray data are avail-
able for SbC15°POC13, [TiCl4’POC13]2 and SnCl4'2POC13, an
investigation of the solid—state effects was possible.

A calculation of line splitting as a function of the
Sternheimer parameter was made assuming that the field
gradient produced by charged ions situated in the crystal
lattice dominated the charge-transfer effects. This calcu-
lation, which assumes a model that replaces the charged ions

by point changes whose magnitudes are dependent on the

ionicity of the bonds in which the ions are involved, pushes
to the limit some segments of the NQR theory. Thus results
from this work may be used to evaluate this theory.

The molecular field gradients, which were obtained from
the experimental absorption frequencies after allowance was
made for solid-state effects, were then used to evaluate

the extent of charge transfer.

I. THEORY AND BACKGROUND

Physical Theory

A. Absorption Frequencies

1) Basic Equations
The overall Hamiltonian HEL describing the interaction

between a charged nucleus and the surrounding electronic

charge may be written as
pe(re)pn(rn)dvedvn ’ (1)

H =+f
EL V r

 

\ /
Nuclear
\ // K" surface

f //

 

Figure 1. Pictorial representation of the various
vectors and volume elements.

where pe is charge density of the electrons external to the
nucleus in the volume element dVe at position re with
reSpect to the center of the nucleus under discussion, on

is the charge. density of the volume element an within
the nucleus at a position Vn with respect to the center of
the nucleus. Also, Vn is a vector from dVn to dVe and Gen

is the angle between r and r as shown in Figure 1. From

e n

the law of cosines

1 '2'
'— = (r 2 + r 2 - 2r r cos 9 )
r e n en (2)
r 2 2r -%
= l- (1 + (-2) - -—3 cos 9 )
r r e
e e e
rn
which can be expanded in a power series in-;— to yield
e
r I" 2
_1.= 1 _11 _I1 +....
r r (1 + r P1 + (r ) P2- ), (3)
e e e
where PE is the Legendre polynomial of cos Gen; i.e.,
P1 = cos een
- 4. 2 _ (4)
Pg 2 (5cos Gen 1)
etc.

The first term of this power series corresponds to an
electric monopole, the second to an electric dipole, the
third to an electric quadrupole and, in general, a term in

2. We shall

Pg corresponds to'a multipole moment of order 2
be concerned with the term in P2. In particular we are
interested in the energy levels which arise due to this term.

Substituting Equations 5 and 4 into 2 we obtain the equation

_ 1 (5)
H — f f V 2p -§ (5 cosaeen -1)pe(re)/re3 andVe

9 V5; Vri n n

for the nuclear electric quadrupole interaction. This
equation is valid only if re)»rn, since it is only under
these conditions that the expansion (Equation 5) is valid.
This restriction has the effect of excluding from our con-
sideration electronic charge which actually penetrates the
nucleus. This is not serious, however, since only s
electrons have a non-zero probability of penetrating the
nucleus and because of their Spherical symmetry they have no
interaction with the nuclear quadrupole moment. Equation 5
may be expanded in Cartesian coordinates using the relation-

ship

r r cose = Z X X to yield
n e en 1

ni ei
H = r f (r )[é-Z x x x x - ;-r 2r 2] (6)
Q 4 Dn n 2 .. ni nj ei ej 2 n e
Ve Vn l

X pe(re)/re3dvndve.

However, if we define Qij and.(vE)ij by the relationships

= _ 2
Qij é pn(Vn) (5xnixn-j éij rn )dvn
n

(7)

 

X .X . + X -X .
= f on(vn) [ 5( n1 ”3 n3 n1) - 5--r 21dV

Vn 2 13 n n
and
_ ~ .1
(VE)ij - - éepe(re)8/BXi d/ij( re)dVe (8)
= - é pe(re)/re5 [5XeiXej - éijre2]dVe

e

 

pe(re) xeixej + xejxei 2
- -J —;;S—- [5<; 2 > '- oij re ]dVe.
e
Then,
1 = =
= - — Z .. .. = :
HQ 6 ij013 (vmlj Q vs (9)

where the double dot indicates a scalar product of two

second rank tensors; this may be verified by direct expansion
of Equation 9 using the first form of Equation 7 and the
second form of Equation 8. Thus, we have seen that HQ can

be completely described by two tensors S (the quadrupole
tensor) and -V_-E (the electric field-gradient tensor) whose
elements Qij and (vE)ij have been defined by Equations 7

and 8, reSpectively. Furthermore, the two tensors are sym-
metric and it can be seen by inspection of Equations 7 and 8
that both a and 6E are traceless.

Ramsey (10) has shown that the elements of the Q tensor

Qij may be represented in the form

Q = C[5(<Ii)<lj) + (Ii)(Ii))

_ "2*
ij 2 5 I 1 (10)

ij N
where Ii and Ij are components of the nuclear spin operator

I and C is a constant scalar quantity. The arbitrary constant
C may be expressed in terms of the scalar nuclear quadrupole
moment Q which is a measure of the departure of a nucleus

from the shape of a perfect Sphere. By definition

2;. 2_ 2
Q _ e f pn,mI=I[szn rn ]an. (11)

where the subscript m = I indicates that the integral is

I

carried out for the nuclear state whose magnetic quantum

number mI = I. Q has the dimension of length squared.

It is positive for a prolate Spheroid and negative for an

oblate Spheroid. But

.4 2_- 2 - .

e.f pn,mI=I [5Zn rn ]an 18 equal to the matrix element
<I II Q33( I I> = c < I I |5(IZ)2 - 12 I I >

= C[5I2 - I(I+1)] = c I (21-1), (12)

using Equation 11. Hence,

I I + I I

eQ i j yj i _
ij 'ITEI:IT [5( 2 ) éijlg]. (15)

Q

It is of interest here to point out that while nuclei
of Spin I > 1 have non-zero quadrupole moments, nuclei of
Spin I = 0 and I =-% do not necessarily have to have a zero
quadrupole moment (14). It often has been written that
nuclei with I < 1 have zero quadrupole moments, this is in-
correct. However, it is impossible to observe a nuclear
electric multipole moment of 23 greater than that correspond-
ing to 2 = 21. This is easy to prove. From Equations 5 and
1 we can see that insofar as the nuclear coordinates are con-

2

cerned the interaction for the 2 th moment is proportional to

f r p (r )P dV . (14)
Vn n n n E n

but if wn is the nuclear part of the total wave function

W

_ - 2 *
total - wewn,Equat1on 14 becomes 5 rn ¢nP£¢nan.

n
However, if the angular momentum of the nucleus is I then

wn must be an eigenfunction corresponding to an angular
momentum of I. Since 5i has no angular dependence but PE
has an eigenvalue of 2 under operation by the angular
momentum operator, rfiwn and Pgwn correspond to eigenfunctions
with angular momentum eigenvalues of I and between I + fl

and II - 2 l, respectively. In order that Equation 14 not
vanish rfiw; and Pgwn must correspond to the same eigen-
values; hence, I must lie between I + Z and II - fl .

This can only be true if E‘s 21 hence for nuclei Of'Spin I
multipole interactions of order 22 where Z > 21 cannot take
place.

Returning to the quadrupole interaction let us examine
the electric field gradient tensor 57?. The elements (VE)ij
previously given are identical to Vij' where Vij =§%E%§f ,
and V'is the electrostatic potential at the nucleus
3)

(the units of Vij are cm‘ . In the usual notation.X1=x',

X2=y', and X3=z' where the primes indicate that we are not
yet in the principal axis system. Since (7E is traceless
and symmetric

Y'Y' + Vz‘z' = O (15)
and we need specify only five elements to completely Specify

the tensor.

10

These elements are:

(VE)0 = % V2.2.

1 .
(VE)i1 7JE‘Vx'z' 4.1Vy.z.)

.21.
(VE)12 - 2J6 (Vx‘x' -vy'y' i'zvx'y')

Any symmetric tensor may be diagonalized, this diagonalization
corresponding to a transformation to the principal-axis

system. The diagonalized tensor has components

_ 1, 2.1
(VE)Q - 2 sz — 2 eq
(vs)i1 = o (16)

1 1
(VE)42 - 2J6 (Vxx-Vyy)- 2J6 n eq.

This correSponds to the definitions

_.1
q — e sz and
(17)

(v -v )/v

n xx yy zz .

Using the convention I VXX (g_l Vyy lg_|vzz|, n may vary

from 0 to 1. For n = 0, V = V = - 2-V and for n = 1,
xx yy 2 zz
V = 0 and V = -V . The first condition corresponds to
xx yy zz

cylindrical symmetry. For chlorine atoms involved in single
bonds it is a very good approximation to assume cylindrical
symmetry, therefore the assumption is usually made that n = 0.
An expression must now be derived which will relate the
observed resonance frequencies to the quantities q and n.

We proceed by writing an expression for the quadrupole energy

level designated by the quantum number m, where m can take

11

the values m = +I, I-1, .... -I, these numbers corresponding to
the allowed spin orientations in the electric field gradient.
Thus, it is necessary to calculate the matrix elements
(mlHolm'> for the two cases of axial (fi=0) and non-axial

(n#0) field gradients. To calculate the matrix elements we
need only know the general behavior of wave functions ¢n(m)
with the angular momentum Squared operator I2 and the angular

A . A A A .
momentum operator I, With components Ix, Iy and I2, 1.e.,

(mllem'>==m6mm' and (mllxiilylm'>= [(I m)(I¢m+1)] ém¢1,m'

(18)
where 6 is the familiar Kroneker delta. Using these relation—
ships we can write (Equation 19) the only non-zero matrix

elements (15). Since

 

= _.1 = eQsz 2_ 2 eQ(Vxx:YYY)
HQ 6 §.Qij( E)ij 41(21-1)[512 I 1 + 41(2I-1)
j 2 2]
I - I
and [ X y '
_ _ _ =e2 2—
(mlHQIm>—-< mlHQl m> 4I%%I:I) [5m I(I+1)] and (19)
<m[Hle12>==<-m|HQ|-mi2>==<mi2|HQ|m>==<-mi2|HQl-m> ; then
2399... .n 2' -i
E = [I(I+1)-m(m+1)] [(I+1)I-(m11)(mi2)] ;

41(21—1) 2

the quantity e2qQ is commonly called the quadrupole coupling
constant and is identical with qu' which is another common
notation Since q'E eq. For n = 0 we have only diagonal non-
zero matrix elements <mIHQ|m> and use of Equations 18

immediately yields

12
Em = <mIHQ|m> = A[5m2 - I(I+1)] (20)

where we have used the common notation A = e2qQ/4I(2I-1).
We see immediately that all levels except m = 0 are doubly
degenerate. Thus, for half-integral Spins there are I +-§

energy levels and for integral Spins there are I + 1 levels.

2) Absorbtion Frequencies and Selection Rules

 

In order to derive the selection rules it is necessary
to consider a mechanism by which transitions between energy
levels are produced. Although it is possible in theory to
induce transitions by application of an electric field
gradient, in practice this would require a field gradient
which is too large to be produced in the laboratory. In order
to induce an observable number of transitions, we must,
therefore, turn to an oscillating magnetic field which can
interact with magnetic dipoles; that is, electromagnetic
radiation. The time dependent Hamiltonian representing this

interaction may be written as
H(t) = -yh(HXIX + Hny + HZIZ) (21)

where 7 is the magnetogyric ratio, h is Planck‘s constant,
Ix, Iy and I2 are the components of the angular momentum
operator and Hxl'Hy and H2 are the components of the linearly
polarized oscillating magnetic field. The matrix elements
<mlH(t)'m‘>2will then be proportional to the transition prob-

abilities and may be calculated with the aid of Equation 19.

15

We then find that the transitionslAmJ = 0 and 1 are allowed;
these then are the selection rules for the case of n = 0.

Furthermore, it can be shown.following the treatment of Pake
(15) for the case of magnetic resonance.that maximum transi-

tion probability occurs when the Bohr condition

 

w = - (22)

is satisfied. We may now write, using Equations 20, an

expression for w:

a. = {115 (2|m|+1). ’ (25)

There are (I + %)doubley degenerate energy levels for half—
integral spins and I + 1 doubly degenerate levels for integral
nuclear Spins. If I and m are known, which is usually the
case, then equ/h (in units of MHz) may be calculated
directly from the measured value of absorption frequency.

If the m value is not known, and this situation may only arise
for spins I > 5/2, the values of ml and ma may be uniquely
determined by measuring the ratio -$:-= %%E:+$—% .

For the case of n # 0 the problem of writing down ex-
pressions relating ean, n and w becomes much more complex.
Now we must also consider matrix elements of the type calcu-
lated in the second of Equations 19. This results in the mix-
ing of the pure magnetic dipole states with states differing
in m by.i 2. Because of this the selection rules 'Am|= 0.1

no longer hold and for values of n) 0.1 the probability for

14

observation of transitions correSponding to lAm|= 2 becomes
quite large. Reddoch (15) has observed the 93Nb(I = 9/2)
resonance in NbCls. The observed spectrum contains lines due
to transitions for which IAm|= 2 and even IAmI= 5. The
calculated relative intensities for n = 1/5 in the transi-
tions lAmI = 1, [Aml = 2 and lAml = 5 are, respectively,

129, 54 and 7.8. In some cases the degeneracy of the doubly
degenerate levels is removed. For the case of I = 5/2 we

now have to consider the matrix elements Hm,mi2 =< mlHQImiZ>
in addition to the matrix elements Hmm <m|HQ|m>; the

Hamiltonian matrix now becomes

0 Hi” i’ -' E 0 Hi , _ .3
H =
H__é_’§_ O H‘fi-é‘ - E 0
O H‘B'Ié‘ O H__3__a_ - E

where Hi Epi-E = 5A, gi-§.i-§ = -5A and 34-4'1-3 =If5 A n.

This matrix may be put into the diagonal form by simply re-
arranging rows and columns. When this is done two submatrices

are obtained along the diagonal, the first of which is

Hes” Hit-4
3-43 H44”

15

This submatrix yields a secular equation E2 -5A2 (54-n2) = 0,
using the previously tabulated values of the matrix elements.
This equation can be solved exactly to yield Eg.=:22gg(i+%;)§
and E_§ =-:EZQQ(1+%E)5. Solving the second matrix gives

E9 = E-g and Efi = 31%? thus, the mixing of the magnetic
dipole states does not remove the energy level degeneracy.

Using the Bohr condition one then obtains

.32 1_12339. 113*}
w‘*2_’iz)-2(h”1+s)- (24)

In a similar manner the other secular equations may be de-
rived. Except in the case of I e 1 it is not possible to
obtain an analytical solution for these equations. For the
case I = 1 it is found that the degeneracy of the levels is

lifted; in this case two frequencies are predicted
=éeng _=§e‘2_qQ _
w+ 4( h )(1 + n/5) and w 4:( h )(1 n/5).

It is thus possible to obtain ‘both n and ean from an ob-

servation of w and w_. It is not possible to measure both

+
e2qQ and n for nuclei with I ?'% (e.g. 35€1,81Br) because
only one resonance frequency is observed. As mentioned
previously the assumption is made that n = 0 for chlorine
resonances; from Equation 24, if n = 0.1 this assumption in-
volves an error of about 150 kHz. This value for n is seldom
exceeded even if a moderate amount of double bonding is
present. The secular equations for the cases I = 5/2, 5/2.

7/2 and 9/2 are tabulated in Table 1; these are the most

important values for the purposes of quadrupole resonance.

16

Table 1. Secular Equations for Nuclei with Half—Integral Spin

 

I“ _====—.

 

I Secular Equation Units of Energy
5/2 52 — 5(5 + n2) = 0 e = E/A
5/2 53 - 7(5 + n2)e — 2(1 — n2) = O a = E/2A
7/2 54 - 14(5 + n2)€2 - 64(1 - n2) 5
+ 55(5 + n2)2 = 0 e = E/5A
9/2 as - 11(5 + n2) 53 - 44(1 - n2) 52
+-%§(5 + n2)2€ + 48(5 + n2)
(1 - n2) = 0 e = E/6A

 

Except for the cases I = 1 and I = 5/2 these equations
are not analytically solvable. Various methods have been
used in obtaining solutions for them. Cohen (18) has given
the numerical solutions of secular equations for I = 5/2,
7/2 and 9/2 and has tabulated eigenvalues for values of n
from 0 to 1.0 in steps of 0.1; Livingston and Zeldes (19)
have tabulated the numerical solution for I = 5/2 in steps
of 0.001; Reddoch (15) has numerically solved and tabulated
results for I = 9/2 and n2 from 0 to 1 in steps of 0.01.
Numerical solution seems to be the best approach. Bersohn
(17) has expanded 8 in a power series in me about n = 0 which
is valid for low values of n(n Z:0.25). When this value for
n is substituted into the Hamiltonian a perturbation treat-
ment allows us to extract expressions for absorption fre-

quencies in terms of n and these are presented in Table 2.

 

'V

c.‘

 

17

Table 2. Formulas for the Nuclear Quadrupole Resonance
Frequencies

 

H
I)
g.»
8
ll

1 5/4 equ/h (1 + 3/5)
5/4 ean/h (1 - n/5)

E
II

I = 3/2 on = Y/Zean/h (1 + nos)?

. 2 '
I = 5/2 wl 5/20(§EQQ)(1 + 0.0926q2 - 0.654n4)

' 2
mg = 6/20(§399)(1 - 0-2057n2 + 0.162q4)

2 ~ I I
I = 7/2 wl = 1/14(§EQ9)(1 + 50.865q2 - 101.29n4)
2 . _
42 = 2/14(3399)(1 - 15.867q2 + 52-052n4)
. 2 i i '
ws = 5/14(3399) (1 - 2.8014q2 - 0.527sn4)

I = 9/2 wl = 1/24(§;99)(1 + 9'0335n2 - 45.691n4)
mg = 2/24(§E99)(1 -_1.5581n2 + 11.724n4)
w3 = 5/24(§;99)(1 - 0.1857n2 - 0.1255n4)
w4 = 4/24(E§g9)(1 - 0.0809n2 - 0.0045n4)

 

It should be emphasized that these equations are only valid
for small n and should be used with caution. Recently
Alexander and Ganiel (20) have expanded the quadrupolar
Hamiltdnian around 1 — n and have calculated the eigenvalues
and eigenfunctions of the fully asymmetric (n==1) Hamiltonian.
This expansion has certain advantages because, since their
Hamiltonian changes Sign upon a rotation of v, certain of the

matrix elements may be set equal to zero unless both the wave

functions involved in the matrix elements have the same phase

 

 

”’0

o—

5;-

‘1 V

V.

fl!
VA

.1.

in

(I!

‘1'

18

factor 7 under rotation of F. Comparison of their results
with the exact numerical results shows that this expansion
is valid in the region of i] from n = 1 to about n = 0.2,
thus this method slightly overlaps Bersohn's expansion.

The value of the power series expansion lies in the insight
which it allows into the eigenfunctions and eigenvalues of
the quadrupolar Hamiltonian but it seems clear that if
accurate values of n and e2qQ are wanted from measured fre-
quencies the numerical solutions of the secular equations

should be used.

B. Zeeman Splitting of Quadrupole Spectra

 

If a single crystal of a material containing a quadru-
polar nucleus is subjected to a weak magnetic field (of the
order of 100 gauss) such that e2qQ>> VhH, where y is the
magnetogyric ratio and H the magnetic field strength, it is
observed that each line will be Split into two or more lines.
This is due to the fact that the magnetic field lifts the
degeneracy of the doubly degenerate levels (Figure 2). It is
observed in this case that four lines are now possible and,
in fact, have been observed. No attempt will be made here to
give the full theory of Zeeman splitting but the simple case
of n = O, I = 5/2 will be treated in outline. Das and Hahn
(16) have treated all cases in great detail. In addition,
Bersohn (17) treated Spins of any value and small n and
Cohen (18) has given a full treatment for half-integral Spins

and arbitrary n. The original study of Zeeman Splitting of

19

 

 

 

 

 

 

 

 

H # 0 _Ԥ
H=O A 2
m =.i-%
5
\ _+_§
_ .V -
(LB (DB
m = i‘%
, \L * +

 

 

Figure 2. Splitting of the quadrupolar levels by a
magnetic field.

a pure quadrupole line was done by Dean (28) and his methods
of analysis are for the most part still in use. AS long as
e2qQ>>th we may treat the magnetic field as a perturbation.
We then wish to calculate the matrix elements of the Hamil-

. , = + . . .
tonian HQ H.Q HM,where HM lS given by the equation
HM = -th(Izcose + IX Sinecos¢ + Iysin951n¢),

G is the angle between the Z axis of the principal-axis

system and the magnetic field direction, and ¢ is the azimuthal
axis for H governed by the particular choice of X and Y for

the principal-axis system. For the states of half-integral

spin and m>§ there is essentially no mixing between states

20

and, for example, the states.i 5/2 are split apart according

to the equation

Em = Atsmg - I(I + 1)] 1F mhyHcose

The matrix elements are not dependent on the Ix and Iy terms
in HM and hence not on ¢; this is because the contribution
due to these terms is small and may be neglected. However,
for the case of m = i.'§ these terms may not be neglected
Since this leads to a mixing of the states m =-§ and m = -§u
That is, two new states arise whose eigenfunctions are desig-

nated by w+ and w_, where w+ = C1¢% + ¢_é_and ¢_ = C3¢%_+ C4¢_§,

Degenerate perturbation theory then leads to energies of

Ei.= A[&-- I(I + 1)]¢'§-hyHcose
where

f = [1 + (I + i) tan29]§7
also,

¢+ = wi sina + ¢_§cOSd.and ¢_ = wdfi sind - Wfi C050 7

+
f 1]

tan d = [f _ 1

It is interesting to note that again we have no dependence
on the azimuthal angle ¢ to the first order. From the above
equations it may be shown that the frequencies of the four

absorptions arising because of the level splitting are given

by
_ 6_A _ ___3-f
wa-— h 2 yHcose
6A 5+f

wB = 7T-- —§-yHcose

21

. _ 6A S-f
wa’ - T?" + —§—-7Hcose
. _ 6A 3+f
wB - T?’ + -§-7Hcose .

These four lines are symmetrical about the line which appears
when there is no applied homogeneous static magnetic field.

It Should be noted that this discussion applies only to
resonance samples in the form of a single crystal. If the
sample is a polycrystalline powder then we have a wide distri-
bution of values of the angle 9 which results in a large
number of lines at varying distances from the zero field line.
Since the amplitude of each line is inversely proportional

to the number of lines this has the effect of smearing out
all lines. Therefore, Zeeman studies cannot be done on
powders; however, this effect is useful in one modulation
scheme.

C. The Effect of an Electric Field on an
NQR Absorption Line

 

Bloembergen and co—workers {21-25) have observed broaden—
ing of nuclear quadrupole absorption lines upon the applica-
tion of an electric field to polycrystalline and Single
crystal samples. Kushida and Saika (26) have also observed
this effect in 81Br NQR Signals in NaBrOa. This effect is
quite generally to be expected when the nucleus under investi-
gation is located in a crystal site which lacks inversion
symmetry. Dixon and Bloembergen (24,25) have investigated
this effect in great detail. They present a phenomenological

theory to explain the macroscopic physical interactions

22

reported in their first paper (24). They then present, in
their second paper (25), microscopic theory in terms of
ionic character and sp hybridization which attempts to pre-
dict the electric Shift in terms of these more basic quanti-
ties.

The macroscopic theory may be understood in terms of a

E * ,
third-rank tensor R* whose elements are Rfimp = §2m2__ =

5E ext
eoqmp/BE£ , where Eext = l EleXt + 3E2ext E
/\
+ kEsext

is the externally applied field and the Vmp's have

been defined previously. Thus, the perturbation in the

. . . . _ *.
electric field gradient components Aqmp is eAqmp - % Rfimp

)(-
EEeXt (25). It Should be noted that REmp is a tensor defined

at constant stress because this is the condition under which
these experiments are performed. However, it is really the

tensor i defined under conditions of constant strain which

*

we desire since strictly speaking. in Equation ZSngmp

should be replaced by R These two quantities are related

flmp'
by the following equation:

+ d ,
flmp Bmp :rSmpqr Eqr

where dfiqr is an element of the piezoelectric coefficient

tensor and Smpqr is a fourth-rank tensor (27) which relates

the changes in the electric field gradient components to the
induced strain components. In most materials the dfiqr
components can be considered small and fi* = i ; however,

care must be taken with those materials which exhibit a large

23

Iqiezoelectric effect. It is also assumed that Eiext = Ei’
‘Mhere Ei is the actual field which is felt by the electrons
5J1 the molecule. This is because the electron distribution
.1n the molecule has an averaging effect on the applied field.
Vtith these assumptions the perturbed Hamiltonian representing

‘Ehe quadrupole interaction may be represented as

HQ' = HQ + HE = [eQ/61(21-1)]; [3/2(IjI + I Ij) -

ik k k
éik I(I + 1)][Vjk + i Ei Rijk] . (26)
Frxnn the unperturbed part of HQ' we obtain the equation
(see 22)
wo(m+1-—+-m) = [3e2qQ/4I(21-1)h][2lm(+1] ;
similarly,
<mlHElm'> = [eQ/GI(ZI-1)][5m2-I(I + 1)]
(27)
E E E
x[ szz --§ (AvXX + Avyy)]
Fuxmn Equation 27 we may then obtain
AwE(m+1 ——> m)= [eQ/(ZI-1)4Ih] [2|m|+ 11pm:i [R133 — g»
i
(28)

(R111 + R122)]].

”III

IJsing the fact that is traceless, Equation 28 reduces to

AwE(m + 1 —+m) = [SeQ/4I(21 - 1)h1[2lm|+ 11 [13312333

+ EeR233 + EiRiss] I (29)

\Mhere AuF is the electrically induced shift in resonance

ov‘

.-

it

I"

u.-

.A‘

bu-

P...

2}.

5..

‘1-

.Il

fiv-
Vs.

24

:frequency. If axial symmetry holds,R233 = R133 = 0;
‘therefore, Amp/mo = R333E3/eqzz, where index 5 corresponds

tn) the z coordinate. If the sample is polycrystalline rather
“than a single crystal,an average must be taken over all
<orientations. The second moment of the line shape, which
(morresponds to this average, has been calculated for this
(case and also for the cases n10, half-integral spin, and

I = 1, ntO. Full details are given in the paper of Dixon and
lBloembergen (24); also presented in this paper_are the
experimental results on a number of selected components in
(electric fields up to 50 kilovolts. In the second paper of
‘this series (25) Dixon and Bloembergen present the microscopic
‘theory'in which they consider the effects of an electric field
cu: the electronic distribution in the molecule. From con-
.sideration of several effects, they conclude that polarization
(of bonding electrons near the resonant nuclei is the dominant
(effect. Dixon has calculated the effect of an electric field
«on qzz for a pure p bond in a diatomic molecule AB with the

field applied as indicated in Figure 5.

A -——————-B E ——————%>

 

. . ea»
R z direction

Figure 5. Assumed electric field direction.

I_ .
,uv‘

.np

1v:-

“Q
h In
h.\.

 

D
(I)

‘
_~r ;

b.“

5‘

~‘

‘-

I
‘u‘

‘-

.11

25

Because the 6-bonding orbitals are directed along the bond
and the 1r-bonding orbitals are directed perpendicular to the
bond the field has opposite effects on the 6 and Tr electronic

distribution. For 6—bonding orbitals the change in qzz(A) iS

quz(A) = -lqat|€6 and quz(B) = +lqatle6,
§ (30)
orlquz/qat(= eEORB/(Z) A . where
- < I I > (A )—l- eE R 2(1-s 2m 2]”‘1? (51)
€6——¢gHEd/e c5 " OB[ 6 6

wg is the ground state eigenfunction of the molecule, here
taken as the bonding LCAO orbital, and we is excited state
eigenfunction, here taken as the antibonding LCAO orbital;
RE is the internuclear distance. E0 is the scalar value of

the applied electric field, S is the 6 overlap integral, A

6

is the average energy separation between the ground and the

6

excited state and eqat is the field gradient due to one un-
balanced p electron in the valence shell. Several approxi—
mations are involved, the most important being 862 = O and
the assumption that there is only one low—lying excited
state. The validity of the assumptions depends on the indi-
vidual molecule but in any event the choice of a value for
A6 is not clear-cut; Dixon has chosen, rather arbitrarily,
twice the value of the bond dissociation energy for this value.

For a double bond the change in the electric field gradient

1 5 ca lculated aS

 

’L

.uv

97‘

vi

 

’v

‘i

‘A

‘i\
sql

;|\

’1-

26

quz‘“ €7T/2 (qatl

quz(B) : _€7T/2 (qat l '

with e.” = eEoRB/(A7r[(1 - SW2)2]3=*).

It is important to notice that these effects are opposite
to those of Equation 20; thus, in a bond which has some
double-bond character, there will be some cancellation of the
effects of the electric field. This has been observed by
Dixon and Bloembergen. Using both variational and perturbation
approaches, they have developed equations which relate the
observed broadening to the Sp hybridization and ionic char-
acter of the bond; at the present time, however, these equa-
tions are too crude to yield meaningful results for the
parameters. As will be discussed later e2qQ may also be ex-
Pressed in terms of these quantities; thus the electric field
effect gives another measurable to determine these parameters.
It is clear that more work is needed on this effect.

D~ The Effect of Temperature on the
EQR Absorption Frequency

It is generally found that as the temperature is lowered
the frequency of an NQR line increases. Studies of tempera-
tLire dependence have been used to determine the temperatures
at; which crystalline phase transitions (28) occur and the
temperature at which the barrier to internal rotation for
1. 2—dichloroethane is overcome (29). These transition

temperatures are recognized because of distinct breaks in

 

..1
II-

I'-

v.
a

.-v

r- ,-

 

A
I
b

(I)

r

27

curves of frequency yersus temperature, the number of lines
due to a particular nucleus may change due to a change in
crystal structure during a phase transition. Frequently
resonance lines which are observable at 770K disappear or
greatly decrease in amplitude when the temperature is raised;
this effect is not well understood although it is generally
attributed to vibrational effects. The disappearance of
quadrupole lines has sometimes been attributed to crystalline
phase changes and undoubtedly in some cases this is true;
however, in other cases the disappearance of the line may be
more realistically attributed to vibrational effects. Several
compounds Show an anomolous effect in that their resonance
frequency increases as temperature increases. Haas and
Marram (50) have recently attempted to explain this abnormal
behavior in chlorine compounds in terms of two competing
effects. First, there is the vibrational motion which tends
to lower the frequency as the temperature is raised since this
increases the amplitude of vibration with a consequent
'averaging out' of part of qzz' It has been found that tor—
Sional motion dominates the vibrational effect. The second
effect is due to the fact that as the temperature is increased
the increased bending vibrational motion tends to break down
the V bonds causing an increase in the population of the
cl'llorine 2pTr orbitals, thus causing the absorption frequency
t<> increase.

Bayer (31) has treated the effect of torsional motion on

the quadrupole resonance frequency. Many refinements have

9‘?

0.4.

III

~..-
ivy
O

‘V

.‘A
5...,

n~~

vy.

RA.
H».
L

.’A

.-
I-.b

28

been introduced for this theory but only the simple theory

is presented here, since the results are not used explicitly
111 this work. It is assumed here that the frequency of the
txxrsional motion is much larger than the quadrupole resonance
frequency and thus we need to consider only the average
effect of torsional motion on the quadrupole resonance fre-
quenncy. This is almost always true since vibrational motions
are: usually in the infra-red or Raman region with frequencies
of? the order of 1013 Hi, while quadrupole resonance fre-
quenncies are in the order of 108 Hz‘ However, if the vibra—
ticnnal frequencies are not much larger than the resonance
frequencies a broadening of the resonance line, rather than a shift
Occurs and is given by the equation Aw (eXp(—- g—T) , where Ad)
is the line width change due to rotational motion and W is the
finitential barrier to rotation. Tatsuzuki (52) has studied
the changes in line width with temperature in 1,2,5-trichloro-

benzene and hexachlorobenzene and his results are Shown in

F j-<3ure 4 .
(a) (b)

Log Aw

 

Figure 4. Line Width change with temperature for
a) Hexachlorobenzene, b) 1,2,5-Trichloro-

benzene.

29

Ta and Th are transition temperatures after which free rota—
tion takes place. Values for W of 6.0 i.O.1 kcal/mole and
12.6;t-2 kcal/mole have been calculated from these data for
the molecules hexachlorobenzene and 1,2,5-trichlorobenzene,
respectively.

Let us consider the effect of pure, very fast torsional
motion on an axially symmetric electric field gradient q

where the tensor, in the principal—axis system, may be

written as
-§- 0 o

0 -§- 0

n-Q II
II
.Q

22
O O 1

If a rotation of 9 about the Y principal axis occurs then

cose O -sin9 -§- 0 O cose O sine
E = o 1 o qzz 0 ~% 0 o 1 o
sine O cose O O 1 -sine O cose

~§cosze + sinae O ~§sin9 cose
0 -§- 0

—§cose sine O —§sin29 + cosge

For small values of 9, sin e g e and cose ; 1; then,
5192-3.» 0 —£-e

ZZ

- r

A
\

'00:

If.

.9. u

r.
5"

DA‘

‘v

 

50

Since we are considering only very fast motion we are
interested only in an average angle <9) and, since <e> = 0

when 6 undergoes symmetric vibrations, we write

\

 

 

3 <92> - '5‘ o o
a = qzz 0 4% O
( o o 1-51 <e2>

 

Finally, taking into account simultaneous rotations about the
X axis, denoting this angle by 9X and average angular motion

about the Y axis as GY we obtain

 

% <eY2> - t o o
3 = qzz O 3<eX2> — t O
_ 2 _ 2
o o 1 Skax > 3<9Y >
( (53)

 

From Equation 55 we see that we must replace qu by

qzzu‘) = qu (1 - a <ex2> - 3 <eY2> ).

Similarly the rotational motion introduces an asymmetry para-

: &(<ey2> - <ex22)
1 - §<ex2> - §<9Y2> '

small value of n we now calculate the resonance frequency as

meter n given by n Neglecting this

a function of temperature. If we treat the system as a rigid
rotator a quantum mechanical treatment gives for the rotational

(torsional) frequency v2

th/kT

47w 2 <92) A = kvz [5 + 1/(e - 1)], (55)

E 2

Where k is Boltzmann's constant and A2 is the appropriate

Inoment of inertia. Using this equation

51

1
w(T) = 1(0) [1 - a h/41r2 Axvzx {4; + 1/(thEX/k'r - 1)}

 

.2, M412 i (.1. + 1/(th2Y/ktr - 1m (56)
AY ZY
and the temperature coefficient becomes

_ h2 1 th.ex/kT thEY/kT 1
50(a—T)v— ' g 412 Ha [3(Jvzx7ki 1)‘2 + AY(th3£y/’<T ‘ 321'

 

 

(57)

But the experiments are performed under conditions of constant
pressure therefore the measured temperature coefficient corres-
ponds to (%%)P which can be related to the theoretical temper—
ature coefficient by the thermodynamic equation
(%bv=(%%)£>+§ 3%T ’ (58)
where d is the thermal expansion coefficient and B is the
compressibility. Thus, to relate theory and experiment we
need to measure the effect of pressure on NQR frequency.
This has been done by Kushida, Benedek and Bloembergen (55)
for C1 in KC103 and p-dichlorobenzene and for Cu in Cu20 and
by Fuke (54) for SnI4, AS406, KBrOa and p-dibromobenzene.
Kushida et al. (55) and McCall and Gutowsky (55) have im-
proved the Simple Bayer theory but it has not been possible
to obtain quantitative agreement with experiment, probably
due to the fact that rotational frequencies are temperature
dependent but also because other vibrational modes besides
torsional motion become important. Fuke (54) has observed

‘this latter effect in AS408.

.
I'-

...\

.0!

3..

0|:

hank

n-

hp.
V.

'd.

‘5-

‘$

«T‘
I I.

e
a.
i

‘A

a(1

52
E. The Effect of Internal Electric Fields
on thegggg Frequencies

The theory of Townes and Dailey which iS discussed in
the Chemical Theory section, is an attempt to interpret NQR
frequencies in terms of chemical parameters. This theory is
strictly true only when the individual molecules are not
allowed to interact with one another, which is true only when
the substances under study are in the gaseous state. Since
pure quadrupole resonance experiments must be carried out on
a solid, a correction Should be made for the effect of the
crystal lattice on the NQR frequencies. Although this adds
considerable complexity to the treatment of NQR data, it
has the advantage of allowing us to investigate solid-state
interactions which could not otherwise be studied. Although
there is no clear division among these effects an arbitrary
division into three different interactions will be made in
order to facilitate discussion.

(1) Direct contributions due to the effect of charges
situated on neighboring atoms in the crystal lattice. This
effect is proportional to r"3 and hence should fall off
rapidly with distance. However, calculations Show that some
contributions are felt from atoms 603 and even 1008 away.
This contribution is enhanced in some cases and decreased in
other cases, by the Sternheimer effect, which is corrected
for by multiplying the calculated ionic field gradient by
1 - 700, where 700 is called the Sternheimer factor and is

gxositive (with a value between 0 and 1) for shielding and

55

negative for antishielding. The effect is due to the fact
that external charges, besides having a direct contribution
to the field gradient, also have an indirect effect due to

a distortion of the closed Shell electrons around the quadru-
polar nucleus. This distortion may decrease or increase

the Shielding of the quadrupolar nucleus and hence is called
antishielding or Shielding, respectively. It could also be
said that the external charges induce an electric quadrupole
moment in the electron distribution around the quadrupolar
nucleus. This causes a redistribution of charge in the mole-
cule which in turn affects the electric field gradient felt
by the quadrupolar nucleus. This redistribution may be such
that it enhances the field gradient (antishielding) or can-
cels part of the field gradient (Shielding). In general small
cations such as Li+ experience Shielding and large deformable
anions such as Cl- and Br- experience antishielding. Stern—
heimer and others (57-42) have calculated this enhancement
factor for a number of neutral atoms and ions. Unfortunately
this calculation is very difficult and often two calculations
for the same atom will not agree. In particular, Sternheimer
has previously calculated a value of -56.6 (41) for 7o) of
the chloride ion; however,experiment (49-54) has indicated

a value of -10 as being more reasonable. Burns and Wikner
(50) have pointed out that, in a solid, higher symmetry and
larger internuclear distances result in pertubations of the

large negative anions, and since Sternheimer used wave

r
uer
.‘uv

\
in: ..

CA,- I

v‘vu‘h

.A'

Ow.

.
h‘,

L3“

p;
(Ii

(I)
l V

1.
L!)
D

TI
4,.

’(‘1
,1 in

All
W

54

functions which only apply strictly to atoms in the gaseous
state, it follows that properties which are sensitive to this
solid state effect cannot be calculated very accurately with
these wave functions. Wikner and Burns (51) tried to correct
this by using what they call contracted wave functions. They
constrained the wave functions to give the correct value

for the average diamagnetic susceptibility for the Cl- ion

in a series of compounds. Using these wave functions they
calculated a value of -27.4 for 700. Recently Sternheimer
(55) has calculated a new value of yaafor the Cl- ion, taking
into account second—order effects,and obtains an improved
value of -45.89. He also states that the solid-state effects
discussed by Burns and Wikner would decrease this value by

as much as 2/5 although he did not make any quantitative
estimate. Another reason for the poor agreement between the
calculated and the empirical value for ya)(Cl-) can be found
in the fact that Yoo is sensitive to the charge on the ion.
This is logical Since the more polarizable an ion, the larger
the antishielding. For example, in most chloro compounds

the charge on the chlorine varies between zero for a chlorine
in a completely covalent bond to -1 for a chlorine in a com-
pletely ionic bond. Therefore, as an ion becomes more polariz-
able (more ionic in the case of chlorine), it follows that the
antishielding factor Should become larger and, furthermore,

a smooth increase is expected. The Sternheimer factor for a
neutral chlorine atom has been calculated by Sternheimer (57)

as +0.42 shielding. This effect is expected to be quite

v-F

9“”

ov-fi

ar‘

.11.

\
L...
h

‘5...

 

p
6
b

‘1’

AA-

" w‘.

 

-
§
§

1‘1 Li
( r

r '1
(I;

“w.
.VI

55

important. Figure 5, which is taken from a paper by Das

and Bersohn (42), illustrates this point. The Sharp increase
in going from He0 to H_ is especially interesting since it
roughly parallels the change in going from C10 to Cl-. In
this case the quadrupole moment induced in the closed shell
electrons of H- is such as to be highly Shielding; however,
it is quite likely that in a series like Cl+, Clo, Cl— a
Similar curve is followed, especially Since we know that 700
(C10) = +.42 and ya3(Cl-) = -45.89. Recent calculations of
field gradients in ionic lattices,with the assumption that
the charged nucleus may be replaced by a point charge in
PrCls (47) and CrCls (48), have yielded reasonable answers
when compared to experimental results using an antishielding
factor of -10. Since these two compounds are expected to be
highly ionic a value closer to -27.04 would probably be more
realistic since the experimental values are for less ionic
compounds. Correspondingly a lower value for compounds
studied in this work is appropriate as they are more covalent
than the compounds used in the "experimental" determination
of the antishielding factor. Unfortunately the calculation
of the contribution of point charges to the field gradient

at a quadrupolar nucleus is very sensitive to the Sternheimer
factor because qzz(crystal) = (1 - 7a))¢zz' where 022 is the
direct contribution to the field gradient from the external
point charges. The large discrepancy between the calculated

and the empirical factor is very disappointing and makes it

56

 

 

 

Figure 5. A plot of the Sternheimer factor (700) versus
ionic charge for helium-like ions.

57

difficult to extract information from a point charge calcu-
lation.

(2) Modification of the electronic structure or molecu-
lar unit as a result of interactions with neighboring mole-
cules. The exact nature of these interactions is not well
understood; however,Van der Waals interactions and dipole
moment interactions probably occur. The latter interaction
results in a small increase in ionic character of the bond
and lowers the crystal energy. Table 5 presents the quadrupole
coupling constants for a number of molecules in both the gas
and the solid state (45). It will be noticed that for
chlorine and bromine the coupling constant decreases in going
from gas to solid. This implies a gain in negative charge
on the halogen atom and, hence, an increase in ionic character.
For iodine in ICl and ICN the absolute magnitude of the
coupling constant increases implying a gain in positive charge
and, hence, an increase in ionicity since iodine has a positive
charge in these two compounds.

(5) Additional bonds may occur between neighboring mole-
cules in the solid. Examples of this are hydrogen bonding
and formation of polymer-type structures in the solid. This
latter behavior has been postulated to explain the NQR re-
sults for solid 12, Bra and ICN. In 12 an examination of the
crystal structure places two near neighbors each 5.543 from
one of the iodine atoms in the iodine molecule. The sum of

the iodine Van der Waals distances is 4.552; therefore, some

«3)

a

nu.

1 t

Qc

n

n s

A

.‘Qnd

- ~

.~.~..J

\

-

..\.

58

 

 

 

o.mwmml 0.0Ndml d>.NmNmI HumH ZQH
o.>momu o.¢¢mml fi>.NmNNI HSNH HUH
o.mmoml m.m¢fiml a>.mmmml Hbma Homo
o.wm>al o.mmmfil H>.Nmmml Hhma Homo
mfi.o 0.6msm- as.mmmm- Htmd NH
0.406 o.mam ms.mms ummk ummmo
m.mmm o.>>m m>.wm> Hmmt ummmu
om.o mm.mm> m>.wm> Hmmt mum
¢.¢>I m.mm| ¢>.m0fi| HUmm HUH
mm.>ml mo.mwl ¢>.moal HUmm HUth
«.mml ¢>.¢>I ¢>.moal HUmm HUmmo
mm.moa| ¢>.m0fil Ho NHU
mm
c Uflaom mmw mumum UHEoum msmHodz masomaoz
UONm vONm UOmw

mumum msommmw mnu CH pom oflaom map CH nuom UmHSmmwS comm

m>mm SUHAS mmasomaoz mcflsflmucoo :mmonm mo mu:Mumcoo msHHmsoo maomsuomso .m magma

59

kind of partial covalent bond must be formed between adjacent
iodine molecules. This type of bonding has also been postu—
lated for some Sb and Bi compounds (45,46). Examples of
hydrogen bonding were studied by Allen (57), and Bray and

Ring (58). Their data are given in Table 4.

Table 4. NQR Data Indicating Hydrogen Bonding

 

 

Compound Reference Frequencies (in MHZ)
CC13CH(OH)2 57 58.190, 59.429, 59.515
CC13CH(OH)(OC2H5) 58 58.516, 58.705, 59.14
CC13COOH 57 39.967, 40.165, 40.240

 

The crystal structure of CC13CH(0H)2 has been determined
by Kondo and Nitta (59). They find three C-Cl bond distances
of 1.79, 1.78 and 1.72A; the two longer distances are at-
tributed to hydrogen bonding of the hydroxyl hydrogens to
chlorines in near neighbors. The quadrupole resonance fre-
quencies for this compound shows a similar grouping, two
lines quite close together and one line lying over 1.MHz
lower in frequency. The explanation for this is that the two
chlorine atoms engaged in hydrogen bonding give rise to the
two high frequency lines and the other chlorine atom accounts
for the lower frequency line. The lower frequency should be

taken when studying the C-Cl bond in the compound and the

.- pa

,-
.100»
‘5..-

. -
ofle
.1. u

a
In‘ .1
\

..~ I

.
~

.F-u
“Ind

A 1

‘ h
H...“
--
a"

9.,“

'1 .

\u.‘~
.

‘s

{I}

40

difference between an average of the higher frequencies and
the lower frequency may be interpreted in terms of a charge
Shift in the region between the carbon and chlorine atoms

due to the formation of the hydrogen bond. This charge shift
will undoubtedly affect the ionicity of the C-Cl bond and,

if this is the only effect, NQR data may be used to estimate
the extent of charge shift and hence the strength of the
hydrogen bond. However, this charge shift may also be accom-
panied by a change in the Sp hybridization of the Cl orbitals
and this would complicate the interpretation. More data are
needed for this type of compound before quantitative state-
ments may be made. For CC13CH(OH)(OC2H5) one hydrogen bond is
expected and the data roughly indicate this but the situation
is less clear-cut; probably the hydrogen bond is not as
strong. In trichloroacetic acid no hydrogen bonds are ex-

pected and the data indicate that none are formed.

Chemical Interpretation of NQR Data

A. Atomic Field Gradients

 

Let us first consider an atom. What will be the contribu-
tions to the electric field gradient at the nucleus from the
electrons of this atom? Suppose we had an electron in an
atom described by the wave function wnfim when n is the princi-
pal quantum number, £ is the azimuthal quantum number and m
is the magnetic quantum number. The quantum number m used

here should not be confused with the nuclear Spin quantum

..w"

.. ~--

.71—
I. l-

U .

. a

u...
1 a

:L
9‘ 1.

‘v-H

‘01»

abv
nub

:..,

s“

\nfl

.\U

\
y
's

V\

41

number m used previously (it is common notation to use the
letter m for both of these quantities). The operator for

; 5cosae—1

q is 322 -—;3———-, where 9 is the angle between the z

22

axis and r. Then, in an obvious notation,

5cosae-1)

anm = ‘9 fwn£m(”—"3'—r (Dngmdv . (59)

If we use this equation we can estimate the relative import-
ance of contributions from p(£ = 1), d(£ = 2) and f(2 = 5)
electrons and also how q varies with the principal quantum
number of the contributing electron. If we use hydrogen-
like wave functions Equation 59 may be evaluated to give the

result

 

qnflm = 2£+5 <f3> 7 (4O)
furthermore,
1 2 2.3
= i
<E3’> 53a31(1 + 1)(2£ + 1) ’ (41)

where Zi is the charge on the atom and a0 is the Bohr radius.
a constant. Combining Equations 40 and 41 we get

4 Zi3 e
qnzm = n33.3(z + 1) (21 + 1) (21 + 5)

 

(42)

Using Equation 42 for some fixed value of Zi and n, qnfim
varies in the ratio 1/50:1/105:1/252 for p, d, and f elec-
trons, respectively. We see then that q falls off quite
rapidly with z. This effect is illustrated in Table 5, in

which both the experimental and calculated (using Equation 42)

 

 

Table 5. Values of qnflo = ggg-for Various Atomic Statesa
Experimental Relative

Electronic Value for Value of

State Atomb qn£0 x 10‘15 anO c
5p I -45.0 1.00
5d Cs -0.51 0.14
5f Cs --- 0.048
6p CS -5.4 0.58
6d Cs —0.16 0.08
6f Cs --- 0.028
7p Cs -1.1 0.56
7d CS -0.09 0.05
2p F -21.0 1.00
5p Na -0.7 0.50
4p Na -0.2 0.12

 

aC. Townes and B. Dailey, J. Chem. Phys., 11, 782 (1949).
bExperimental data are available only for these atoms.

CObtained using Equation 42. Values are relative to 5p
except for F and Na which are relative to 2p.

45

values for q for a given valence are tabulated. It can

be seen that the relatively simple Equation 42 predicts in-
tensities fairly well. In the next section we develop an
equation for the ratio

p -_— eEquO 1
eaoqat

(45)

where qmol is the molecular field gradient at the position
of the quadrupolar nucleus and qat is the field gradient at
an identical free atom nucleus. The values for qat are
obtained from the splitting of atomic Spectra and also from
atomic beam experiments. The atomic beam values are much
more accurate. In obtaining qat the Sternheimer factor must
be taken into account due to the polarization of the inner
electrons by valence electrons; this effect must also be

considered for q Most chemical interpretations of NQR

mol'
are given for p rather than ean and it has been previously
assumed that taking the ratio cancels out the effect of
polarization of the inner shells but for this assumption to

be true 700 for free chlorine atoms must equal 700 for a
chlorine in a covalent bond. Let us examine this assumption
more closely. If the bonds of a molecule are covalent enough
that the direct contribution to the field gradient from extern—
al charges may be considered to be essentially zero, then

the measured coupling constant e20q may be considered to arise

entirely from the valence p electrons of the nucleus. These

electrons will certainly distort the inner electrons inducing

44

enielectronicquadrupole moment characterized by a Sternheimer
factor of 70S; hence,the measured coupling constant e2qQ e
e2qm01(1 - 70$)Q. However, the free atom field gradient

qat also arises because of the gradient due to valence p
electrons (although it is not the same as qmol due to charge
distortions arising from bond formation) and induces a quadru-
pole moment in the inner Shell described by 70;. Thus,

ezqétQ = eaqat(1 - 703)Q, but because the same mechanism causes
the inner shell distortion it is believed that 705 = was; then
p = qmol/qat’as desired. This is probably a good assumption.
However, when there is appreciable ionic character in the
bonds to chlorine (for example, in SnCl4, HgClg, SbCls and
other similar compounds) the contribution to the field gradient
due to external charges and valence electrons is expected to
be more nearly equal and the measured coupling constant must

be written as

ean =e2<2[(qmol(1 - 705) + 4’22” - ymn, (44)
where '

705 + 7a): €20¢zz(1 - 700)

must therefore be calculated and subtracted from the measur-
ed equ before p is calculated.
B. The Townes and DaileyfiTheory of
Molecular Field Gradients
The following treatment is taken,in part,from Das and
Hahn (8). It Should be kept in mind that no completely gener—

al treatment for the molecular field gradient has been given;

45

the theory of Townes and Dailey was developed for the particu-
lar case of the singly bonded halogens although it may be
generalized for other atoms if they are fairly electro-
negative. In general, however, it is better to consider each
nucleus separately and test each approximation of the Townes
and Dailey theory to see if it applies in the particular case.
All the NQR resonances reported in this work are chlorine
resonances; therefore, the original development of Townes and
Dailey seems appropriate. The arguments of Townes and Dailey
should be regarded as heuristic rather than rigorous. Let us
consider how qat of chlorine is modified when the chlorine is
bonded to another chlorine in the C12 molecule. The bond is
not expected to have any appreciable ionic character, double-
bonding or pd hybridization; however, a small amount of sp
hydridization may take place. The bonds use the chlorine pz
orbitals and the direction of the z principal axis is along
the chlorine-chlorine bond; cylindrical symmetry may be as-
sumed. Then the electronic distribution in the valence shell
of the bound chlorine atom may be described by the following

four wave functions:
¢6= a? s + (1 «not pZ

wx=px wy=py

¢£p'=(1_a)és- Qipz

The measured value for qat corresponds to the integral

of atomic wave functions

46

_ 5cosae-1
_. = -x- .
qat _’qn£m (w nEO ( r3 ) wnfiO dV ’
m = 0
for p electrons E = 1 and we must also consider the atomic

field gradients qn£1 :nd an-1 which are related to anO by
= .. L . ' = =
‘45) qnzm qn£O[1 1(e+1)]' thus' 1f qn£0 qat’ qnz1

an-l = -§-qat. This means for a chlorine with one pz electron
we get sz (atomic) = qat and—Vxx = Vyy = - i-qat, but if the

electron were in the px orbital then VXX = qat’ Vyy = - fi-qat

and sz = - é'qat' In order to describe the electronic state

of the chlorine atom in this molecule we consider the wave func-

' ,, ; . = + + + .
tions wé,w£p wx and wy then q an6 nfipq‘gp nqu nyqy
where n = the number of the electrons and, for example,

* 5 829-1
qcs = ((6 (—9%3—-—) ‘(6 9"

*(5cos29-1
‘err—-—9

* 5cosae-1
(-——s————)

dfs st + (1-d)fpz r pde

+-dé'(1-coéjs*(§9%§i§:;)pzdv + 12(1-a)§ fpz*(§£%§3§:;) sdv.

The cross products are ignored because the atomic wave

2—
functions are orthogonal and fs*(§£9§3§—i)sdv = 0 because

the s electrons are spherically symmetric; hence, q6 -

2-
(1-d)fpz*(§99§3§—i)pzdv = (1-c0qat. Below are listed the

contributions to the molecular Vxx’ Vyy and sz from the

various wave functions.

47

 

 

Number of
Electrons in
Orbital the orbit V V V
xx gyy 22
(o 1 —i~~(1-a)qat -g-(1-o:)qalt (1-o)qat
(X 2 ant -qat -qat
(0 _ _
Y 2 qat ant qat
((1 ._ _
Ep 2 Oqat Oqat 20gat
§‘(1-oz)qat §(1-wqat (-1+c1)qat
We can see from the above that q E sz = (--1+'CL)qat and n = 0.

If our bond had some fractional ionic character I, then the
number of electrons in $6 would be (1+1) and if the bond had
some fractional double bond character‘flpthen the number of
electrons in wx and ¢y would be (2 - g),so q = [(-1+a)+
(1-O)I -l-Tr]qat but 1} still is zero.

Let us now consider a chlorine atom in a planar molecule
such as a chlorobenzene, then only the pX orbital takes part

in double bond formation so that the orbital populations P

become
P(6)=1-I
P (x) = 2 —'rr‘
P (y) = 2
P(£p)=2

and the field gradients become

vxx = [§(1-a)(1-I) -7T]qat
vyy = [141-a) (1-I) + 5777 qat
q = sz = [(1-a)(I-1) + 17771.”
= 512‘. 1
n 2 p °

48

Thus, if n can be determined for these molecules an independ-
ent determinationcflTTTis possible. We now attempt to derive
the above equations in a more rigorous manner. For an ICl

molecule we may write an LCAO wave function

2(c1 + i (I
w =(1 + i2 + 213)%' (46)

 

where S is the overlap integral fwlwcldv and i is relative
contribution of (I to the total wave function. The ionic
character of a bond is defined as I = %—i—%§-with ionic
character in the bond being allowed for by the parameter i.
However, if we consider the bond as being formed by the pz
orbitals of I and Cl then it is known that a stronger bond
will be formed if we allow some admixture of other states
with the pure pz state. Energy and symmetry considerations
suggest that the most likely states to mix with pz are s and

dzg states; with this in mind we write the atomic wave func-

tions as

(c1 = (1-dsé)% pz(Cl) + d? s(Cl) + 6% dzg (c1)

(47)
WI = (l-a‘~5')§ pz(I) +(a')§ s(I) + (6')é-dzg(l).

Four different contributions to qmol at the chlorine nucleus
will now be considered. They are: 1) The two electrons in
the molecular orbital Equation 46; 2) The two pairs of pX

and py electrons on the chlorine atom: 5) The electrons which

were in the 552 orbital in the free atom. These electrons

49

were previously accounted for with tap because in the mole-
cule they are lone pair electrons; 4) The inner shell elec-
trons.

1) The two electrons in the bonding orbital give rise to

2
q ='J¢*(5CO: 6-1) ¢dV

__"2 .2 .
_ (1+12+Zis)% [quC1 + l qII + 21q1c1] ’

 

where, in an obvious notation,

qICl E ((1 (5co::9-1)wC1 dv'
The term qII gives the contribution of the bonding electrons
to the field gradient at the chlorine nucleus when the elec-
trons are near the iodine nucleus. Because of the %3-term,
qII is very small and is neglected. The term qICl arises
because of contributions from the overlap region. The value
of qICl is certainly less than quCl although not as small as
qII' Furthermore, it is multiplied by 2i where i is less
than unity. If the bond which contains the chlorine nucleus
is quite ionic then i is small, but in the case of ICl
Townes and Dailey estimate the ionic character as 0.25 and
from this i =(l775. Reddoch (7) has stated that for i = 1
the error involved in neglecting qICl is no more than 10%;
however, he does not say how this estimate was made.

Although we will neglect qICl this may not be correct for co—

valent compounds. If we use Equation 47 for (C1 we obtain

50

= _ _ ‘ é- .
quCl (1 Cl é)qat(Cl) + qu22(Cl) + Edi-0 qsdzz(Cl),

where we have neglected two cross terms which are zero be-
cause of symmetry.

2) Each of the four electrons in the pX and py orbitals
contributes -§-qat to field gradient as discussed previously,
giving a total of - qat'

5) The two lone pair electrons contribute nothing to the
atomic field gradient but in the molecule the pure s state
gains some pz character. They then contribute an amount ~2d
qat'

4) The inner shell electrons of chlorine should contribute
nothing to the field gradient but because of polarization by
the valence electrons small corrections should be made to qat;
however, these may be made by using a value of qat which has
not been corrected for polarization when we calculate the
ratio p = Egggja . This correction has been discussed, it
will not suffize for qdzg and qu22 but we are planning to
neglect them so will not bother with a correction. Collecting

all the contributions to the molecular field gradient qzz(Cl)

we write

_ 2 __ it.
qzz(Cl) - 1:12:2i5 [qat(1 d 5)+éqd22 + Zdéb qSfiz?]'

(48)
In order to Simplify this equation into an easily usable

form, we wish to neglect éqazg, dédéqsazg and the overlap

51

integral product 2iS in the denominator. The term éqd.2

may be safely neglected because both 6 and qd 2 are quite
small, 6 being usually less than 5%, and Tabl: 5 shows ap-
proximately an order of magnitude decrease in the qat result-
ing from d electrons compared to that from p electrons. The

product débéq

sd 2 may not so easily be neglected. There is
‘ 2

no simple way to calculate qsd 2 and no experimental values
2

are available. Although its value is eXpected to be smaller

5%

than q , E qat’ is expected to be smaller than d5, hence

92
the product dédg is less than d. For these reasons Townes

and Dailey neglect dédtp Let us now consider the denomi-

sd 2'
nator of Equation 48,(1 + :2 + 2iS)-l. A typical value for

S falls in the range 1/5, hence for a molecule like C12 or

Bra where i = 1 the denominator becomes equal to [1 + 1 +
2(1)(%)] = 8/5: Therefore, according to Equation 48, for
these molecules p =-§:%§-—- should equal 5/4 if we neglect sp
hybridization. .However,athe measured p values for these

two molecules are very close to unity, which is the expected
value if we neglect overlap. Gordy (60) has discussed the
inclusion of S in the Townes and Dailey formulation. He
argues that the overlap term is included to take into account
the contribution to the molecular field gradient which comes
about because of some charge migration from around the quadru-
polar nucleus to the overlap region and this charge must

come from the outer regions of the quadrupolar atom. Since

the major contribution- to the field gradient comes from the

52

electronic charge close to the nucleus the effect of the
overlap migration is negligible. This argument does not
seem valid as it only considers the direct effect of the
charge migration and does not consider indirect contribu-
tions to the molecular field gradient which must occur as

a result of decreased distortion of the inner shells by the
outer shells. Furthermore, the Townes and Dailey theory
attributes the difference between the free atomic field
gradient qat and the field gradient of an atom in a chemical

molecule qmo entirely to the valence electrons which, of

1
course, are the electrons which migrate into the overlap
region; Gordy conveniently overlooks this point. A more
reasonable argument is advanced by Das and Hahn, who refer

to some calculations by Schatz of coupling constants for 35C1
in the compounds HCl and CH3Cl (61), and by Das (62) of the
coupling constant for 11B in some boron compounds. They find
that due to a contraction of atomic orbitals on molecule
formation qu may not be strictly equal to qat’ This effect
may be partially corrected for by neglecting the overlap
integral in the denominator of Equation 48. This explanation
for the consistent interpretation of NQR data with the overlap
integral set equal to zero, in terms of two cancelling effects,
seems more reasonable than Gordy's argument. It also suggests
that we must be careful to watch for cases in which we do not

get a self-cancellation of effects. After neglecting the terms

just discussed Equation 48 becomes

55
_ _:21-w6) _
qzz(C1) - I 1 + i c1.at + 2(1 wqat] (4.9)
. . . _ 1 - 12 .
which, substituting I — 1 i Equation 49.becomes
qzz(Cl) = [(1-oc+c5-I) + I(a+<5)]qat- (50)

We neglect the second order terms Id and Id (although in

rare cases Iczmay need to be included) to obtain
qzz(Cl) = (1-d + é-I)qat. (51)

If we wish to correct for double bonding we define a quantity
'Wras the electron density in the px(or py) orbital of a free
chlorine atom minus the electron density in a pz (or py)
orbital of a bound atom and call this quantity the fractional
double bond character. The population of each px (or py)
orbital is (ZJHT and qp (C1) = - (é -7T)qp (C1); the pX and
py electrons now contribute an amount q” =z-2(15U76at to

qzz(Cl) instead of -2qat. Including this correction in

Equation 51 gives
qzz(c1) = (1-a&é=n=l)qat. (52)

This is commonly referred to as the Townes and Dailey equation
as these two authors derived it originally and it has been
used successfully in interpreting NQR data from hundreds of

compounds. In a similar manner Equation 55 may be derived:

q(I)= [1-o&é+I:U]qat(I)o (55)

54

Cotton and Harris (65) have recently developed an equation
similar to that of Townes and Dailey but from the molecular
orbital, rather than from the valence bond, formalism.

These authors claim that under appropriate limiting conditions
their equation reduces to the Townes and Dailey equation but
they do not explicitly state these conditions. It is interest—
ing to note that their derivation is much more general than
that of Townes and Dailey, not requiring an explicit intro-
duction of hybridization. Their proof is no more rigorous

than that of Townes and Dailey, although they do attempt to pro-
vide a numerical corroboration of their most important assump-
tion. The derivation of Cotton and Harris is given below.

It is desired to calculate the quadrupole coupling
conStant ezoaqa for a molecule which contains a quadrupolar
nucleus designated by a. The wave function for the molecule
may be expressed by a product wave function Y =7gik, each wk
containing Nk electrons. Each molecular orbital wave function
wk may be expressed in the LCAO-M0 approximation as:

wk = r21 Cik(>1 (54)

i=1
where n is the total number of atomic orbitals ¢i of the atoms
in the molecule and all the ¢i are required to be orthogonal.
The total field gradient in the molecule thmay be written as

NUCL C

q_ = Z qu k-+ NUCL where q is the contribution to qa

from the charged nuclei of the surrounding molecule and

neighboring molecules and qaf is defined by the equation

55
k 2 - k
qak= M *(i‘aisfl) 1 av . (55)

Using Equation 54, Equation 55 becomes

_ k ,k k lj. NUCL; .
qa-E§§NC1C. qa+qa (56)

‘

3

where

qij _ f¢: (5cosa re-1)¢i dV .

Cotton and Harris then break down Equation 56 into three
sums, one for each of the following types of qij:
1) qii, one-center integrals in which both Ii are on
the quadrupolar nucleus.
2) Two-center integrals qij and qgé, where i refers to

atomic orbitals centered on the quadrupolar nucleus,

and
5) qgfwhere neither j nor fl refer to atomic orbitals
on the quadrupolar nucleus.

With this arbitrary grouping of terms they now write Equation

56 as
_ k jj K k ij
qa - 2:ka [ZiIICi qu (11+ ZICj I2 qa + chi Cj qa +
z c. kc kqul + qa NUCL . (57)
3'13 j E

Equation 57 must be simplified as it would be impossible to
solve this equation in its present form by any presently
known methods for most molecules of any chemical interest.

In order to make simplifications the following three

56

approximations are introduced: 11 The sum over all core
orbitals on atom unwill be taken as a constant P. Although
this contribution should ordinarily be zero, the Sternheimer
effect will cause some contribution to qa; thus, Elcikleqaii
becomes 1

in in
a

2 'l'l 2
EICi'kl q; l + :2 lci"k| q
r 1"

III
M
0

ij" + q NUCL

2) The sum over two-center integrals go. a, ,where j"

refers to a core orbital, will be approximated by a constant

CORE

a which corresponds to contributions from all charged

q

nuclei and their core electrons external to atom a.

5) The sum over all non-core two-center terms qzq, plus one-
half of the sum 2 Cikcjkqtg, is assumed to exactly cancel
i,j

Core. Cotton and Harris attempt to justify this assumption

a
by computing the field gradient at one chlorine atom due to

the net effective charges on all atoms of PtCl4-. They find,
that in this case, the error made in neglecting this effect
amounts to about 2.5% of the total field gradient. They do

not, however, give anough details of this calculation to allow

an estimate as to how good it was. 4) All three-center integrals

are neglected. With these assumptions we may now write

k'z i'i' k k i'j'
[i.lci' qa +§I>i'ci, cj, qa ]+ P .

k

qa

=ZN

k

Using the Mulliken-type approximation (57)
i‘jf _ i'i'

qa -Siljl q(l I

we write

57

_ i'i' _ k k 2 k k

I 3., 1],
C1. i' 1 k j'>i' 3 1'j

(59)
where fi' is the molecular orbital expression for the occu-

pation of ¢i° When Equation 59 is multiplied by eerswe get

2

2 = 2 i'i' e 055

e Qaqa E. "‘Ei'[e qa Qa+ >3 fi' 1 ° (60)
il

The term in the square brackets is then replaced by eaoogat’
then with Nk replaced by 2-Nk (since chlorine has one hoIé

in the p shell) we finally get

e20 q
pa=‘—z——Q‘L = Z
l

e Qaqat l 3

z (Z-Nk)[‘Ci¥l2 + ' Z c.k c.k s. ..1.
k .

(61)

This equation has many potential advantages over that of
Townes and Dailey although much more extensive computation
is needed when it is employed. However, it is not yet clear
whether the assumptions involved are any better than those of
Townes and Dailey.
C. Evaluation of the Parameters of the
Townes and Dailey Equation

From Equation 52.p = (l-afié-I:"Y, and since we know
ezqatQ and may measure e2qQ this equation may be used to
interpret our experimental data in terms of bond parameters.
However, we have only one measureable, p, and four parameters;
therefore, we must estimate three of the parameters by other

means in order to calculate the fourth from our experimental

58

data. It should be emphasized that all methods discussed in
this section apply only to the interpretation of halogen NQR
data. Townes and Dailey (65), and Gordy (66), have discussed
approximations for obtaining these parameters. Gordy has
madetnwaapproximations both of which neglect hybridization.
In the first he sets 0,5 andjn—equal to zero and calculates
the bond ionicity from the equation p = 1 - I. For compounds
in which some double bonding is expected Gordy sets the
ionicity I = fi-AX where AX is the difference in electronegativ-
ity between the two atoms forming the bond. He then calculates
77 from the equation p = (1-IJWT: again neglecting hybridiza-
tion. Values of 77-calculated using his second approximation
are quite reasonable but his neglect of hybridization is not.
For example the compound ICl has a coupling constant of 80

MHz and eaQqat(Cl)= 109 MHz; no double bonding is expected

in this compound hence, neglecting hybridization, about 28%
ionic character is calculated. This seems much too high and
it is reasonable to invoke hybridization to explain this dis-
crepancy. Gordy‘s assumption of I = fiAX is probably roughly
correct, but it gives ionicities which are too high in the
region of AX = 2. Whitehead and Jaffe C67) have used this
same approximation but they use modified electronegativities.
Townes and Dailey have also used two approximations, in the
first dp hybridization has been neglected. This is reasonable
for the halogens since the difference in energy between the

p and d states is large and an upper limit of 5% probably may

nay

“va-

.0‘

"r
~\

5

(I,

“J

59

be set on dp hybridization for the halogens. They also

neglect double bonding and estimate 0 according to the

following rule: if the atom to which the halogen is bonded

is less electronegative than the halogen by 0.25 units or
more,then d== 0.15, otherwise a.= 0; 6 is always less than

0.05. This rule was proposed by Townes and Dailey partly

from a consideration of compounds of the group V and VI "elements"
where 5 character of the bond may be estimated from the

formula

= cos y .
a 'I:E$E$ (62)

where ¢ is the angle between the bond in compounds where the
group V and VI element is the central atom. Dailey (68) has
re-examined this rule for a series of simple alkyl compounds.
He finds that for halogens involved in C—Cl, C-Br or C—I

bonds the factor 0.15 in the Townes and Dailey equation should
be replaced by 0.156, 0.086, and 0.016, respectively. This
takes into account both Sp and dp hybridization. Coulson

(69) has calculated that maximum overlap occurs at about 50%
sp hybridization but the curve of overlap versus sp hybridiza-
tion is quite flat and 25% s hybridization would not cause

a large decrease in overlap. The percentage of s hybridiza-
tion is governed by two competing effects, the energy needed
to promote s electrons into the p orbital so that hybridiza-
tion may take place and the bond energy gained by reason

of additional overlap. (Thus, 5 hybridization in the

6O

neighborhood of 25% is favored. In addition, the s hybridi-
zation of the group V and VI elements as calculated by
Equation 62, varies between 10 and 25%. Finally, it is known
that the amount of hybridization increases as the ionicity
of a bond increases. All these facts indicate that the
Townes and Dailey treatment of hybridization is quite reason-
able.

When double bonding is expected to be important, Townes

and Dailey use the equation

= aiRi + 532R2
R a1 + 532 , (65)

first derived by Pauling. In this equation R is the ob-
served bond distance in the compound under study, R1 is the
sum of the single-bond radii for the two atoms involved in

the bond, R2 is the sum of the double-bond radii, and a1

and a2 are the fractional importance of the single and double
bond structures, reSpectively. Since R1 and R2 have been
tabulated by Pauling (70), and by Townes and Schawlow (71),
and since a; + a2 = 1, a2 E Trmay be calculated if R is

known. To correct for some anomalies observed in internuclear
distances in fluorine compounds Schomaker and Stevenson (72)

have suggested that R; be modified to R1' by the equation

R1' R; -0.09 AX, where AX is the electronegativeity dif-
ference. However, in other compounds the correction itself
introduces anomalies so it is probably better to disregard

it. For well defined covalent bonds, such as a C- C or C— H

61

bonds, Equation 63 is fairly reliable, but for bonds like
Sb-Gl or P-Cl it has more qualitative than quantitative
significance. Using these rules to obtain a and;(, Townes
and Dailey have calculated the bond ionicity I in a number
of compounds and have constructed a graph of ionicity versus
AX from which it is possible to estimate the ionicity of
any bond with the aid of a table of electronegativity.
Their graph is reproduced in Figure 6, along with those of
Gordy and of Pauling,for comparison. Townes and Dailey
argue that their graph is more accurate than Pauling's
because Pauling based his values on an incorrect interpre-
tation of dipole moment data.

Although the Townes and Dailey equation (Equation 55)
is probably quite good, and for the purposes of comparing
a series of similar compounds quite reliable, their treatment
loses much accuracy when the various rules are applied to
evaluate the parameters in individual cases. Townes has
estimated that these approximations are accurate to about 25%.
Equation 61 derived by Cotton and Harris,offers certain ad—
vantages since their parameters may be calculated much
more accurately than those of Townes and Dailey and thus
interpretations for individual compounds will be more re-
liable. The best approach at present to the interpretation
of the NQR data must be to interpret changes within a series
of chemically related compounds as a function of the change

in one specific parameter.

1.0-L

O’Bq'b

Ionic character

 

 

62

 

Figure 6.

1'. 0 2‘1 0
Electronegativity difference

Ionicity versus electronegativity difference
according to the approximations of Pauling (70),

, Gordy (60), and Townes and Dailey (44).

63

Previous NngStudies of Charge
Transfer Complexes

 

Douglass (2) was the first to study a charge-transfer
complex with NOR techniques. He studied complexes formed by
chloranil with several donors. The only compound in which
an NQR absorption could be found was the complex of chloranil
and hexamethylbenzene. If charge transfer takes place as
expected from the hexamethylbenzene to the chloranil, a charge
shift from the chloranil ring to the attached chlorine atoms is‘
expected. This charge shift, by increasing the ionicity of
the bonds,should decrease the BQIINQR absorption frequency.
Douglass observed a slight increase in the absorption fre-
quency which he explains by invoking solid-state effects.

In substituted benzenes the crystal splittings are about 200
kHz and Douglass points out that the frequencies which result
when 200 kHz is subtracted from his measured frequencies
correspond to an increase in ionicity in the C-Cl bond of
chloranil in the complex. On this basis he obtains an upper
limit to charge transfer. There is, however, no good reason
for expecting a crystal field effect of this magnitude or
even this direction. In organic complexes two types of
electron donors are commonly recognized. The first is a
w-donor, which donates charge from wabonds, such as carbonyl

bonds, multiple bonds, etc. or donates charge from the w-

I
cloud above an aromatic ring. The second is an n-donor which
donates charge from lone-pair electrons. Charge-transfer

complexes formed by transfer of W-charge are known to correspond

VA
Iv'

 

5n

to.

UT.

RA
5v

5!-

~l.‘

II

64

to the weakest charge transfer (75). Moreover, charge
transfer into the w-cloud of chloranil may not redistribute
itself in a simple manner. HOOper (5) has studied the
resonance frequencies of 35C1 in a 1:1 complex of CC14 and
p-xylene and the 79Br NQR spectrum in CBr4.p-xylene and
Bra-benzene. The halogen resonancesin.CCl4, CBr4 and Bra
show only a negligible shift in frequency upon complex form-
ation. Since the above complexes are uncomplicated by #-
cloud effects on the acceptors these results indicate that
the charge transfer is too small to measure by this method.
Duchesne et al. (4) have studied a series of charge transfer
complexes between bromine and some substituted benzenes and

the results are given below.

Table 6. Frequency Shifts Upon Complex Formation Between
Brg and Some Substituted Benzenes.

 

 

Compound Br Frequency Shift (MHz)
C6H5°Br2 +0.107
C5H5F-Br2 —0.04
C5H5C1°Br2 -0.026
C6H5Br°Br2 '1.706

 

The frequency shift for the bromine in CeHsBr is —10.384
MHz, while the frequency shift of the C1 in C6H5Cl is only
-0.004 MHz. These results generally support the work of

HOOper and Douglass except in the case of the CeHsBr'Brg

65

complex. Duchesne et al. explain their results in the follow-
ing manner. For the first three complexes the only mechanism
for complex formation is a donation of charge from the #-
cloud of the ring to the bromine molecule and this type of
charge transfer increases the electron population in the anti-
bonding 4pz orbitals of the Br atoms. This distribution
should be spherical to a first approximation and thus have
little or no effect on the Br NQR absorption frequencies.
Nevertheless, if any appreciable charge transfer takes place
it is puzzling that no frequency shift takes place for the
chlorine frequency in chlorobenzene. In the complex CaHsBr'Brg,
however, another type of charge transfer complex may be formed
in which the bromine atom of bromobenzene may donate some
charge from its lone—pair electrons to the bromine molecule.
This type of complex is much stronger than a W-complex (75).
Accordingly large shifts for both the bromine molecule and
the bromine atomcflfbromobenzene are found. It is unfortunate
that it was not possible to find an absorption in the complex
C3H51°Br2 as CeHsl is also expected to be an n-donor.
Grechishkin et al. (6) have studied the 1218b, 35Cl and
81Br resonances in a series of molecular complexes of SbCla
and SbBr3 with substituted benzenes and ketones. They find
only negligible shifts for the halogens (in those compounds
where it was possible to find halogen resonances) and larger
shifts for the antimony. These data agree well with the data

previously discussed for w-complexes. Since the antimony is

66

the recipient of the w-charge it is logical that larger shifts

121Sb is about 10 times

are observed; however, e2Qqat for
that for 35C1 so the relative shift for antimony is negligible.
From the above discussion it may be concluded that NQR studies
have revealed only a negligible shift in the resonance fre-
quencies for quadrupolar nuclei involved in w-type charge-
transfer complexes. The probable reason for this is that such
a small charge is transferred in the formation of the w-type
complexes that other things obscure the effect of charge trans-
fer on the NQR data; on the other hand, as exemplified by the
CsHsBr°Br2 data, n—type charge-transfer complex formation

has a noticeable effect on the NQR resonance. For this reason
a series of n-type charge transfer complexes formed between
quinoline, pyridine and some pyridine derivatives with ICl

and IC13 were synthesized during the present work.
Unfortunately, a search on several of the compounds over a
frequency region which should have contained the 35Cl resonance
frequencies for ICl and IC13 did not yield any absorptions.
There is no apparent reason for this failure.

Much stronger charge transfer complexes have been studied
by Dehmelt (8) and by Biedenkapp and Weiss (9). These com-
plexes are strong enough so that they may be considered to be
formed from a Lewis acid-Lewis base reaction and in these the
shifts in the chlorine resonances studied averaged greater
than 1 MHz. It was thought (74) that this was outside the

range of frequency shifts which may be attributed to crystal

b"
it

V i
(Y‘

of.

\A/
an

H
H r

o.\

n

67

field effects. Of particular interest are the shifts in the
two complexes ASClg'POCls and SnCl4°2POC13; the chlorine
resonance frequencies together with the previously measured
frequencies for the pure components are given below in

Table 7.

Table 7. NQR Resonance Frequencies in Charge Transfer Com—

plexes Compared to the Resonance Frequencies in
the Pure Compounds

 

 

 

Resonance Resonance
Frequenc1es Frequencies
Compound (MHz) Compound (MHz)
POC13 28.995 SnCl4 24.294
28.958 24.226
AsCls 25.406 24.140
25.058 25.719
24.960
SnCl4-2P0C13 50.215 ASC13°POC13 29.208
50.117 29.168
21.146 29.154
19.807 24.481
19.055 25.125
24.799.

 

An inSpection of Table 7 reveals that each complex has

two distinct groups of frequencies.

group may be associated with the chlorine resonances of P0C13

The higher frequency

u
‘91-. *
I .

4.4! ‘-

u .
I. -.

‘1: Hr

in *5

3" ‘.I
‘6‘ 1..

R5“,
5VAL~
.

4.
...a_

n
.
"deu
‘Vcl.

(I,
’ A
’. :

(n
MP-

\-

68

and the lower frequency group with those of the Lewis acid.
We find that the chlorine frequencies in SnCl4-2POC13 have
large shifts relative to the uncomplexed molecules. These
may be qualitatively explained in terms of a simple model
in which the charge transfer from the oxygen atom of POC13
to the tin atom results, by induction, in an increase of
electron density on the chlorine atoms of SnCl4 leading to
an increased ionicity in the Sn-Cl bond and a decrease in
ionicity in the P-Cl bond. Thus, the NQR frequency of the
chlorine atoms of SnCl4 should decrease while that of the
chlorine atoms of POC13 should increase as is, in fact,
observed. For the AsC13°POC13 complex, only negligible
changes from chlorine NQR resonance frequencies of the pure
compound are observed. This may be explained on the basis
that no complex, or at most only a very weak complex, is
formed as indicated also by data from Raman spectroscopy
(74) and from thermodynamic studies (75).

In this study we have prepared a fairly large series of
P0C13 complexes, although it has been possible to find
resonances in only four of them. It was thought that the
shifts in the 35Cl.resonance frequencies in the complex rela-
tive to those in the uncomplexed components would give a
measure of the acid strengths of the Lewis acids involved in
these complexes. In addition, since quite accurate X-ray
structures were available for several of these complexes, it

was thought that calculations of the field gradient induced

69

by the charged nuclei in the crystal lattice, combined with
the observed splittings of the NQR lines, would yield some

information on the solid state interactions in these complexes.

lunar
Lah'bé

int:

#IL

7..

Der;

Q

33);!

II. EXPERIMENTAL

A. The Nuclear Quadrupole Resonance Spectrometer

1) Introduction

 

The problem of finding NQR absorptions is simple in
concept. All that is needed is a spectrometer which pro-
duces electromagnetic radiation in the proper frequency
range, and whose frequency may be varied until an absorption
is detected. Since all known quadrupole resonances fall
into the frequency region between 0 and 1000 MHz, we need
a Spectrometer which Operates in the radiofrequency region.
In this investigation we shall be concerned with chlorine
quadrupole resonances, which are expected to fall into the
frequency region 0-55 MHz; most of the NMR absorptions of
commonly observed nuclei also occur in this frequency region.
Thus, it is not surprising that many of the experimental
methods are the same. It is not practical to use the
balanced-bridge method since the frequency must be scanned,
requiring that the bridge be continuously rebalanced. It
had previously been thought that the nuclear induction method
was unsuitable for the purpose of detecting NQR absorptions
because the twofold degenercy of NQR energy levels did not
permit any net nuclear induction to appear. Recently,

however, it has been found that the application of magnetic

70

9AA",
nix/H“

Q

0"
‘01 L)
F.

‘P‘.
so; '

y
«83‘

J
a a

71

modulation of about 50 gauss amplitude removes the degeneracy
well enough so that it is possible to detect NQR resonances by
this method. Hartmann et al. (76), using a Varian Wide-Line NMR
Spectrometer, have recently detected chlorine NQR absorptions
in bis-ethylene diamminodichlorocobalt(III) chloride-HCl-Xflgo.
They detected three resonances at approximately 5, 10 and 15
MHz due to igéi-é‘ ; ig—i-ig-and :t%-%:1:-§- transitions,
respectively, by simply tuning the variable frequency Varian
VF-16 oscillator by hand and observing the output on an oscillo-
scope while the sample was in the probe and the field was modu-
lated with an amplitude of about 50 gauss. However, the

most common method for observing NQR absorption is by means

of either marginal or supergenerative oscillator—detectors.
These consist of a radiofrequency oscillator which is modified
in such a way that it detects when the frequency is swept
through a resonance. Marginal oscillators are in common use

in wide-line NMR but superregenerative spectrometers are less
commonly used because of troublesome Sidebands, even though
they were originally introduced by Roberts (77) for use in

NMR. In NQR work, however, the superregenerative oscillator

is used almost exclusively, as it is much more sensitive than
the marginal oscillator. This is an important consideration
since, in general, NQR lines are much weaker than NMR lines.
From now on we shall confine our discussion to super-

regenerative oscillator-detectors as they have been used

exclusively in the present work.

72

It is of interest to examine the factors which determine
the signal-to-noise ratio AS/An in the output of our spectrOm-
eter. Pound (79) has calculated this ratio for the case of

nuclear quadrupole resonance and found that

_ v.35 oi Af hBNQCIE‘)é 7 v)3 (I + m) (I - m + 1)
n 2(1 + 1) 16 kT(kTBF)?T1E

 

*1:

for single crystals; this ratio should be reduced by a factor
of 2/5 if the sample is in the form of a powder. VC is the
effective volume of the resonant circuit, Q is the well-known
quality factor of the resonant circuit, A is a constant very
close to unity, f is the filling factor, V the magnetogyric
ratio, No the number of resonant nuclei per cc, v the
resonant frequency, T1 the relaxation time and (kTBF) an
effective temperature T, bandwidth B, noise figure F for

the spectrometer; T2*is a line width parameter roughly
analogous to the Spin-spin relaxation time in NMR. It may be
shown (16) that the optimum signal-to-noise ratio is obtained
when 72H12T1T2*(I + m)(I - m + 1) = 1, where H; is related
to the output voltage of the Spectrometer. Since T1 is gen-
erally quite small (typical values being in the range of 1
millisecond) large values for the rf voltage are needed to
satisfy this equation. This is one of the reasons why super-
regenerative oscillators are preferred, since typical rf
voltages of 20-150 volts may be developed across the coil of

the tank circuit. Marginal oscillators typically only reach

75

about 0.5 volts, although Special circuits (82) are avail-
able which can attain voltages in the range of about 20
volts.

2) Superregenerative Oscillators

In Figures 7 and 8 are given the wiring diagrams for two
oscillators which were constructed during the course of this
work. The first has its circuit parameters chosen so that it
works well in the frequency region of 15-55 MHz while the
second works well in the region of 2-20 MHz. The lowest fre-
quency NQR line observed was that of PrC13 at 4.5 MHz and
the highest was that of CC14, which has its highest frequency
line about 41HMHz, but the oscillators worked well as low as
2 MHz and as high as 55 MHz.

In order to make clear some of the difficulties encountered
in frequency measurement we will now briefly sketch the theory
of the superregenerative receiver. The distinct feature of
this type of oscillator is that the oscillation is periodically
dampened or quenched. Two different modes of operation may
be distinguished, coherent and incoherent. In the coherent
mode the next oscillation cycle is initiated before the decay
of the previous cycle to noise level, while in the incoherent
mode the next cycle starts from the noise level. The inco-
herent mode is more sensitive and most radio and radar appli-
cations of the superregenerative receiver use this mode but
in our applications we require transmitting and receiving

properties so use the coherent mode. Operation in the coherent

74

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75

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m u
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76

mode gives rise to discrete frequencies rather than a single
one. These frequencies consist of a center frequency, which
correSponds to the actual frequency, of the oscillator, and
two series of sidebands. If v0 designates the center fre-

quency and v is the quench frequency, then the frequencies

Q
of the first series of sidebands correspond to the formulas

v0 + v v0 + 2v v0 + 3v while the other series

0' Q' Q ° ' ' ’

correspond to the formulas v0 - v v0 — 2v v0 - 5v . . . .

Q' Q' Q

Thus, a quadrupole resonance absorption consists of a whole
spectrum of lines, one of which is v0 and the rest are side-
bands. Although in theory the amplitude of the sidebands
should decrease as they are further removed from the central
frequency, in practice the first upper and lower sidebands
often have the same amplitude as the central band. This situ-
ation is not too bad as we may pick the central frequency of
the triplets as the center frequency. However, it often
happens that the first and second upper sidebands are compara-

ble in size to the center line while the lower sidebands are

quite low in intensity or vice versa and in this situation it

 

is impossible to pick out the center band. Both this problem
and that of the closely spaced doublets and triplets of NQR
lines will be discussed more thoroughly in the section on
frequency measurements.

The quenching action is brought about by periodically
driving the voltage of the grid of the oscillator tube to a

negative enough value so that current flow is stopped,

there
then
ing c

v
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exte:

77

thereby dampening the oscillations. The oscillations are
then restarted by withdrawing this voltage and again allow-
ing current to flow in the oscillator tube. There are two
methods for applying this quench voltage. In the first,
commonly referred to as external quenching, a periodic voltage.
usually a sine wave of appropriate frequency generated by an
external oscillator, is applied to the grid of the oscillator
tube. It was found by running test experiments under varying
conditions that the best voltage for the external frequency
was in the region 4-9 volts. The higher the voltage used

the higher the quench frequency that may be used but as the
quench voltage is raised undesirable modulation of the oscil—
lator output is introduced. In general, it is desirable to
quench at as high a frequency as possible consistent with the
condition that a small amount of noise be alflDwed in the
oscillator output. This noise generally increases as the
frequency of the oscillator increases, and to keep the noise
level down the quench frequency must be continuously raised
as the oscillator frequency is increased. Increasing the
quench frequency also increases the coherency of the oscil-
lations as is evident from the preceding discussion. Thus,
we try to keep the quench frequency as high as possible while
still allowing enough noise for the proper operation of the
oscillator. Raising the voltage of the external quench in-
troduces more noise (correSponding to more incoherency) thus

allowing us to raise the quench frequency, but it also

in¥f

fin
NU
-

C1Y1

78

introduces amplitude modulation. At low oscillator fre-
quencies it was sometimes necessary to lower the quench
frequency so much that a sharply decreased sensitivity was
noted. In summary then, the voltage and frequency of the
external quench are adjusted in conjunction to obtain the
highest quench frequency (although not too high) consistent
with the proper noise and the least amount of amplitude
modulation. In the second method, called self-quenching,

the oscillation is dampened by the following action. During
oscillation current flows in the oscillator tube, this results
in a small gridhleak current which flows through the variable
resistor R1 to ground and back to the cathode, thus complet-
ing the circuit. During its passage some of the grid-leak
current is diverted to charge capacitor C; which in turn
causes a negative potential on the grid. As more current
flows the capacitor becomes more highly charged and the grid
becomes more negative until current flow through the tube is
cut off. The capacitor then discharges to ground through R1,
decreasing the negative potential on the grid until current
may again flow in the tube, then the whole process is re-
peated. The quench frequency is mostly controlled by the
product of R1 and C1. In the circuit of Figure 7, R1 = 2 Meg-
.ohm and C1 = 50 pf, permitting quench frequencies in the range
20-40 kHz. This control is logical since the larger is R1,
the more slowly is C1 discharged to ground and hence the lower

the quench frequency. Again R1 must be continuously adjusted

79

as the frequency of the oscillator is changed in order to
maintain the prOper noise level. The advantage of self-
quench is that it is slightly more sensitive than external
quench. However, external quench has the advantage that it
does not need to be adjusted so frequently as the oscillator
frequency is changed and changing frequency does not affect
the oscillator frequency; these are both significant ad-
vantages. The oscillator can only detect rf power absorp-
tion (which would indicate a nuclear absorption frequency)
during the build-up of oscillation amplitude following a
period in which the oscillation has been quenched. The method
of detecting a resonance is to detect a slight lowering of

the rf voltage at the plate of the oscillator tube. This
lowering comes about in the following manner. For a self-
quenched circuit, an absorption of power lowers the base volt-
age upon which a new oscillation cycle must start, thus it
takes a longer time for the grid to reach the cut-off voltage,
corresponding to a decrease in quench frequency. Since a
decrease in quench frequency means fewer bursts of rf voltage
at the plate in a given time, the average rf voltage at the
plate decreases; this decrease is the basis for detection of
the absorption. For an externally quenched frequency circuit
the quench frequency is fixed but the average amplitude of

the rf bursts is lowered by an absorption, which the plate
sees as a drop in average rf voltage. The high-range oscil-
lator may be operated as either a self-quenched or externally-

quenched oscillator. In order to operate it with external

80

quench, R1 is switched from ground to a BNC connector at
which the output from the quench oscillator is injected

and the value of 31 is then decreased until self-quenching
stOps. Capacitors C2 and C3 are adjusted by experiment to
obtain the most sensitive Operation of the spectrometer but
as a general rule if one is more open the other should be
more closed. For this reason they are connected in tandem

in the low-range oscillator such that as one opens the other
closes. The frequency of the oscillator within a given range
is varied by tuning the tank capacitor C4. The range of the
oscillator may be changed by changing the tank coil L1.
Typical coils allow a range of about 10 MHz. The sample to
be studied is inserted directly into the tank coil and since
most searches and measurements are made at liquid nitrogen
temperatures some extension of this coil is needed outside
the oscillator. At first this was done by means of a standard
shielded cable RG-SB/U but this caused problems because it
introduced increased capacitance into the tank circuit.
Although the problem was partially solved by using Special
low-capacitance cable RG-62/U this was not completely satis-
factory because shielded cable was not rigid enough, the
oscillator being very sensitive to vibration, and it was very
inconvenient to change coils. All these problems were over—
come in the following manner: A-é inch O.D. brass tube

6 inches long was rigidly mounted to the spectrometer chassis

and fitted at the bottom with a male BNC connector. A-fi inch

81

solid brass rod was then run down the middle of the tube,
being careful to keep the rod and the tube electrically iso-
lated since the tube was grounded. The end of the rod was
reduced and sharpened and used as the pin in the BNC con-
nector, the other end of the rod being connected to the side
of C4 which was above ground. The various coils were then
mounted on female BNC connectors thus making coil changing
quite simple and easy.

In the process of building high frequency oscillators
certain good practices should be followed. It is well-known
that length of leads is critical but only in certain parts
of the circuit. The most critical lead lengths are the
lengths of wire between resistors, capacitors, etc. and the
oscillator tube. Thus, for example, a resistor which is to
be connected to the tube should have its connecting wire cut
off as close to the resistor body as possible, allowing only
a long enough lead to insure a good solid joint; the lead on
the other side of the resistor body is not important. It is
also good practice to get a chassis much larger than needed
and to place the oscillator tube socket in the center allow-
ing plenty of hand room so that the elements directly attached
to the tube may be squeezed in quite closely. Lead lengths
in the tank circuit do not seem to be critical but they should
be of heavy gauge bare wire, preferably the tin coated variety.
They should not be placed close to the walls of the chassis,

if possible, as the wall and the wire tend to form a capacitor.

.1 n

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82

All grounds in the oscillator should be to one firm ground
and the tube socket center should a130 be grounded to this
same ground. This helps to avoid ground loops and parasitic
oscillations. Finally, particular care should be taken that
all components are mounted solidly and rigidly.

5) Modulation and the Lock—in Amplifier

 

In NMR work a resonance absorption may be detected di-
rectly by a drop in rf power at the receiver but in NQR work
this drop in power is too small to be directly detected.
Accordingly, a method has been adapted from radio technology
called modulation. As applied to the observation of nuclear
resonance absorptions the concept of modulation is quite
simple. In NQR there are two types of commonly used modu-
lation, frequency modulation and magnetic, or Zeeman, modu-
lation. When the frequency of the oscillator is passing
through resonance both types of modulation cause the rf power
absorption to appear at the frequency of the modulation, thus
causing a signal to appear in the oscillator output at the
modulation frequency, although this signal is not necessarily
in phase with the audio generator producing the modulation
signal. When no absorption is taking place the modulation has
no effect on the oscillator output. Thus, the appearance of
a component in the oscillator output at the modulation frequency
means that the frequency of the oscillator coincides with an
NQR absorption frequency in the sample under study. This sig-

nal is much easier to detect than a drop in rf power.

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85

In frequency modulation the frequency of the oscillator
is constantly varied over a small frequency range which is
determined by the amplitude of the modulation. The modulation
amplitude should be determined by the width of the resonances.
Wide resonances need large frequency excursions when sweeping
through them; hence, large modulation amplitudes are needed;
narrower lines require a smaller amplitude. Since excessive
modulation amplitude tends to distort and broaden absorption
lines the minimum amount of modulation should always be used.
This is particularly true when using the lock—in amplifier
recording technique. The frequency of modulation is another
consideration. The most important consideration is that the
modulation frequency must be small compared to the absorption
line width. Since line widths have been observed from about
2-50 kHz, modulation frequencies generally should not exceed
300-400 Hz. It is also not advisable to use 60 cycles,or any
harmonic or sub-harmonic,when using the recorder technique
due to the danger of picking up line noise. Aside from this
consideration many workers seem to prefer higher frequencies,
typically 280 Hz, in order to avoid flicker noise but this is
not a very convincing reason since flicker noise is only im-
portant for frequencies below about iOHz. In this work
several standard signals were recorded at widely varying
modulation frequencies. The results showed a surprising
‘Variation in signal-to-noise ratio with modulation frequency.

(HPtimum modulation frequencies usually fell around 59 Hz so

 

this
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pres

84

this modulation frequency was adopted. No explanation can
be offered for the variation in signal amplitude with modu—
lation frequency.

Although there are many schemes for frequency modulation
of superregenerative oscillators the one adopted in the
present work is believed to be the best. It consists of
placing a 1N950 diode D1, which acts as a capacitor, in
parallel with the tank capacitor. The diode then has the
property that its capacitance varies with the voltage applied
to it. Thus, if a periodic voltage is applied to D; the fre-
quency of the oscillator is varied periodically. For example,
the 1N950 varies in capacitance from 0-88 pf with a variation
of 0-150 volts. The slope of a graph of the capacitance of
the diode versus applied voltage changes in different voltage
regions so the diode is biased with a d.c. voltage to bring
the voltage into the region with the desired slope. Figure 9
shows the auxiliary unit used for frequency modulation in this
work. It can accept either 60 Hz line voltage, which is
stepped down to 6 volts rms with a filament transformer, or
1-10 rms volts of audio voltage supplied by an audio oscillator,
in this case a Hewlett-Packard Function Generator Model 202A.
In either case the audio frequency is supplied to an inter-
stage transformer with a 2:1 ratio which steps up the voltage
and also acts as an impedence matching device for the audio
oscillator. The auxiliary unit also supplies a d.c. bias

using a standard Eveready 45-volt battery.

 

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In magnetic modulation the absorption is made to appear
and disappear periodically by applying a periodic magnetic
field to the sample. As previously explained, the application
of a magnetic field of sufficient size to a polycrystalline
sample will cause the resonance to broaden out and disappear.
Thus, when a square wave or half—wave rectified sine-wave
voltage is applied to a Helmholtz coil or a solenoid in which
the sample is placed, the resonance disappears during the on-
period and appears during the off-period. If an unrectified
sine wave is applied, the situation is more complex but
essentially the signal appears and disappears twice during a
modulation cycle, since both positive and negative voltage
producetflmzsame magnitude magnetic field (although Oppositely
directed), and the broadening of NQR absorption lines depends
only on the magnitude of the applied field. Accordingly, the
induced frequency in the oscillator output appears at twice
the modulation frequency.

Magnetic modulation in this work was applied by means
of a solenoid wound in four layers around a cylindrical Dewar
vessel. The sample is placed inside the Dewar vessel in the
sample coil and both are immersed in liquid nitrogen. The
wire was of small enough gauge to permit winding forty turns
per inch over the length of three inches and the diameter of
the Dewar was three inches. The sinusoidal current was
supplied from the Hewlett-Packard Function Generator which was

fed into a Fisher lOO-watt power amplifier. This amplifier

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87

supplies currents in the range 0.1 to several amperes rms;
three amperes roughly corresponds to a field of 400 gauss
rms at the center of the solenoid.

The signal-to-noise ratio for many NQR signals is so
low that it may not be easily observed on the oscilloscope.
In this case some device must be found which improves the
signal-to-noise ratio. Abragam (78) has shown that the
narrower the band width around the modulation frequency which
we observe, the better the signal-to-noise ratio. Thus, if
our modulation frequency is 59 Hz and we observe all signals
in the output of our oscillator in the frequency range 59.i
0.1 Hz our signal-to-noise ratio will improve compared to
signals observed in the range 59 :,1 Hz. The narrower this
bandwidth the more improved will be our signal-to-noise ratio
but there is a practical lower limit to the bandwidth. We
'wish,'then, to use a narrow—band amplifier to amplify only
signals at the modulation frequency in the output of the oscil-
lator. The oscillator output will also contain some noise at
the modulation frequency at which the narrow-band amplifier is
centered, but the phase of this noise will not be fixed but
random. The signal induced by the modulation will be of fixed
phase although not necessarily the same phase as the modula-
tion. If we pass the output of the narrow-band amplifier into
a phase-sensitive detector, then the output of the detector
A is proportional to Aincose, where 9 is the phase angle

out

between the input signal from the narrow-band amplifier and

CCI‘.
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no
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88

the modulation signal; the noise will then be greatly
reduced. The input to the phase-sensitive detector is put
into phase with the modulation by passing it through a phase-
shifter circuit, the amount of phase shift being set by
maximizing a strong known signal. The output of the phase—
sensitive detector is then rectified and fed to a recorder.

A signal may be detected by noting marked changes in the
level of the d.c. output to the recorder. An amplifier which
consists of a narrow-band amplifier followed by a phase-
sensitive detector is called a lock-in amplifier. For further
discussion of the lock-in amplifier see references 78-81.
Since the modulation amplitude is set at only a fraction of
the line-width when using a lock—in amplifier the output of
the amplifier is proportional to the slope of the absorption
line and a first-derivative curve is obtained instead of an
absorption curve. If desired, an output proportional to the
change in slope of the absorption line may be obtained by
detecting at twice the modulation frequency; a second deriva-
tive of the absorption line is then obtained. This is desir-
able if amplitude modulation is troublesome. Also, if an
unrectified sine-wave magnetic modulation is used it is
necessary to detect at twice the modulation frequency. A home-
made lock-in amplifier constructed according to a circuit
diagram by Bolte (81) was first used in this work but it was
found that there were several mistakes in the wiring diagram

and even when these were corrected the amplifier never worked

89

reliably. A Princton Applied Research Associates Lock-in
amplifier Model JB-4 is now used and has worked quite satis—
factorily. No NQR spectrometer would be complete without a
lock-in amplifier since approximately half of the signals
reported in this work could not be observed on an oscilloscope.

Figure 10 shows a block diagram of the spectrometer.
All the important parts have been discussed. A typical re-
corded NQR spectrum is shown in Figure 11.

4) Frequency Measurement

If the NQR absorption line whose frequency we wish to
measure is a single sharp line strong enough to be easily
observable on an oscilloscope, frequency measurement is rela-
tively straightforward. The method is based on the fact that
when the quench frequency is changed by an amount Av the

Q

first upper sideband moves up in frequency by an amount AvQ .
the second upper side band increases in frequency by ZAVQ . etC-I
the lower sidebands similarly move to lower frequency. The
center frequency, in theory at least, does not move but this

is strictly true only for externally quenched oscillators;

in self-quenched circuits,changing R1 slightly does alter the
central frequency and this movement of the central frequency

can greatly confuse the measurement. However, once the high
frequency oscillator was modified so that it could be ex-
ternally quenched this uncertainty was removed. From the

above discussion it is clear that the sidebands far removed

from the center frequency move quite radically upon small

90

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92

changes in the quench frequency. Without changing the quench
voltage, which usually greatly alters the line shape, changes
of about 5 kHz in the quench frequency may be made. Such a
small change does not alter the positions of the closer side-
bands on the oscilloscope screen so there is usually still
some ambiguity'.regarding the center line. A further problem
is that when an external signal is coupled to the oscillator
it is received as a series of sidebands and a center band.
The problem then becomes one of superimposing the central
band of the external signal source upon the central line of
the resonance spectrum. A useful technique is to pick out
the three or four strongest lines from the external source
and the sample absorption. Each sample line is then tuned
onto the oscilloscope in turn and tested with each of the
external source lines. Each external line is imperfectly
superimposed on the absorption signal, the quench frequency
is then varied and the two lines observed to see if they move
relative to one another. This technique is usually successful
with strong lines. However, even if the center line of the
oscillator and that of the external source are correctly
identified, it is very difficult to superimpose them exactly
since there is a marked difference in line shape between
absorption lines and those from the signal generator. This
may lead to an error which has been estimated at.1 kHz from
trial.nmasurements on NaClOs. If the NQR line is not a singlet
the absorption spectrum becomes quite complex, due to over—

lapp-ing of the sideband patterns. In this work the POC13

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95

lines in both TiCl4‘2POC13 and (TiCl4-POC13)2 overlapped. In
the case of (TiCl4-POC13)2 it was possible to resolve the
spectrum into three lines after a considerable time spent
studying the spectrum but it has not yet been possible to re-
solve the spectrum of TiCl4°2POC13. In the case of the more
complex Spectra the best procedure is to pick out the strong-
est lines and measure their frequency by superimposing what
is judged to be the center line of an external oscillator on
them. The quench frequency is then changed and the measure-
ments repeated. From a study of the results, keeping in mind
how sidebands behave upon changing the quench frequencies, an
attempt is then made to distinguish the number and frequencies
of the center lines. Needless to say, this procedure is not
infallible. In the case of (TiCl4'P0Cla)2 additional COD?
fidence in the results is gained from the agreement between
the experimental results and the line multiplicity as predicted
from the X-ray structure of this compound. In all cases ten
frequency measurements were made for each line and an average
used for the line frequency. From the precision of individual
measurements of the same line, and from previous trial
measurements on NaClOs and p-dichlorobenzene, it is believed
that all frequency measurements made by the above techniques
are accurate to.i 3 kHz.

When absorption lines are too weak to be observed on the
oscilloscope screen a different technique must be used. The

follxjwing method was found to be the best of several methods

"A.

VJ

1+
CI)

94

tried. The line was first recorded repeatedly while chang-
ing oscillator settings, modulation amplitude and lock-in
amplifier settings, until the best recorded spectrum was
obtained. This spectrum was then studied in an attempt to
determine if it was a singlet or not. The most likely

center lines were then picked out and the spectrum rerun at
the slow speed of l/SOO rpm and stopped on each of the likely
lines in turn. An effort was made to stop at the exact zero
point of the first derivative, but this was not always pos-
sible, because of a lag between the recorder and the lock-in
amplifier. Furthermore, it was not possible to tell if the
recorder was stopped at the correct spot. The correct center
line from the external oscillator was then centered on the oscillo—
sc0pe and this line was then centered on the frequency at
which the oscillator was stopped by observing the output of
the narrow band amplifier on another oscilloscope. The pro-
cedure was then repeated at another quench frequency and by
comparison of the shifts induced by the change in quench
frequency the center line was decided upon. By comparison
'with measurements on known compounds.i 10 kHz is believed to be
the accuracy of lines measured by this method. The precision
of measurement is, however, somewhat better. Unfortunately.

.i 5 kHz was the maximum change in quench frequency which could
‘be obtained. Since the uncertainty in measuring the quench
frequency was :t 10 kHz this allowed some ambiguity in the

choice of the center line.

t«

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5.

95

It is believed that any line whose frequency was
measured on the oscilloscope is accurate to.i 3 kHz while
those measured on the chart are accurate to.i 10 kHz.
However, especially in the latter case, there is a chance
that a sideband was mistakenly chosen as the center line.
This possibility is inherent in all frequency measurements
involving superregenerative oscillators but is often ignored
by authors when assessing their possible errors.

5) Spectrometer Operation and Problems in

Detecting Resonances

Searching for an NQR absorption is often frustrating and
disappointing. Relatively minor things may cause the line to
be missed. For example, some lines are quite sensitive to
modulation while others are not. For no apparent reason some
lines are quite intense while others with the same number of
resonating nuclei per unit volume are quite weak. In some
cases the latter phenomenon has been attributed to subtle
differences in crystal structure although no one cares to go
into this matter too deeply. For example, it is found that
certain liquids which are rapidly cooled to liquid nitrogen
temperature give no resonance signals but if they are cooled
very slowly they do have resonance absorptions. This behavior
is attributed to the fact that rapid cooling probably developed
strains in the crystal lattice and these strains somehow
erased the signal. Order-disorder phenomena also have an ef-
:fim:t as shown by the following phenomenon observed by Dean

(85): no signal was found for chlorine in p-chlorobromobenzene

2+
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96

but when a small percentage of p-dibromobenzene was mixed with
the p-chlorobromobenzene a chlorine signal appeared. The ab-
sence of absorption was explained on the basis of a certain
randomness in the crystal structure of p-chlorobromobenzene
due to the fact that the halogen sites have equal probability
of being a bromine or a chlorine atom. When the p-dibromo-
benzene was added the crystal structure became more ordered
since there was now a higher probability that a halogen site
would contain a bromine atom. Khotsyanova (86) has explained
some of his results in a similar manner. He has studied the
spectrum of C6C15F which consists of 3 lines of 770K, while
at 1950K no lines are observed. He ascribes this behavior

to a crystalline phase transition to a totally disordered
phase.

It is also found that impurities have an effect on NQR
lines. Some types of impurities have a more marked effect
than others, but all impurities tend to broaden an NQR line
and lower its intensity.

Another factor which contributes to the difficulty of
finding NQR lines is the wide range of frequencies at which
they may occur. This difficulty is eSpecially troublesome in
elements which have a large quadrupole moment. Compounds
containing these nuclei have potentially a very large absorp-
tion frequency, yet if they are involved in a highly ionic
bond.the absorption frequency can be quite low. An example

of this is 1271 (Q = -O.75) whose d: 5/2 ->:t 3/2 transition

freque:
Fartun
predic
but ca

SUCK a

Eltroc

liquid

97

frequency ranges from 29.5 MHz in CdIg to 902 MHz in ICl.
Fortunately the expected frequency range for 1271 may be
predicted from studies on similar 85Cl containing compounds
but calculated predictions have not been succeSSful for nuclei
such as 55Mn (Q = 0.6) and 57Co (Q is expected to be of the
same order of magnitude as Q for 55Mn) and it is difficult
indeed to predict where NQR absorption will take place in com—
pounds containing these elements.

Finally, it should be mentioned that NQR absorptions are
missed in many compounds for no apparent reason whatsoever.
This happens more often than is desirable and is one of the
principal drawbacks to the widespread use of nuclear quadru-
pole resonance.

The frequency sweeps in search of unknown resonances were
made so as to minimize as many of the above mentioned draw-
backs as possible. First, the sample was packed as tightly
as possible into a glass vial to maximize the filling factor,
or,if the sample could be melted without decomposition, it
was melted into the sample tube. It was then annealed in an
oven overnight at a temperature just below its melting point
to minimize strains. If the sample was a liquid, or a solid
near its melting point at room temperature, it was precooled
overnight in a refrigerator then slowly cooled to 770K by
gradually lowering it into a Dewar vessel containing liquid
nitxnogen which had been pretreated by adding a small amount of

Lhmrid nitrogen and allowing it to stand long enough to

98

establish a temperature gradient in the rest of the Dewar.

Various methods were tried for adequately sealing
sample tubes which contained substances highly reactive with
air. At first rubber stoppers were inserted and sealed
with plastic tape. This was not successful as the corrosive
samples were found to attack both the rubber and the tape.
Then Nylon stoppers were machined and inserted into the glass
tubes containing the sample; these were sealed in with a tape
especially resistant to chemicals and the top of the tube
was coated with paraffin. At first this method was success-
ful, even though the samples attacked the tape,but repeated
immersions of the sample into liquid nitrogen soon flaked
off all the paraffin. The final measurements were made on
samples sealed into glass tubes. This seems to be the only
satisfactory way to handle corrosive samples.

In order to avoid temperature gradients, samples were
kept in liquid nitrogen for half an hour prior to beginning
the search. This was much longer than necessary but was a
convenient time since it took this time to warm up the
spectrometer and make some preliminary adjustments.

The range of a particular coil was governed by the in-
ductance of the coil, the larger the inductance the lower
the frequency range of the coil. Thus, the larger the number
of turns in a coil the lower its frequency range. In order
to obtain a good Q for the tank circuit these should all be

of the same size and the coil should be wound neatly with

99

closely spaced turns. All coils used in this work were

1.5 cm in diameter. However, if too many turns were wound
on a coil, the coil became quite unwieldly. Conversely, in
coils intended for a high frequency the number of turns
became too few causing a serious drop in rf power in the
coil. Both of these problems were solved when it was noted
that a coil wound with fine gauge wire always had a larger
inductance than a coil with the same number of turns of
heavier gauge wire. Coils with a few turns were wound with
heavy gauge wire while those intended for the low range of
the oscillator were wound with small diameter wire; those
for intermediate ranges had their wire gauge chosen to give
a convenient number of turns. Below is given a table of
coil size and gauge together with the frequency range of the
coil.

Table 8. Physical Dimensions of the Coils Used with the
High Range Oscillator

 

 

Number of Frequency Range
Turns Wire Gauge in MHz
9 18 15-22
12 16 21-27
7 16 24-52
5 14 28-56
4 14 52-42
3 14 36-48

 

si;

582

[L‘

"1

100

The settings for the lock-in amplifier are maximized
prior to the beginning of each run by use of a strong known
signal. This signal should be as close to the expected
sample frequency as possible.

When all is in readiness, a low frequency modulation
amplitude is chosen and the frequency range provided by the
coil being used is swept. This is done by means of a Holtzer-
Cabot motor of 120 inch-ounce torque and 1 rpm speed which
is fed to an INSCO speed reducer that may be set to provide
reductions of 1:1, 2:1, 5:1, 20:1, 50:1, 100:1, 200:1, 500:1,
and 1000:1. The speeds of 1/500 and 1/200 were most often
used. If the recorder trace showed no signals, the frequency
range was swept again with a larger modulation amplitude.

This was repeated with severalsdifferent modulation amplitudes.
In some cases both frequency and magnetic modulation were used
although frequency modulation was used most often. The noise
level of the spectrometer was kept at a level which was de-
termined through trial and error on known signals.

All frequency measurements were made with a BC-221
Frequency Meter whose frequency was then counted with a
Hewlett-Packard Model 524C Electronic Counter. The direct
reading on the electronic counter was compared to the cor-
rected frequency read from the charts on the BC-221 and in all

cases agreement was excellent.

sL
~.E

101

6) Temperature Dependence of the 27.512 MHz
Resonance in SbCls-POClg

It was decided to measure the temperature dependence
of the strong 35Cl line of SbC15 in SbCls'POClg to see if
a crystalline phase transition took place. For this purpose
three slush baths were prepared to cover the temperature
range from liquid nitrogen (770K) to room temperature
(2970K). These were carbon disulfide, ethyl acetate and
carbon tetrachloride. An ice-water mixture was tried but
could not be used because the mixture damped out oscillations.
Each bath was made by adding about 200 cm3 of reagent to a
500 cm3 Dewar vessel and then adding liquid nitrogen in small
amounts. The mixture must be vigorously stirred otherwise
the two liquids quickly separate. The mixture finally
solidifies and is allowed to melt until a thick slush is ob—
tained. This mixture easily holds its temperature.i 10K
for about 50 minutes, after which it must be resolidified.
The samples were allowed to equilibrate with the slush baths
to eliminate temperature gradients and the resonance pattern
centered on the oscilloscope screen. The frequency of the

line was then measured by the method given previously.

B. Chemical Syntheses

 

The methodsibr the preparation of all samples and
standard compounds are given below.

1) Trans—dichlorobisethylenediamine Cobalt(III)
Chloride-HCl-xfigo

frec

mate

102

This compound was desired as a standard for the low
frequency oscillator since it has 57Co resonances at approxi-
mately 5, 10 and 15 MHz and a weak asCl resonance at about
16 MHz. It was prepared by the method of Bailar (87). At
first it was not known that the HCl occluded in the lattice
was essential to observation of the 57Co resonances so that
no precautions were taken to retain the HCl which is very
volatile and evaporates if the complex is air dried. When it
was realized that HCl was essential the complex was dried in
a desiccator over concentrated sulfuric acid with an open
beaker of concentrated hydrochloric acid also inside the
desiccator. The procedure is as follows: Six hundred grams
of a 10% (by weight) ethylenediamine solution was added while
stirring to a 2-liter flask containing 160 gms of CoC12°6H20
in 500 ml of water. A vigorous stream of air from the air
jets in the hood was filtered through glass wool and blown
into the solution overnight. Three hundred milliters of
concentrated EKIL was added, the whole mixture poured into a
large evaporating dish and then heated on a steam bath until
a crust was formed over the surface. The bright green
crystals of the complex were filtered off and quickly washed
with alcohol then ether. The crystals at this point had
partially turned to a dull green indicating some loss of HCl.
They were then transferred to the desiccator and dried in an
atmosphere of HCl gas. During the drying process they re-

gained their bright green lustre.

S)

n;
"\

'(J

C)

(\7

105

2) The Cu(I) Complexes of Some Thiosemicarbazones

 

These 1:1 complexes were synthesized so that an attempt
to find 63Cu(I) resonances in diamagnetic compounds could be
made. Thiosemicarbazones of the following ketones and
aldehydes were made and complexed with CuCl:acetone, cyclo—
hexanone, benzaldehyde, o-chlorobenzaldehyde, o-methoxy-
benzaldehyde and m-nitrobenzaldehyde. Each was made by react-
ing the corresponding ketone or aldehyde with thiosemi-
carbazide in a reaction quite similar to that used in forming
hydrazones and oximes. The following procedure was adopted
from the method of Sah and Daniels (89): 0.05 moles of thio—
semicarbazide, 100 ml of water and 10 ml of glacial acetic
acid were warmed on a steam bath until the thiosemicarbazide
dissolved and the solution then added immediately to an
alcoholic solution of the ketone or aldehyde. Usually a pre-
cipitation of the product occurred immediately but sometimes
it was necessary to cool in an ice bath. The copper com-
plexes were made as follows (Gingras et al. (88)): 0.05 moles
of the thiosemicarbazone were dissolved in methanol (about
200 ml) and heated to reflux in a three-necked flask equipped
with a stirring motor. To this solution was added dropwise,
while stirring, 0.05 moles of CuCl dissolved in about 100 ml.
of ammonia solution (0.9 Specific gravity). The mixture was
then stirred and refluxed for an additional thirty minutes,
cooled to room temperature and the complex filtered off in

the form of a dark Sludge ranging in color from light gray to

104

a dark olive green. The complexes were purified according

to individual methods as recommended by Gingras. In the case
of the o-methoxybenzaldehyde complex, which was not made by
Gingras, the procedure for the p-methoxybenzaldehyde complex
was followed. It Should be mentioned that these complexes

do not seem to be soluble in any of the common solvents

hence recrystallization, the most reliable purification method
for solids, could not be used. The purification procedures
consisted of washing with various solvents and solutions.

It is not known how pure these compounds are. The complexes
seem to be quite stable and have been stored in plastic topped
bottles for over a year without noticeable decomposition.

5) Mercuric Chloride Complexes

 

Mercuric chloride has a strong NQR absorption at about
22 MHz; hence, several complexes were made to see if the
resonance line shifts upon complex formation. The preparation
of HgC12°(CH3)2SO followed one of the methods of Selbin et al.
(90).

Approximately 20 ml of dimethylsulfoxide was heated on a
steam bath and saturated with mercuric chloride. Upon cooling
transparent crystals separated. An attempt was made to re-
crystallize these crystals from acetone; however, an oil
formed. Addition of ethyl ether followed by scratching the
Side of the beaker with a glass stirring rod, however, pro-
duced a white transparent precipitate of good crystalline

form. The melting point as given by Selbin et al. was

 

:U

.‘4

\I,L
\G.

A!
t, h

adv
5L

105

125-60C and the first time the complex was prepared it had

a melting point of 125-60C. The second time it was prepared
a waxy rather than a crystalline material was obtained which,
when recrystallized from ethyl ether, yielded a compound with
a melting point of 77-80C. Although this compound was put

in a vacuum desiccator connected to a vacuum pump for several
weeks no complex with a melting point 125-60C was obtained.
It is suggested that this compound may be HgC12-2(CH3)2SO

but no attempt was made to determine its formula because

neither complex yielded an NQR resonance.

 

The four complexes (Pyridine)2°HgClg,(2-Picoline)2»HgC12,
(S-Picoline)2-HgClg and (4-Picoline)2-HgC12 were made accord-
ing to the following procedure: To a saturated ether solution
of HgC12 the base was added and the white flocculent precipi—
tate which appeared immediately was removed by filtration and
washed 5-6 times with cold ether. It was then recrystallized
from methanol, placed in a vacuum desiccator and the desiccator
connected to an oil pump for several days.

Preparation of the dimer of the 1:1 complex of triphenyl-
phOSphine mercuric chloride (91). When a solution of tri—
phenylphosphine in absolute alcohol (5.2 gms per 250 ml) was
added to a solution of mercuric chloride in hot absolute
alcohol (5.4 gms per 250 ml) the complex immediately precipi-
tated in the form of glistening white Scales. These were

collected and dried in a vacuum desiccator.

 

106
4) The Complexes of ICl with Pyridine
and its Derivatives

The complexes of pyridine, S-cyanopyridine, 2-bromo-
pyridine and quinoline with iodine monochloride were prepared
with a method adapted from Meyer (92).which depends on the
fact that ICl and all the organic bases are quite soluble in
CCl4 but most of the complexes are not. The method is as
follows: The base and ICl were each dissolved in CC14 in '
approximate one-to-one molar ratios, the two solutions mixed

together and the complex allowed to precipitate. The colors

J.“u‘v:-n ' ll " "

of the precipitates ranging from mustard yellow quinoline-1C1

 

to bright yellow 2-bromopyridine-IC1. This precipitate was,
however, mixed with some brownish red particles, also the
solution remained brownish red. Evidently the complex forma-
tion does not go to completion, the reddish brown color being
attributed to ICl. The original solution was decanted, fresh
CCl4 added, and the whole mixture gently warmed on a steam
bath. After a time this solution was also decanted, and the
process repeated until no more red particles could be ob-
served mixed with the complex and the CCl4 remained trans-
parent in color. The complex was then air-dried.

5) Binary Complexes of POC13

Since the complexes are quite difficult to prepare, and
to various extents react with moisture, no attempt will be
made to give a general preparation, as has been done for the
compounds previously discussed, but each preparation will be

described individually. The compounds all have in common the

107

fact that they are hydrolyzed quite easily by the moisture

in the air and every precaution must be taken to ensure as
little contact as possible with the atmosphere. All Operations
involving extensive handling of these compounds were carried
out in a dry box under nitrogen atmOSphere. All reactions

were carried out under an atmosphere of purified nitrogen

 

which had been passed through a drying column. After the re- lrfih
action was completed the reaction flask was quickly sealed

and opened only in the dry box. The physical appearances of

these compounds are quite diverse, some are low-melting waxy [

solids, while others are powders. It was found that the waxy
solids were more stable and could be handled in the air for
longer periods of time without decomposition.

The complexes SbCls-POClg, TiCl4-2POC13, SnCl4-2P0C13
and (TiCl4-P0C13)2 were all made by the same general method.
Two 250 ml Erlenmeyer flasks were first flushed out with
nitrogen, then about 25 ml of the acid was quickly added to
the first flask and the flask was weighed again. In the case
of the TiCl4 complex, POC13 was then carefully weighed into
the other flask on an OHAUS CENTIGRAM balance, such that the
molar ratio of P0C13 to TiCl4 was either 2:1 or 1:1. The
P0C13 was then quickly added to the TiCl4 and the flask again
stoppered. Immediately an exothermic reaction took place
and the solution became bright yellow; upon cooling the
whole mass solidified. The mixture was then melted, stirred

and allowed to resolidify to ensure good mixing of the

 

108

components. The solid was then completely melted and allowed
to solidify except for the last few milliliters which were
discarded. This process was repeated twice. The complexes
were then stored in a vacuum desiccator over P205. In the
case of SbCls and SnCl4,only one complex is formed with P0C13
so that a little excess reagent was added to ensure complete
reaction. At first excess P0C13 was added as recommended by
Gutmann (93) but this did not work as well as excess acid,
Since excess acid was much easier to remove when the complex

was pumped on with a vacuum pump. The SbCls complex was a

 

pale lemon yellow color, which may possibly have been due to ,_w
a slight impurity of SbCls, while the SnCl4 complex was color-
less. BiC13°P0C13 and SbCla-POClg were also made by this
method but since only a slight warming of the solution occurred,
and the mixtures were cloudy liquids after cooling, there is
some doubt that the complexes actually formed. Raman data
Show that frequencies are only Shifted slightly in the mixture
so the complexes are weak or nonexistent.

The preparation of 2FeC13-5POC13 and FeCla-P0C13 followed
a modification of the procedure of Gutmann and Baaz (94).
FeCla which was slightly wet was dried in the following manner.
A three-necked one-liter flask was fitted with a reflux con-
denser whose top was closed off with a Drierite tube, a
dropping funnel and a connection which allowed dry nitrogen
gas to be constantly passed through the flask. This flask

was flushed out for 50 minutes with dry nitrogen and about 20

 

109

gm «of wet FeCla and 100 ml of thionyl chloride was added.

The mixture was refluxed on a steam bath for about three
hours, until the thionyl chloride had reacted with all the
water. The condenser was then put into distilling position
and the excess thionyl chloride distilled off. A large excess

of P0C13 was then added to the dark black anhydrous FeCla

 

through the dropping funnel The resulting solution is a I‘m“
deep brownish red and was refluxed for an hour to ensure com-

plete reaction. It was then transferred to a 250 ml Erlen-

myer flask and the solution partially evaporated by use of

an aspirator while warming the flask in a beaker of hot water. .,-

When the mixture was reduced to a rather viscous appearance
it was transferred to the freezing compartment of a refrig-
erator and allowed to solidify. This process may take several
weeks. The solid was allowed to warm at room temperature, at
which point it remained a solid but with some drops of excess
P0C13 still adhering; these were removed by evaporation in

a stream of dry nitrogen. The complex, which is a dark red-
dish brown spongy solid,was then transferred to a drying
pistol and evacuated: the pistol wasyleft connected to a
vacuum pump until a constant weight Was obtained. This latter
process may also take several weeks. The complex is very
easily hydrolyzed and Should be handled quite carefully.
Another preparation, due to Dadape and Rao (95), was tried
with much less success. In this method advantage is taken

of the fact that while FeC13 is not soluble in CC14 the

 

110

complex is quite soluble in hot CC14 and POC13 is quite

soluble in CCl4,hot or cold. A large excess of anhydrous

FeCl;; is placed in a one-liter flask and 600 ml of dry CC14

is added along with 50 ml of POClg. The mixture is heated

for an hour on the steam bath with constant stirring and the
liquid decanted from the remaining FeC13 and cooled in an

ice bath at which point the complex precipitated and was fil-

tered off. Perhaps some arrangement could be made to carry

out these operations in a dry atmosphere and a better yield
could be obtained but the only time this method was tried
mo st of the complex decomposed during the filtration step.

In all other preparations of this complex the first method

was preferred. FeCla'POC13 was made from the 2FeC13'5P0C13

as follows: 2FeC13-5P0C13 was placed into a drying pistol,

the temperature raised to about 550C by refluxing acetone,

and the pistol connected to a vacuum pump. After several

hours the brown 2FeC13-5P0C13 changed to greenish yellow

FeCla-POCIS by loss of P0C13.
The complex BCla-POClg was made by the following pro-

cedure: A 250 ml Erlenmeyer flask was first flushed out with

dry nitrogen, then cooled in a slush bath of dry ice and

isopropanol. BC13 gas was condensed in the cooled Erlenmeyer

flask and an amount of POC13 added such that the BC13 was in

large excess. The very volatile excess BC13 was evaporated
with an aspirator leaving behind a white powder. During the

removal of the excess BC13 it was discovered that the complex

 

111

sublimes at room temperature under reduced pressure. The

complex was stored in a vacuum desiccator over P205.

The two complexes AlClg-POCla and 2AlC13°3P0C13 are prob-

ably the most difficult to prepare. Groenveld and Zuur (96)

have studied the temperature versus composition diagram for the
system AlClsaPOCla and they report three complexes, AlCla-POCls

(m-p. 1860C), A1c13-290c13 (m.p. 1640C) and AlC13;POC13 (m.p.

410C) . They report making these compounds by sealing

stoichiometric quantities of the reactants in heavy-wall glass

tubes and melting the mixture. They also report making

 

A1C13°P0C13 (m.p. 1860C) by dissolving AlCla in P0C13 and re-

moving the excess POC13 with a vacuum pump. Gutmann and Baaz

( 94:) , on the other hand, on the basis of conductivity measure—
Iments find that the only possible complexes between AlCla and

Pool3 are AlCls'POCla (m.p. 1800C) and 2AlC13'5POC13 (m.p.. >

1600C) and do not mention a low-melting complex. It is

interesting to note that Gutmann and Baaz obtain 2A1C13-5POC13

by a method identical to that described by Groenveld and

2“lur (96) for the preparation of AlCls'P0C13.' These reports

are not encouraging to one who wishes to make these complexes

with a minimum of fuss and bother. In all the preparations

the A1013 used was first purified by vacuum sublimation. In
the first attempt to make these complexes AlC13 was dissolved

in POCla, the mixture placed in a vacuum desiccator and

Pumped on with an oil pump. A dirty white powder was obtained

Whose melting point was about 500C. This was pumped on for

112

several weeks without any change. Finally the powder was

transferred to a drying pistol which was heated with reflux-
ing acetone. The melting point of the complex then started
to rise as POC13 was removed and continued to rise until all
the POClg was lost. No complexes were obtained and several
variations of this procedure also produced no results. In a
second attempt to prepare these complexes, several thick-wall «
g lass tubes were obtained with sealed bottoms and constricted
necks for easy sealing. The tubes were about five inches

long with about three inches of the tube below the constric-

 

tion. Approximately one gm of AlC13 was weighed into each
tube and stoichiometric amounts of POCla added to each tube
Corresponding to the AlC13:POC13 ratios of 1:1, 1:2 and 2:5.
The tubes were quickly dipped into liquid nitrogen to prevent
reaction or vaporization of the reagents while the tube was
be ing sealed off with a gas—oxygen torch. The constrictions
Were wiped clean with a cotton swab and sealed. The tubes
Were then allowed to come to room temperature. With suitable
Precautions in case of an explosion each tube was heated with
a. Fisher burner until the contents melted together. These
Were the samples which were used in the NQR experiments.
6) Ternary Complexes of POCla
In addition to the binary complexes of P0C13, a number of
ternary complexes were also made. [A1(P0C13) a] [SbCle]s (97)
was prepared in a 5-necked 1-liter flask which was continually

flushed with dry nitrogen and was equipped with a stirring

115

rn<>t:or and dropping funnel. A 10‘1 M solution of SbCls in
POClg was placed in the flask and a 10‘1M solution of AlCls.
Jill POC13 added dropwise until a ratio of 5:1 was reached.
firllee resulting precipitate was filtered in a dry box and
vvaisshed with dry CCl4. It was then transferred to a vacuum
éieessiccator to remove any CC14 and POC13 remaining. A similar
Eazrcocedure was followed in preparing [Al(P0C13)5][FeCl4]3 (97).
ssLllostituting FeC13 for SbCls : also the AlCls was added to
t:r163 solution of FeC13 until a color change from red to pale
gyxreeen occurred. K[TiC15°POC13] was made by the following
berc>cedure: Using the same set-up as the previous preparation,
1Pj_<214 was added dropwise to a suspension of KCl in P0C13
llrltzil a molar ratio of 1:1 was attained. The solution was
c=C>lrlcentrated in gaggg_until a good crop of yellow crystals was
C51)1:ained. The flask was then transferred to a dry box where
titles crystals were removed by filtration and washed with dry
(3C3314. They were then dried in a vacuum desiccator over P205.
s1~'>C215°TiCl.;,-5POC13 was prepared by the following procedure
( 98) : SbCls and TiCl4 were dissolved in a 1:1 molar ratio in
city ethylene chloride and P0C13 added in excess. The mixture
‘VEiS concentrated under vacuum, filtered in a dry box and
Vmashed with dry CC14. Finally, the resulting crystals were
sublimed in 33939 at a temperature of 180-2000C.
All solvents used in this work were dried with Drierite
and then with magnesium sulphate. The solvent was then de-
canted and distilled taking only the middle cut. They were

stored over Drierite.

III. CALCULATION OF THE CONTRIBUTION TO THE
MEASURED FIELD GRADIENT FROM CHARGES
SITUATED IN THE LATTICE

I&.. Introduction

As mentioned in the theoretical section, contributions

t:<> the quadrupole coupling constant may result from charges

eezcternal to the molecule being investigated. These charges

atzre situated at fixed points in the lattice and the approxi-

:nmaition is often made of replacing these charged atoms by

js>c>int charges. In order to avoid confusion in subsequent

C3;i.scussions the following definitions are made. The molecular
ffj_eld gradient tensor EmOl at a nuclear Site is due only to

e lectrons within the molecule and is the gradient which would

kbee measured if the molecule was completely isolated. The

C21:ystal lattice field gradient acrys arises due to solid

SState effects and is a property of the crystal lattice.
3511 this thesis a model has been introduced which ascribes
t:his effect to point charges Situated in the lattice; thus,

tihe term crystal lattice field gradient will often refer to

(zontributions from this source. This calculation is not a

asimple one for several reasons. As previously mentioned a

<:orrection must be made by use of the Sternheimer factor for
the fact that the chloride ion is highly polarizable. The

uncertainty in assigning a value for 7a) (Cl-) has been

114

115

discussed. Another problem is that, for the compounds we
wish to discuss, it is not certain exactly what charge to
assign to each point because the compounds which are investi-
gated in this work are partially covalent. Thus, it is not
realistic to assign the charge of the fully ionic species,
but the partial charge on the ion is very difficult to
determine. Sharma and Das (99) have shown in calculations on
A1203, Fe203 and C‘r203 that a rather large contribution to
the electric field gradient comes about from the dipole in-
duced in the highly polarizable 02" ion. These contributions
have been neglected in the present case partly because, Since
all the ions involved are much less polarizable, this contri-
13111:ion is much smaller than that expected from 02‘, and partly
13€e<2ause this effect would be extremely difficult to calculate
in our case. The above three approximations introduce enough
mlicertainty into the actual lattice sum calculations that the
results of the calculation Should be used with caution in
quantitative predictions. The lattice sum results are,
hOwever, quite valuable as a measure of the differences in
environment of crystallographically different but chemically

similar chlorine atoms. In particular this is of value

when trying to determine the relative acid strength of a series

of Lewis acids. It is important to make sure that the chlorine

atoms one is using as test probes be in roughly equivalent
Crystal atmOSpheres. An attempt is made here to get an idea

Of the size of the external contributions to the field

116

gradient. When these contributions are determined, it must
1363 decided whether their effects overshadow chemical effects.
IKIIthher reason for evaluating these sums is to explain the
(31>:served multiplicity of the NQR lines. The splittings have
toeeeen attributed to chemically Similar atoms in crystal-
ILcaggraphically nonequivalent lattice Sites. However, few
a:t:1:empts have been made so far to explain even qualitatively
t:r1<ese splittings by use of the crystal structures. Furthermore,
j.ff these crystal lattice sums could be evaluated in a more
satisfactory manner, detailed information on solid state
interactions would be obtained.

One final problem with these calculations should be men-
tliuc>ned. The calculations essentially consist of summing a
iftlrlcmion of e and r"3 over various sites in the crystal lattice.
This summation procedure is continued until the sum converges.
IIr1 theory this convergence should be rapid because of the r'3
'teezrnn in practice, however, this is not found to be the case
lbsecause the lattice sums are conditionally convergent rather
'tlléan absolutely convergent. The usual practice is to pick a
sE3°here of arbitrary radius (usually 20-602) around the atom

a"'-“-which the lattice sum is desired and then to sum over all
a4:0ms contained within this Sphere. For crystals in which the
m<Dlecules are close packed, this may correspond to summing
<3ver 250,000 atoms. Even with the use of high speed computers,
this procedure is very time consuming and convergence is by

no means assured even for this number of atoms. An alternative

117

Exrwocedure is to mathematically change the conditionally con-
xzeexrgent sum to an absolutely convergent sum. This was the
rneat:hod applied by DeWette (100) and DeWette and Schacher
(:L()1-102). DeWette (100) first deve10ped his method for
czz:)rstals with a fourfold or sixfold axis. The method had the
disadvantage that the direction of the field gradient princi-
E>EilL axis must be known. Jones, Barnes and Segal (105) applied
I)eeVVette's method to the calculation of the field gradient in
21 Imumber of ionic halides. They assumed that the principal
EI><:i.S'was along the sixfold axis. Unfortunately this is true
only if the atom whose field gradient is being calculated lies
(DI). the sixfold axis which is not true for several of the mole-
czuilLes studied by them, introducing a considerable error in
1Zl'leese cases. In order to find the principal-axis direction
3Lt: is necessary to calculate all nine components of the field
€31TEidient tensor and then diagonalize the tensor; qzz will be
'trIEit component of the diagonalized tensor which is largest
:111 absolute magnitude. DeWette and Schacher have extended
DEEWrette's original method so that all nine components of the
field gradient tensor may be calculated for any crystal sym-
Infietryu This work is the first attempt to use this new method
‘fCDr the calculation of crystal field gradients. Dickmann
(IL04) has computerized the method of DeWette and Schacher for
tile purpose of calculating the electric field in a crystal due
‘to permanent dipoles in the lattice. This program LATSUM

has been obtained from Dr. Schacher and suitably modified for

118

the present purpose. This modification consisted Of adding

several subroutines, which first diagonalize the calculated

tensor by rotating the axis system to the principal-axis

system in order to obtain q and n. The tensor is then ro-

tated to the principal-axis system of the molecular field

gradient in order to evaluate the contribution of the crystal

lattice to the measured field gradient. The main program

was also modified so that the electric field gradient rather
than the electric field is calculated and also so the program

may be cycled for the several hundred lattice sums needed,

rather than separately for each one.

B - Theory

For the sake of completeness, a brief discussion Of the

tI‘Leory involved in the calculation Of the electric field
gradient at a nucleus due to external charges Situated in

a crystal lattice will be given.

In order to calculate the full tensor Q two types Of sums

I“List be evaluated
. 5v.2~-r.2
AXial sums vi =5; Ell—#314 and
3

Off“ '1 =26. .v, r.5 (65
ax1a sums va j JpJ J/ J )

Where the va are the elements Of the tensor 5, the index j

ideally runs over all the atoms in an infinite crystal, and ej

is the charge at the j th atom. Both Of these sums were

119

derived under the point-charge assumption. Previous workers,
taking their cue from Bersohn (105), have aimed at the direct
evaluation Of these sums for all the lattice sites contained
in a Sphere Of radius ranging from 20-1003 which is about
the largest Sphere for which this direct summation procedure
is practical. However, in some cases these limits do not
include enough atoms to ensure convergence. This problem
can be critical as the value of the sum is usually quite
small compared to individual terms since these terms are
both positive and negative and the final sum is a small dif—
ference between two large terms. Although the terms fall
Off quite rapidly as distance from the central nucleus in-
creases, terms quite far away from the nucleus can make Sig-
nificant contributions to the lattice sum. Thus, workers
using this method should prove convergence of their sums but
this is not easy to do and has been neglected in most cases.
In our particular case a sphere 1003 in diameter would con-
tain about 400,000 atoms. Since this is too many for the
CDC-5600 computer to dO in a reasonable time we looked for a
method which ensures faster convergence Of the lattice sums.
DeWette used another approach, first evaluating the sum
in each plane and then adding these sums for the complete set
of planes. Each sum may then be made to converge absolutely
in each plane which may be seen by considering the following

Simplified version Of our lattice sums method:

CD

S = f(n), (66)
n=1

120

where f(x) goes slowly to zero as x -%~OO and may be infinite
at x = 0. This is exactly the behavior of the general terms
in our sums (65) because Of the r"3 term. In order to ensure
good convergence for (66) we introduce an auxiliary function
F(x) which is finite at x = 0 and goes to zero rapidly as
x -$>OO; now (66) may be rewritten as
oo o:
S = Z f(n) F(n) + Z f(n)[1-F(n)] . (67)
n=1 n=1

The first sum of Equation 67 is absolutely convergent but
the second is not. However, if f(x)[1-F(x)] is a smoothly vary-
ing function of x then its Fourier transform is a rapidly con-
verging function in Fourier Space. Utilizing the property
that a sum of a function over a lattice in real space is equal
to the sum of its Fourier transform over the reciprocal lattice
in Fourier space, we can evaluate the second sum. A third
condition on F(x) is that it must be such that f(x)[1-F(x)]
be a smooth function at x = 0 even if f(0) = on. For the
functions f(x) with which we will be concerned, it is always
possible to find an auxiliary function F(x). Thus, we see
from the above discussion that the sums Obtained in this work
may always be made absolutely convergent by introducing an
auxiliary function and dividing the original sum into two
parts, one being summed over the ordinary lattice and the other
being summed over the reciprocal lattice. However, if f(x)
is not infinite at x = 0 and is fairly smooth it is not

necessary to find an auxiliary function. Instead the Fourier

121

transform Of f(n) is taken directly and summed over the
reciprocal lattice; only one sum then needs tO be evaluated.
Schacher and DeWette have given the necessary formulas for
the evaluation Of these sums and they are embodied in LATSUM.
It turns out that if the sums are first evaluated in a plane
the summation may be replaced by an integration. The sums
are therefore not evaluated in a sphere, as in the usual
practice, but in a cube. It is also more convenient to con-
sider each atom in the unit cell separately. A lattice sum
over all atoms at the equivalent position in each adjacent
cell is taken, including enough adjacent cells to ensure
convergence. The coordinates Of the position are chosen so
that the atom at which the field gradient is desired is at
the origin Of the unit cell. Each nonequivalent chlorine
atom of the unit cell will have associated with it a total
field gradient. For each total field gradient calculated,
nine sums, one for each Of the components Of the tensors,

are evaluated, multiplied by the charge Of the Site at which
they were evaluated and added tO the sum of the previous
components calculated, which have also been multiplied by their
reSpective charges. In this way an electric field gradient
tensor is Obtained with reSpect to a chosen coordinate system.
The tensor is then diagonalized to transform it to the
principal-axis system. The maximum contribution to the field
gradient which may be Obtained in this lattice can thus be

Obtained.

122

To illustrate this process consider a fully ionic mole-
cule MClg with two molecules per unit cell. Suppose further
that each of the chloride ions associated with a particular
M2+ occupies a crystallographically nonequivalent position

M2+ ions and 4 Cl- ions

so that the unit cell consists of two
at three nonequivalent positions. Because MClg is totally
ionic the measured field gradient would be expected to arise
entirely from external contributions Of the crystal lattice.
Then, unless both nonequivalent Cl_ sites accidently experience
identical Van der Waals forces and identical electric fields
due to charges in the lattice, two quadrupole resonance absorp—
tions would be eXpected. Furthermore, the difference between
the two measured gradients should give some measure Of the
solid-state interactions which occur, since in the gas phase
both Of the chloride ions should be identical. In order tO
Obtain the contribution tO the field gradient from the charges
in the lattice,sums at each Of the nonequivalent positions

must be evaluated. Designating two Of the chlorines as Cl(A)
and the other two as Cl(B) the whole lattice is divided intO sub—
lattices,each Sublattice with a different atom from the unit
cell at its corner. Since the unit cell contains six atoms
there will be Six sublattices; each Sublattice consists Of
atoms Of the same charge. TO find the lattice sum at Cl(A)
this atom is placed at (000) and the coordinates Of the other
five atoms with respect to this origin found. The sums are

evaluated to yield a tensor at each of the six points. These

125

tensors are each multiplied by the prOper charge and added
together to yield the total field gradient at site A with
respect to a chosen coordinate system. To Obtain the field
gradient due tO external charges at Site B this whole process
must be repeated with one Of the Cl(B) atoms at the origin.
To Obtain the principal values Of the tensor and the rela-
tion between the principal-axis system and the chosen system,
the tensors were diagonalized to give the principal values
and the resulting eigenvectors gave the angular relation be-
tween the chosen axis system and the principal-axis system.

C. Some Details Of the Modification and
Use Of LATSUM

 

LATSUM, as it was originally set up, calculated the con—
tributions to an internal electric field in the crystal from
the electric dipoles situated in the lattice. This was done
by evaluating nine sums such as Equation 65; since the tensor
system is symmetric and traceless, there are only five inde-
pendent components to evaluate. The input data consist Of
the three unit cell lengths a, b, and c and the three angles
a, 8 and y for the crystal unit cell. Another card must be
punched with the convergence limit and the maximum number Of
cells N to be summed over. The program sums over successive
cells until the value contributed by the next cell is less
than the convergence limit or until the number of neighbor
cells summed over is equal to N. Values Of N and the con-

vergence limit should be chosen as some compromise between

124

speed and accuracy. If N is made large enough the sums may

be made to converge to any desired accuracy but this may

make the summation process too time-consuming. Values Of N=20
and a convergence limit Of 10‘7 were used at first. However,
it was found that some sums which were very close to the

plane containing the origin Of the cell did not converge so
the convergence limit was changed to 10'”5 and N set equal to
80; with these limits all sums converged satisfactorily. The
final output data which the original program needed were

the coordinates Of the atom in the unit cell whose sublattice
was to be summed over. Each sublattice then required a
separate computer run which is unsatisfactory. For example,
(TiCl4'POC13)2 has 80 atoms in the unit cell and there are
seven crystallographically nonequivalent chlorine sites in

the unit cell; this means that 560 sums must be performed.

The first change in LATSUM,then,was to allow multiple sums to
be done in one computer run. Furthermore, these sums are
grouped so that all the sums for a particular lattice site are
done consecutively, added, multiplied by their charge and
printed out so that the contributions from different Sites may
be evaluated. In terms Of the previous example of MClg this
means that the two Cl(A) contributions are added together,
multiplied by -1.0 and printed. Because of this modification
additional information must be supplied to LATSUM, namely, the
number of sublattices, the number Of nonequivalent atoms at

which the field gradient is desired, the number of atoms in

125

the unit cell which belong to a particular nonequivalent site
and the charge associated with this Site.

The second change introduced was to add two subroutines
which diagonalize the field gradient matrix when it is Ob—
tained for a particular site. One of these, SMDIAG, which
diagonalizesaasquare matrix by the method of Jacobi, was
kindly supplied by Professor Richard Schwendeman. In addition
to these major changes in LATSUM, numerous minor changes were

also made.

D. A Test of LATSUM

 

Before LATSUM was used on the rather complex structures
involved in this work, it was desired to test it out on some
simpler systems first. The two systems chosen were the low
temperature form of CrC13,which was done by Morosin and
Narath (48% and CdIa which was done by Jones et al. (105).
The former was picked Since it had 24 atoms in the unit cell
and was the most complex previous calculation' and also be-
cause a reading of the literature indicated that this calcu—
lation was done correctly. CdIz was chosen because it had
two nonequivalent sites in the unit cell. Although Jones et
al. were not correct in their choice of the principal z axis
along the sixfold axis in some Of their compounds, their
choice was correct in this particular compound. This is veri-

fied by the fact that, with the same choice Of the z axis,

126

our calculated tensor was very close to diagonal. The results
of the LATSUM calculation are compared to those on CrCls
(which were calculated by direct summation in a sphere) and
those on CdIa (which were done by the earlier method Of
DeWette) in Table 9.

Table 9. Comparison of q and n as Calculated Both by LATSUM
and by Other Authors

—
L

 

 

 

LATSUM Other Calculations
Compound q n q n
CrCls -0.45000 0.5240 -0.42602 0.5219
_ a
CdIg I (2b) -0.00580 0.1701 -0.00579 --
ca:2 I-(2a) —0.00584 0.1108 —0.00585 —-

 

aThe notation 2a and 2b refers to crystallographically non-
equivalent iodine sites.

As can be seen the agreement is excellent. The slight differ—
ence between values Of q and n for CrCls is probably due tO

the superior convergence Of LATSUM. Since the CdIg calculations
were made using the same method (that of DeWette) and the same
crystal data, it is reassuring to see such good agreement.

E. The Crystal Lattice Field Gradient
Model and Programs ROTATE and DIAG

 

a) The First Model

Before a calculation Of the solid-state effects could be
attempted some kind Of a model upon which to base the calcu—
lations had to be developed. In this case it was decided to

try to explain the line splittings as due to the effect of

of‘

r‘

D—v-i

127

charged ions in the crystal lattice. This effect was expected
to be large for two reasons. First, the ionicity of the bonds
in the complexes averages about 50% with the result that the
charge on each Of the sites is Significant. Second, because
the atoms are unusually closely packed, the density of

charged sites is greatly increased compared to previous crystals
on which these calculations had been tried. vThuS, even though
the full ionic charges were not used, significant contributions
to the measured field gradients were expected. In considering
only the contribution Of the charged sites, contributions due
to induced dipoles, dipole-dipole interactions, Van der Waals
interactions and partial chemical bonds formed between the
chlorines in adjacent molecules are neglected. Nevertheless,
for reasons given above, this model was expected to give a
good first approximation. It was further assumed for the sake
of mathematical simplicity that the charged ions could be re-
placed by point charges. Using this model it is necessary
first tO assign a charge tO each site. This is not easy

since there are nO gOOd rules for Obtaining the ionicity Of
bonds. The approximate relationships of Pauling (70) and Of
Gordy (60), involving the electronegativity, have been used to
estimate the ionicity. Pauling's relation has been criticized
as being based upon an incorrect interpretation Of dipole
moment data and Gordy's method is not really based on any
experimental results. Townes and Dailey, working from quadru—

pole resonance data, have developed a graph Of bond ionicity

128

versus the difference in electronegativity Of the two atoms
involved in the bond (71). This graph was used to assign
charges to each of the chloride and oxide ions, the charges
on the other atoms were then chosen to maintain charge
neutrality in the molecule. It was assumed that, in the com-
plexes, there was a single bond between the oxygen atom of
POC13 and both the phosphorus atom and the central atom Of
the Lewis acid. This assumption may be justified, at least
in the case Of SbClS'POCla, by Observing that the Sb-O distance
in this complex is 2.188 (107) while the Sb-O distance in Sbgos
is 2.27 (108). Using the charges selected as described above
the calculation Of the point-charge field gradients was
carried out.

2) An Improved Model

After the calculation was completed it was thought that
a better assignment Of charge could be made if the coupling
constants actually found by NQR spectroscopy for POC13, SbCls,
TiCl4 and SnCl4 were used. According tO the theory Of Townes
and Dailey the measured quadrupole coupling constant ratio
p is given by p==1-I-a. ‘Using the rule of Townes and Dailey,
a,= 0.15 if the difference in the electronegativities Of the
two atoms involved in the bond is greater than 0.25; otherwise,
a,= 0. The ionicity (I) can then be calculated if the NQR

resonance frequencies are known.

Since NQR data are available only for the chlorine nuclei,

the charges on the phOSphorus and oxygen atoms and on the

129

central atoms<fifthe Lewis acids are still undetermined.

If the charge on oxygen is determined, and is separated into
contributions from the central atom and phosphorus, the
charges on these atoms may be determined because Of the
charge neutrality Of the molecule. The only way to do this
is to use the electronegativity differences. The following
procedure, explained by means of an example, was used. For
a hypothetical molecule Cl-M-O, if we assume there is some
linear relationship between electronegativity and bond

ionicities, we may write

I(Cl) = AA¥(MC1), (68)
where I(Cl) is the ionicity Of chlorine and AX(MC1) is the
electronegativity difference between atom M and chlorine.
Since AX(MC1) is known and I may be calculated from NQR data
we can calculate A from Equation 68. It is reasonable to
assume that the same relation will hold for the M-0 bond,

hence
I(O) = AAX(M0) . (69)

Using these relations the ionicity of the oxygens was calcu—
lated. In our compounds the oxygens were bonded to two atoms;
therefore, using SbCls-POCla as an example, in an Obvious
extension Of Equation 69, I(O) = AAX(Sb-O) + BAX(P-O), where
A and B can be calculated from NQR data on SbCls and POCls.
Table 10 lists the charge assigned to each atom. For the

oxygen atom in [TiCl4'POC13]2,I(O) = AAX(Ti-O) + BAX(P-o).

150

In this case A was not calculated from the TiCl4 NQR data
because it was felt that these data had too large an un-
corrected crystal effect because Of the high ionicity Of the
Ti-Cl bond and the consequent low value Of p. The value of
A calculated from the NQR data would then be tOO large and,
in fact, the calculated A was much larger than the A's
calculated for SbCls, SnCl4 and POC137 an average Of the
other A's was therefore used. In the most elegant approach
this set of charges would only be the first approximation

to the true charges. They would be used to refine the
measured NQR data to extract the molecular field gradients.
These molecular field gradients would then be used in the
Townes and Dailey relations to Obtain a new set Of charges.
This process would be repeated until self consistency was
reached. However, it was felt that the model on which the
calculations are based is not accurate enough to warrant this
procedure. Table 10 gives the charges used in the LATSUM
calculations. Since there are two kinds of chlorine atoms
in the complexes, Cl(A) designates the chlorines attached

to the phOSphorus and Cl(B) the chlorine attached to the
central atom Of the Lewis acid. The LATSUM results using
these charges are the ones used in further calculations.
Townes (71) has estimated that the ionicity calculated using

this method is within 20% Of the true value.

151

Table 10. Charges Used in LATSUM

 

 

Compound Atom Charge
Sbc15 Sb 1.625
Sbc1s c1 -o.525
Sbc15-Poc13 Sb 2.185
Sbc15-Poc13 Cl(A) -o.322
SbCls-POCla Cl(B) —o.525
SbCls'POC13 P 1.467
SbCls-POClg o -1.061
SnCl4-2POC13 Sn +2.806
SnCl4-2POC13 Cl(A) -0.322
SnCl4-2POC13 Cl(B) -o.411
SnCl4'2POC13 P +1.467
SnCl4-2POC13 o —1.082
[TiCl4-POC1312 Ti +5.952
[TiCl4°POC13]2 Cl(A) -o.522
[TiCl4-POC13J2 Cl(B) -o.741
[TiCl4°P0Cla]2 p +1.46?
[TiC14'P0C13J2 0 -1.489

 

5) ROTATE

LATSUM calculates a field gradient tensor due tO point
charges in the lattice according to a particular choice for
the directions Of the X, Y and Z axes. This tensor may be
diagonalized by a rotation to its principal-axis system.

On the other hand the molecular field gradient at a chlorine
nucleus has its principal axes oriented such that the z axis

is along the bond. Since we assume cylindrical symmetry for

152

the molecular field gradient the orientation of its X and Y
axes is arbitrary. Hence, it is only necessary tO rotate

the Z axis Of the calculated crystal lattice field gradient
tensor SO that it is aligned along the bond; then, since the
X and Y axes Of the molecular field gradient are arbitrary,
the two coordinate systems will be aligned. We can then
directly combine the 22 component of each tensor. A computer
program, ROTATE has been written which performs this rotation.
ROTATE works in the following manner; any tensor 8 with
matrix elements Qij may be rotated to any arbitrary direction
by the matrix transformation ST Q S = Q' where Q' is the
matrix Of the rotated tensor, S is the matrix Of direction
cosines and ST is the transpose of S. This rotation may take
place in two (or more) successive rotations if this is more
convenient. If the two direction cosine matrices are repre—
sented by S; and 82 then S = 8152 and ST = SgTslT, hence

Q' = SgTslTQslsg. In this case two successive rotations are
performed one in the original XY plane by an angle a.and the
other tipping the original Z axis by an angle 8. Program
ROTATE is given the coordinates Of the two atoms involved in
the bond and the unrotated tensor. ROTATE then calculates
the bond direction relative tO the Z direction Of the original
choice Of coordinates, calculates S and ST and performs the
necessary matrix multiplication. It prints out the rotated
matrix and also a, 8 and the bond distance as a check on the

calculation. Figure 12 shows how o.and 8 are defined with

Figure;12.

 

155

ACZ'

 

 

Definition Of the angles d.and 8 as used by
ROTATE.

YO

In

F—l

LC)

’13

Fr.

154

respect to the molecular bond axis Z and the axis system Of
the unrotated tensor X', Y' and 2', which are equivalent
to the crystalline a, b and c axes, respectively, for orthor—
hombic symmetry. ROTATE is listed in the Appendix.
4) PROGRAM DIAG
As a first approximation, one may take the 22 component
of the rotated tensor and combine it directly with the
measured field gradient to extract the molecular field grad-
ient. Another more accurate method is available, however.
The field gradient actually measured has principal axes
slightly different from the molecular field gradient (although
the molecular field gradient is expected tO dominate the
measured value) because when the rotated crystal lattice
gradient tensor is added to the molecular field gradient
ten sor the resulting tensor is no longer diagonal. The
Principal-axis orientation Of the measured gradient relative
to the bond direction may then be Obtained by diagonalizing
the resulting cumulative tensor. The largest element along
the trace Of the diagonalized tensor will be the experimentally
mea sured field gradient. An asymmetry parameter 7} due to
the solid-state effects may also be calculated from the
diegonalized tensor. Ideally the solid—state effects Should
be the only contributors to this parameter so that the calcu—
lated I} should correspond tO the measured 1].
At this point another complication, the Sternheimer factor,

must be introduced which may increase or decrease, according

155

to its sign, the contribution of the crystal lattice effects.
This has already been discussed but must now be taken into
account. If it were known eXactly this would pose no prob-
lem.as we would Simply multiply the calculated crystal
leattice field gradient tensor by the appropriate factor.
Lhafortunately, for several reasons already discussed (Section
:I-Ji), the factor is not known. In addition to the previous
discussion it should be noted that, although we always treat
tries Sternheimer factor 700 as a scalar, because it depends
or) the polarizability Of the chlorine atom it should probably
be: a second rank tensor. At present it is not possible to

take this into account. Or, more accurately, we assume the

E 700 0 0 _
OO 0 ym 0 .
0 0 700

If we assume that the Sternheimer factor is known we can

tensor is Of the form

{ll

Ca-:Lculate the molecular field gradient from the rotated crystal
la‘itice field gradient tensor and the measured field gradient
by the following procedure. Knowing the measured field
gre~dient we guess a molecular field gradient which we assume
is cylindrically symmetric. In the axis system in which: the

Z axis is along the bond direction this trial molecular field

grecfilient may be represented as a second-rank tensor Of the

£0 llowing form

a
-2 O O
E mOl(trial) = O -% 0 .
0 0 a

156

This is then added to the rotated crystal field gradient
tensor and the resulting tensor diagonalized. The absolute
value of the largest element on the trace Of the diagonalized
tensor is then subtracted from the measured field gradient.
This difference is compared tO the difference calculated for
the previous iteration. If it is smaller than the previous
difference we are going in the proper direction and the trial
field gradient is incremented by an element Of the same sign
and magnitude aS that used in the previous iteration. If the
difference is larger than that of the previous iteration the
Sign Of the increment is changed and if the largest value Of
the diagonalized tensor oscillates tO one side and the other
Of the measured value the magnitude Of the increment is cut
in half. This process is continued until the diagonalized
teIlsor converges to the measured tensor. The other two values
on the trace Of the diagonalized tensor can be used to calcu-
late the asymmetry parameter due to the crystal effects and
the eigenvectors Of the diagonalized tensor may be used to
determine the relative orientations Of the principal axes
of the experimental field gradient. The trial field gradient
is now the molecular field gradient. A computer program,
DIAG, has been written tO perform these iterations and is.
listed in the Appendix. The iteration procedure is repeated
for a number Of values Of the Sternheimer factor. The method
for assigning a Sternheimer factor to a chlorine atom will be

illustrated by an example. Consider again MC127 in the gaseous

157

state both chlorine atoms are equivalent, therefore their
molecular field gradients are identical. Since in the solid
the two chlorines have different experimental field gradients
this is clearly a solid-state effect. If we know the crystal
structure of MC12 we can apply LATSUM, ROTATE and DIAG.

This results in a set Of molecular field gradients as a
function of the Sternheimer factor. We then pick the Stern-
heimer factor which makes the two molecular field gradients
identical. This procedure necessitates the assignment of

the correct eXperimental field gradients to sites A and B;
however, this may usually be done from an inSpection Of the
results of ROTATE. Also, if there is reason to believe that
at least a part of the splitting between two nonequivalent
sites is due to a difference in the molecular field gradient,

this procedure will no longer be valid.

IV. RESULTS

A. Assignment Of Absorption Frequencies to
Specific Atoms in the Complexes

 

With the aid of chemical considerations, relative intensi-
ties and ROTATE it is possible to assign each NQR absorption
tO a Specific chlorine atom in the molecule. Each compound
will now be discussed separately. The crystal structure Of
SbCls-POCla was determined by Lindqvist and Branden (106) and
the atomic arrangement for the complex is shown in Figure 15;
each numbered chlorine atom denotes a crystallographically
nonequivalent site. In a similar manner Figures 14 and 15
Show the atomic arrangement for the complexes in SnCl4°2POC13,
as found in the X-ray analysis Of the crystal structure by
Branden (108), and for the complex [TiCl4'POC13]2 from the
X—ray work of Branden and Lindqvist (109).

1) SbClsfPOCla

 

At 770K six absorption lines are Observed for this com-
pound, two lines grouped at about 50.5 MHZ, one at about 27.4
MHz, two grouped around 26 MHz and one at about 24.4 MHg.

The intensities Of the four lowest lines are in the approxi-
mate ratios Of 2:1:1:1. From chemical considerations we
expect four different resonances, one from the three POC13

chlorines, one from the axial chlorine atom on the SbCls.

158

159

 

.mHOOm.mHonm mo masomgos a

Amoao

 

 

AmoHU

.ma wusmflm

 

 

.mHOOmm.¢Hocm mo mesomnos 2 .ea magmas

     

 

140

&

 

 

 

141

.NHMHUOm.¢HUHBH HOEHU OS“ MO OHSUOHOE fl

.ma onsmflm

 

142

one from the chlorine atom trans to the POC13 oxygen and one
from the two chlorine atoms gig to the POC13 oxygen atom.
Reference to Figure 15 shows that there are six nonequivalent
chlorine atoms in this complex. AS will be discussed, it is
expected that charge transfer will be indicated by an in-
crease in the resonance frequencies Of the POC13 chlorine

atoms and a decrease in the resonance frequencies Of the

 

chlorine atoms Of the Lewis acid. Thus, the two absorption
frequencies at about 50.5 MHZ must be assigned to the POC13
chlorine atoms. Furthermore, the resonance due to a chlorine

atom at site 5 should be twice as intense as that due to

 

atoms at Site 4. It is Observed that the higher frequency
line is much less intense than the lower frequency line and
the higher frequency line is therefore assigned to site 4.
This assignment is confirmed by the results of the crystal
lattice field gradient calculations which calculate an un-

crys Of +0.5 for site 4 and -0.05 for site 5

corrected q
(it should be recalled that the molecular field gradients

are all positive). The last four lines may be assigned to
chlorine atoms bonded to antimony. The highest frequency line
is unmistakably more intense than the other three lines each
of which has approximately the same intensity. Therefore,
this absorption is assigned to the two axial chlorine atoms
(Site 6). Each Of the three equatorial chlorine atoms

occupies a nonequivalent site SO we expect three separate

resonances as observed. Two of these resonances are split

 

 

 

 

145

by less than 500 kHz while the other resonance lies 1.6 MHz
lower in frequency. Hence, the lowest frequency is assigned
to the Cl at Site 5, trans to the POC13 oxygen. The point-

crys of -0.12 for

charge calculations give an uncorrected q
site 1 and +0.5 for site 2, hence, the lower frequency is
assigned to site 1 and the higher to site 2. i

2) SnClg-ZPOCla

At 770K five resonances are found for this compound, which
is unfortunate because Figure 15 Shows seven nonequivalent
chlorine sites, four for the POCls chlorine atoms and three
at the SnCl4 chlorine Sites. Two absorptions may be associ-
ated with the POC13 resonances instead of the four predicted.
They were assigned to either sites 4 and 5, or 6 and 7, since
these belong to different POC13 molecules and the most likely
phase transition would be one in which the POC13 molecules
are aligned in an equivalent manner. This point will be dis-
cussed in more detail in the discussion. The LATSUM
calculations were then used to assign the measured frequency
to a particular site. It is interesting to note that sites
4 and 6, which should become equivalent if the POC13 mole-
cules are rotated into equivalent positions, are always
assigned the higher frequency line. The resonance at highest
frequency Of the three which come from the SnCl4 chlorine
atoms is assigned to Site 5 on the basis Of intensity.

crys Of +0.57 while

Site 2 has a calculated uncorrected q
qcrys for site 1 is +0.42; hence, the line at higher frequency

of the two remaining is assigned to site 2.

144

3) _ [TiCl4-POC13]3_

 

For this compound only the POC13 chlorine resonances
could be Observed. Three lines are measured for this com-
pound and three nonequivalent chlorine sites (Sites 5, 6 and
7) on the POC13 molecule are predicted. Hence, the NQR and
X-ray results are in gOOd agreement for this compound.

Since all three resonances are about equal in intensity (also
predicted from the crystal structure), we must rely on the
point-charge calculations to assign the frequencies. These.
calculate uncorrected qcrys values Of -0.18, -0.09, and 0.00 for
Sites 5, 6 and 7, respectively. For this reason the highest
frequency absorption was assigned to Site 7 and the lowest

to Site 5.

4) Pure SbCl5

In SbCls McCall and Gutowsky (110) have Observed three
lines at 770K. These lines are themselves multiplets but
McCall and Gutowsky report that they seem to center about
27.88, 28.5 and 50.4. It is likely that the two closer spaced
lines are associated with either the axial or the equatorial
chlorine atoms and that the high frequency line is associated
with the other. This spectrum was re-examined in the present
work; however, it was not possible to decide whether the high
frequency line or the low frequency pair was to be associated
with the axial position. The only basis for this decision
was the intensity ratio because, since it is believed that

the molecular field gradients at the axial and equatorial

145

positions should differ, ROTATE results can not be used.
However, the lines were too complex to yield a reliable
intensity ratio. Furthermore, X-ray data on SbCls (118)

taken at -500C Show only two nonequivalent chlorine sites in
the molecule corresponding to the axial and equatorial
positions. In an effort to Obtain some new information to
help solve this difficulty new NQR measurements were made

on SbCls at -25OC; this temperature was chosen because it is
quite close to the temperature at which the x-ray data were
taken. The frequency region 51 MHz to 20 MHz was searched
using the recording technique and two strong lines were

found. These lines are quite intense and easily observable on
the oscilloscope. There is no doubt that each is a single line.
The two lineswere Observed at frequencies Of 25.114 MHz and
25.585 MHZ. Furthermore a comparison of the relative intensi-
ties Of the recorded signals clearly shows that the lower
frequency line is less intense and the intensity ratio closely
approximates 5:2. Hence, the 25.585 MHa line is assigned to
the equatorial chlorine atoms while the 25.114 MHz line is
assigned to axial chlorine atoms. This assignment parallels
the observations of Holmes et al. (111), who found for the tri-
gonal bipyramidal molecule PCl4F two lines at 52.54 and
28.99. They also assigned the higher frequency line to the
equatorial chlorines on the basis of intensities. It is
obvious that a phase transition involving a change in the

crystal structure between 770K and 2500K (-25OC) has taken

146

place, both from the change in line multiplicity and the
abrupt drop in frequency (~v5 MHz). Working back from these
results and using both the known behavior Of lines which have
undergone phase transitions, and the fact that the line
separation at 2500K (2.5 MHz) and at 770K (2.5 MHz) are equal,
it seems quite likely that the lines centered at 50.4 MH;
should be assigned to the axial position.

B. New Resonance Frequencies and Their
Temperature Dependence

 

 

In this work new resonances were found in the compounds
Fec13-90013, SbC15~POC13, TiCl4°2POC13, and (TiCl4oP0C13)2.
In addition,the room temperature frequencies were measured
for SnCl4-2POC13. The temperature dependence of the most
intense SbCls line in SbCls-POClg was also studied. The input
to DIAG requires knowledge of the measured field gradients.
This quantity is Obtained when the measured quadrupole
coupling constant is divided by 23%1941.I where Q(Cl) is the
quadrupole moment of the 35Cl nucleus, e is the electronic
charge and h is Planck's constant; this factor has the value
-2.9552 x 106 when q is desired in units Of statcoulombs per
cubic Angstrom (esu/Rs). The factor was calculated with
h = 6.627 x 10-27, e = 4.80 x 10‘10 and 0 = -0.085. Since
all the quadrupole coupling constants were negative this made
all the measured field gradients positive. Although it is

impossible to assign a Sign tO ean as measured by pure

quadrupole resonance, the sign is taken to be negative for

147

all compounds Of chlorine in which the chlorine has a charge
more positive than -1. This conclusion is drawn from data
on gaseous chlorine compounds measured by microwave spec-
troscopy where the sign Of the coupling constants can be
determined eXperimentally. The data indicate that e2qQ be-
comes more negative as the chlorine becomes more positive.
There is every reason to believe that the sign Of the coupling
constant does not change upon changing from the gaseous to
the solid state. Table 11 lists the resonance frequencies
of all the compounds measured in this work. Data were
measured at both liquid nitrogen and room temperature for all
resonances fimrwhich this was possible. All chlorine resonances
which were ascribed tO the POC13 part Of the molecules dis-
appeared at about 2000K. Table 12 lists the results of a
temperature study on the most intense line Of SbCls in SbCls-
POCla. This line is listed as Cl(6) in Table 11 and has been
assigned to the axial chlorines in SbCls as discussed above
(Section IV-A). Table 15 presents the coupling constants and
the field gradients derived from the resonance frequencies.
All frequencies are numbered for convenience of reference in
the discussion. Figure 16 gives the data Of Table 12 in
graphical form.

Table 14 gives the temperature coefficients for all
resonances which were observable at room temperature. These
coefficients are based upon measurements at only two tempera-

tures but only their signs and rough magnitudes are needed.

148

Table 11. Resonance Frequencies for the Compounds Studied
in This Work

 

Compound

Temperature (OK)

Frequency (in MHz‘)

 

SbC15°P0C13a
c1(1)
01(1)
01(2)
01(2)
01(5)
01(5)
01(4)
01(4)
01(5)
01(5)
01(6)
01(6)

SDC14° 2POC13
01(1)
01(1)
01(2)
01(2)
c1(5)
01(5)
01(4)
01(4)
01(5)
01(5)

(11014-90013)2
01(5)
01(6)
01(7)

FeC13 ' POClg
TiCl4' 2POC13

b

 

around 50.1 MHz could nOt

Sb015C
Equatorial

Axial
Axial

SbCls
Equatorial

Axial

77
297
77
297
77
297
77
297
77
297
77
297

77
297
77
297
77
297
77
297
77
297

77
77
77

77

25.882
25.570
26.186
25.949
24.454
24.465
50.652
50.565

27.527
26.890

19.807
19.110
19.055
18.875
21.462
20.945
50.215

50.117

29.987
50.112
50.515

50.265

77 Several lines centered

77
77
77

250
250

be resolved.

50.4
28.5
27.88

25.585
25.114

 

*

aThe number in parentheses refers to the numbered atoms in

Figures 15, 14 and 15.

bready Been discussed.
The 77 K measurements on SnCl4-2POC13 are taken from
Biedenkapp and Weiss (9).
The 77 K measurements on SbCls are taken from McCall and

Gutowsky (116).

This frequency assignment has al-

149

Table 12. Temperature Dependence Of the Most Intense Line
of SbCls-POCla (Line 6 of Table 11)

‘
.-_ _

 

 

Temperature (OK) Frequency (MHZ)
77 27.327
165 27.145
190 27.118
250 26.974

297 26.890

 

150

Table 15. Coupling Constants and Field Gradients for the
Compounds Studied in This Work

 

 

 

—*

 

 

 

 

 

Compound Tempgrature eaQq/h (MHz) q(esu/Ra)
K

SbCls'POCla
(1) 77 —51.644 17.476
(1) 297 -50.740 17.170
(2) 77 -52.572 17.722
(2) 297 -51.898 17.562
(5) 77 -48.868 16.556
(5) 297 -48.950 16.557
(4) 77 -61.264 20.751
(5) 77 -61.150 20.686
(6) 77 -54.654 18.494
(6) 297 -55.780 18.198

smut-290013a
(1) 77 -59.614 15.405
(1) 297 -58.220 12.955
(2) 77 -58.070 12.882
(2) 297 -57.746 12.775
(5) 77 -42.292 14.511
(5) 297 -41.890 14.175
(4) 77 -60.426 20.447
(5) 77 -60.154 20.549

(TiCl 1:001:92
7(7T 77 -60.626 20.515
(6) 77 -60.224 20.400
(5) 77 -59.974 20.294

FeC13°POCla_ 77 -60.526 20.481

§2§lab
Axial 77 -56.18 19.011
Axial 250 -46.228 15.645
Equatorial 77 -60.8 20.574
Equatorial 250 -50.766 17.179

 

a770K measurements on SnCl4°2POC13 bleiedenkapp and.Weiss (9).
b770K measurements on SbCls by McCall and Gutowsky (110).

151

.OHUOm.mHOQm mo mUGOGOmOH macaw mmemusfl umoE mew mo GOHuMHHm> medumnmmEmB .ma mnsmwm

AMOV ousumummea

 

oom omm _ omm owe ope
- n d d 1
1.93
V
q
S
O
I
d
3
T.
O
. u
so 5...
I
8
b
n
w
nTII. O
J )
/ .m.
/ .m.
/ .rN.s.N
/
II
/
/
I
/

 

152

Table 14. Temperature Coefficients for the Chlorine
Resonances Of Complexed SbCls and SnCl4

 

 

- 2:: "
i-m _i I

Compound Atom Temperature Coefficient
(in kHz per degree)

 

SbC15°POC13 1 -2.5
SbC15°POC13 2 -1.1
SbCls-POCla 5 +0.14
SbC15°POC13 6 -2.0
SnCl4-2POC13 1 -5.2
SnCl4'2POC13 2 -0.74
SnCl4-2POC13 5 -2.4

 

Moreover, the Cl(6) resonance in SbC15°P0C13 which was studied
in more detail shows that the graph Of resonance frequency

versus temperature is quite linear.

C. Compounds in which NO Resonances were Found

 

A large number of compounds were examined in the NQR
Spectrometer. Unfortunately, for a number of reasons, most
of these failed to yield absorbances in the frequency ranges
studied. It was suSpected in some cases, particularly the
HgCla complexes and the POC13 complexes, that impurities
caused the signals to be missed. It is desirable that these
compounds be synthesized again and another attempt be made
to find Signals. Another attempt should also be made on the

n-donor complexes Of ICl and IC13 because impurities may

155

have also caused these signals to be missed. The resonances
of ICl and IC13 themselves are not tOO strong and, since it
was found that the intensity Of SbCls and SnCl4 resonances
in their complexes was greatly reduced, it is possible that
the Signals in the ICl and IC13 complexes are too weak to

be found by present methods. However, if care were taken to
Optimize all conditions it might be possible tO find signals
for these complexes. It would also be interesting to look
for the nitrogen quadrupole resonances in these complexes as
they have been reported for the pure pyridine derivatives.
Differences in the nitrogen quadrupole coupling constants in
the pure and complexed molecule could be interpreted in terms
of w-electron populations. It is not known why the copper,
cobalt and manganese resonances could not be found although
they may not be in the frequency range Of the Spectrometer.
Table 15 gives the compound examined, the frequency range
searched and the conditions Of the search for a number of
compounds in which no Signals could be found. In order to
Simplify and condense the conditions the following abbrevi-
ations have been used: fm = frequency modulation, this is
followed by two numbers in parentheses. The first refers to
a relative attenuation of the voltage from the modulation
unit with numbers ranging from one to six, where one refers
to zero attenuation, two refers to a sixth of a turn Of the
10 K potentiometer which is acting as a voltage divider,

three is two-sixths Of a turn, etc. The second number refers

154

Table 15. Compounds in Which NQR Absorptions Were Missed

W

Frequency Region.

 

Compound Searched (in MHz) Conditions
p-C6H4FC1 20-40 77°, fm(5, .05)
(C5H5CH=N-NHz-NH2)CU 20-40 77:, fm(5, .02)
770, fm(5, .02)
77 fm(1, .02)
((CH30)C3H4CH=N-NHfi-NH2)CU 20-40 770: fm(1, .02)
HgC12-2(C5H5N) 17-25 297:, fm(1, .05)
2970 fm(S, .05)
297: fm(1, .02)
77o; fm(1, .05)
77 fm(5, .05)
HgC12°2(5-CH3C5H4N) 17-25 77°, fm(1, .05)
[(C5H5)3P-HgC12]2 17-25 2973(2, .05)
2970(6, .05)
77 (5, .05)
HgC12‘(CH3)2SO 17—25 778 fm(1, .02)
770 fm(1, .05)
K3[Co(CN)5N0] 15—54 297° zm(.2)
297° zm(1.0)
29702 fm(1, .02)
297 fm(1, .05)

K3[CO(CN)5I] 15-54 Same conditions as
K3ICO(CN)5NO]
K3[Mn(CN)5N0] 15—54 Same conditions as
K3[CO(CN)5NO]
CSHSN'ICl 50-45 77° fm
C9H7N'ICl 50-45 77°, fm
C9H7N-IC13 25-55 77° fm
2-BrC5H4N°ICl 50-45 77° fm
5~NCC5H4N-IC1 50-45 77°, fm
SbCls-TiCl4-5POC13 18.5-41 77: fm(7, .05)
77 fm(1, .02)
TiC14°K01-5P0C13 24.8-54 77°, fm(4, .05)

repeated above at

77 K

 

Continued

Table 15 - Continued

155

 

 

Frequency Region

 

Compound Searched (in MHZ) Conditions
BC13'POC13 24.8-54 77°, fm(4, .05)
5 Different O
241013-90013 24.8-54 770' fm(4, .05)
Complexes 77 , fm(1, .02)
81013-p0013 24.8—54 77:, fm(4, .05)
77 , fm(1, .02)
Sb013-90013 24.8-54 77:, fm(4, .05)
77 , fm(1, .02)
[A1(P0C13)8][SbC16]3 24.8-54 773, fm(4, .05)
77 , fm(1, .02)
[A1(P0C13)8][FeCl4]3 24.8—54 77:. fm(4, .05)
77 , fm(1, .02)
(TiCl4-P0C13)2 5.5-10.5 77:, fm(1, .02)
77 , fm(1, .01)

 

156

to the reference attenuation control on the lock-in amplifier.
These two settings are the only information needed to repro-
duce any of the modulation conditions Of this experiment.
Zeeman modulation is denoted by zm followed by a number in
parentheses which gives the current in amperes that was passed
through the modulation solenoid. The other condition given
is the temperature at which the searches were conducted.

Most of the searches were conducted at liquid nitrogen
temperature (770K) but others were also repeated at room
temperature (2970K). It should be noted that, in addition to
searching with recording techniques, visual searches were

also carried out in all cases.
D. LATSUM, ROTATE, AND DIAG Results

1) Tabulated Results Of LATSUM and ROTATE

In the hexagonal SbCls crystal the z axis for LATSUM
was chosen parallel to the sixfold axis and the x axis was
chosen along the crystalline a axis. This means that the
tensor for the axial chlorine atoms Should be almost diagonal.
This is expected Since the axial chlorines almost lie on this
crystal sixfold axis; for this same reason it is expected
that n should be very close to zero. Both of these expecta-
tions are realized. The three complexes are orthohombic in
their crystal symmetry;zhence, the X4‘Y, Z axes of LATSUM
were chosen along the crystalline a, b and c axes,

respectively. LATSUM was applied to 22 nonequivalent chlorine

157

atoms; the results from both LATSUM and ROTATE are summarized
in Tables 16-57. The numbering Of the chlorine atoms refers
to that used in Tables 11 and 15 and in Figures 15, 14, and
15. Each table gives the results Of LATSUM and ROTATE for a
Single chlorine site. "Tensor" refers to the crystal field
gradient tensor calculated with respect to the original

choice Of X, Y and Z atoms as given above. "Rotated Tensor"
refers to this same tensor after it has been rotated so that
its Z axis lies along the bond direction. In order to determine
the principal values and the directions of the principal axes,
the undiagonalized crystal field gradient tensor, as calculated
with respect to the original choice Of coordinates, was trans-
formed tO the principal-axis system by diagonalizing it. The
eigenvector matrix for this transformation is given in the
tables under the heading Of "Eigenvectors." If the axes Of
the new coordinate system are denoted by X, Y and Z and those
of the Old coordinate system are denoted by X', Y', and 2',
then the elements Of the eigenvector matrix are the cosines Of
the angles between the X and X' axes, X and Y' axes, etc.

The angles along the diagonal Of this matrix are Of Special
interest as these correspond to the angles between the X' and
X axes, the Y' and Y axes and the Z' and Z axes, respectively.
For convenience the arc cosines, rounded to the nearest degree
of the elements of the eigenvector matrix:are collected in the
section Of the table labeled "Direction Cosine Angles."

Finally, the elements on the diagonal of the diagonalized

158

Table 16. LATSUM andaROTATE Results for the SbCls Axial

 

Chlorines
Tensor
-0.45550 0.00011 0.00000
0.00011 -0.45516 0.00000
0.00000 0.00000 0.86646
Eigenvectors
1.00000 0.00000 0.00000
0.00000 1.00000 0.00000
0.00000 0.00000 1.00000

Angles for the Direction Cosine (in degrees)

0 90 90
90 0 90
90 90 0
qxx = -0.45516 = 0.86646
= -0.45550 = 0.00016
qyy U
Rotated Tensor
-0.45550 0.00009 0.00000
0.00009 —0.45516 0.00000

0.00000 0.00000 0.86646

 

159

Table 17. LATSUM and ROTATE Results for the SbCls Equatorial

 

Chlorines
Tensor
-0.14857 -0.00061 0.00000
-0.00061 0.29075 0.00695
0.00000 0.00695 -0.14125
Eigenvectors
1.00000 -0.00174 0.00154
0.00177 0.99979 -0.02017
-0.00151 0.02018 0.99980

Angles for the Direction Cosines (in degrees)

0 90 90
90 1 91
90 89 1
qxx = -0.14145 = 0.29095
q = —0.14950 n = 0.02774
YY
Rotated Tensor
-0.14125 -0.00872 0.00000
-0.00872 0.29075 -0.00077

0.00000 -0.00077 -0.14867

 

160

 

Table 18. LATSUM and ROTATE Results for the SbC15°POC13
Cl(1) Chlorines
Tensor
0.11550 0.00004 -0.21298
0.00004 -0.15028 -0.00001
-0.21298 -0.00001 0.05679
Eigenvectors
0.76721 -0.00155 0.64159
0.00008 1.00000 0.00200
-0.64159 -0.00148 0.76721

Angles for the Direction Cosines (in degrees)

40 90 50
90 0 90
150 90 40
qxx = -0.14127 q = 0.29155
q = -0.15028 n = 0.05090
YY
Rotated Tensor
0.27098 0.00005 0.09210
0.00005 -0.15028 0.00005
0.09210 0.00005 -0.12069

 

161

Table 19. LATSUM and ROTATE Results for the SbCls'POCla
Cl(2) Chlorines

Tensor
0.21654 0.00000 -0.18190
0.00000 —0.15559 0.00000
-0.18190 0.00000 +0.08095
Eigenvectors
0.90561 0.00000 0.42855
0.00000 1.00000 0.00000
-0.42855 0.00000 0.90561

Angles for the Direction Cosines (in degrees)

25 90 65
90 0 90
115 90 25
qxx = -0.15559 q = 0.50277
q = -0.16718 n = 0.10454
YY
Rotated Tensor
-0.16568 0.00000 —0.02647
0.00000 -0.15559 0.00000

-0.02647 0.00000 0.50127

 

162

Table 20. LATSUM and ROTATE Results for the SbCls‘P0C13
Cl(5) Chlorines

 

Tensor
-0.00845 0.00000 0.21982
0.00000 -0.15804 0.00000
0.21982 0.00000 0.16647
Eigenvectors
0.82754 0.00000 0.56141
0.00000 1.00000 0.00000
—0.56141 0.00000 0.82754

Angles for the Direction Cosines (in degrees)

54 90 56
90 0 90
124 90 54
qu = -0.15756 q = 0.51560
= -0.15805 = 0.00155
qyy n
Rotated Tensor
0.25266 0.00000 0.16067
0.00000 -0.15804 0.00000

0.16067 0.00000 -0.09462

 

Table 21. LATSUM and ROTATE
Cl(4) Chlorines

165

Results for the SbC15°POC13

 

Tensor
0.26864
-0.00017
0.14878

Eigenvectors
0.94897
-0.00054
0.51557

Angles for the
18 90
90 0
72 90

-0.15904
-0.17904

qXX
qyy

Rotated Tensor
—0.17654
-0.00006

0.05658

-0.00017
-0.15907
0.00000

-0.00012
1.00000
0.00141

0.14878
0.00000
-0.12960

-0.51557
-0.00158
0.94897

Direction Cosines (in degrees)

108

90

18

q = 0.51808

n = 0.12575
-0.00006 0.05658
-0.15904 -0.00016
-0.00016 0.51558

 

164

Table 22. LATSUM and ROTATE Results for the SbCls-POC13
Cl(5) Chlorines

 

Tensor
-0.04165
-0.19965
-0.07007

Eigenvectors
0.60594
0.59175

-0.55596

Angles for the
55 120

54 57

122 71

-0.15128
-0.17527

qxx

qyy

Rotated Tensor
-0.15674
-0.05556
-0.04667

-0.19965 -0.07007
0.14861 0.15515
0.15515 -0.10699

-0.49779 0.62247
0.80524 0.06824
0.52712 0.77967

Direction Cosines (in degrees)
52
86
59

0.52655
0.07546

q
W

-0.05556 -0.04667
0.18488 0.21284
0.21284 -0.02816

 

165

Table 25. LATSUM and ROTATE Results for the SbC15°P0C13
Cl(6) Chlorines

 

Tensor
-0.05492 0.05879 0.00598
0.05879 -0.00829 -0.11598
0.00598 -0.11598 0.06521
Eigenvectors
0.52045 0.84905 -0.09102
-0.70910 0.57056 -0.60001
-0.47571 0.57682 0.79480

Angles for the Direction Cosines (in degrees)

59 52 95
155 68 127
118 68 57
qxx = -0.05554 q = 0.14857
q = -0.11522 n = 0.52420
YY
Rotated Tensor
0.04555 -0.00545 -0.11845
-0.00545 -0.05241 -0.05989

-0.11845 -0.05989 0.00706

 

166

Table 24. LATSUM and ROTATE Results for the SnCl4°2POC13
Cl(1) Chlorines

 

Tensor
0.15626 0.51417 0.00000
0.51417 0.04055 0.00000
0.00000 0.00000 -0.19658
Eigenvectors
0.76858 -0.65975 0.00000
0.65975 0.76858 0.00000
0.00000 0.00000 1.00000

Angles for the Direction Cosines (in degrees)

40 150 90
50 40 90
90 90 0

qxx = -0.19658 q = 0.41776

q = -0.22118 n = 0.05889

YY

Rotated Tensor
-0.19658 0.00000 0.00000
0.00000 -0.22028 0.02588

0.00000 0.02588 0.41687

 

167

Table 25. LATSUM and ROTATE Results for the SnCl4-2POC13
Cl(2) Chlorines

 

Tensor
-0.10000 -0.19751 0.00000
-0.19751 0.29115 0.00000
0.00000 0.00000 -0.19114
Eigenvectors
0.92294 -0.58495 0.00000
0.58495 0.92294 0.00000
0.00000 0.00000 1.00000

Angles for the Direction Cosines (in degrees)

25 115 90
67 25 90
90 90 0
qxx = -0.18258 = 0.57555
q = -0.19114 n = 0.02545
YY
Rotated Tensor
-0.19114 0.00000 0.00000
0.00000 -0.18175 -0.01897

0.00000 -0.01897 0.57288

 

168

Table 26. LATSUM and ROTATE Results for the SnCl4-2POC13
Cl(5) Chlorines

 

Tensor
-0.16016 -0.00225 0.11825
—0.00225 -0.20257 -0.02924
0.11825 -0.02924 0.56254
Eigenvectors
0.95905 -0.18980 0.21024
0.20424 0.97770 -0.04904
-0.19624 0.08997 0.97642

Angles for the Direction Cosines (in degrees)

16 101 78
78 12 95
101 85 12
qxx = -0.18485 q = 0.58946
q = -0.20465 n = 0.05084
YY
Rotated Tensor
—0.18666 0.00810 0.05455
0.00810 —0.20070 0.00547

0.05455 0.00547 0.58757

 

169

Table 27. LATSUM and ROTATE Results for the SnCl4-2POC13
Cl(4) Chlorines

Tensor
-0.18220
0.01279
0.00771

Eigenvectors
0.96885
-0.02597
-0.24657

Angles for the
14 89

91 1

104 90

-0.15220
-0.18448

qxx

qyy

Rotated Tensor
-0.15416
-0.00769
-0.00068

0.01279 0.00771
0.55656 -0.00056
-0.00056 -0.15416
0.02464 0.24651
0.99970 -0.00574
-0.00055 0.96912

Direction Cosines (in degrees)

76

90

14

q = 0.55667

n = 0.09588
-0.00769 -0.00068
-0.18025 -0.05425
-0.05425 0.55441

 

170

Table 28. LATSUM and ROTATE Results for the SnCl4-2POC13
Cl(5) Chlorines

 

 

Tensor
-0.06271 0.06668 0.18255
0.06668 -0.08149 0.12282
0.18255 0.12282 0.14419
Eigenvectors
0.84217 —0.26575 0.47050
0.10115 0.95599 0.54269
-0.52964 -0.24104 0.81525

Angles for the Direction Cosines (in degrees)

55 105 62
84 21 70
122 104 56
qxx== -0.15201 q = 0.50150
q = -0.16949 n = 0.12451
YY

Rotated Tensor
-0.16528 0.01014 -0.01521
0.01014 -0.15520 0.05552
-0.01521 0.05552 0.29847

 

171

Table 29. LATSUM and ROTATE Results for the SnCl4-2TOC13
Cl(6) Chlorines

‘M

TEn's'Or ,
0.25254 -0.12295 0.00000
-0.12295 -0.11008 -0.00000
0.00000 0.00000 -0.14226
Eigenvectors
0.95592 0.29564 0.00000
-0.29564 0.95592 0.00000
0.00000 0.00000 1.00000

Angles for the Direction Cosines (in degrees)

17 75 90
107 17 90
90 90 0
qxx = -0.14226 q = 0.29010
= -0.14784 = 0.01925
qyy n
Rotated Tensor
-0.14226 0.00000 0.00000
0.00000 -0.14715 -0.01758

0.00000 -0.01758 0.28941

Ii

 

172

Table 50. LATSUM and ROTATE Results for the SnCl4°2POC13
Cl(7) Chlorines

Tensor
-0.17155 —0.01846 -0.02790
-0.01846 -0.05017 0.25611
—0.02790 0.25611 0.20150
Eigenvectors
0.99794 0.01725 -0.06182
0.01900 0.84070 0.54117
0.06150 -0.54125 0.85864

Angles for the Direction Cosines (in degrees)

4 89 94
89 55 57
86 125 55
qxx = -0.17559 q = 0.56882
q = -0.19545 n = 0.05976
YY
Rotated Tensor
0.28085 0.00467 -0.20465
0.00467 -0.17559 0.00040

-0.20465 0.00040 -0.10724

 

175

Table 51. LATSUM and ROTATE Results for the (TiCl4-P0C13)2
Cl(1) Chlorines

 

Tensor
0.10915 -0.14095 0.20545
—0.14095 0.26921 0.05101
0.20545 0.05101 -0.57854
Eigenvectors
0.74710 -0.55866 -0.56020
0.56114 0.82054 -0.10875
0.55651 -0.12088 0.92652

Angles for the Direction Cosines (in degrees)
42 124 111

56 55 96
69 97 22
qxx = 0.10125 q = -0.46184
q = 0.56059 n = 0.56154
YY
Rotated Tensor
-0.27098 0.07019 —0.26557
0.07019 0.55078 0.00584

-0.26557 0.00584 -0.07981

 

174

 

Table 52. LATSUM and ROTATE Results for the (TiCl4-P0C13)2
Cl(2) Chlorines
Tensor
0.56558 -0.25411 0.09752
-0.25411 -0.25465 -0.01975
0.09752 -0.01975 -0.51092
Eigenvectors
-0.96149 0.22749 0.15422
-0.25444 0.52466 0.81240
0.10590 -0.82055 0.56254

Angles for the

Direction Cosines (in degrees)

16 77 81
105 58 56
84 145 56
qxx = -0.51277 q = 0.65805
qyy = -0.52528 n = 0.01961
Rotated Tensor
-0.52141 -0.01677 0.01959
-0.01677 -0.10120 -0.59827
0.01959 -0.59827 0.42262

 

175

Table 35. LATSUM and ROTATE Results for the (TiCl4-POC13)2
Cl(5) Chlorines

 

Tensor
-0.24047 0.22476 0.12810
0.22476 0.59100 0.57115
0.12810 0.57115 -0.15055
Eigenvectors
0.88856 0.27751 -0.56551
-0.40189 0.85487 -0.52815
0.22124 0.45858 0.87115

Angles for the Direction Cosines (in degrees)

27 74 111
114 51 109
77 64 29
qxx = -0.51024 q = 0.65428
q = —0.54404 n = 0.05166
YY
Rotated Tensor
-0.52560 -0.06758 0.07827
-0.06758 -0.05657 —0.45761

0.07827 -0.45761 0.56197

 

176

Table 54. LATSUM and ROTATE Results for the (TiCl4-P0C13)2
Cl(4) Chlorines

Tensor
-0.25476 0.04995 -0.28551
0.04995 -0.28522 -0.21410
-0.28551 -0.21410 0.55798
Eigenvectors
0.74071 -0.60407 -0.29401
0.56175 0.79695 -0.22217
0.56851 -0.00060 0.92962

Angles for the Direction Cosines (in degrees)
42 127 107

56 57 105
68 90 22
qxx = -0.52091 g = 0.67874
q = —0.55784 n = 0.05441
YY
Rotated Tensor
—0.11555 0.15127 —0.57604
0.15127 -0.25000 -0.29802

-0.57604 -0.29802 0.54544

 

177

Table 55. LATSUM and ROTATE Results for the (TiCl4-POC13)2
Cl(5) Chlorines

 

Tensor
-0.00561 0.22498 0.04590
0.22498 0.11156 0.09510
0.04591 0.09510 -0.10794
Eigenvectors
0.68479 0.58681 -0.45211
-0.65190 0.77550 0.04901
0.56500 0.25949 0.90049

Angles for the Direction Cosines (in degrees)

47 54 116

129 59 87

69 76 26
qxx = -0.12480 q = 0.51168
qyy = -0.18689 n = 0.19921
Rotated Tensor

-0.09195 -0.11476 0.02851

-0.11475 0.26581 —0.07192

0.02851 -0.07192 -0.17585

 

178

Table 56. LATSUM and ROTATE Results for the (TiCl4-P0C13)2
Cl(6) Chlorines

Tensor
-0.05496 -0.18458 -0.05695
-0.18458 0.15611 0.06092
-0.05695 0.06092 -0.12115
Eigenvectors
0.85574 -0.51158 0.09706
0.52065 0.84155 -0.14519
-0.00758 0.17448 0.98465

Angles for the Direction Cosines (in degrees)

51 121 84
59 55 98
90 80 10
qxx = -0.15577 g = 0.28086
q = —0.14708 n = 0.04759
YY
Rotated Tensor
—0.10799 -0.09482 -0.05485
-0.09485 0.20052 0.15726

-0.05485 0.15726 -0.09255

 

179

Table 57. LATSUM and ROTATE Results for the (TiCl4-P0C13)2
Cl(7) Chlorines

Tensor
-0.04414
-0.05579

0.18877

Eigenvectors
0.81450
-0.26075
-0.51859

Angles for the
55 72

105 18

121 89

-0.14558
-0.15289

qxx

qyy

Rotated Tensor
0.08197
0.12112
0.18642

-0.05579 0.18877
-0.15275 -0.06654
-0.06654 0.17687
0.51225 0.48952
0.94992 -0.17224
0.01267 0.85495

Direction Cosines (in degrees)

61

100

51

q = 0.29827

n = 0.02518
0.12112 0.18642
-0.08255 0.10275
0.10275 0.00058

 

180

matrix qxx’ qyy' and qzz E q are collected, along With the
crystal field asymmetry parameter n.

2) Comparison of the Lattice Sum Results Using
Both the First Model and the Revised Model

In order to facilitate the comparison of calculations
using the charges assigned by the method of Townes and Dailey
(old charges), and those using charges calculated from the NQR

data (new charges), values of q E and n calculated using

qzz
both the old charges and the new charges are collected in
Table 58. As can be seen, the results are quite sensitive to
the charges assigned to the sites which is a not unexpected

result.

5) DIAG Results

 

In Table 59 the results of DIAG, as applied to chlorine
atoms which should have identical molecular field gradients
but occupy nonequivalent sites in the crystal lattice, are
given. Thus, the difference between the two measured field
gradients should be due entirely to solid state effects. The

size of these effects, following our model, will be determined

mol + crys

by the Sternheimer factor. If we write q2 = qzz 22

then lqu z(meas)l = zlqzz(a)-qzz(b)l = Ichrys|= lqcrys(a) _
qggys(b)l, where qz is the measured field gradient, qul and
crys

22 have been defined previously, and qzz(a) means the field
gradient at site a. Application of DIAG to the calculated
and measured field gradients then allows us to estimate a
Sternheimer factor. This is done by applying DIAG to the

measured field gradient, using a number of different Stern—

heimer factors, and a series of molecular field gradients as

181

 

 

 

 

 

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185

a function of the Sternheimer factors is obtained. Let us,

as an example, consider Cl(1) and Cl(2) on SbC15°P0C13 (see
Figure 15). These two chlorine atoms are expected to have
identical molecular field gradients since they both occupy
equatorial positions gig to the POCla oxygen atom. We com-
pare the results of DIAG for these atoms and see that for

a Sternheimer factor of +0.4 the experimental results obtained
at liquid nitrogen temperatures yield the same molecular field
gradient. It should be recalled that DIAG calculates a
molecular field gradient with a series of trial Sternheimer
factors. For a pair of chlorines which occupy nonequivalent
positions in the crystal lattice.but should be identical in
the isolated molecule, the "experimental" 700 is then taken

as that 700 which yields an identical molecular field

gradient at each of the two chlorine sites. With a Sternheimer
factor of +0.07 the room temperature experimental results
yield an identical molecular field gradient. These, then are
the "experimental" ybo's. For SnCl4°2POC13 four nonequivalent
positions (two on each P0C13 molecule) are predicted for the
P0C13 chlorine atoms; however, only two resonance lines are
observed. For reasons to be given in the discussion of the
temperature dependence of the absorption lines, it was assumed
that these two measured lines resulted from only one POClg mole-
cule but it is not knoWn whether the POCls molecule containing
Cl(4) and Cl(5), or that Containing Cl(6) and Cl(7) gives rise

to the absorption. Therefore, the DIAG results for each pair

184

 

 

 

 

 

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185

were applied to the experimental splitting and a separate
Sternheimer factor obtained for each pair of sites. It should
be remembered that the value of the calculated ¢zz is enhanced
by the Sternheimer factor. That is, qggys (calculated) =

(1'- Voo)¢zz’ when¢zz is the 22 component of the LATSUM tensor
after its coordinate system has been rotated to its final
position by DIAG. As a first approximation (1 - 7a)) could
have been obtained from the 22 component of the tensor which
resulted from the application of ROTATE to the results of
LATSUM. This is a very good approximation if the rotated
crystal field gradient tensor is nearly diagonal. DIAG essen-
tially allows the off-diagonal elements to be taken into
account so the use of DIAG becomes more important as the value
of the Sternheimer factor increases. In the column of Table
59 under lA¢zz[ is listed the difference in the calculated

field gradients after the corresponding tensors have been ro-

tated to the final coordinate system by DIAG. For purposes of

crys

22 I have also been in-

comparison the measured splittings lAq
cluded. The first column of Table 59 specifies the two atoms
whose field gradients are being compared. Table 40 lists all
the atoms upon which calculations have been performed. Since
some atoms (for example those at sites 5 and 6 for SbCls'POClg)
besides occupying nonequivalent sites, are also expected to
differ from the other atoms in the molecule in their molecular
field gradients, it is not possible to obtain a "experimental"

value of yanor these sites. In these cases the values of

700 obtained for chemically related sites are used when applying

186

DIAG to the experimental frequencies measured for these
lines. In Table 40 are collected the values of (fizz (the 22
components of the final rotated tensor),the values of ncryst

(the asymmetry parameters arising from solid state effects),

and the values of ngl

(the corrected molecular field gradients).
In addition the angles between the axis system obtained by
applying ROTATE to the results of LATSUM (X', Y', Zf) and the
final principal-axis system (X, Y, Z) are given for each site.

All this information may be obtained from DIAG. ROTATE and

DIAG have already been described (Sections III-E-5 and III-E-4).

V. DISCUSSION

A. Temperature Dependence of the Absorption
Frequencies and Phase Transitions

The NQR absorption lines from these complexes show an
interesting temperature dependence in that, while the POC13
resonances observed at a temperature of 770K are very intense, no
POC13 resonances are observed at room temperature. 0n the
other hand, the resonances due to SnCl4 and SbCls in their
respective complexes are observable both at liquid nitrogen
temperature and at room temperature. Also, their frequencies
show the normal negative temperature coefficients as listed
in Table 14 except for Cl(5) in SbCls'POCla. The temperature
dependence of the Cl(6) line in SbCls-P0C13- was studied in
more detail and is listed in Table 12 and plotted graphically
in Figure 16; the plot shows a possible break indicating a
phase transition between 770K and 1650K. Two other observa—
tions, while not directly related to temperature dependence,
are also of interest. First, while the crystal structure
predicts four nonequivalent sites for the chlorine atoms of
P0C13, and the crystal field gradient calculations show large
differences in the gradients calculated for these sites, only
two absorption frequencies are found for the chlorine atoms
of P0C13 in the SnCl4-2POC13 complex. Second, the observed

splittings of the resonances attributed to P0C13 in SbC15°POC13

187

 

 

188

and SnCl4'2POC13 are much smaller than those expected from
crystal field effects, while the splitting and the multi-
plicity of the POC13 lines in [TiCl4'POC13J2 and TiCl4-2POC13
are about what is expected (this point will be discussed more
thoroughly in a later section).

It appears that some sort of phase transition is taking
place. One possibility for the phase change would be if a
change in the actual crystal structure took place. This could
explain all of the observed phenomena except the line disap-
pearance. Dean (112), and Kubo and Nakamura (115), have ob-
served phase transitions due to a change in the crystal
structure in a wide variety of organic and inorganic compounds.
In all cases this phase change is accompanied by an abrupt
break in the curve of resonance frequency versus temperature.
If there is a change in the number of nonequivalent sites
after the transition the line multiplicity will also change.
However, in no case which is known to this author do the NQR
absorptions completely disappear well below the melting point
when the crystal undergoes a phase change which is only
associated with a change in crystal structure. This observs;i
ation, while not completely ruling out a change to a new
crystal form as an explanation for the disappearance (fade out)
of the POC13 lines, at least makes this explanation unattractive.
It would also be difficult to explain why this new crystal
form would affect only the POCla chlorine resonances and not

those of the SnCl4 and SbCls chlorine atoms. At least a change

189

in the number of nonequivalent sites in these acids may be
reasonably expected if the crystal changes structure. All
the data collected so far indicate that only the POC13
chlorines are involved in the phase change.

Gutowsky and McCall (111,55) have observed a fade out
of the NQR signals well below the melting point in several
compounds. In all of these compounds either molecular or
internal reorientation is possible. Dean (28) has also ob-
served a fade out of the chlorine resonance in CC13CC13 on
warming up. Although completely free internal rotation does
not seem likely in this compound because of the high barrier
(116), it is quite probable that restricted rotation takes
place about the C-C axis. In C5H5CC13, in which a fade out
of the signal also occurs, a restricted rotation about the
C3 axis of the trichloromethyl group is possible as well as
ring reorientation. NMR studies by C. Holm (115) on
p-C3H4(CF3)2 show that both the CF3 groups and the ring re-
orient in the solid. According to Gutowsky and McCall (55)
a comparison of molecular models for this compound and that‘of
C5H5CC13 indicate that such motions should also occur in the
latter. In all the complexes studied so far there is a
possibility of restricted rotation about the P-O bond in the
P0C13 molecule, it is therefore proposed that the phase transi-
tions in these complexes are associated, not with a change in
crystal structure, but with molecular reorientations in the

solid. This restricted rotation could explain all the features

190

so far observed including the temperature dependence, multih'
plicity and anomalously small splittings. The onset of
rotations is expected to be a gradual process rather than a
sharp transition. As the transition temperature is approached
the fraction of the molecules able to overcome the barrier

to internal rotation increases. This would have an Laveraging;
effect on the crystallographically nonequivalent chlorine
atoms, decreasing the splitting between the P0C13 lines while
not directly affecting the resonance frequencies of the SbCls
chlorine atoms. Since the chlorine atoms on the two POC13
molecules in SnCl4°2POC13 see different environments it is
likely that the barrier to rotation for each of the two P0C13
molecules is different. Therefore, it is quite possible that
at 770K the resonances of one of the POC13 molecules would
have already faded out. .The fact that the splittings of the
POCla lines in [TiCl4°POC13]2 seem to follow the calculated
gradients may be explained by postulating that this compound
is farther from its transition temperature than the other two
compounds. It is interesting to note that TiCl4'2POClg shows
a very complex absorption pattern at liquid nitrogen tempera-
ture, with about 5-6 lines spread over about 500kHz. Since
TiCl4t2P0C13 is isostructural with SnCl4-2POC13 (117) four
lines are expected if the barriers to internal rotation are
high enough at 770K so that no fade out occurs for the
chlorine resonances of the two P0C13 molecules. Thus» the

observed pattern may be four lines, and, if this is true, it

191

indicates that the transition temperature for this compound

is also high. The fading out of resonances was observed by
Gutowsky and McCall well below the actual temperatures of

the phase transitions. The latter were known from the heat
capacity and dielectric constant measurements of Rushner et
al. (116). In the case of (CH3)3CC1, however, fade out
occurred at the lower of two transition temperatures. Hence,
the temperature at which fade out of the resonances in the
complexes studied here occurs would not be expected to corre-
late well with the actual temperatures at which the phase
transitions occur but may be expected to give a qualitative
idea of the relative barrier heights. Unfortunately, since

no measurements on heat capacity, dielectric constant or other
physical prOperties which undergo an abrupt change at a

phase transition, are available for the complexes studied here
it is not known where their phase transitions take place and
there is no way to check the conclusions drawn above at
present. X-ray data, however, also suggest the possibility of
restricted rotation. As shown in Table 41, the temperature
factors for the x-ray scattering by the chlorine atoms of the
POC13 molecules in SnCl4°2P0C13 are unusually high. A value
of 582 is considered normal and anything larger than 632 is
considered very large. It may be seen that, although all the
temperature factors are high, those for the P0C13 chlorine
atoms (chlorine atoms 4, 5, 6, and 7) are unusually high as

would be expected if the P0C13 molecules were undergoing

192

a
Table 41. Temperature Factors for SnCl4~2P0C13

 

m * f; ‘ =5

 

Atom Temperature Factor (in 22)
Sn 5.58
Cl(1) 6.55
Cl(2) 5.87
Cl(5) 4.87
0(1) 4.21
0(2) 4.65
P(1) 5.05
9(2) 4.51
Cl(4) 7.84
Cl(5) 6.58
Cl(6) 7.88
Cl(7) 7.44

 

aC. Branden, Acta Chem. Scand. 11, 759 (1965).

restricted rotation around their threefold axes. Unfortu-
nately, the temperature factors for the individual atoms are
not listed but an average factor of 4.5 22 was used for
[TiCl4’P0C13]2. Since this is only an average value it is
not possible to conclude much from it, although 4.5 32 sug-
gests an abnormal structure. Branden and Lindqvist have also
estimated the temperature factors for SbCls-POCla (150).

The factors for the two nonequivalent P0C13 chlorine sites
are 4.9 and 5.2 22. These are again very large and indicate
abnormal motion of the atoms. In conclusion it may be said

that, although no conclusive evidence is present, the proposal

195

of restricted rotation explains all the available data. In
this connection it would be interesting to obtain the
temperature dependence of the chlorine resonances for the
chlorine atoms of POC13 in the complexes. Such a study

should include some temperatures below liquid nitrogen
temperature to determine, if possible, the temperature at

which the restricted rotation is "frozen out" since it seems
likely‘that a good percentage of the P0C13 molecules in
SbCls-P0C13 and SnCl4-2P0C13 are undergoing restricted rotation

even at 770K.
B. Calculation of the Point-Charge Field Gradient

Semin and Fedin (122) have stressed the importance of
evaluating the influence of the solid-state effects on the
NQR absorption frequencies. Although these effects are
usually much smaller than chemical effects, this is not always
true. Because of the close-packed structure of the charge-
transfer complexes studied here and the moderately large
fraction of ionic character in the bonds it was expected that
the crystal7lattice field gradient tensor Ecrys would be
comparatively large. As previously discussed, it was assumed

that the most important contribution to Ecrys

came from the
charged atoms situated in the crystal lattice. This is be-
lieved to be a good assumption since an examination of the

crystal structures of these compounds show that all chlorine-

chlorine distances are large enough to preclude the possibility

194

strong intermolecular interactions and Bersohn (120) has

shown that dispersive and short-range repulsive forces

(Van der Waals forces) do not appreciably affect the measured
field gradient. At the beginning of this work it was decided
to calculate the crystal lattice field gradient ¢zz at each
chlorine site, multiply them by the factor 1-yoo.using -10

(51) for ya),and use these qualitatively, if not quantitatively
to estimate the importance of solid state effects. It soon
became apparent, however, that such a simple interpretation

of the calculated data was not possible as shown by a critical

 

examination of the "experimental" value of ya). The expected
value (700 = -10) was taken from Burns and Wikner (51) who
argue that, although Sternheimer has calculated a much larger
value, solid-state effects will cause this value to be greatly
reduced; the value Va): -10 was deduced from ultrasonic
experiments and thus is considered to be an “experimental"
value. The quotation marks refer to the fact that no com-
pletely unambiguous method has yet been found to measure 700.
The ultrasonic experiments all were made using highly ionic
alkali halides; therefore, the fact that most of the experi-
mental values of Woo measured in this work are much more
shielding than —10 is not incompatible with the results of
the ultrasonic experiments, since the chlorine atoms involved
in the charge-transfer complexes are much less polarizable.
However, the chlorine atoms of P0C13 in SbCls-POC13 and one

of the P0C13 molecules in SnCl4-2POC13 are found in our

195

calculations to be much more shielded than would be expected
(as mentioned.yoo for a neutral chlorine is +0.46).
Undoubtedly some other effect is obscuring the effect of the
charged lattice sites on the field gradient of these chlorine
atoms. One possible effect, restricted rotation about the

P-O bond, has already been discussed and seems to be the most
likely explanation. On the other hand the calculated values
of 700 for [TiCl4-POC1312 show fairly good agreement with

the other calculated values of 703' In addition, the internal
consistency of the values of Va) calculated for the three
splittings of the POC13 lines in [TiCl4-POC13]2 is very satis-
factory although it may be partly fortuitous. Temperature
may also affect the results in other ways. Vibrational motions
of the molecules containing the quadrupolar nuclei can cause

a decrease in the absorption frequency due to an averaging

effect. Thus the absorption frequency m at some temperature

T

T can be represented as w = wo(1 + aT + bT‘l), where wo is

T
the absorption frequency in the absence of vibrational motion
in the lattice. Obviously we should compare our calculated
field gradients with the corresponding values of mo. However,
determination of mo requires points below 770K and, at

present, it is not possible to work in this temperature range
in the Department of Chemistry. Another effect of the
temperature is that, as the temperature is lowered, even though
no phase change occurs, the positions of the atoms may be

slightly shifted. Unfortunately, the point-charge field-

gradient calculations are very sensitive to changes of this

196

type which probably accounts for the major part of the large
difference between the "measured" values of woo at room tempera-
ture and liquid nitrogen temperature and the fact that the 2
values of 700 at room temperature seem to be more reasonable
deSpite the fact that the observed frequencies at room
temperature are farther from we than are those at liquid
nitrogen temperature. Another factor which may affect the
results is the neglect of the contribution of dipolar polari-
zation to the field gradient. This contribution is always
smaller than the point-charge contribution. In our case this
contribution should even be smaller because the chlorides

and oxide ions, which vwnxkl give the most important contribu-
tion due to this effect, are not nearly as polarizable as

they are in the wholly ionic compounds in which this effect
has so far been evaluated. However, this polarization may be
important when we try to reproduce such small effects as the
splitting of NQR lines by solid-state effects. Many authors
(e.g., 105, 122, 125) have_tried to account for the entire
measured field gradient in ionic crystals by means of the
calculated 022(1 - 700). Bersohn and Shulman (124) have
strongly criticized this approach, maintaining that the point-
charge contribution has been given too much importance by
using a value of lyool which is much too large. These authors
claim that the largest part of the measured field gradient

is due to p-electron defects on the halide ion (i.e., covalent

bonding). Of course,sthe effects of covalent bonding have

197

been included implicitly in previous calculations by permit-
ting such large values of 700. A large value of 700 implies
a large amount of polarization of the charge cloud around the
chlorine and, thus, is equivalent to introducing some co-
valent character into the bond. However, it is artificial to
try to include covalent bonding in this manner. The arguments
of Bersohn and Shulman are undoubtedly correct to some extent;
it is certain that the value of (700' has been overestimated
in many cases, the general practice being for authors to
choose, from the several available values for ya) (all large).
that value which most closely fits their data. However,
Bersohn and Shulman may have gone too far to the other extreme.
In fact, the majority of the values of 700 "measured" in this
work,where other effects do not interfere, seem to lie very
close to yoo = 0. Nevertheless, it seems likely that more
ionic chlorine atoms will exhibit a somewhat larger yoo'

In the one case in which the percentage covalent bonding
obtained by Bersohn and Shulman, was directly comparable to
the percentage covalent bonding as measured by ESR the agree—
ment is rather poor (16% for NQR as compared to 10% by ESR).
Bersohn and Shulman explain this difference by reintroducing
the point-charge contribution which, with 700: 0, reduces the
NQR covalent bonding to 15%. One is tempted to think that a
slightly larger Ivaal would have explained all the difference.
Another effect which should be mentioned is that the Stern-
heimer factor is not constant as a function of distance from

the nucleus. Calculations (121) show that 7a)(Cl-) is fairly

198

constant after about 5ao(2.658). In the compounds studied
here most ions were more distant than 2.65 3 except the atom
directly bonded to the chlorine under consideration.

-Although no calculations exist which give any insight into
this source of error it is not thought to be important.
Morosin and Narath (48) have criticized the point-charge

model as applied to the nearest neighbor ions of the nucleus
under investigation. Unfortunately, it is a characteristic

of this type of calculation that the nearest neighbors make

a most important contribution to the final value so that

if the assumption of point-chargesjkn:the nearest neighbor
sites is seriously in error the effect could be quite large

on the calculated crystal-lattice field-gradient tensor.
Although the calculations done so far have not shown that this
effect is important, neither has anyone tried to apply these
calculations in a consistent manner in situations which make
serious demands on the accuracy of the calculations. The
present work is the first attempt to make stringent demands

on the calculations. For this reason there are not yet

enough determinations of experimental and calculated splittings
available to permit comparison with the results of other
workers. Regarding the present data it may be said that the
calculations made so far seem to indicate that 700' in these
only partially ionic complexes, must be given a much lower
value than Va): -10 which has usually been used for more ionic
structures. In particular, a value in the range 0 to -5 seems

the most reasonable and a value of 0 is not too inconsistent

199

with the data. Very probably no single value of 700 can

be used but each compound must be considered individually.

A more definitive statement than this awaits more compari—
sons. Because of the uncertainty in 700 it is not possible
to use these calculations quantitatively but the calculated
values of ¢zz should be reliable in a relative sense. The
asymmetry parameters calculated by DIAG are quite interesting,
although they are somewhat lower than those usually found
for chlorine atoms in covalent bonds. These measured values
of n usually fall in the range 0.05-0.1. However, the dif-
ference can easily be accounted for by the introduction of

a small amount of double bonding: also, it should be

noted that, in estimates which use n to give the fractional
double-bond character in a bond, a serious error could be
introduced by neglecting the contribution of solid-state
effects to n. Some of the X-X' and Y-Y' angles of Table 40
are quite large. This is expected since ROTATE fixed the X',
Y', 2' system under the assumption that the X' and Y'
directions are arbitrary. When some asymmetry is introduced
into the field gradient by means of crystal effects, these
directions become fixed and it is not surprising that the

X' and Y' directions must be shifted to conform to the fixed
directions. It is significant that the solid—state effects
did not shift Z from Z' to any appreciable degree, in agree-

ment with experiment.

200
C. Frequency Shifts in the Complexed POClg Chlorine:Atomsr

In a simple model of charge transfer we may think of
a POC13 molecule donating electronic charge from the oxygen
lone pair electrons. This donation may go so far that the
P-O double bond is broken. Electronic charge is drawn from
the chlorine atoms of POC13 toward the phOSphorus atom by
induction. This charge migration is reflected by an increase
in the molecular field gradient at the chlorine atom of
POC13 which is reflected in an increase in the NQR absorption
frequency. In all the complexes studied so far, an increase
in the absorption frequency of the POC13 chlorine atoms has
been noted. It seems clear that this change in the field
gradient should be attributed to inductive withdrawal of
charge from chlorine by the oxygen atom of POC13. Until the
X-ray structures of some of this type compound were done it
had been postulated (95) that the charge transfer took place
from one of the POC13 chlorines to the Lewis acid. This
structure can be rejected on the basis of the NQR results.

Before a more quantitative treatment may be attempted
it is necessary to evaluate the contribution of the crystal
lattice to the observed shifts. An examination of the ¢zz
values calculated for these positions shows that, if an
average of the observed resonance frequencies are taken for
SnC14-2POC13 and SbC15°POC13, while the highest frequency line
is taken for (TiCl4°POC13)2, a shift which is fairly free

from solid-state effects should be obtained. This is

201

especially true since there is some evidence that 703: 0.
It should be kept in mind, however, that solid-state effects
could still be large enough to cause a reordering of the
acid strengths.

Badgley and Livingston (125) have studied POC13 by
electron diffraction; their results, together with the results

of X-ray studies on the complexes, are listed in Table 42.

Table 42. Bond Angles(in Degrees)and Bond Lengths(in
Angstroms)of POC13 in Various Complexes From
X-Bay Investigations

ll

Bond Length
or

 

Bond Angle POC13 SbC15°POC13 SnCl4-2POC13 (TiCl4-POC13)2
P-O 1.45:.05 1.46i.02 1.44:.05 1.44:.02

P-Cll 1.99:.02 1.95:.02 1.95:.05 1.95i,01

P-Clg 1.97i.02 1.931.05 1.98i.01

P-C13 , 1.89:.05 1.961.01

p-014 2.00:.03

Cll-P-Cll 105.5 105.6 105.7 107.0
Cll-P-Clg 107.4 105.4 106.6
Clg-P-Clg 112.5 104.1
Cla-P-Cl4 101.2

 

The designations C11, C12, C13 and C14 simply designate non-

equivalent chlorine atoms. It is not necessary to identify

202

them with specific sites in the crystal lattice. An inspection
of Table 42 shows that, aside from some distortion in bond
lengths and bond angles, which were expected because the data
were obtained for gaseous rather than solid POC13, the

geometry of complexed POC13 is quite close to that of pure
POC13. This is strong evidence that no change in Wbbond
character in the P-Cl bonds, and probably no great change in

s hybridization at the chlorine sites, has taken place upon
complex formation. Let us consider the basic equation of

Townes and Dailey (Equation 52)
p = 1 - I - 0 -|| + 0 ;

then, if we designate the 0 measured for complexed POC13 as

p1 and that for the pure POC13 as pg,
Ap = p1 - p2 = -AI — Aa.- A1I} A0,

where the other symbols have been defined previously (Section
I-F). From the fact that the geometry of POC13 does not

vary to any marked extent, the hybridization is not expected

to charge very much if a small charge shift takes place,hence As,

A0 and A7T'may be set equal to zero. Then,
Ap = -AI

so that if 0 increases upon formation of the complex the
ionicity of the P-Cl bond decreases in agreement with simple

induction considerations. Dilke and Eley (126) have studied

205

heats of formation for the reaction between benzaldehyde

and a number of Lewis acids. The results are given in

Table 45 along with values of p and AI for all the complexes
studied in this work. The p valuesrquotéd are average values
for SbCls-POC13 and SnCl4-2POC13, the highest frequency
resonance line is used for (TiCl4-POC13)2, and only one line
is observed for FeC13'POC13. The compounds are arranged in
order of decreasing p. Since AI is negative in all cases,

AI values may be interpreted as providing the fraction (AII

Table 45. Electronic Charge Lost by the POC13 Chlorine Atoms
Estimated from NQR Data

 

 

a Heats of Reactionb
Compound p AI kcal/mole
SbCls-POClg 0.556 -0.028 21
(TiCl4-POC13)2 0.552 -0.024 17
FeCla-POC13 0.551 —0.025 27
Snell-290013 0.549 —0.021 14

 

aAverage p for POCla is 0.528 (151).

Heats of reaction as measured for reaction of these acids
with benzaldehyde (150).

of an electronic charge which has moved from the chlorine atom
to the phosphorus atom. For example, our measurements say
that 0.028e of electronic charge has migrated from each
chlorine atom to the phosphorus atom in SbCls°POC13. The AI

values in Table 45 enable us to order the four Lewis acids

204

studied according to decreasing acidity, as SbCls > TiCl4 >
FeCls > SnCl4. It may be argued that, since SnCl4 accepts
two POC13 molecules, the AI for this compound should be
doubled. This is a matter of definition but it is interesting
to note in this respect that infrared studies reveal that the
negative shift of the 1500 cm"1 P-O bond of POC13 upon
complex formation was 95 cm-1 in both TiCl4°2POC13 and
(TiCl4-POC13)2 while that of 5110143290013 was 85 cm‘1 (128).
The larger shift is correlated with a larger charge transfer
from the P-O bond, hence, IR results predict that TiCl4 is a
stronger acid than SnCl4 and also suggest that TiCl4 accepts
the same amount of charge from POC13 whether it coordinates
with one or two molecules. It should be noted that the
thermodynamic data disagree with the ordering of the Lewis
acids proposed here. However, this is not surprising since
the base used in the thermodynamic studies was benzaldehyde,
and it is often found that the order of acid strength is .
changed when the standard base is changed. For example, infra-
red data and the present NQR results show that, with respect
to POClg, TiCl4 is a stronger acid than SnCl4 but the reverse
is true if the ordering base is (C6H5)2PO (152).
D. Shifts in the NQR Spectra of SnCliiand
SbCls Upon Complex Formation
1) General Comments
Although NQR data for only two Lewis acids, involved as

components of a complex, are available, it is still prOper to

205

point out a few similarities between the spectra of the two
complexed Lewis acids. The general appearance of the two
spectra is quite similar, both spectra have a group of
absorptions at a low frequency (two for SnCl4 and three for
SbCls) which are quite close together. In both cases these
absorptions belong to the chlorine atoms which lie in a
plane, which for SbCls would correspond to the equatorial (basal) P
plane of the free molecule (assuming that the POC13 approaches
SbCls in the basal plane), and for SnCl4 would correspond to

a somewhat analogous plane. The other absorption line, which

 

in SbCls is due to the axial chlorine atoms, lies about L
2 MHz higher in frequency than that for the basal chlorine
atoms. This pattern is not due to solid-state effects as the
point-charge results indicate that, if this were the case,

the resonance line due to the Cl(2) chlorine atom of SbCls-
POC13 would be at a higher frequency than the resonance line
due to the two axial Cl(5) chlorine atoms which is contrary to
observation. Furthermore, the point charge effects by them-
selves would put the NQR line due to Cl(1) of SnCl4'P0C13
higher in frequency than those due to Cl(2) and Cl(5), again
contrary to observation. The available data suggest that the
metal bonding orbitals directed towards the "basal" plane
positions (from Sb to Cl(1), Cl(2), Cl(5) and O in SbC15°POC13
and from Sn to Cl(1), Cl(2) and the two POC13 oxygen atoms in
SnCl4'2POC13) are different from those directed towards the

"axial" positions. Possibly there is some similarity between

206

the "basal" metal atom orbitals in the SbCls complex and in
the SnCl4 complex; some similarity may also exist between
the bonds to the "axial" positions in the two complexes.
More data is needed to substantiate or disprove this sug-
gestion.

2) SnCl4-2POC13

 

Livingston (127) has studied the NQR spectrum of SnCl4 at
770K using a regenerative oscillator. He found four very
closely spaced lines whose average frequency is 24.095 MHz.
All the measured frequencies for SnCl4-2POC13 which have been
assigned in this work to the SnCl4 molecule are lower in
frequency than the average value of 24.095 MHz which he re—
ported. This is expected if the change in frequency is due
to an inductive gain of electronic charge by the SnCl4
chlorine atoms when the tin atom accepts charge from the POC13
oxygen atoms. The difference between the frequencies of the
"basal" chlorines and the "axial" chlorines has already been
interpreted to suggest a difference in the nature of the
metal bonding orbitals directed towards the "axial" and "basal"
positions. Van Der Doorn and Drago (129) have recently
studied the bonding in the trigonal bipyramidal phosphorus(V)
chlorofluorides by means of extended Hfickel calculations.

They have interpreted the difference in the phosphorus bonding
orbitals as a difference in the electronegativity of these ‘

orbitals. Because the equatorial bonds have a large 3 hybridi-

zation they are more electronegative while the more

207

electropositive orbitals are directed towards the axial
positions. Thus, the more electronegative atoms will be

in the axial positions; this assumption suffices to predict
the structuresci'all the phosphorus chlorofluorides. Also,
PC14F,which is thought to retain its trigonal bipyramidal
structure in the solid state (PCls does not),has been studied
by NQR (111). The results show that the absorption of the
axial chlorine lies about 5.5 MHz lower in frequency than

the absorption of the equatorial chlorine atoms. This would
be consistent with the higher ionicity of the P-Cl axial bond
which is expected if the phosphorus bonds to the axial posi-
tions are more electropositive and in fact points to a quite
sizeable difference in ionicity between the axial and equa-
torial P-Cl bonds (AI“’0.07). Furthermore, measurements
performed during the present work on SbCls at 2500K show

that the axial chlorine atoms absorb at about 2.4 MHz lower
in frequency than the equatorial chlorine atoms (AIA/0.05).
These are the only NQR measurements made on molecules which
are known to retain their trigonal bipyramidal geometry in
the solid-state. For the Cl(1), Cl(2), and Cl(5) NQR absorp-
tions in SnCl4‘2POC13 the calculated 022 values would group
the Cl(2) and Cl(5) absorptions closely together and put the
Cl(1) absorption at a somewhat higher frequency. At first
glance this may seen to fit the observed pattern but two
things strongly argue against accepting this assignment of

lines. First, from X-ray data it is apparent that the Cl(5)

208

absorption should be twice as intense as the absorption due
to either Cl(1) or Cl(2). The highest frequency line is
noticeably more intense than the other two lines. It seems
reasonable, therefore, to assign this absorption to Cl(5).
Second, if Cl(1) is assigned to the highest frequency line on
the basis of crystal lattice effects, in order to account

for the observed splitting in terms of the calculated 422
values (1 - 703) must be taken to be 42.0 which is quite un-
reasonable. It seems then that the splitting between the
high frequency line and the two low frequency lines is due to
a difference in the molecular field gradients at the "axial"
and "basal" chlorine sites. Since it is unlikely that the

s and d hybridization at the different chlorine nuclei would
change very much, the difference must be accounted for by dif-
ferences in ionicity and w-character of the Sn-Cl bonds.

Both of these differences would arise due to nonequivalence
of the tin bonding orbitals. No additional information is
gained if the Sn-Cl bond lengths for the complexed SnCl4 are
studied as these seem about equal, within the standard
deviations of the X—ray data. If, as a working hypothesis,
we assume that the difference is entirely due to a difference
in the ionicities of the two types of Sn-Cl bonds, it is
possible to calculate the actual charge transferred. This is
a logical extension of the idea that all the tin bonding orbi-
tals are not equivalent, for if, as in the case of the phos-

phorus(V) chlorofluorides, the main difference between the

209

tin bonding orbitals is that one set is more electronegative
than the other, it is natural to expect that the more electro-
negative orbitals will get a larger share of the charge
transferred to the Sn from POC13. The Sn-Cl bonds which are
formed with the more electronegative orbitals will then show
a larger gain in ionicity and consequently the chlorine atom
involved will have a lower resonance frequency. Table 44 is
constructed to show this effect quantitatively. The column
labeled AI shows the change in ionicity calculated from the
equations

p = 1 - I - a JTU_+ 0 and

0(SDC14'2POC13) - p(SnCl4) 3 AP = - AI(AQ« = AT: A0 =0)

From the definition of Ap it is obvious that a positive AI
corresponds to an increase in the ionicity of the Sn-Cl bond
under consideration. The column under "corrected AI"(Table 44)
was calculated after correcting thelchlorine absorption fre-
quencies for solid-state effects assuming 70) = 0. This was
done more as an indication of the error involved in neglecting
solid-state effects rather than as a realistic attempt to

make corrections since no X-ray data exist for SnCl4. The
chlorine resonance frequencies for SnCl4 and SnCl4-2POC13

at 770K were used. The total charge transferred from the
oxygen to the tin-atom may then be calculated from the uncor-
rected values of AI by taking the weighted sum 2(0.054) +
2(0.076) = 0.260e. This is a reasonable answer but it is

clear that more data on SnCl4 charge-transfer complexes of

210

Table 44. Charge Transfer in Complexed SnCl4

 

 

Compound p AI AI(corrected)
SnCla , 0.459 -- --

SDCIL' ZPOC 13

01(3) 0.585 0.054 0.064
Cl(1) and
Cl(2)a 0.354 0.076 0.087

 

aAverage of the p values measured for Cl(1) and Cl(2).

211

known crystal structure must be obtained in order to confirm
or deny the conclusions drawn here.

5).SbC15°POCla

The abnormal behavior with temperature for chlorine
resonance frequencies in SbCls has already been discussed in
Section IV. Because there are no data available (such as
values of dielectric constant as a function of temperature)
which Could give any information on phase changes, either for
these complexes or for those of SbCls, the cause of this
abnormal behavior is not known for certain. Although it is
normal for absorption frequencies to change abruptly at a
phase transition, the dr0p in frequency of 4.5 MHz observed
for the chlorine resonance in pure SbCls is distinctly abnormal
(about 0.5 MHz would be normal). A phase transition would
account for the observed changes but X-ray data taken at 770K
along with a study of the variation of the NQR spectrum with
temperature would be needed to establish whether this is the
correct explanation. The very large variation in frequency
strongly affects the interpretation of the observed chlorine
resonances for the chlorine atoms of SbCls in SbC15°POC13.
If the interpretation of the NQR results for the complex are
based on the data for SbCls at 2500K there would be an un-
explained rise in frequency for the axial chlorine atoms
whereas a drop would be expected. Similarly the drops in
frequency for the equatorial chlorine atoms would become

smaller than expected. It would not be easy to explain these

212

changes, especially since the X-ray data show no dramatic
changes in the bond lengths of the Sb-Cl bonds and large
decreases in s hybridization and/or double bonding in the
Sb-Cl bonds would be needed to explain these changes (an
examination of Table 40 will show that solid-state effects
cannot account for the changes). On the other hand, if we
accept the NQR results at 770K and also assign the higher
frequency group at 50.4 MHz to the equatorial chlorines, the
results agree quite well with those found for SnCl4. Again,
the axial chlorine atoms receive a smaller charge than do

the equatorial chlorine atoms. If, as expected, the complexed
SbCls retains some identity with the uncomplexed SbCls there
is every reason to believe that the Sb-Cl bonds involving
Cl(1), Cl(2), and Cl(5) will be different from those involving
Cl(6). Further,if theresults of Van der Doorn and Drago can

be extended from PC15 to SbCls, and this seems like a reason-
able extension, then the basal positions should receive the
largest change. Table 45 presents results similar to those

of 44 using the frequencies for SbCls'POCls and for SbCls
measured at liquid nitrogen temperatures. The values of p

for the equatorial SbCls chlorine atoms and for Cl(1) and Cl(2)
of SbCls-POCla are obtained by taking an average of the observed
resonance frequencies.v The column "AI corrected"(Table 45) gives
the value of AI calculated after correcting the observed ean
for the solid-state effects assuming 7a): 0. In this case

the correction is quite small. However, it should be emphasized

215

Table 45. Charge Transfer in Complexed SbCls

 

 

Compound p AI AI(corrected)
SbCls _
(axial) 0.512 -- —_

(equatorial) 0.554 -- __

 

SbCls'POClg
Cl(1) and
01(2)a 0.474 0.080 0.083
01(3) 0.445 0.109 0.106
Cl(6) 0.498 0.014 0.014

 

aAverage of p values measured for Cl(1) and Cl(2).

that these corrected values of AI are probably not any better
than the uncorrected values and only serve to give an idea of
the error involved if the solid-state effects are neglected
since there is considerable uncertainty over the value of 700'
Also, in correcting for the solid-state effects only p for
the complex has been corrected and solid-state effects in
SbCls and SnCl4 themselves have been neglected. The total
charge transferred from POC13 to SbCls may be calculated as
2(0.080) + 2(0.014) + 0.109 = 0.297e. Comparison of this
result with that calculated for SnCl4-2POC13 (0.260e) shows
that both are about the expected magnitude and their relative
magnitudes also look right. It is also interesting to note

that Cl(5) receives a larger share of charge than the other

214

basal chlorines. This is in agreement with Brgnden et al.
(151) who find that bonds to chlorine atoms trans to the donor-
acceptor bond are generally stronger than the bonds from

the acceptor atom to other chlorine atoms.

SUMMARY

The nuclear quadrupole resonance Spectra of several
charge transfer complexes between POC13 and some Lewis
acids have been obtained. The absorption frequencies have
been assigned to various chlorine atoms in the complexes by
comparison with X—ray data and point-charge calculations
of solid-state effects.

The spectra have been interpreted in terms of charge

 

transfer upon complex formation and the changes in the NQR t
absorption frequencies of the Lewis acids have been taken

to indicate a nonequivalence in the bonding orbitals of the

central metal atom of these acids when they are complexed

With POC13 .

215

(1)
(2)
(5)
(4)

(5)

(6)

(7)

(8)
(9)

(10)

(11)

(12)
(15)

(14)

(15)

(16)

(17)

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P. Cornil, J. Duchesne, M. Read and R. Cahay, Bull.

, Classe Sci. Acad. Roy. Belg., 59, 255 (1964).

V. Grechishkin and I. Kyuntsel, Fiz. Tverd. Tela,§, 948
(1965).

V. Grechishkin and I. Kyuntsel, Optics and Spectroscopy,1§,
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APPENDIX

The computer programs ROTATE and DIAG, written during
this work, have already been discussed; they are listed here
along with a description of their input parameters. It should
be noted that, although ROTATE is completely general, it
should be used with care for any crystal whose unit cell is
less symmetric than hexagonal. Also, DIAG was written for
the case in which the molecular field gradient is cylindically

symmetrical. The input parameters are discussed below.

1) ROTATE

NCASE-IS format gives the number of tensors to be rotated.

X1, Y1, Z1, X2, Y2, Z2 - The coordinates of the two atoms
forming the bond to which the z-axis of the calculated tensor
is to be rotated, X2, Y2, 22 refer to the coordinates of the
quadrupolar nucleus.

A1, A2, A5 - The crystalline unit cell a, b, c parameters.
These must be in the same order as used for LATSUM.

ALPH, BET, GAM - The angles between A2 and A5, A1 and A5
and A1 and A2, respectively.

Q(I,J) - The elements of the tensor to be rotated.

The value of NCASE is only given once, the other input

parameters must be repeated for each case.

225

 

 

224

2) DIAG

(Q(I,J) - The elements of the rotated tensor as obtained

from ROTATE.

V(I) - The first guess for the molecular field gradients

on the diagonal (for example V(5) refers to qzz(mol)).

ST - The starting value for (1 - 700).

VV(I) - The diagonal elements of the measured field
gradient tensor. At present only VV(5) = q(exp) is used in
the program.

NN - The continuation parameter, if NN = 0 the program
stops, otherwise it reads the next set of Q, V, VV and ST

values.

 

 

 

15

20
16

21

22
25

17

225

PROGRAM ROTATE
DIMENSION s(3.3).ST(3,3),Q(5.3).QR(3,3),SQ(3,3)
READ 15,N0A5E

FORMAT(IS)

D0 14 M=1,NCASE

READ 1,X1,Y1,Z1,X2,Y2,22

FORMAT(6F10.0)

PRINT 2

FORMAT(///,*INPUT PARAMETERS*,/)

PRINT 5,X1,Y1,Z1,X2,Y2,Z2
E0RMAT(3P12.6,/,3P12.6)

READ 20,A1,A2,A5

READ 20,ALPH,BET,GAM

FORMAT(5F10.4)

FORMAT(5F12.6)

PRINT 16,A1,A2,A3

PRINT 16,ALPH,BET,GAM

PI=ATANE(1.)*4.

CONV=PI/180.

AA=CONV*ALPH

BB=CONV*BET

G=CONV*GAM

THETA=(GAM-90.000)

T=ABSF(THETA)*CONV
D=ASINF(SQRTF(COSF(AA)**2+COSF(BB)**2-2.*COSF(AA)*

1COSF(G)*COSF(BB))/SINF(G))

x2=x2*A1

X1=X1*A1
IF(THETA)21,22,22
Y1=A2*COSF(T)*Y1
Y2=A2*COSF(T)*Y2

so T0 23
Y1=(A2/COSF(T))*Y1
Y2=(A2/COSF(T))*Y2
Zl=A5*COSF(D)*Z1
z2=A3*005F(D)*z2
R2=(X2-X1)**2+(Y2-Y1)**2+(22-Z1)**2
R=SQRTF(R2*

z=z2-z1

B=ACOSF(Z/R)

Y=Y2-Y1

x=x2—x1

A=ATANF(Y/X)

PRINT 4,A,B.R
F0RMAT(3P12.6,/)
PRINT 17

F0RMAT(/,*TEN50R*,/)
D0 5 I=1,5

READ 6, (Q(I,J),J=1,5)

5
6

11
10

18
12

15
14

226

PRINT 6.(Q(I,J),J=1,3)
FORMAT(5F10.5)
8(1,1)=COSF(A)*COSF(B)
8(1,2)=-SINF(A)
s(1,3)=SINE(B)*COSF(A)
S(2,1)=SINF(A)*COSF(B)
S(2.2)=COSF(A)
S(2,5)=SINF(A)*SINF(B)
S(5,1)=-SINF(B)
s(3,2)=0
s(3,3)=COSE(B)

DO 7 I=1,5

DO 7 J=1,5
ST(I,J)=s(J,I)

DO 8 I=1,5

D0 8 J=1,5

SUM=0

DO 9 K=1,5

SUM =SUM+5T(I,K)*Q(K,J)
SQ(I,J)=SUM

DO 10 I=1,5

DO 10 J=1,5

SUM=0

DO 11 K=1,5
SUM=SUM+SQ(I,K)*s(K,J)
QR(I.J)=SUM

PRINT 18
PORMAT(///,*R0TATED TENs0R*,/)
DO 12 I=1,5

PRINT 13,(QR(I.J),J=1,3)
P0RMAT(/.3P14.6,/)
CONTINUE

END

 

59
12

10

15

16

18

19
20
25
25

227

PROGRAM DIAG

DIMENSION Q(5,5).V(5),VV(5),VL(5),T(5),A(5,5),VALU(5)
1,VAL(3),QQ(3.3)

COMMON A.QQ.VALU,ITER,ITP
DO 2 I=1,5

READ 1,(Q(I,J),J=1,5)
FORMAT(5F10.0)

READ 3,(V(I),I=1,3),ST,(VV(I),I=1,3)
FORMAT(7F10.0)

PRINT 4

FORMAT(*INPUT PARAMETERS*,//,*TRIAL.QS*,/)
PRINT 5,(V(I),I=1,5),(VV(I),I=1,5)
FORMAT(5F15.5)

PRINT 6,ST

FORMAT(/,*ST= *,F6.5,//)
DO 7,I=1.5

PRINT 8,(Q(I,J),J=1,3)
FORMAT(5F12.5)

DO 57 K=1,10

ITER=1

ITP=0

D0 39 I=1,3

D0 59 J=1,3
QQ(I,J)=Q(I,J)*ST

DO 12 I=1,5

VL(I)=V(I)

DEL=0

AB=100.

KTR=0

DELTA=0.1
VL(1)=VL(1)70.5*DEL
VL(2)=VL(2)-0.5*DEL
VL(5)=VL(5)+DEL

DO 13 I=1,5
QQ(I,I)=QQ(I,I)+VL(I)
CALL QDIAG

KK=4

DO 16 I=1,3
T(I)=ABSF(VALU(I))

DO 17 I=1,3

KK=KK~1
IP(T(1)-T(2))18,18,19

J=2

00 T0 20

J=1

IE(T(3)-T(J))21,23,24
PRINT 25
F0RMAT(//,*MISTAKE*,//)

 

21

24

17

52
60

15
28

29

50
22

11
54
56
45

55
57

55
56

228

GO TO 17

VAL(KK)=VALU(J)

T(J)=o.

GO TO 17

VAL(KK)=VALU(3)

T(5)=0.

CONTINUE

AA=ABSF(VAL(5))-ABSF(VV(5))

AA=ABSF(AA)
IF(AA-0.001)11,11,52

DO 60 I=1,5

QQ(I,I)=QQ(I.I)-VL(I)
IF(AB-AA)15,15,22

KTR=KTR+1

VL(1)=VL(1)+0.5*DEL
VL(2)=VL(2)+0.5*DEL

VL(3)=VL(3)-DEL

DELTA=-DELTA
IF(KTR-5)22,22,29

DELTA=DELTA/2.

DD=ABSP<DELTA)-0.00001
IP(DD)11,11,30

KTR=O

DEL:DELTA*VL(3)

AB=AA

ITER=ITER+1
IE(ITER-1OO)1O,1O,11

DO 9 I=1,3

PRINT 34,(A(I,J).J=1,3)
FORMAT(//,5F12.6)

PRINT 36,ITER

F0RMAT(//,I4,* ITERATIONS*,//)
PRINT 45,(VALu(I),I=1,3)

FORMAT(*TRACE ELEMENTS*,3P12.6,/)
PRINT 35,K,(VL(I),I=1.3)

FORMAT(/,*END BLOCK*,I3,//,3P12.6,//)
ST=ST+0.1

READ 55,NN

FORMAT(I5)

IE(NN)38,56,38

CONTINUE

END

SUBROUTINE QDIAG

DIMENSION B(3.3),A(3,3).QQ(3,3),VALU(3)

COMMON A,QQ.VALU,ITER,ITP

N=5

D0 4 I=1,5

DO 4 J=1,3

 

229

4 A(I,J)=QQ(I,J)
CALL SMDIAG(A,VALU,N)
IF(ITP-ITER)1,1,2
ITP=ITP+10
PRINT 3,ITER,(VALU(I),I=1.3)
3 PORMAT(/,*ITER=*,13,4x,3E15.5)
2 CONTINUE
END
SUBROUTINE SMDIAG(A,EX,N)
DIMENSION A(3,3),T(3.3), EX(5), RI(3),RJ(3),CI(3),CJ(3)
EPS = .00001
LLM = 10
LL = 1
100 D0 110
D0 105
105 T(I,J)
110 T(I,I)
120 NCNT =
130 D0 350 K=2
NN=N+1-K
D0 345 I=1,NN
=K+I-1
x = 2.0*A(I,J)
IF(EPS-ABSF(X)) 150,150,340
150 Y = A(J,J) - A(I.I)
IF(Y) 160,170,160
160 R = SQRTF(X*X+Y*Y)
COS = SQRTF(0.5+0.5*ABSF(Y)/R)
SIN = ABSF(X)/(2.0*R*COS)
IF(X/Y) 165,180,180
165 SIN = -SIN
00 T0 180
170 SIN = 0.707106781186
COS = SIN
180 MA = I+1
D0 190 M = MA, J
190 RI(M) = A(I,M)*COS - A(M,J)*SIN
200 MA = J+1
D0 210 M= MA,N
RJ(M) A(J,M)*COS + A(I.M)5SIN
210 RI(M) A(I,M)*COS - A(J,M)*SIN
220 M2 = I-1
D0 230 M= 1,Mz
CI(M) A(M,I)*COS - A(M,J)*SIN
230 CJ(M) A(M.J)*COS + A(M,I)*SIN
240 M2 = J-1
DO 250 M=I,Mz
250 CJ(M) = A(M,J)*COS + A(I,M)*SIN

H

I

O" IICIH
POE-‘ll

1
N
0
0
N

o
o
I

 

260

270
280

290

520

550

540
545
550
560
570

580
590
400
410

250

T1 = A(I,I)*COS*COS + A(J,J)*SIN*SIN-2.0*A(I,J)*SIN*COS
T2 = A(I,I) + A(J,J) - T1

DO 270 M=1,J
A(M,I) = CI(M)
A(M.J) = CJ(M)
MA = I+1

D0 290 M=MA,N
A(I,M) = RI(M)
A(J,M) = RJ(M)
A(I,I) = T1
A(J,J) = T2

A(I,J) 0.0

D0 330 M=1,N

T1 = T(M,I)*COS — T(M,J)*SIN
T(M,J) = T(M,I)*SIN + T(M,J)*COS
T(M,I) = T1

GO TO 345

NCNT = NCNT+1

CONTINUE

CONTINUE

IF (N*(N-1)/2-NCNT) 370,370,400
D0 580 I=1.N

EX(I) = A(I,I)

DO 580 J=1,N

A(I,J) = T(I,J)

RETURN

IF(LLM-LL) 370,370,410

LL = LL + 1

GO TO 120

END

 

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