3.31% 53:73:53 83:32.3 CRYS‘E‘A ES

Tlmsis {my five Deqmo a-‘E 737:: D.
MICEEGM SYAYE UMVEESETY

James Ciycie Was-an
:99793

THES": m

LIBRARY ;-
Michigan State
UDiVCfSity Gib-

 

This is to certify that the

thesis entitled

AN ESR STUDY OF RADICALS IN SOME
IRRADIATED SINGLE CRYSTALS

presented by

James Clyde Watson

has been accepted towards fulfillment
of the requirements for

Ph .D .1 degree in Chemistry

fl
42/5411 1‘ Ov/O/a

Major essor

Date 03—4 92;lclé? .

0-169

\‘L'. ‘

ELL-

 

ESR spect

~"
"fl‘q

unaticn in s

:zzction cf te

.;.s and the :

 

 

ABSTRACT

AN ESR STUDY OF RADICALS IN SOME
IRRADIATED SINGLE CRYSTALS

BY

James Clyde Watson

ESR Spectra of radicals produced by electron and y-ir-
radiation in six single crystals were investigated as a
function of temperature. The radicals produced in the crys-

tals and the temperature range over which they are stable,

+
NHz

are: c12‘ (770x-1230K) and éHz-c-NH2 (1230K-1930K) from
acetamidine hydrochloride y-irradiated at 770K;
CH2 0
CH3-C — C-NH2 (77°K-1930K) and E-butyl radical (779K-
CH3
3000K) from trimethylacetamide y-irradiated at 779K;

0 CH3 . O

:CH-C-NHZ (77°K-1930K) and >C-C-NH2 (770K- 3000K)
CH3 CH3

CH2

from isobutyramide y-irradiated at 770K; Clz- (77°K-1930K)
in y-irradiated hydrazinium dichloride at 770K; Brz- (770K-
1130K) in y—irradiated hydrazinium dibromide at 779K; and
hydrogen atoms (77°K-1930K), an unidentified radical pair
(779K-1930K) and a radical,possibly N2H6+,(193°K-3OO°K) in

hydrazinium difluoride y-irradiated at 779K.

 

In the car
|
‘-'.'i::chlcride '

tense: and g

a 7 center in

Stable at mte

D"!- A

...,c:fir.e Spli

35 “electron
1395 Cf ~5.4

In ‘I‘irra

 

 

James Clyde Watson
In the case of the C12- radical anion in acetamidine
hydrochloride it was found that the hyperfine splitting
tensor and g tensor exhibited the anisotropy expected for
a V center in a monoclinic crystal. The radical CHz-C-NHz .
stable at intermediate temperatures, exhibited principal
hyperfine splitting values of -35.9 gauss, -23.1 gauss,
and -7.5 gauss for one proton and -36.2 gauss, -19.0 gauss,
and -5.8 gauss for the second proton. These values are in
reasonable agreement with predicted splittings for a-protons
of v-electron radicals. .A further interaction with the —NH2
protons was detected giving principal proton hyperfine Split-
tings of -6.4 gauss, -4.1 gauss and —1.7 gauss.
In y-irradiated trimethylacetamide single crystal
cnz 0

both Efbutyl radical and CH3-C -C—NH2 radical were present
I
CH3

after irradiation at 770K. Both radicals appear to be re-
orienting faster than 107 sec"1 since only the isotropic
hyperfine splittings were observed in each case. The

CH2 0

CH3-C -'C—NH2 radical was stable only from 77°K- 1930K.
I
CH3

It was possible to obtain the maximum 13C hyperfine Split-
ting QQZ gauss) for Efbutyl radical at 770K. This value

was used to show that the tfbutyl radical is probably slightly
non-planar with the C-C bonds tipped about 3-40 from the

average radical plane.

 

 

Isc'sutyrar
station at 77

rpmtcn princ;
-20.3 gauss, a:
:ecrienting 51;
fire splittings
:haza teristic
:aiicals. The
53.35 that the

25:31:29 the tw:

 

 

Q ‘ C
:‘qu

.u.u‘y.‘. The |
C

‘v.,.“
"VU

.lC is-proto:
.:;.'.g 23.0 gau:
{.51th with n

:‘Irradia

1;;Ififis; “
vu.4.ce Cr},

8

:Ese hf ‘
V hidraz

o: ‘
N tie ._
“IPErfi
36:6.“- .
._ wlth t
In .
.‘Evc ‘_
c“Estes
A:

James Clyde Watson

Isobutyramide single crystal gave two radicals upon ir-

' O
CH 2 ”

radiation at 779K. ~In ;::CH-C-NH2 radical the equivalent
CH3

d-proton principal hyperfine splittings of -24.2 gauss,
—20.3 gauss, and -17.8 gauss show that the -CH2 group is
reorienting slowly at 779K. :The B-proton principal hyper-
fine splittings of 22.8 gauss, 18.9 gauss and 12.2 gauss are
characteristic of fi-hyperfine splittings in -C-CH-XY type
radicals. "The isotropic fidhyperfine splitting of 18.0 gauss
shows that the B proton is oriented 93° from the plane con-
taining the two carbon atoms and the p” iorbital of the a
ca3 9
carbon. The ;:C-C-NH2 radical exhibited essentially iso-
CH3
tropic firproton hyperfine splittings, the principal values
being 23.0 gauss, 21.7 gauss, and 21.7 gauss. This is con-
sistent with nearly free rotation of the CH3- groups at 779K.
y-Irradiated hydrazinium dichloride and hydrazinium
dibromide crystals contained V centers at 770K. ~In the
case of hydrazinium.dichloride C12- radical anions were
found to be oriented along (110) directions in the crystal.
In hydrazinium dibromide Br2_ exhibited principal values
of the hyperfine splitting and g tensors which were con-
sistent with the monoclinic symmetry of the crystal.
In y-irradiated hydrazinium difluoride hydrogen atoms
were detected at 779K, along with a radical pair. The
presence of the pair was verified by the observation of

lines at g 3'4. Because of insufficiently resolved spec-

tra over a range of orientations in the magnetic field it

 

 

as net possum

 

.
:::.s and two 6;
33:: could ex;

I ICIIEthI'l ’

electrcn to 5:2

3:: three e;

a
0",”
6U..ua.lcn C

- ‘In 4 .
Z-‘CI‘G 10?.

a... . ‘
I.: 5lrsg‘il Sh a?“ ,-

nsl ‘

 

James Clyde Watson
was not possible to identify the radical pair. Upon warming
to -700 a spectrum was observed which indicated a radical
in which the odd electron interacts with six equivalent pro-
tons and two equivalent nitrogen nuclei. -Three possiblities
which could explain the Spectra observed were postulated;

a) formation of N2H33+ radical cation, b) addition of an
electron to N2H6++ cation to form the radical N2H6+
with a three electron bond between the nitrogen atoms, or
c) formation of an F center by trapping an electron in

a fluoride ion vacancy. .Further work will be required to

distinguish among these possiblities.

AN ESR.STUDY OF RADICALS IN SOME

IRRADIATED SINGLE CRYSTALS

BY

James Clyde Watson

A THESIS

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

DOCTOR OF PHILOSOPHY

Department of Chemistry

1970

 

 

 

1 1.4"! II

 

To Sandy

ii

ACKNOWLEDGMENTS

The author would like to take this opportunity to ex—
press his appreciation to Professor M. T. Rogers for his
helpful suggestions and encouragement during this research.

The author is also indebted to Mr. George Giddings
and Mr. Gary Blair for performing the y-irradiations, Mr.
Pat Hock for performing the dbctron irradiations, Mr.
Norman Fishel for aiding with the x—ray analyses, Dr. H. A.
.Eick for the use of the x-ray equipment, and Mr. Tom Krigas
for helping with the computer simulation program.

Finally thanks are extended to the Atomic Energy
Commission for a research assistantship and to Michigan

State University for a teaching assistantship.

iii

TABLE OF CONTENTS

Page

INTRODUCTION . . . . . . . . . . . . . . . . . . . . 1
HISTORICAL BACKGROUND . . . . . . . . . . . . . . . 4
I. Proton Splittings in v-Electron Radicals . 4

.A. a-Proton Hyperfine Splittings . . . . . 4

B. B—Proton Hyperfine Splittings . . . . . 9

C. y-Proton Hyperfine Splittings . . . . . 14

D. 14N-H Proton Splittings . . . . . . . . 16

II. 14N Splittings . . . . . . . . . . . . . . 19

III. 13c Hyperfine Splittings . . . . . . . . . 20
IV. V Centers . . . . . . . . . . . . . . . . . 28

V. {Free Atom Hyperfine Splittings and 9 Values 32
THEORETICAL . . . . . . . . . . . . . . . . . . . . 34

I. Basic Theory of Electron Spin Resonance . . 34
A. Classical Treatment . . . . . . . . . 34

B. .Electron.Dipole-Nuclear Dipole
(Hyperfine) Interactions . . . . . . . 35

C. First-Order Quantum Mechanical
Perturbation Theory . . . . . . . . . 39

D. :Spin-Orbit Coupling . . . . . . . . . 41

E. .Second—Order Perturbation Theory . . . 43
II. -Evaluation and Interpretation of Spectral

Parameters . . . . . . . . . . . . . . . . 47

.A. Experimental Determination of Hyperfine
Splitting and 9 Values . . . . . . . 47

iv

-r-_ll

 

115:?”

352.3 0? CCX'Z‘E‘.

11- Spect.
III . X-Ra‘ .

 

 

IV. Mater;

TABLE OF CONTENTS (Continued)

III.

B. Interpretation of Hyperfine Splittings
and Their Signs . . . . . . . . . . .

1; Isotropic Splittings . . . . . .
2 Anisotropic Splittings . . . . .

Planarity of Radicals . . . . . . . . .

EXPERIMENTAL . . . . . . . . . . . . . . . . . . . .

I.

II.
III.

IV.

VI.

RESULTS

I.

Analysis of ESR Data for Irradiated Single
Crystals . . . . . . . . . . . . . . . . .

Spectrometer System . . . . . . . . . . . .

X-Ray Structure Determination and Optical
Crystallography . . . . . . . . . . . . .

.Materials . . . . . . . . . . . . . . . . .

A. Acetamidine.Hydrochloride . . . . . .
B. Isobutyramide . . . . . . . . . . . .
C. ,Trimethylacetamide . . . . . . . . . .
D. -Hydrazinium Dichloride . . . . . . .

E. :Hydrazinium Difluoride . . . . . . . .
F. :Hydrazinium Dibromide . . . . . . . .
Procedure . . . . . . . . . . . . . . . .

A. Crystal Growing . . . . . . . . . . .
B. Radiation Procedure . . . . . . . . .
C. Mounting Crystals . . . . . . . . . .
D. .Rotation Spectra . . . . . . . . . .

E. Temperature Studies . . . . . . . . .

Standard Samples and Conversion Factors . .

Irradiated Acetamidine Hydrochloride . .
A. Crystal Structure . . . . . . . . . .

B. Identification of Radicals Produced in
Irradiated Acetamidine Hydrochloride .

1 Low-Temperature Radical -Clz- . .

2 High—Temperature Radical -CH2-C—NH3

+NH2
V

Page

51

51
58

62
65

65
67

68
71
71
72
72

- 72

72
73
73
73
74
76
82
83
83

85
85
85

86

86
99

TABLE OF CCNTE

II. Irrai

 

 

 

 

 

IV. 1:186

DiChl

 

B. ‘

Irrad
D1510

'7

com

TABLE or CONTENTS (Continued)

Page
II. Irradiated Trimethylacetamide Single Crystal 116

A. .Crystal Structure . . . . . . . . . . . 116
* CH2 0
B. EfButyl Radical and ens-C --C-NH2 Radical
at 77°K . . . . . . . C33 . . . . . . 118
C. Temperature Studies . . . . . . . . . . 123
D. 13C Splitting for ErButyl Radical . . . 126
III. Irradiated Isobutyramide Single Crystal . . . 129

A. Crystal Structure . . . . . . . . . . . 129

CH; O
B. Low—Temperature Radical “CH-C-NH2 . . 129
CH;
C. Radical Stable at Higher Temperatures
CH O
146

3.
‘\
C—C-Nflzooooooooooooo
CH§/’

IV. Irradiated Single Crystals of Hydrazinium
.Dichloride . . . . . . . . . . . . . . . . . 153

A. Crystal Structure . . . . . . . . . . . 153
B. Presence of C12- at 779K . . . . . . . . 153

V. Irradiated Single Crystals of Hydrazinium
Dibromide . . . . . . . . . . . . . . . . . . 159

A. Crystal Structure . . . . . . . . . . . 159

B. Bra- Radical in Crystals Irradiated
at 770K . . . . . . . . . . . . . . . . 159

C. Temperature Studies . . . . . . . . . . 171
VI. Irradiated Hydrazinium Difluoride . . . . . . 173
(A. Crystal Structure . . . . . . . . . . . 173
B. -Hydrogen Atoms Formed at 770K . . . . . 173
C. .Radical Pairs at 77°K . . . . . . . . . 176
D. -The Radical at -7o° . . . . . . . . . . 178

vi

1152.3 0? CCN’I‘E)

33331.35 ICNS

 

I. Radlca
Hydro:

RS

HI- Radica

Iv. v Gen,
Dihal;
w
P

5.;4

 

 

TABLE OF CONTENTS (Continued)

CONCLUSIONS

I.

Radicals in Irradiated Acetamidine
Hydrochloride . . . . . . . . . . . . .

A.

C13" Radical '-. . . ; . g . . . .u;

B. CHg-C-NHz Radical . . . . . . . .
II

+NH2

II. .Radicals in Irradiated Trimethylacetamide

III.

IV.

VI.

A.

C.

A.

B.

EfButyl Radical . . . . . . . . .

CH3
I
13C Splitting in H3C-13C' . . .
o I
CH2 0 CH3
I II
H3C-C - C—NH2 Radical . . . . . .
I
CH3
.Radicals in y-Irradiated Isobutyramide
° 0
.CH2 ”
LZCH- -NH2 Radical at 779K . . .‘
CH3

CH3 . 9
;C-C-NHa Radical . . . . . .
CH3

V Centers in y-Irradiated Hydrazinium

A.

B.

A.
B.
C.

.Dihalides . . . . . . . . . . . . . . .

.Clz- Radical Anion in y-Irradiated
Hydrazinium.Dichloride . . . . . .

Br2_ Radical Anion in y-Irradiated
Hydrazinium Dibromide . . . . . .

~Radicals in y-Irradiated Hydrazinium
.Difluoride . . . . . . . . . . . . . .

~Trapped Hydrogen Atoms . . . . . .

Radical Pairs at 779K . . . . . .
-The Radical at -700 . . . . . . .

Summary . . . . . . . . . . . . . . . .

vii

Page
193

193
193

196

199
199

201

202

203

203

206

207

207

208

210
210
211
211
216

 

TABLE OF CCXT‘

REFERENCES .

APPEKDIX . .

 

TABLE OF CONTENTS (Continued)

Page
REFERENCES . . . . . . . . . . . . . . . . . . . . . 218
APPENDIX . . . . . . . . . . . . . . . . . . . . . . 227

viii

r1

 

as
In!

C
in

II.

III.

HI.

HHL

XL

HI.

I.?‘
kl

a-Prc:
carbon

f-Pret
carbon

7-Prot
carbon

Hlperf
bound

 

14w I?
the cd

nitrgg

13C l1:

LIST OF TABLES

TABLE Page

I. a-Proton hyperfine interactions in hydro-
carbon radicals . . . . . . . . . . . . . . . 5

II. B-Proton hyperfine splittings in hydro-
carbon radicals . . . . . . . . . . . . . . . 10

III. y-Proton hyperfine splittings in hydro—
carbon radicals . . . . . . . . . . . . . . . 15

IV. Hyperfine splitting constants for protons
bound to 14N . . . . . . . . . . . . . . . . . 17

V. 14N hyperfine Splitting tensors . . . . . . . 21

VI. 14N hyperfine splitting tensors in radicals where
the odd electron is delocalized over two
nitrogen atoms . . . . . . . . . . . . . . . 24

VII. 13C hyperfine Splittings . . . . . . . . . . . 26

VIII. Hyperfine Splitting constants and g values
for V centers . . . . . . . . . . . . . . . . 30

IX. ‘Free atom hyperfine splittings and g values 33

X. <Representative 13C and '14N isotropic
splittings . . . . . . . . . . . . . . . . . . 55

XI. ~Deviation from planarity for some substituted
methyl radicals . . . . . . . . . . . . . . . 64

-XII. Principal hyperfine splitting and g values
and their orientations for C13 radical in
irradiated acetamidine hydrochloride . . . . . 98

«XIII. Principal values of the hyperfine splitting
tensor for the two nonequivalent a-protons in
-CH2-C-NH2 radical . . . . . . . . . . . . . . 113

+NH2

ix

 

LIST OF TABLES

X‘.’ .

XII .

I31.

'. Hyperf

in .CI

Hyperf.
trimet)
Hyperf.
H2C\\

/C:

H3C
HYperf;
in the |
PrinCiE
tenSQr

hydraz;

Hyperf1
hydIng

RddiCaJ

 

LIST OF TABLES (Continued)

TABLE

XIV.

XVII.

XVIII.

XIX.

Page

-Hyperfine splitting values for -NH2 protons

in ~CH3-C—NH2 radical . . . . . . . . . . . 117
+NH2

Hyperfine splittings for radicals in irradiated
trimethylacetamide . . . . . . . . . . . . . . 124

-Hyperfine Splitting tensors for protons of the

O

H2C\~ u

’,CH-C-NH2 radical . . . . . . . . . . . . 149

H3C

Hyperfine spliating tensor for methyl protons
CH3 "

in the L>C-C-NH2 radical . . . . . a . .'. 153
C33

Principal values of the hyperfine Splitting
tensor and g tensor for Bra in y-irradiated
hydrazinium dibromide . . . . . . . . . . . . 163

-Hyperfine splitting tensors for nitrogen and

hydrogen in the -70° radical . . . . . . . . . 190

-Radical pairs . . . . . . . . . . . . . . . . 212

 

 

."V'RE
' i
t M13.

10.

12.

. ESR ene

- Spin p:

° RElatiQ}

and Si:
radical

to the
is Show:
dotted 1
eleCtrm:

V

 

' Princlp.

teflsor 1

Signs a
Values
PIOtOn

Single

Single

Dewar c

APPEIa1
magREt:

FIGURE

1.

10.

11.

12.

LIST OF FIGURES

~ESR energy level diagram for a Single electron

and Single nucleus . . . . . . . . . . . . . .

'Spin polarization for a hydrogens in w-electron

radicals O I O O O O O C O O I I O O O O O O 0

Relationship of nucleus at S—position relative
to the odd electron orbital.e?A -C-CH fragment
is shown looking along the C-C bond with the
dotted line outlining the pr orbital of the odd
electron . . . . . . . . . . . . . . . . . . .

Prinbipal directions of the hyperfine splitting
tensor or g tensor for an a proton . . . . .

Signs and relative magnitudes of the principal
values of the dipolar coupling tensor for an a
proton illustrated-for a.-C-H fragment . . . .

.Single crystal holder . . . . . . . . . . .

Single crystal mounted in crystal holder for
transfer to ESR cavity . . . . . . . . . . . .

.Dewar container for ESR single crystal studies

-Apparatus for rotating single crystals in the

magnetic field . . . . . . . . . . . . . . . .

Crystallographic axes for acetamidine hydro—
chloride . . . . . . . . . . . . . . . . . . .

-ESR spectrum of irradiated acetamidine hydro-

chloride showing C12 at 770K. H> is 50° from

.a in the ac* plane . . . . . . . . . . . . .

~ESR spectrum of irradiated acetamidine hydro-

chloride showing C12 at 770K. H> is 400 from
c* in the ac* plane . . . . . . . . . . .

xi

Page

40

52

57

60

61

77

79

80

81

87

88

90

 

VI
I - - ‘i f
‘ ...._.

123': OF FIG'JRE;

 

1

FIRE
13. ESR speq
chloride
a in ti
14. ESR speé
gflane .
15' ESR Spe
plane .
16- BE’Perflr
in the
17' Hyperfn
in the
13' Hi'Perfl;
in the
w' PlOt Of
the be
20. pm Cf
the ac
U. plgt Of
the a:
22. ESR Sp“
9
.3, ESR SD
frgm ‘,
24_ ESR p
1000
h,
ESR SP
1400

LIST OF FIGURES QContinued)

FIGURE

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

-ESR spectrum of irradiated acetamidine hydro-

chloride showing Clz- at 77°K. H'> is 60° from

.a in the ac* plane . . . . . . . . . . . . .

-ESR spectrum of C12- with H’ll b in the ab

plane . . . . . . . . . . . . . . . . . . . . .

ESR spectrum of C12” with fi5|| a in the ab
plane . . . . . . . . . . . . . . . . . . . . .

'Hyperfine splitting of C12- gs angle of rotation

in the bc* plane . . . . . . . . . . . . . .

Hyperfine splitting of C12- gs angle of rotation
in the ac* plane . . . . . . . . . . . . . .

Hyperfine Splitting of C12- yg angle of rotation
in the ab plane . . . . . . . . . . . . . . .

Plot of 9 XS angle of rotation for C12- in
the bC* plane . . . . . . . . . . . . . . . .

Plot of g y§_angle of rotation for C12- in
the ac* plane . . . . . . . . . . . . . . . .

-Plot of 9 XS. angle of rotation for C12- in

the ab plane . . . . . . . . . . . . . . . .

:ESR spectrum of CHz-C-NHz radical with H) 60°
' II

+NH2
from b in the ab plane . . . . . . . . . .

+
NHz

-ESR Spectrum of éHg‘C-Nflz radical with HI> 50°

from b in the ab plane . . . . . . . . . .

~+
NHz

-ESR Spectrum of CHz-CeNHz radical with H)

100° from b in the ab plane . . . . . . .
+
NH2
ESR Spectrum of CHz-C-NHz radical with H.>
140° from b in the ab plane . . . . . . . .

xii

Page

91

92

93

95

96

97

100

101

102

103

105

106

107

 

m' E
LIST OF FIucR

.7 13m

26. Angular

Splitt;

27° Angular

fine 5;
radica;
28. Angularl

fine S;
radical

29. ESR Spe

With fi

30.

 

 

31.

32.

33.

34.

35.

LIST-OF FIGURES (Continued)

FIGURE page

26. -Angular variation in the ab plane of hyperfine
+NH2
splittings for a protons in CHg-C-NHz radical 110
27. rAngular variation in the bc* plane of hyper-
+NH3
fine splittings for a protons in CHz-C-NHz
radical . . . . . . . . . . . . . . . . . . . . 111

28. Angular variation in the ac* plane of hyper-

+NH2
fine Splittings for a protons in CHa-C-NHz
radical . . . . . . . . . . . . . . . . . . . . 112
. +NH3
29. 'ESR Spectrum of deuterated CH2‘C’NH2 radical
with H> II a in the ac* plane . . . . . . . 114
+NH 2
30. ESR spectrum of deuterated CHz-CeNHz radical
with H> || c* in the ac* plane . . . . . . . 115

31. Crystallographic axes for trimethylacetamide . 119

32. -ESR spectrum of irradiated trimethylacetamide
crystal at 77°K. :H is 60° from b in the
a*b plane . . . . . . . . . . . . . . . . . . 121

33. ~ESR Spectrum Of irradiated trimethylacetamide
crystal at 77°K. .H 13 60° from C in the
a*c plane . . . . . . . . . . . . . . . . . . 122

34. ESR spectrum of an irradiated trimethylacetamide
crystal warmed to -80°. H >1| c in the a*c
plane . . . . . . . . . . . . . . . . . . . . . 125

35. .ESR Spectrum of an irradiated trimethylacetamide
crystal warmed to -80°. H is 40° from C in
the a*c plane . . . . . . . . . . . . . . . . 127

36. ESR first derivative spectrum of irradiated tri-
methylacetamide crystal at 77°K showing 130 lines.
H is 10° from b in the a*b plane . . . . . 128

xiii

r!

 

 

 

LBTOF FIGURE

333$
37.

w.

39.

40.

41.

42.

Q.

44. .

45.

4s.

 

Cryscai

 

 

ESR Spi
at 77°}

ESR 5;:
amide :
ah ple

ESR Spe
at 770K

Angular
0H2

LIST OF FIGURES (Continued)

FIGURE
37.
38.

39.

40.

41.

42.

43.

44.

45.

46.

Page
Crystallographic axes for isobutyramide . . . . 130

ESR s ectrum of irradiated isobutyramide crystal
at 77 K. H is 10° from b in the ab plane. 131

-ESR spectrum of irradiated deuterated isobutyr-

amide crystal at 77°K. AH> is 10° from b in the
ab plane . . . . . . . . . . . . . . . . . . . 133

-ESR spectrum of irradiated isobutyramide crystal

at 77 . H “ c* in the bc* plane . . . . . 134

.Angular plot of line positions for the

O

CH3;CH
w-C-an radical in the ab plane . . . . 136
CH3

Variable temperature study of the spectrum of the

° 0
CH3 ._>
“CH-C-NH3 radical with H || a . . . . . . 138
CH3
Variable temperature study of the spectrum of the
° O
CH3

,L‘CH—C—NH2 radical with B’|| b . . . . . . 141
CH3

Variable temperature study of the spectrum of the
CH3 9 . . ._>
“CH‘C*NH3 rad1cal W1th H II c* . . . . . . 144

cnj'

CH3\ 0

-Plot of line positions for /,CH-C-NH3 radical
CH3

as a function of field orientation in the bc*

plane . . . . . . . . . . . . . . . . . . . . . 147
CH3 9

Plot of line positions for :)CH-C-NH3 radical

' CH3

as a function of field orientation in the ac*
plane . . . . . . . . . . . . . . . . . . . . . 148

xiv

 

IIST OF FIGL'RI

FREE

47.

48.

49.

50.

51.

M.

53.

M.

H,

M,

5L

a.

59.

ESR Spt

E’Ht

ESR Spi

‘>

We

ESR Spi
Chlorl:
aa' ;;

ESR Spa
Chlori;
aa' p:

ESR Spg
Chloric
aa' P:

ESR Spg
cthIic
from

 

LIST OF FIGURES (Continued)

FIGURE 0 Page
CH3 , u
47. .ESR spectrum of the :;C—C-NH2 radical with
_. CH3
H>|| b in the ab plane . . . . . . . . . . 151
CH3\. 9
48. -ESR spectrum of the IIC-C-NHZ radical with
_. CH3
'H>|| c* in the ac* plane . . . . . . . . . 152

49. ESR Spectrum of irradiated hydrazinium di-
chloride at 77°K. -H is 450 from a in the
aa' plane . . . . . . . . . . . . . . . . . 154

50. .ESR spectrum of irradiated hydrazinium di-
chloride at 77°K. H is 135° from a in the
aa' plane . . . . . . . . . . . . . . . . . 156

51. -ESR spectrum of irradiated hydrazinium di—
chloride at 77°K. .H is 900 from a in the
aa' plane 0 O O O O O O O O O O O O O O O O 157

52. ‘ESR spectrum of irradiated hydrazigium di-
chloride after warming to -80°. H is 450
from a in the aa' plane . . . . . . . . . 158

53. Crystal axes for hydrazinium dibromide . . . 160

54. -ESR spectrum of irradiated hydrazinium di-
bromide at 77°K. -H is 30° from b in the
be plane . . . . . . . . . . . . . . . . . . 162

55. -ESR spectrum of irggdiated hydrazinium di-
bromide at 779K. H is 300 from c in the
a*c plane . . . . . . . . . . . . . . . . . 164

56. Hyperfine splitting of Br2- versus angle of
rotation in the a*b plane . . . . . . . . . 165

57. Hyperfine splitting of Br2- versus angle of
rotation in the be plane . . . . . . . . . 166

58. Hyperfine splitting of Br2- versus angle of
rotation in the a*c plane . . . . . . . . . 167

59. Plot of 9 versus angle of rotation for Brz-
in the a*b plane . . . . . . . . . . . . . 168

XV

 

125T OF FIGURE‘

FIGURE

66

M.

62.

63.

64.

66.

67.

~’
C.)
-

Plot c4
in the

Plot 0:
in th

 

First |
hydraz
in the

Crysta
fluori

ESR S;
ium d;
the h-
the “

ESR s
ium 6
D20 .

LIST or FIGURES (Continued)

FIGURE
60.

61.

62.

63.

64.

65.

66.

67.

68.

69.

70.

Plot of 9 versus angle of rotation for Bra-

in the be plane . . . . . . . . . . . . .

Plot of 9 versus angle of rotation for Brz-

in the a*c plane . . . . . . . . . . . .

First derivative ESR spectrum of irradiated
hydrazinium dibromide warmed to -160°; HII
in the a*c plane . . . . . . . . .

Crystal reference axes for hydrazinium di-
fluoride; c is the threefold axis . . . .

~ESR spectrum of electron irradiated hydrazin
ium difluoride at 77°K showing the spectrum of

the hydrogen atom (outer doublet). H>|| c
the be plane . . . . . . . . . . . . . .

ium dig uoride which has been exchanged with
D20. H I] c in the bc plane . . . . . .

ESR spectrum of y-irradiated hydrazinium di—
fluoride at 77°K with Hx>|| c in the bc
plane. The outer seven lines on each side
are attributed to a radical pair . . . . .

h drazinium difluoride at 770K with H> || c;
a position of the g = 4 lines relative to

C

in

-ESR spectrum at 77°K of y-irradiated hydrazin-

.First derivative ESR spectrum of y-irradiated

the resonance at g = 2, b) the g = 4 lines

with better resolution . . . . . . . . . .

~ESR spectrum of y-irradiated hydrazinium di-

fluoride warmed to -70°. H> || c in the bc
plane . . . O C C O C C . O . . . . . C . .

-ESR spectrum of y-irradiatgd hydrazinium di-

fluoride warmed to -70°. H> is 400 from c
in the ho plane . . . . . . . . . . . . .

rESR Spectrum of y-irradiated hydrazinium di-

fluoride warmed to -70°. H> is 30° from the
a -axis in the ab plane (plane l to c- -axis).

xvi

Page

169

170

172

174

175

177

179

180

181

183

184

LIST OF FIGURES (Continued)

FIGURE

71.

72.

73.

74.

75.

76.

Page
.ESR Spectrum of y-irradiatgg hydrazinium di-
fluoride warmed to —70°. H is 120° from the
a axis in the ab plane . . . . . . . . . . . 186

Angular variation of the hydrogen hyperfine
splitting in the ab plane for the -700 radical 187

Angular variation of the nitrogen and hydrogen
hyperfine Splitting in the bc plane for the
-700 radical . . . . . . . . . . . . . . . . . 188

Angular variation of the nitrogen and hydrogen
hyperfine splitting in the ac plane for the
-70° radical . . . . . . . . . . . . . . . . . 189

-ESR spectrum of y-irradiaged deuterated hydrazin—

ium difluoride at 77°K. H> is -100 from the c
axis in the ac plane . . . . . . . . . . . . 191

~ESR Spectrum of y-irradiated acetamidine hydro-

chloride powder at 77°K. a) Observed spectrum
b) Computed Spectrum.. . . . . . . . . . . . . 195

xvii

INTRODUCTION

Irradiation of organic compounds by X—rays or yerays
produces free radicals by adding or removing electrons or
by breaking chemical bonds. If single crystals are irradi—
ated well below their melting points the radicals may be
trapped in the crystal and may be partially or completely
oriented.

The molecular and electronic structures of the radicals
are determined from ESR studies. If the odd electron inter-
acts with nuclei which have magnetic moments hyperfine
structure is observed and usually serves, along with the
measured 9 values, to identify the radical. If the radi-
cal is oriented the hyperfine Splitting constant for each
nucleus, as well as the 9 factor, are second—rank tensors
whose elements are determined by obtaining ESR Spectra'for
various orientations of the magnetic field with respect to
the crystal (or radical) axes. The hyperfine splitting
tensors thus obtained have both an isotropic part and an
anisotropic part; the former is related to the odd electron
density in s. orbitals and the latter to the odd electron

density in p orbitals.

 

The ESR S
:zed by giving:I
sglitting tens
:: by giving 5
itisctrcpic p:

::e equations

 

 

 

 

13(.

E
\:E’\n+
\:¥
5 w
.. 1th
21* b
“4 Y
‘Jdro
“~ \
‘s '5-
’ Qt
:.‘ ‘Q'

2
The ESR spectra of the radicals may then be character—

ized by giving the principal components of the hyperfine

splitting tensor for each nuclear Interaction Axx’ Ayy' Azz
or by giving separately the isotropic portion Aiso and the
an1sotrop1c portion Bxx’ Byy’ 322. These are related by
the equations

BXX + Byy + Bzz = 0

+ + =
1/3(Axx Ayy Azz) Aiso
Axx = Bxx + Aiso
A =B +A

yy yy iso

Azz ' Bzz +Aiso .

The relative signs of the principal components of the A
tensor are found experimentally but the absolute Signs are
not usually obtained. The principal components of the g
tensor (gxx' gyy' 922) are also found from the Spectra.

The most common type of radical from irradiated organic
compounds is of the type 'CRR'R" or 'NRR'R" where the bonds
to the three groups R, R', R" lie approximately in a plane
and the odd electron is largely in a p orbital directed
perpendicular to the radical plane; such radicals are
commonly called w-electron radicals.

*In typical w—-electron radicals the odd electron may
interact with the nucleus of the atom on which it is centered
and with hydrogen (or other) atoms on adjacent carbon (or

nitrogen, etc.) atoms (a-hydrogens) or on carbon atoms more

distantly removed (5, y-hydrogens, etc.). The convention

 

fcr designati:

Irradiatt
radical 'R
13.6 Sig-bu tvl

23?. studies ha

 

 

 

 

 

:izeth'dacetai
Few S tud l
irradiated sa‘

'.0
a. .
A Q
‘

"whce. hyd.
ii'lrazimum (3
6.3345 and t“

:I‘:-S:al ESR s

3
for designating these is illustrated by the radical
R

>C-CH3 -CH2 -CH3 .
H B y 6

a

Irradiated amides RCONH2 usually give the trapped
radical 'R ; it would be of interest to know whether
the gggfbutyl and Efbutyl radicals are planar or not, hence
ESR studies have been made of irradiated segfbutyramide and
trimethylacetamide.

Few studies.have been made of the radicals produced in
irradiated salts such as acetamidine hydrochloride or the
hydrazinium halides.) Single crystals of acetamidine hydro—
chloride, hydrazinium dichloride, hydrazinium dibromide and
hydrazinium difluoride have therefore been irradiated with

y-rays and the radicals produced identified from single

crystal ESR studies.

 

 

I. Pr:th 3:;
N

There are
:5 3:?511ic rad

351 matrices.

 

HISTORICAL BACKGROUND
I. Proton Splittings in v-Electron Radicals

There are now available ESR data for a large number
of organic radicals which have been studied in single crys-
tal matrices. It is found that the hyperfine splitting
tensors for a protons tend to be similar as do those for
the splittings by the S or‘y protons or by the central
atom. .Data from the literature for each class of inter—

action will be collected and discussed below.

A. a—Proton Hyperfine Splittings

 

Isotropic and anisotropic splittings for the a hydro-
gens of a number of hydrocarbon radicals are listed in
Table I. The list is not complete but is representative of
the results which have been obtained.

-It has been shown theoretically (113) that a Single
F electron induces a Spin density of about -0.05 in the ls
orbital of an a hydrogen atom corresponding to predicted a
splittings in the range —20 gauss :‘Aiso :.-25 gauss. .From
Table I it can be seen that most of the isotropic split-
tings fall in the range predicted by theory with some exe

ceptions. The negative Sign for the isotropic splitting has

been shown to be correct (1).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I . . if ..I.|..|.
(URL—C?“ Ammzfimv 4
MN >% XX Own
0050 mm mm mm 4N .mwnvfi «Wyn .
luwubm UHWJHQCde€ UemOMUOEH a .U HEUNNHU TOUGHUMHRH
may: flddfl naum .nwcflnfiHthx—fl
0 I...- ~ ENFU.‘ Ivfix. niAHndlherviUFUMN~J>.-.~ ah‘ Enhau‘,l,svidloc HIL- N-I.‘ FUR. ‘ N -.Uo..‘\.fia§ aufii‘nviaiii h.

 

 

 

o“ m.m u fi.H+ m.w + m.mfiu moooumwanrouoom mooouomoanIUIQem
o o
mfi.vfi n.oHu v.Hu m.mH+ H.mmn nooouoouzom mooounmouZNm
+ . .
m~.ma “.ma: w.a+ e.oa+ m.mHn moooumwnoem mooouAnmzvmounmouo
H.Ha| H.a+ o.m + m.mfi|
HH m.oHn fi.H+ o.m + m.Sfiu nooonmbnom +eq accounmUuom
o“ m.oHu w.o+ o.oH+ «.man noooumwuom +x nooouomouom
m m.ouu >.o+ m.m + m.omn mooonmwnom mooounmouom
m «.mfiu n.m+ m.oH+ m.omu moooumbuermovuooom mooonvflomovuooom
o.aal v.0: o.HH+ «.mfil . .
n v.HHu H.e+ e.ofi+ o.omu mooonmwueAnmuvuooom mooouoxnmuvuooom
o m.m s fi.n+ m.w + n.mmu moooummunmuaooom moooufinmzvmuuomouooom
m fi.anu v.ou H.aH+ w.HNu «Amooovwm «Amoouvemo
m.o~u v.n+ m.m + m.mmu _
v n.m u H.fl+ m.ofi+ e.Hmu mooosbnm «Amooovamo
m.m v.fifin v.ou n.oH+ v.Hmu moooumbunmouooom moooquomovuooom
mmmsmmv dumsmmg
sum mam xxm omflm -
IHMWMM .i, camouuomflcm camouuomH Hfiofiomm Hmumhno nonmacmhuH

mmcfiuuflamw osfluuwmmm

 

.mamoflUmH sonumoonpmn so mGOAUUMHouGH mcwmnomhn cououmlflo .H magma

 

 

 

 

”mute—Ca - - i .l mm~.~fl.mv
. X Omfl .
mum xxn X m < Hmudfimm Hmumkhb EQQMNUMHAH
0020 II, 01.. OhJCTMde UHAMUHJOWH .

levavflm who—ewnudd

—.

 

 

 

411;; it

mum. 9:6“. HUEX:

 

 

 

a. . nu.:..uv . ~ 6c~.~....~.

 

. Lid-IN IIL h, a
.- . .. . .1
. 5.51.9
.. a. .. .d.

moooqumzvmounmounomom

 

 

mmcfluufiamm wnflmuommm

om o.o~u m.o+ o.m + m.omu mooonmwaomonnomom

mm m.b I m.o+ m.b + $.vHI IOImOIOIUOOI mIUOO mz

«m m.o u ¢.o+ m.o u «.mmu omo. comm.mzoooomo

mm e.oHu H.o+ o.H~+ m.Hmn «mZuonmwuuuzem emanouomonouzum

o o o 0

mm s.m u n.mu m.m + m.mHn mooonmbimZuouzom mooouemuumZuouznm
o 0

Ha n.m u o.Hu o.w + m.sns mooonmwnonnmouooom mooounmououomonooom

om m.fifiu w.on S.HH+ m.nfin +M nooonmwnouomo +M nooouomououomo

oe o.He- om e.HH+ o.mm- new-ouemz nemuuouemz
o 0

ma m.ofln >.Nu o.mH+ m.fiuu omoumwuooom mooonmouomo

ea o.ma1 m.wn m.ma+ o.mmu «manonmvunmouomo nmzuonnAomovnomo

o o
be H.fiHu m.au o.mH+ o.mmu «eroumwuomo «mauouemouomo
. o o
Ammdmmg Ammsmmv
.... NNm. mwm xxm omH<
IHMWMM camouuomwcd camouuomH Hmofiomm Hmummuo pmuMflpmnuH

 

A.ucoov .H manna

 

@Ume
IHQW m.“

,NN

. $31.2-..»
Q %% X rmeH
x .
2 mm Q <
Umnfinoudomfleed. UflnHOHUCmuH
flmeflUJ -w #5me mvCflH HQQN:

 

 

Hmoetmm

 

 

444/

H MU moanU Um!“ MUHUMHHH

A\ I JRQRUHJUU

 

I,“

‘ ‘6 V 1‘04...

d

.

 

 

mm m.m a m.H+ m.e + m.oea -ooA+omzvemwumonmuomo moouumounfiomovnmuomo
., new .
Hm m.HHn m.H+ v.oH+ o.omn uoooumwuomoquomovuzom o«m«.moooumouvflomuvuznm
m
nHo+ us
on >.oeu e.o+ m.oH+ m.omn mooouumoumwnooom moooumoum0nooom
mm ~.m u o.nu m.oH+ m.mHu neomoumwnomo +x unencumonmo
mm m.flfiu N.fi+ m.oH+ m.omu «mZnonmwuomUIUIZom «mzronnAumovuwsz«m
o o o o
«.mfiu n.o+ H.~H+ m.fimu .
so v.eeu n.e+ H.oe+ o.eu- -oooemo. oemn.exoooemoven
5N osmonuomH o.fiHo.mNI «mu. CumN.«AooonmchN
Ammdmmv Ammsmmv
Mum .wmm- xxm. owed
UHMWMM camouuomflcd camouuomH Hmoflpmm Hmummuu cmumwcmuHH

mmGAHUflHmm ocflmnommm

 

A.ucoov .H manna

 

 

 

 

Q

>xnm~

xx

 

 

Ufinwnuhdomfiltw

manor—fl #8 .H film arnflHlexw:

mu

 

 

 

 

 

 

 

 

:2

th—-Ht\
O a.
m..<

UdeNCHJOMH

«:2

adoenmm

 

 

 

 

 

 

 

N m5 mkhb mom.“ m HUEHMH

 

 

.14

 

 

 

a. . unfdhvv - ~ .o~.~...~.

e.een e.e+ o.o + n.em-
on e.oen m.e+ w.o + m.em- «mauwuomb

m0
.
Oflml 0m
-
m 0

o I o
\\x. .1// \m
an m.flfin m.ou s.fifi+ o.nfis ouw m m .w
mum\z/ouo muouom
o be m

 

 

 

. i . IIQA“
Ammsmmv Ammsmmv.4 « . :9
, NNm mam .xxm Omwfl NZ
mono camoquchd OflQoHuomH HMUflUMm

lemmm , .-.mmCHuuflHmm mcflwuwmmm

Hmummno ooumflpmuuH

A.ucoov .H.manma

The anis

 

‘n

n: an a-prc:

5ch .B.

For

 

TI)

32? flat the

”fin“

“Well (2) \

 

ientauy in
11‘ that the

EXPIQSSiQn

mat-ins ti:
tame“ the
35:20“ 3nd

:‘Aa‘ s '
~“ with
O

.
‘

.F
a‘J‘V

{W‘Etica

9
The anistropic splitting tensor has been calculated
for an a-proton and the values +14, -2.9 and.—15 G obtained
for ‘Bxx’ Byy' B22 (170). <The observed values (Table I)

are in fair agreement with the theoretical prediction.
B. B~Proton:§yperfineSplittings

For 5 and y protons it has been shown by McConnell
'(2) that the splittings should be nearly isotropic. Mc—
Connell (2) was the first to observe B~splittings experi-
mentally in irradiated succinic acid. It was found empirical-
ly that the isotr0pic splittings could be described by an

expression

A = Bo + Bacos2 9

B
relating the isotropic S splitting to 9, the dihedral angle

between the axis of the odd electron W orbital on the a
carbon and the plane containing the.NH or CH bond in the B
position. -This expression is discussed further in the
theoretical section. Because of the dependence on 6, the
Splittings observed experimentally for B protons can be
quite different from one radical to the next as can be seen
from Table II. It should be noted that the anisotropy is
either very small or was not detected.

(For a radical with two B protons, it is necessary to
calculate two angles, 61 and 92, with an angle 6 for each
proton. . ~The relationship of Bo and B2 to the observed
Splittings is given in the theoretical section in Equation 59.

The relationships above for 9 are valid assuming that the B

carbon is sp3 hybridized.

 

 

 

 

\ ».um2mdu
. %% XX Omd
.00me NM: 2 m .4‘): 604 n.
|Hmwnu0~m anuChdcmmCxN UmLCHJCNH H .3.“ HNUQNHU MVQUMUHMUNHHH.

ETC. I. . Hnuvfl «VCHM 7.3%:

 

 

 

I :5. Hflyhu flnvlih F-fiVnahuUfiu,h-v\fl.n~ nu ‘ auvan - a .9 i Nani! 55.. u G utiv.~\h- .~nv u..- -...~ . .x . h I .3 ~ .w-...~

 

10

m.ޢ

 

 

m onomeomH m.vm moooaemoumwuooom mooounmoumonooom
uao+omz
we uHmomsomH “.mmum.mm mooonmwuomo mooonmounmo
mm onomaomH o.m muAmovmonmqumovmonm anAmOVmouAmovmouAmovmoum
\onm \oom
um m.ou o.ou m.H+ v.mm mooonv/ ‘ mooono/ ,
oom and com
o.m
om onomaomH H.5m .
w.mv moooumwuomo mooouAamzvmounmo
he oHdomaomH o.mmuo.Hm «azioumwuomo «mauounmUIomo
o o
\oem .\oom
he m.ou H.on o.fi+ e.fim «mauouw/ «manoumo/ .
.. 0 mm .. U mm
o o
H.eu H.e- H.m+ o.em mo .
/
mm o.mu m.on m.m+ o.m \ounmouemouooom mooouofinmovnooom
o
Ammsmmu Ammsmmv
mono NNm mam xxm owesN m
luomom l.oflmoHuomflc¢ owmoHuomH HMUHUMM Hmum H0 pounaflmuuH

mmcqumHmm ocMWuomam

 

11111

enamowwww Gonwmuouvmz GA mmGHUUHHmm mcwmummhn cououmlu

.HH magma

 

meCmv
lHTUMMvm

I|z mu ijifsielvll‘
N N x x
m Q

Uflqnoudom.‘ CAN
whoeiddeeemm

 

 

 

A. mmzr. .o
xx 0min.
Q Q

4

 

UHanHUOmH
QC duh H01}:

 

 

Honest:

 

 

 

 

 

N mu manU memo GHUMHHH

 

 

N I 5....wrbv .1 ‘~ o.I‘.\uv.\.

11

 

 

o.e- o.ou e.H+ v.om emouomo
we :.u I u
“.mn o.o+ m.~+ o.mm moon w ooom mooo mw ooom
omounmo
onomaomH A«moved. moon
. u . u . . .
o a m o m m+ o . m we . on «mo- ooom mooou on «mo: ooom
no w on on m o+ A movm an emo «mu
m m
o. n- w. H+ m. m+ m. S . mm mw
we Aemo sonmv .ounmouooom mooouonnmouooom
o .I o l- o o o p
m H e o m m+ m m omo emu
«mo: «mo- «mo #6: «no: «mo
Ho m.mu v.Hu H.n+ H.wm fl a flu H
«moumwanIU «moanmoumZuo
o o
m.ou m.on n.m+ m.sm .
ow uaommZIeA«movuemoanIUOOn _ .
m.Hu m.o+ m.o+ e.wm commnHOnmzieA«muvuflnmzvmonooom
+
m
on w.fin «.fiu m.m+ o.om moooumonmm-ooom mooonmoumonooom
Ammsmmg Ammsmwv
mono Mum mam xxm omwfl moa mm m ammo o ma MHHH
Inmmom camouuomflcm vamoHuomH H .U H u o u .p

mmcfiuuwamm mcflmuwmmm

 

A.u:oov yHHmHnma

 

 

 

.....4....J\ rmmauflu.mv
MN >% XX Omd
mWUCQ m m mu .AN
lumuwflw UflAHAVHiaomfiah/u‘ UflfladHJomH Hmoflnmm

m7: .e u... walm OCTHHTQAZ

I r

HMO mxflHU UmeflJfiu-WHMH

 

 

 

 

 

 

 

 

 

 

 

 

12

fi.nm

 

 

mm onomaomH .
«.mfi nooflemzvmouomoumwnmnomo moooamouefinmovumumo
1.. NEW
on onomBOmH m.mm mooouomoumbnooom moooumoumUuooom
mm oHdomaomH m.ono.mm unomOImbnomo +Mnoomounmouomo
we m.ou H.ou H.H+ofiemovm.mm nooouAmmzvmoupermuv mooouflnmzvmoumonAemov
mm onomsomH o.vm .
o.fim «mZIUumwuomonouznm «m2nounflomovn012nm
o o o 0
mm oHdomBOmH m an
«.ma mooonmonomouoomom mooouflomzvmounmosuomom
no onomaomH m.m .
v.mH mnemounmouonom «Amuomounmououomv
. . .hmmSMWV .flmmsmmv
OUGO NNfl \Cam Nunm Omflfl 8H. mm m th0 O ma MHHH
summom owmdnuomwcd camouuomH H .U H u o u .0
mmcfluUHHQm ocamummmm I)

 

 

A.u:oov .HH manna

 

 

 

N %% XX. One
QUCO R Q m 4

 

 

HonUEZ Hfismkhb UmufiwfithH

 

.. .CHJCWWCAN . CHJCQH
my: a do .— QOu 0:..enuhnwlcmxaa

I."

lhmwhmawu

 

{4411141441} 4| [4414

41444..
. 4.1 I‘iilflll 1|.“ ‘III 1’ I1"! |.|‘Il | I

 

 

 

14.41141' 4411!}1

 

all, ‘11:.hufifefini... a.“
‘ \..u
If.
I

n—

13

 

«m2

 

 

«we m.ou o.oy o.” v.oo communmoubnnxoav nooonflemzvmonnmuon
no mo .
HmH H.ma m.o m.n o.oH moooubnmonooom moooufimovmoufimovmonooom
no
mo onmnom
cumuom mm m
m o w |||.n//
mum/x \xm mmAm m ox:
OHW\m m .w Ill/O\\\\_
mm onomaomH n.mm w miwnom _ mnwuom
\\ [I s m m z m
mum no o\ /“wu,9
o z a.
\\ o z
/o \ /o\
u -
. . «m2 «m2
Ammsmmu dmmsmwv
mono mum mam xxm owed
luomom UflQOHHOmficfi UHmoHuowH Hmowomm Hmummuo pounaflmuuH

mmcfluuflamm osflmuommm

 

.....

A.ucoov .HH manna

 

723' consider;

sylittings 1
fact, Whiffs
be less tha:
line width.
in aliphatic
trsn irradie
are smaller .

Bailey 6:
Stuplings a:
at the carbc
11:195 for 7

rather Sma l;

 

 

14

C. y-Proton Hyperfine Splittings

For protons further removed than the S position from
the atom on which the unpaired electron is centered, the
splittings become quite small in aliphatic radicals. In
fact, Whiffen (47) postulated that these Splittings would
be less than 1.8 gauss and so would usually be lost in the
line width. However, these small Splittings were detected
in aliphatic radicals by Fessenden and Schuler (48) in elec-
tron irradiated liquid hydrocarbons where the line widths
are smaller. These results are given in Table III.

Béiley and Golding (49) have calculated proton hyperfine
couplings at various positions in aliphatic radical fragments
by considering a second-order expansion of the Spin density
at the carbon nucleus. Using this approach isotropic coup—
lings for y protons were predicted to be only 0.05 gauss,
rather smaller than observed. Agreement was better for a-
and fi-proton splittings; a value of -23.2 gauss was obtained
for a.proton splittings and a value of -1.6 gauss was ob-
tained for B Splittings. The peculiar value obtained for
y splittings was due to a lack of available values for cer-
tain of the exchange intergals used in the calculation.

Recently Underwood and Givens (50) used extended Hfickel

theory to predict the y-splittings in aliphatic semidiones.

Table III.

Irradiated

 

 

33’ (C82 )3'Ci

CH2
/
as, \ C:

\ CHz/

 

 

 

15

Table III. y-Proton hyperfine splittings in hydrocarbon
radicals.

 

 

 

Aiso Refer-
Irradlated Host Radical (gauss)ence
CH3-CH2-CH3 (liquid) CH3-CHz-CH2 0.38 48
CH3-(CH3)3-CH3 (liquid) CH3-CH2-CH-CH2-CH3 0.45-0.50 48
CH3 CH2
z/’ .
CH2 \CH2 (liquid) CH2/ >CH 1 .12 48
CH2 \CH2
CH2— CH2 CH2—— CH2 .
>cn2 (liquid) | >CH o .53 48
CH2— CH2 CH2_' CH2
CH2-—CH2 CH2-—CH2
‘\ . - // ‘\\°
CH2 / CH2 (11qu1d)CH3 CH 0 .71 48

/
\CH2"'—_CH2 \CH2_‘CH2

 

rite treatme:
different c:

These result

 

} splitting
pt ted by F6

ENDCR (
sible to de:
casing incre.
Iteractions

fine normal Bi

 

5e discussed

‘5 35d elem
Her: ..

e oh
“i in lrr

16
The treatment was also tested with propyl radical in which
different conformations and B substitutions were considered.
These results predicted the temperature dependence of the
y splitting for propyl radical within 12% of the values re-
ported by Fessenden and Schuler (48).

ENDOR (Electron Nuclear Double Resonance) makes it pos—
sible to detect small hyperfine splittings and so is be-
coming increasingly useful for studying long-range proton
interactions. The ENDOR technique is quite different from
the normal ESR technique used in this thesis and will not

be discussed further.
D. “N - g Proton §plittings

Protons attached to nitrogen can give hyperfine split-
tings also; the hyperfine components are similar to those
obtained in the case of a protons bound to carbon. When
the odd electron is centered on nitrogen the isotropic com-
ponent for an a proton is slightly greater than 23 gauss,
the value obtained in the case of protons bound to carbon.
Radicals Showing this type of coupling are quite commonly
found in irradiated amino acids and in some irradiated in-
organic compounds. Examples of the magnitude of these coup—
lingsame given in Table IV. The anisotropic components for
a-protons are about the same as in hydrocarbon radicals and
for B or y protons are small. Of particular interest in
this project are N-H couplings in radicals resulting from

irradiated hydrazine compounds.

¢LC¢
IHUWQK

>
mu 2

Ken

  

xx

2

CV...

   

4.

 

UdmnuHJCMw _ C4
MTCHJJ w Ham

DJ wnqavHueva

0: m H Hal}:

 

HMUwUmm

     

u m3: mumvu fiflMVFuHHH

 

'2'“

Al».& Unnjfivfia

 

 

nfinhpvru AVLAH

 

”5.qu

:J-:.. ‘N-hAUVU

Tun-d v “u ‘ We“

hie-1,5 .ei.§\A- l>u m.vs.~|1.~.

17

 

 

. \ , // . wamuv/l
Ho e.m I e.oI m.m + flows.8+ sol/x oo Aemuwmnov emu//. ou
mzx\\ mz\\\
o.w n.ono.oe NV .
vm A V A +mm2llmz. Aamumhuovlao+mmszOUInmz
o.HHI e.uI v.vH+ o.¢dIAHV ‘Amv AHV
N.N I m.nI m.m + m.mN+ .
mm H.N I H.HI v.m + H.mm+ IoooImw. AHmunmuuvInooInmw
. I . I . . a m
m m e o m m + m a + + m2 + as
no m.oHI o.mI v.mH+ ¢.oHI +emo¢ AeonmmuoveOnomomnz
ANV m z Aamummnovz
z
m/ \\ //o\\ fivoIzem /m xnwazum
. a\u,, = _ o.e.. e-
. I .w . + . I . zIm In
3 Ha o om mug w“\n./o\ //zooz\/\
m.» I m.HI n.m + n.8IAHV \ = x m
0 s
AHv+m .I IHo+m
amnsumv Ammsmmv .
nu x» xx one
ooso m m m .4
Iuwmmm owmoHuochm UnmouuomH Hmuwdmm umom pmumwpmunH

mmcfiuuflamm ocwmuommm

.Zvu ou canon msouonm Mom mucmumcoo mcfluuflamm osflmuommm

I>HIOHQMB

 

 

 

 

 

I .
“I. II t h I ZINK HI. 4 .Vll’l'llilllll
mmmjflmv 4mm3nwnwv
xx flvmfi
0050 NNS tail 3 .c. U
IHWUKQNN Nude-n... HIanumwmfiulN UufiaflnJIflUAva Ham. flfivflwx

 

U m0~u~ MUMvU “flNd-rULIHIHHI

 

 

 

mind: _ -dJ .— Flmfl 0n~iINI,~nueuxh-

 

 

 

 

 

 

 

18

 

 

 

one n.m I m.o+ m.m + A>Vm.mI eszoImpIomoIoIzumAHmonmuuvanIoIA«movIoIznm
o o o 0

mm H.m I v.HI o.ofi+ H.NHI manImz Aaoonmuov NszoIszom
o 0

mm m.maI n.H+ m.mH+ n.muI Amomvmz. Aannnmuov oomznmx

so w.o I e.oI H.e + w.amI +em¢IIeom Aeonnmuov +emz IIoon

on o o o m.mm+ +omz. Annunmuov «cavemz

on m.NHI e.oI o.ue+ «.mmI .zrm Aemnumuov eoomeAemzv
+

Ammsmmv Amwdmmu
mono mum mam xxm omw<
Iuomom oflmonuomwcd cammuuomH Hmowomm umom nonmavmnuH

mmsfluuflamm ocflmnwmmm

 

 

A.unovv .>H manna

 

II. “N S:

For i:
{I= 1: are
spectra in
plittings.
fie isotar;.
and the an;
The theore:
lated using
26550 gaus
that only a
tram molecu
61.: functigj‘
Efi this va
ting Cortes;
.3331 is CC:
the: the fr:
5:: “N mOst
3&ita1,

The 14:
firradiCalE

3".
ME

I
‘argest

 

‘12: -

 

19

II. 14N-Splittings

For irradiated crystals where splittings due to 14N
(I = 1) are present, it is possible to analyze the resulting
Spectra in much the same manner as was done for a-proton
splittings. When the odd electron is centered on nitrogen
the isotorpic coupling for 14N is usually about 8-20 gauss
and the anisotropic coupling shows nearly axial symmetry.
The theoretical spin density for was for 14N has been calcu-
lated using Hartree-Fock wavefunctions (60,61) and is equal
to 550 gauss. So if Aiso (14N) < 23 gauss this implies
that only a small amount cfs character exists in the odd elec-
tron molecular orbital. Calculations with Hartree-Fock (60,
61) functions also yield the theoretical 2p Spin density
and this value equals 17.1 gauss. If the anisotropic split—
ting corresponding to the direction parallel to the p or-
bital is compared with the theoretical 2p spin density
then the fractional p character can be measured. Generally
for 14N most of the unpaired spin density is in a 2p
orbital.

The 14N hyperfine splitting tensor Shows axial symmetry
for radicals with the odd electron centered on nitrogen.
The largest principal value of the tensor corresponds to
the direction parallel to the p orbital containing the
odd electron. The smaller values are associated with the
two perpendicular directions and are usually nearly equal

but are of opposite sign to the parallel value. This may

 

be seen if

Since the 2

g 2
"h
(I)
II
o

:rbital the
per: adieu)

The 11
are present)
sale Specie
eq’.‘iva lent l

radicals 0t

 

 

20
be seen if the form of the anisotropic splitting is examined,

Since the anistropic part of A, A = B<(3cos2 6-1)/r3>;

aniso
if 6 = 0 corresponds to the Splitting parallel to the p

orbital then A = 2B; if 9 = 7/2 then A = -B

aniso aniso

perpendicular to the 2p orbital.

The 14N hyperfine couplings for a variety of radicals
are presented in Table V. Listed in Table VI are data for
some species containing two nitrogen nuclei which couple
equivalently to the odd electron. Of special interest are
radicals obtained from hydrazine compounds and the diatomic
Species, N2-, which is similar to the V centers observed

in irradiated alkali halides.
III. 13cpgyperfine splittings

Hyperfine splittings can result from interaction of the
odd electron with 13C (I = 1/2) in a radical and will be ob-
served if there is a high enough concentration of 13C present
relative to 12C, the most abundant naturally occurring iso-
tope. Since 13C is present in only 1.1% natural abundance
it is usually very difficult to detect any ESR signal from
13C in natural abundance. It is usually necessary to sub-
stitute 13C by synthesizing the required compound starting
from Ba13CO3 or some other appropriate available reagent.
The radicals formed are the same but now the carbon nucleus
is capable of giving hyperfine interaction in addition to
that from any attached protons, nitrogen, etc. Hyperfine

interaction with the 13C nucleus of the atom on which the

21

Aamummnov

mm o.mI o.NI o.m+ o.¢+

 

on n.HHI m.oI m.Hm+ m.mH+ Aeounmnov eonZAms

 

 

 

 

 

 

on H.m I n.oI o.m + o.oe+ Aeoummuov eoeoemz
. \omo . \omo
be o.H I m.oI o.“ + A>Vm.fi+ oszoIbl, Aamummuov «szoImUII.
_ m emu m emu
mm e.o H m.ou v.o n onm.mu InooIA+emszmw AenunmuovmooqumuIznm
m _. m
. z Aamummuov . z
\\ 27 x,
n \z/o QIZNm n \z/o\ /oIz«m
an n.o : n.oI o.mH+ o.m+ mox/ m wIm o m~.mIo// m “In
.\ \
z / \ Iz / \
\\ U \\ U
+m .. 1H0+m .-
Ammsmmv Ammsmmv
mono mum ham xxm omfifi .
Iummmm o«mouuom«c¢ oomoHuomH Havapmm umom omumwomHHH
omeflonom magenta II II
IIII'Ii ill-II“

.muoocmu UCHUUHHQm OGHMHOQXS an

.I + 1.1.... I (In. PseutUMLLx lfljjoivullllll

 

 

 

 

mmmdwmwv Nmmdwmv 44
NN %% XX, OWH
@Ucw Q Q E .4
levawNm UHANOHUOWHCAN UflfiNOHu—CWH HNUflmUnm-NN memo: UUUUHUNHHH
ETCddUflHlufl Opuflkhmvlifin

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

22

Hmumauov

 

 

mm w.fi I o.HI m.m + A>vo.m+ «szoImenmUIoIzum oszoINMnmovIoIZNm
o o o o
v "mu V «8
Ho m.fi I m.oI e.fi + Amvm.HI no on Aaounmuov mo 00
.1, x. I/ \\
mz m2
on «.meI o.eI H.om+ o.oH+ .zIm Aemuomuov eonmefiemzv
+ .
Aamummuov
no n.w I s.wI m.efi+ >.HH+ «mamoIMIszomoo uszuIszszomoo
m
we «.mfiI m.HH m.vm+ m.mH + «Infieomvz. Aemunmuov «Aeomvmzns
m
z 2
no m.o I m.oI e.mH+ m.oe+ \\\ xx . \\. //
«molllnmu Annmamv «mvlllumu
em e.meI ¢.oI m.me+ m.oe+ +em¢IIeom xenonmnov +eszeon
Ammsmmv Ammsmmv
ooso Mum mam xxm owed
Inmmmm afimouuomwc< UHmmHuOmH HMUHUMM umom pmumwwmunH

masons mates

 

i

IIIIIII'lIiIII|I\

A.u:ouy .s oNQme

 

 

 

 

 

’ llllll \ mmmfimmV
NN %% XX Omd
0020 a Q m .<
lhwwwm UMQOHUOTeC< UHQOHUCTH HMUMUMK HMO; UUUUHUMHHH
mmCHJUHHQW OCfiuhwlhz

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

N I II.- niA.vle V I > Sui ~ . N .5.

 

 

23

 

NZ

Aamummuov

 

 

. + .. Immo \mmo
mo w.o I v.oI m.H + A>vu.n+ IoooImoIo/d IoooImoImo,M
. emu n . mo
+ m2
.MOI/ moll AmOmmmamv
mo o.oeI o.oHI o.om+ mm+ \erm no .szm eased u m uozIm
o c
on e.e I m.oI o.me+. m.m + meoIemz Aemunmnov eszuIzIom
o o m
..w Annsmmv Annsmmv
mono Mum mam xxm ones
Iuomom camoHuOmfic¢ owmoHSOmH Hmoaomm umom poumfiomuuH

mmcwuuwamm ocwmnommm.

A.uoouv .> menus

I

:

UanOhJCm m :<

 

 

 

I‘ll'l

N. 4

meChucmH

 

Ufi IN Hmwlxfiuk

u we: womb m .HmumwhHH

 

 

 

 

ahAJIN .Id (VFIV H all?

TUCauUMHQm

"Iv-(IVA a

Era}.

ImuEanHw :mnvaquIHUfl-K 03d Ide>nu

3H nU-3 T- n 50 In, ublnL

an

echoenhcni o aunh u .e a a H-nu

Stu. ‘ I... In. .1: N\.h-

Numvvw .m. N Fervfiu ~ are

2'~ I q> HW~A\IH.~.

 

 

 

on o.n I H.oI w.oe+ m.o + Iez “Hounxnov «Anzvmm
oo o.w I m.HI e.oe+ w.me+ Iez Aeoonauov 8282
no o.o I m.vI m.oe+ «.HH+ Iez Aeouoxnov HM oomoo Imo
no n.o I e.¢I n.ee+ H.oe+ Iez Aeounmnovnmx oomoo Imo
no m.n I e.vI o.oe+ w.oH+ Iez Aemnnxuoveox oomoo Imo
_4 no d.m I ¢.mI s.oe+ o.oH+ +emo¢ Aenuumnoveo«omomez
2
II II .8 + NH+ .
no II II .m + ¢H+ +emN¢ Aamonxuov eomomoZeq
o.e I n
o.ve o.on o.en
on e.oI H.NHI mueeI o.oe+ o emmImz. AeounmnovIHo+emzmzooIemz
. o .
Ammsmmv Ammsmwv
. MN x» xx one
mono m m m m
Iuommm UfimoHuomflcd camouuomH annapmm umom pounafimuuH

mmcfluuaamm mswmnommm

.mEoum somouuflc 03» Ho>o pouflamooHop
me souuooam poo ozu mum£3 mamoflpmn CH muomcou meauuflamm ocflmuommn ZvH .H> manna

25
odd electron is centered are Similar to those found for 14N
interactions in radicals with the odd electron centered on
nitrogen.

Hartree-Fock calculations (60,61) have been performed
to calculate the theoretical isotropic hyperfine splitting
for an odd electron in a carbon 2S or 2p orbital. It was
found that the theoretical isotropic Splitting for a 2s elec-
tron was 1190 gauss while that for a 2p electron was 32.5
gauss. It is possible to obtain an estimate of the amount
of s or p character in the odd electron orbital in ex-
actly the same manner as was done for 14N. The amount of 3
character in the case of 13C is small, as it was for 1“N.
The odd electron is therefore primarily localized in the 2p
orbital and so the anisotropic hyperfine tensor should be
axially symmetric. The anisotropic splittings are therefore
equal to + 28 parallel to the p—orbital containing the odd
electron and -B perpendicular to this direction for interac-
tion of the odd electron with the 13C nucleus of the atom on
which it is centered.

Some examples of the magnitudes of 13C hyperfine Split-
tings are given in Table VII. It is obvious that the aniso-
tropic components Show axial symmetry. Where deviations
from cylindrical symmetry occur it is usually a result of
delocalization of some of the spin density from the 13C nuc-

leus to one of the other nuclei in the radical.

3 2.3.00» «:0

 

 

 

 

mmmjmmv dflfiflfimv
0.0me NNQ \nxnm xxm OMfidw
IHQMG“ UHQOHJCTHCK‘ UififlOHUmeH HmwhvfimVnwm HMUWANU muva-WHMVHMHIHH.

mum-hflJJ fidflflm OCH“ Hrfinw>-

 

 

 

 

 

 

 

 

 

 

Inuit-.1 u U! .5411 .3... fi na!.\.fl.§ IIIII I |.t

 

26

 

 

on mcenueamn ensexme unsom w.mm+ moooAmovoneInmoIooom .

. com.moooIAmovmoIomoIUOOIemz
on m.omI H.8eI v.eo+ m.eo+, IenowH Axenooavemo
mu mcwuuflamm Esaflxme mmdmm mw+ mlmmeIUIumz aszUIummu

. m I»-o.
mm a.» I o.m + m.m + H.s + IomoIoIInoo ozoooIm
mm H.6NI m.HNI m.e¢+ m.mm+ mooooeImenmoIooom moooInAnmovIooom
we H.NNI o.omI w.H¢+ m.wm+ nmzoonmowe umzooemo
as o.mmI o.¢HI o.n¢+ Hem+ emwa emzoommo
m.on

«a o.mmI n.mmI .nv+ n.em+ emowe comm.mzoooemu
so o.nNI m.mmI o.ov+ o.nw+ «AIoonvmome «Asoomvemo
me ¢.HNI «.mHI m.mv+ m.m¢+ AInoov+omsze AIoouvnmo+omz
no w.nnI m.m + m.¢m+ m.vo+ Amuoovemowe AIeoovnmU+omz

we.ee o.omI o.eeI m.mo+ m.mn+ «Ameoovmumw. «Ameoovemo

Ammsmmv Ammsmmv I
mono Sum mam .xxm omfN m
Iummom camoqumwcd camouuomH Hmowpmm Hmpm Ho pmuMHUmHHH

- mmsfiuuflamm ocflmuommm

 

 

+

mmcwuuflamm ocflmuomms UmH .HH> manna

QUCW
lhwmmwm

pmmSGCV
NN xx XX
3 m m
U .nnflCHdOmwa/N
mmuCMUUfiHQW MUCHIHH

 

 

 

 

CWWTEEv
omd
.AN
UMQCHUOWH
Onwxnm

 

emoenmm

ill.

HMUMNHU UUUMHUMHHH

 

 

 

27

 

 

 

Io
on m.wHI o.nmI m.no+ n.om+ l/woeImeemu mOOUImmIemo
o omz «m2
on w.oHI o.HHI o.em+ H.eoe+ Ieooee ozooom
QO/ .
he m.omI m.omI m.oo+ e.mHH+ \xoeeIeco Axeuuoev nooOeoo
Ammsmmw Idmmsmmv
- an x» xx 0nd
mono m m m .4 mod mm m mmuo 6 ma MHHH
Iuommm onouuoch< UHmoHuOmH H .U H u p u .U

mmGHuuHHQm osHmnommm

 

A.ncouv .HH> oHnoa

 

I)" W

uradiati

 

centers in the
he to an elec
center may be
new centers (V
in the otherwi
Ir. a later Pal:
'I’ centers in 8
wish the radic
seen to be nor
:her. be shared
Since the
ire hyperfine

nuclear 3 pin 0

nnnnn

28

IV. V Centers

Irradiation of alkali halides produces paramagnetic
centers in these materials. Besides the F center, which is
due to an electron trapped near an alkali vacancy,another
center may be formed. Kanzig (80) was first to detect these
new centers (V centers) and attributed them to holes trapped
in the otherwise filled electron Shells of the halogen ions.
In a later paper (81) Castner and Kanzig investigated these
V centers in some detail and were able to identify them
with the radicals F2-. C12“, and Br2—. The diatomic species
seem to be more stable Since the electron deficiency can
then be shared with a neighboring halide ion.

Since the electron is shared equally by both nuclei
the hyperfine splitting pattern will depend on the total
nuclear spin of the diatomic Species. This means I = 1,3,3
and 5 for F2-, C12-, Br2-, and Iz-, respectively. Another
complication to the hyperfine splitting arises from the
presence of more than one naturally occurring isotope for
C1 and Br. Chlorine has two isotOpeS, 35C1 in 75.4% abundance
and 37C1 in 24.6% abundance. Bromine has two isotopes, 79Br
:nn 50.6% abundance and 81Br in 49.4% abundance.

A problem also arises in evaluating components of the
«g tensor. The principal g values are quite different
from the free spin value 9 = 2.0023 primarily as a result
of spin—orbit coupling. An explanation is given in

Slitflrter's book (82) where it is Shown that the g anisotropy

I\
“I 3 v. Vuvgf‘

 

is primarily
: ground st
9
c principa
'i'Y
I a E
922 ll'lCh mg
The alka
should Show a
354 the g \

gzz=gH a!

1103 of Table

three differI
gli’Cine hYdI
21‘s are non

aa‘

["2 in iIra
EEN- -

" 1“ the
..;eIQXylamin

‘L‘ s
Tue dla

29
is primarily due to a mixing of a fig excited state with the

cg ground state. The net effect is to change the and

gxx

g principal values from the free-spin value and to leave

YY
unchanged.

922

The alkali halides are all cubic in structure and so
should show axial symmetry in both the hyperfine splitting
and the g values. This means that gxx = gyy =JEi-'
gzz = 9|] and AXX = Ayy = 1., A22 = All. From an examina-
tion of Table VIII it can be seen that this is indeed the
case. When the internal symmetry is not as high as cubic,
as in the case of irradiated glycine hydrochloride (86) and
hydroxylamine hydrochloride (85), it is possible to get
three different principal values for either 9 or A. Both
glycine hydrochloride and hydroxylamine hydrochloride crys-
tals are monoclinic. The greater g and A anisotropies
are expected since the environment about the bond axis of
C12— in irradiated KCl is more symmetrical than the environ-
ment in the case of irradiated glycine hydrochloride or
hydroxylamine hydrochloride.

The diatomic V center Iz- was detected later than the
other V centers. Boesman and Schoemaker (87) first found it
in irradiated KCl doped with.KI. This species has also
recently been detected in irradiated PH4I single crystalK88).

In addition to the V centers formed from two identical
halogen nuclei there have also been cases where hetero-

nuclear V centers have been detected. These include FCl'

(89,90), FBr_(90), PI” (90), and ICl' (91). The analysis

 

 

 

 

 

 

III NucmXMU
UUCU mQMHm> Ammsmmv m®3H0> HQQHUCHMQ «@QOHOTHV DOOM
. UCHUUHHQM QCHWHQQ I NMUHUEK _u
IHQWQK HmwaflflUCflHnu . . lwmorImIIefi.
I .1,- sIv --.I-ndIIJ \I in»! Boned.- H.!.\) u; caused 91 ~.-:dvt.~.a.s ~...- . e . ~.~.I .I.. . . ..I.~.;.. -

 

 

30

NN
omo.HI m

 

 

 

x» xx a» x
on HwH.NI I m Hon aux m Hmwuunm AHwJHwVIsum nmemz
Nun
mm smoo.mu u m can «Ixxd o.souuu4 AnmInvanHo Hoemz
ooo.Hquo
a»
osH.mu m a»
so osH.muxxm own swans nnvuuud AHmIHmVIeum ems
oHoo.muuum
a»
havo.mu m a»
un
Hm omeo.mux m on uxx< mousse AomInnvIsHo Hooz
oeoo.muuum
mm
swvo.mu m as .
xx xx N
Hm mmvo.mu m on I a Hoeun a AnnIonvIsHo Hos
Hmoo.muuuo
a»
ammo.mu o a»
Non Nun NN
Ho smao.mu m on" «I a soon 4 AoHIoHVIem med
ovum .noMHm> Amwsmmv mmsHm> HmmHosHHm AoQOHOmHv Hmumwww
Inomom HmmHocHum mcHuuHHmm ochnmmam IHnoHpmm IHomHHH
.muoucoo > How mmSHm> m can mucmumcoo mcHuuHHmm ochnommm .HHH> mHnt

nnvo.NIIoc H.wnIII<

 

0 II. N I 0 III N N.
no bnno NIs o n N7. d. «nnInmCI «H0 HUEOnIZ
QUCmv WMVMHflx/ AmmuSMMUv DQSHMV> HWQ..~.UC..~.IHAW «.mnwOUOQHC Nmu 54>}th
lHUlHImHW— 451mm .nCiCLIImnu .{14II . WT—nfldnw fidnwuw 92.1% IA.3M..N.\'.W~ H ewIUIHIUP...“ l ehhenvww

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I;

31

 

 

NN NN
mm moo.oflmomwuu m fifimwmu ¢
moo.ofimfio.au uxxm oHHmwu uxxm Amflumfivuum ammo
NN NN
vmomwuu m v.womu a
mm omfio.mu uxxm Amfiumfivuum mam
NN NN
omomwmu m o.mmmu «
xx
mm vfimo.mu u m o.omn ¢wxx¢ Amfiumavuam mg
NN
«Homw u m H.»mmnnu«
van
mm ommow u,. u m o.uwu uxx< Amfiumflvuam mmz
NN
Hoo.ofifiomwfiu m «.ofim.mmmuuua
van
mm Ho.ofimu.mu u m o.mfifio.muu uxx< Aumfi-umfivuaH vam
NN
mo¢mm>< o.mmvu <
um «mm.fiu m o.oHHu uxx< Aumfiuhmflvuua quaux
umo.munmm m.¢uunm¢
_omo.muuum n.m¢uaa« «
om .mmm.fiuafim u.oHHuHH< Ammunmvnuau moon- mw
uHo+ «m2
mmmm.Hunmm m.moflnnm<
mmwo.~u««m fi.mmu««<
mm umno.mufiam H.~HuHH¢ Ammunmvuaau Homemmz
mocm mmmHm> Nmmnmmv mmsHm> Hmmflocflnm AmmouomHv Hmuwwmw
lummmm Hmmflocfinm ....,\mmcwuuwamm mcflmummmm afloavmm vamHHH

 

 

A.pcouv

.HHH> magma

 

 

of these hete
pcle interac
his type

::t be treat
Y. Free Ate

In some
ated materia
1:: critente
55 a result
Table 1x gix
ferent atoms
339 Some re:
irradiated s
2235 agree
ally in the

It has

t 1'
0A-;

Gatdne:

.r
(.3

32
of these heteronuclear V centers is complicated due to quadru-
pole interactions and second-order effects. Since none of
this type of center was detected in this work, they will

not be treated further.
V. Free Atom Hyperfine Splittings and 9 Values

In some cases free atoms have been detected in irradi-
ated materials. Since these are small particles and are
not oritented, they exhibit essentially isotropic splittings
as a result of their random distribution in the matrix.
Table IX gives a summary of the ESR data obtained for dif-
ferent atoms in various matrices. Also included in Table IX
are some results for free atoms which have been detected in
irradiated single crystals. The observed hyperfine split-
tings agree quite well with theoretical predictions especi-
ally in the case of hydrogen atoms where Aiso = 508 gauss.
It has not been possible (94) to detect halogen atoms
in irradiated crystals or matrices by ESR. A recent article
by Gardner (102) which reported Cl' has been shown (103)
to be in error; the radical is Cla- with the outermost lines
of low intensity. The reason for the failure to observe
Cl- is that the interaction between the matrix field and
the orbital angular momentum produces a large enough magnetic
anisotropy to broaden the resonance lines beyond recognition
(94). However, these fragments have been observed in the

gas phase by Vanderkooi and McKenzie (104) and the results

are included in Table IX.

33

 

 

 

Table Ix. Free atom hyperfine splittings and g values.
Hyperfine
Irradiated Host Radical :?11E3;338) 9 2:22:-
lso

CH4 (solid) H’ 504.0 + 0.01 2.0021 94
NH3 (solid) H° 508.9 95
H2 (solid) H' 506.1 i 0.01 2.0023 {94.96
CaFg (crystal) H' 522.9 2.0023 97
HClO4 (solid) H' 502.5 2.0022 98
H2804 (solid) H‘ 505.6 2.0024 98
H3904 (solid) H' 508.3 2.0024 98
NzH4'HCl (crystal) H' 510.0 99
02 (solid) D‘ 77.7 g 0.01 2.0023 94
CD4 (liquid) D' 77.5 2.0022 48
CaF2 (solid) 0- 80.3 a 0.01 2.0025 97
N2 (solid) N’ 4.3 2.0020 100
H2 (solid) N' 4.1 2.0020 100
NH3 (solid) N' 4.0 2.0020 95
02 (gas) 0' Single line 1.5009 101
F2 (gas) F' 1.3333 104
Bra (gas) Br' 1.3333 104
C12 (gas) Cl 1.3333 104

 

THEORETICAL
I. Basic Theory of Electron Spianesonance

A. Classical Treatment

In electron spin resonance (ESR) spectroscopy, as in
other types of spectroscopy, the spectra obtained are related
to the allowed transitions between energy states. These
transitions follow certain selection rules to be mentioned
later. -ESR is concerned with interactions between free or
unpaired electrons and magnetic fields which may be internal

or external in nature. The type of interaction is expressed

in Equation (1)

——> >
E — -uJ °H (1)

where I; is the magnetic moment of the jth electron, E)

is the magnetic field, and E is the resultant interaction
energy.

The basic ESR experiment is concerned with interactions
of electron magnetic moments with magnetic fields arising,
from two sources. In one case a large external magnetic
field is applied resulting in a coupling known as the Zeeman
coupling. The other coupling results from the fact that the
nuclei are spinning charged masses and as such generate their

34

a .

 

 

on magnetic

where E; i
with magneti
is being mea
and Vis th

35 interacti.

31PC1€ inter.-

”mere ED is
The tOta

and can be de

I
I".

35
own magnetic field of the form given in Equation (2)

E; = -V x [3; x (‘11?)] (2)

‘where ‘2; is the magnetic field created by the Ith nucleus
‘with magnetic moment E; , r is the distance at which E;
is being measured relative to the position of the nucleus
and Vis the familiar gradient operator. The second type
cof interaction called the hyperfine interaction, or dipole-
<iipo1e interaction, has the form given in Equation (3)

—> '—>
ED - -uJ {HI (3)

\Mhere ED is the dipolar energy.

The total interaction energy is the sum of the energy
contribution of the Zeeman type and the dipolar interaction

and.can be denoted by Equation (4)

—> -> ->
ET _ -uJ (Hext + i HI) (4)

>

V9 e ‘w
her no Hext
—>

Eis defined above. Notice that this field, i-e. HI , is

is the external magnetic field and E; is

Summedrover all nuclei I.

B. -§lectron DipoleeNuclear Qipole (Hyperfine)g;nter-

actions

Some further rearrangements need to be made in the ex—
pression for the hyperfine interaction. The spin magnetic
moment of an electron is defined by Equation (5)

E5 = -g B S; (5)

 

where g is
texts (105).

associated wi

 

ngslar momen1
lament arisinc
disregarded .

in a similar 1
mlear g fact

is the spin v

At this
5:3“ for the

*3?

“ It is fist

idion (8 .

' how

36
where g is the spectroscopic g factor defined in several
texts (105), B is the Bohr magneton and S3 is the vector
associated with the direction and magnitude of the spin
angular momentum. For the present the contribution to the
moment arising from orbital angular momentum 39 ‘will be
disregarded. The nuclear magnetic moment 'U> can be defined

I

in a similar manner (Equation 6) where and 5N are now the

9N
mxfleer 9 factor and nuclear magneton,respectively.and 1*

is the spin vector associated with the nucleus of interest:

> _>

At this point it is convenient to rearrange the expres—
sion for the magnetic field created by the nuclei to the

forms given in Equations (7) and (8)

0
—§ ii; [(707%) - W

+r(v-1- - u; - (E;-v>(v%)i (7)

is?

- i“ [fiva % - (a; -V)(V%)1 (a)

nun» it is necessary to examine Equation (8) to consider what
happens as r -—+> 0 and r 75 0. It is found that for r 75 0

Equation (8) adequately describes the interaction. For

 

r > 0, however, the following expressions are obtained

 

[-

‘Jhere 5 a
The to

DECWO part

m
H
(A! m

37

5.: =22. 5’5““ 'V><V”i - “IV“ '3'] ‘9’
a _ z[§1fi;é (;>) — 4m E; <5 (E’H (10)
= g1 in; as (‘r") (11)

where 0 (I?) is the Dirac delta function.

The total hyperfine energy, E is therefore composed

DI
of 'twvo parts and can be written

—> 2 _ ->.— -> ->
El LLJ r 3(0J r )I'(LL )
IS

(12)
If the expressions for the spin magnetic moments given
in liczuations (5) and (6) are substituted in Equation (12)

thEBI). one obtains the relation

-87T —> —>
ED - §-gNBNgbé(r> ) 2 II SJ

—> —> —> —> —> ->
S 'I 3(S ' r )(I ' r )
J I J I
-g B 96 Z - (13)

 

 

1* “Kare convenient rearrangement can be made resulting in

Equations (14) and (15):

 

 

- 8m —- —- -—
En ‘ 33— QNBN955(I >) Z I; '53 (14)
‘ I
T _ r' ‘
(r3-3x2)/r5 -3xy/r5 -3xz/r5 IXI
- 5 2- 2 5 _ 5 =
~gNBNgB 2(SxJ SYJ'SZJ) 3xy/r (r 3y )/r 3yz/r IYI
_ 5 _ 5 2- 2 5
_. 3xz/r 3yz/r (r 32 »EJL?Z£.

 

 

 

where A is
titer thing t
3 x 3 matrix

:‘ten be writ

where the fj
55% been if
element of 1

The sis
15 that the
iliependent
.:0 ' and
LEE dipolar

u.‘ '

4i ‘

38

00

__ —> —>.—>_ —>.=_->
- 3 QNBN955(r ) E II >SJ QNBNQB i SJ A II (15)

where A is the matrix defined by Equation (14). One fur-
ther thing to note at this point is that the trace of the
3 x.3 matrix is zero. The total dipolar interaction can

then be written in the following simplified form

= _>
= O | .

(16)
where the first term and the constants g, gN, B and 5N
have been included in i as constants multiplying each
element of the matrix.

The significance of the separation in Equations 9-12
is that the term containing the Dirac delta function is
independent of direction, i4g; it vanishes except where
.r = 0 , and is referred to as the isotropic contribution to
the dipolar coupling, whereas the second term is dependent
on direction and is referred to as the anisotropic contri-
Tbution. It is possible to separate the two contributions
if the matrix i' can be determined. «All that needs to be
(done is to take 1/3 the trace of i', as in Equation (17),
to obtain the isotropic contribution .

T i'
A. = R3 (17)

 

!rhe anisotropic terms are naturally the terms remaining
after the isotropic contribution has been abstracted. i'
\flill be referred to as the hyperfine splitting matrix in

this thesis.

 

C. Fl

Effect
fields are
the system
theory. F0
first-order
interaction
Standpoint

I

Equation ( 1

is.

C

E
PQIt

it: an d

39

C. First-Order Quantum Mechanical Perturbation Theory

.Effects arising from electrons interacting with magnetic
fields are considered perturbations of the total energy of
the system and these effects can be treated by perturbation
theory. For most cases to be dealt with in this thesis
first-order perturbation theory is adequate to describe the
interactions. The total energy of the system from the
standpoint of first—order theory can be expressed by

Equation (18)

E = E + <YIH3 I‘D (18)

total unperturbed

where Y is the unperturbed ground-state wave function for
I

the system and H is the perturbing Hamiltonian operator.

The brackets denote that a matrix element needs to be evalu—

ated to obtain the perturbation energy.

I
In the case of ESR,)* is the Hamiltonian operator which
may be obtained from Equation (4). It can now be re-expres-

sed as
H'=ga§;..§> +2.23%?» (19)
I

The perturbation energy is therefore given by
spat = 96 <W 15: - “£2.00 + Ems; 5' -‘I';Iw><2o>
‘ I .

In the case of first-order theory it is usually assumed

that S3 and ii: are quantized along the direction of

_9. and if we define this temporarily as the z direction,

Hext

 

such that

The seiect'l'
ticns betwe
'11 3 0. Ti
Lateracting

corre5pondi‘

40

_> I
such that Hext — Hoz, then we obtain

Epert = 96 Ho mS + Z A m m (21)

I 22 s I

The selection rules for first-order theory allow for transi-
tions between energy levels to occur only for Ams = i 1,

AmI = 0. Therefore for the simple case of one electron
interacting with one proton (I = 1/2) the energy level scheme

corresponding to the allowed transitions is given in Figure 1.

 

 

 

 

m -l' m =1
//__7T__—'I-2' s 2
j \ 1 1
// =5 mI=_2-' ms=2
_9@H0 I
\
\\ -—J——m =-l ma’l
\ / I 2 s 2
m1 2’ s- 2

 

 

Figure 1. ~ESR energy level diagram for a single electron
and single nucleus.

For the case of more than one nucleus coupling with
time electron the scheme would naturally be more complicated.
Also, more transitions would be allowed for nuclei having
I > 1/2 since ‘mI can assume all values I Z.mI.: -I.

If the hyperfine interaction contribution to the per-
turbation energy is examined it can be easily seen that it
would be possible to determine completely the components

Of 45' in a principal-axis system using only first-order

 

 

theory. I!

tion is of

W if the
cmsidered
ternal fiel
then it wow;
amply by a
5irection c

ccmE’Gnen ts

I

In San
it‘d the Crt

‘-‘
m; V ,
.e.acthn

tt‘Q‘EQ"
\‘ ele
‘e «not
A
VI

41
theory. In a principal—axis system the hyperfine interac-
tion is of the type

E= 2011 §>-'1=\' -?r'>|\r>
I, I. I

= i <WHSxJAxxIxI + SyJAnyyI + SzJAzzIzIHY> ‘22)

Now if the spins of both the nuclei and the electron are
considered to be quantized along the direction of the ex-
— ->

ternal field in some arbitrary direction, ngt =-Ho h .

then it would be possible to determine A . A . and A
xx y zz

simply by appropriate alignment of the crystal along the
direction of quantization h§ to give each of the three

com onents A . A , and A
p YY 2

xx 2'

D. Spin-Orbit Coupling

In some cases coupling of the spin angular momentum S
and the orbital angular momentum E) becomes important.
The Classical Hamiltonian which describes this type of

interaction is of the form

>

 

— —> —>
H _ _|s|;;> . 2 31.11;" ”/2 VJ ‘ V11 (23)
_ c J I r3
IJ
*where Z is the charge on nucleus I, E” is the distance

I IJ

ibetween electron J and nucleus I, and V; and IV; are

the vector velocities of electron and nucleus, respectively.

'rhis interaction reduces to the form

‘.
‘- L‘xr-r ‘~..;

 

where the 1

)~ V) ~
t..at I _

where

hrther rec

42

 

 

—> ->
H=-l_e_lu> . Z ZI rIJ (IZPJ) (24)
mc J I r3
. IJ .
where the Born-Oppenheimer approximation has been used so
that ‘9: 3'0 relative to VG. 2A further reduction gives

H=gE—L‘>zv 13’ (25)

 

:mc ”J I IJ
I
where
Z
_ I
VI - - :T (26)
IJ

Further reduction gives the familiar form for the spin-

orbit coupling

_. g§|e| -> . ->
H "'2mc f VI LIJ SJ
- A 2 ii: -§3 (27)
I

The net effect of spin-orbit coupling is to mix in
excited states with the ground state by first-order per—
turbation theory. These modified states are no longer
eigenfunctions of the true spin obtained previously and
the 9 factor becomes significantly different from the
free-spin value, 9 = 2.0023. -An excellent treatment of
this subject is given in Carrington and Mc Lachlan's book
(106) and will not be repeated here.

The reason that spin-orbit coupling is of minor im-

.pcmtance in organic free radicals is that the free electron

 

is usually
If we cons:

oz orbital

A

we

29

and the sp;

8'0.

43
is usually primarily localized in a pz orbital on carbon.
If we consider hydrogen-like wave functions the form of the

pz orbital is

_ 1 3/2 _/
Yap. ‘ 4W. (3,) p e " 2 9 (28>

and the spin-orbit interaction energy is

x<w Z S +1-(L+ ' + — 8+) >
3.0. 2pz|I[LIJz Jz 2‘ IJSJ LIJ J llY2pz

E!
II

. a
= l<i [2 (1h ) s It > (29)
. 2pz I 53 IJ Jz 2pz
= 0 (since sz does not depend on ¢)
z

In cases where spin-orbit coupling is important the
net effect is to change the form of the Hamiltonian so that
the 9 factor becomes a matrix, 3', with properties similar
to i', i;g;_with isotropic and anisotropic components, and

the total Hamiltonian becomes

E. agecond-OIder Perturbatioanheory

When the expressions for allowed transitions were de-

:rived previously it was assumed that the spin vectors, .S>

arui I>, were quantized completely along some arbitrary

 

 

direction l
these vect<
hyperfine i
:he case a:
be directe<
then the C1
theory can:
The t
in the cas.
Thus far tj
ters in wh
'«iiCh A
xx
EEIlVed thc

exzal Symm

44
direction h) of the external field and that components of
these vectors not along h"> were neglected when calculating
hyperfine splitting values. However, in reality this is not
the case and if, for example, the field is considered to
be directed along the z direction such that fi:xt = Ho 2.
then the components Sx’ Sy, IX and Iy in second-order
theory cannot be neglected.

The treatment of second-order effects is complicated
in the case of radicals trapped in irradiated crystals.
Thus far the theory has been successfully applied to sys-
tems in which there is axial symmetry, i;§;_for cases in
which Axx = Ayy = All and A22 = A1: Bleaney (107) has
derived the following Hamiltonian for a system possessing

axial symmetry

H = St'gllesz + gl(HXSX + HySy)] + AylSzIz

+ Ai(SXIX + Sny) - y BN H>- 'i" (:31)
where the term involving H>° I) includes the interaction
of the nuclear spin I) with the external field. The
IHamiltonian in the original paper also includes terms in-
‘volving electron Spin-electron spin interactions and quadru-
‘polar interactions which will be neglected here. By use

<3f the above Hamiltonian it can be seen that the result is

‘to mix in states with different spins that were not allowed

1J1 first-order theory since by definition

 

“lie‘e 8+
:perators

l .
Y

Ultim

Simmetr i c

«s++s_
sx= ———§-—— (32)
s -—s
+ ..
sy= -——-2— (33)

where S+ and S_ are the familiar raising and lowering

operators and similar expressions are obtained for IX and

I 0
Y
Ultimately the expression for the energy in an axially

symmetric system is given in Bleaney's paper (107) by

A1 All +K;'

hv'= gBH + Km + 435i; 2 _J [I(I + 1) - m3]
K

 

 

+ 29530 K deHo

2
A_L All] (21.4-1),“ + ___1._ [ij 2.1.154].
K2 g

x sin2 9 cos2 9 m2 (34)

where K2 2 = A 2 32 9 + A2 2 s'n2 6 a d 9 's the
9 11911‘” 191 1 n 1

angle between the field direction and the direction z cor—
responding to the maximum hyperfine splitting and maximum g
value, 9". The other parameters involved are the measured
value of g for some value 9, the field value 7H0 and
the quantum numbers M, m: M = 1/2 for an electron, and m
is the nuclear spin quantum number.

Other attempts have been made to incorporate second-
<arder effects to account for the discrepancy from first-

<order theory. In an early paper by Breit and.Rabi (108)

 

the exact

35

tings in t
number, 1

defined by

46

the exact energy of an atom in a magnetic field is obtained

as

1
= -AW AW 2m 2 2
W 2(2i+1)i2‘1+i+12x+x) (35)

 

where AW is the separation between the two hyperfine split-
tings in the absence of a field, m is the magnetic quantum
number, i is the nuclear spin and the other terms are

defined by the expressions

x = fix—g) (36)
a ehH =

w 41tmc BH (37)

H " LLoH (38)

Fessenden (109) has treated second—order effects using the
Breit-Rabi equation and expanding the square-root term in

a power series. This treatment was used to obtain more
precise values of the splitting constants for some fluorin-
ated radicals. Maruani (110) has also derived a second-
order expression for use in analyzing the splittings of the
'CF3 radical. The results are applicable to polycrystal-
line spectra. The assumption is made that the spin func-
tions are constructed in the 3' principal—axis system, the
spun Hamiltonian matrix is constructed, evaluated, and third—
and higher-order terms in the secular equation are then

ignored. The end result is the expression

 

where A

andQ a

 

NIH

 

47

2
Ac = v = A0 il%% +-1%5 (39)

where A = (gOB/h) H, H is the magnetic field and a, 0

and Q are defined by the equations

1/2

 

 

 

 

 

 

_ 2 _
gxx LLx
= 40
Q gyy my ( )
u
__ gzz z 4
_ _ 2 1/2
a a a
xx yx zx
0‘ = axy gxxux+ ayy gyyuy + azy gzzu'z (41)
axz ayz azz
2 2 2 '
axx ayx azx 2
1 a
02 = —- a + a + a — -- 42
2 xy yy zy 02 ( )
a a a
L. xz yz zz _
Here the a . are the components of the :' matrix in the

1]
g-axis system, the gii are the principal values of the

3' matrix and the ”i are the direction cosines of H in
the principal-axis system of 3'. The equations are valid

for one nucleus of spin 1/2 only.
11.. Evaluation and Interpretation of Spectral_garameters

.A. Experimental Determination of Hyperfine Splitting

and 9 Values

'rwo methods were used to determine experimentally the

components of the hyperfine splitting matrix, i' , and of

 

the matri
may to ob
external
shelter,
of refere
The matri
matrices

transform

If a
relatin

ind the Sc

we
above .

'0: I.
i‘ th

ue ma t;

48

the matrix 3'. -As was mentioned previously the easiest
way to obtain these Values is by direct alignment of the
external magnetic field along the principal directions.
However, it is usually not possible to do this and a choice
of reference axes in the crystal of interest must be made.
The matrices obtained are therefore not diagonal as are the
matrices containing the principal values but it is easy to
transform them to a principal axis system.

Consider, for example, the hyperfine splitting matrix,

A'. In a non—principal—axis system the matrix will have

the form
.Axx Aiy sz
K' - 'A' ' A' 43
YX AYY yz ( )
Aéx Aéy Aéz

If a measurement is made of the hyperfine splitting
relative to the axis of quantization h (assuming first-
order theory) with Ams =_i 1 and AmI = 0 then the
hyperfine splitting is given by '

a =‘ (K’- A") (44)
and the square of the hyperfine splitting is
(M2 = (m .5) - (i- ~fi>>

=H> -(§-2) ~fi> (45)

The above equation is in a convenient form for evaluation

of the matrix. This may-be seen if it is first assumed

 

that the v
(bx, by, h
and 5 is

the field

plane is d

49
that the vector 39 has associated with it direction cosines
(hx' hy’ hz). :Suppose a rotation is made in the yz plane
and 9 is defined as the angle between the z axis and

the field direction. The square of the splittings in this

plane is defined by

 

 

 

 

(A'2)xx (Anzyxy (A.2)x;' Foo _
(A)2 = (0,sin 9, cos 9) (A'z)yx (A'z)yy (A'z)yz sin 9
_(A'2)zx (A'z)zy (A’2)za _cos GJ

' 2 12 ' :2 2 :2
s1n 9(A )yy+ 251n9 cose(A )yz+ cos 9(A )zz (46)

Rotations in the other two planes, $42; xz and xy, will
give similar expressions.

The experimental procedure for determining either 3'
or 3' in a non-principal axis system is simply to choose
an arbitrary mutually orthogonal set of axes and measure

the square of the hyperfine splitting, (A)2, or the square

of the 9 factor, (g)% as a function of 9 , the angle

between the field direction, fi2xt’ and the axes chosen.

:By choosing three mutually orthogonal planes of rotation

all the elements of the matrices may be evaluated. 'Now it
can be seen that the above matrices are real, symmetric and
that the matrices are therefore Hermitian (Equation 14).

It is possible to diagonalize a Hermitian matrix by a
luuitary'transformation with the resulting matrix containing
only'ciiagonal elements which are the eigenvalues. Therefore,

in Equation 47 the transformation matrix 3 is the matrix

 

of eigenve

reference

the diagor

 

"inland 1
.S methoc
(
\

its»
‘6 Q, r:

50
of eigenvectors relating the arbitrarily chosen orthogonal
reference axes to the principal axes and the elements of

the diagonal matrix are the squares of the principal values

of the 3' matrix:

(Age 0 (1W)xx (2W)my (3'3)xz
(Airy)?! =§-1 (A.2)YX (A")yy (A'2)yz §

(:) (Aéz)2 (Aszyzx (A'2)zy (A'2)zz
' (47)

To obtain the principal values one must take the square root
of each element. One property of this type of transforma-
tion is that the trace of the matrix is preserved so that
there is an absolute guarantee that the anisotropic and
isotropic components of the diagonal matrix are the correct
ones.

The above procedure for obtaining principal values for
3' and i' was generally used in this thesis. If A > 100
gauss in a field Hext 9'3000 gauss then complications arose
ibecause of second—order effects and another method, that of
Schonland.(111), was used to obtain principal values. By

this method Equation (46) can be rewritten in the revised

form
(A)2 = a + B cos 29 + y sin 29 (48)
where or, B, and y are defined by the equations

A: +A:
a = -——ir-—- (49)

 

 

3+ and A_
fine Splitt
the angle f
sPlitting i

Ezuation (4

The e

‘

(It

in“; _
th‘tEd S 1‘;

51

(A2 - A3) cos 29
3= + 2 + (50)

 

(A2 - A3) sin 29
v = + 2 -+ (51)

 

A+ and A_ are respectively the maximum and minimum hyper-
fine splittings measured in a particular plane and 9+ is
the angle from the axis to the position of maximum hyperfine

splitting_in a particular reference plane. The elements of

Equation (46) are related to a. B. and y by the equations

Ayy = a - B (52)
A22 = a + B (53)
Ayz = y (54)
The elements, Aij’ are generated by these equations

and the corresponding ones in the other two planes are ob-
tained similarly and the matrix is then diagonalized by

the usual procedure (see Appendix).

B. Interpretation of Hyperfine Splittings and Their
Signs

1)Isotropic Splittings.

The Hamiltonian which gives rise to the isotropic
cxnrtribution to the hyperfine splitting is derivable from
the classical expression given in Equation (12) which may
be rewritten

8 _. _. ._
H iso = "SE 9N5N935(r>) i1; ' S; (55)

52
The first-order perturbation energy is then simply given by

Eiso = ms iso)» = cmon2 mSmI (56)

where c includes all the constants in the equation above,
2
and |Y(0)| is the spin density at the nucleus, i.e. at

r = 0. The isotropic splitting Ais is then simply given

0
by

Aiso = c]Y(0)]2 (57)

For organic radicals the most important types of iso—
tropic splitting arise from interactions with nuclei a
and e to the carbon atom on which the odd electron is
primarily localized. Because 12C has I = 0 it gives
rise to no splittings but nuclei bonded to the central car—
bon having I > 0 can give splittings. The mechanism by
‘which nuclei in the a position give rise to hyperfine

splitting is known as spin polarization.

 

Efirplre 2. Spin polarization for a hydrogens in m-electron
radicals.

53

As can be seen (Figure 2) the electron in the w orbital
and the one in the 0 bond tend to align in the same direc—
tion resulting in the electron on the proton assuming the
opposite direction. This effect can be explained by molecu—
lar orbital theory as resulting from a mixing of excited states
With the ground state wave function resulting in a small
amount of negative spin polarization at the hydrogen nucleus.

Now the largest spin density on an alpha hydrogen re-
sults if the electron is entirely localized in a ls orbital
on hydrogen. The hyperfine splitting has been measured for
atomic hydrogen (112) and is Aiso 3'506 gauss, in good
agreement with the value computed theoretically (106). From
theoretical arguments it has been shown that a single m
electron on a carbon induces a spin density of about -0.05
(113) in the hydrogen ls orbital, corresponding to a split—
ting from a protons of Aiso 2'-20 to —25 gauss.

For isotropic splittings by the nucleus of the atom on
which the odd electron is centered the isotropic Splitting
takes on more significance than previously. rRemembering
l2

that A.iso a|Y(O) is a direct measure of the amount

, A.

lso
of 5 character in the odd electron molecular orbital.
Two cases which are significant in this work are interac—
tions with 13C, (I = 1/2) and 14N, (I = 1). However, a

2 2

complication arises because now Aiso abl‘l’(0) lls+ cl‘1’(0) [28,
where b and c are the respective weighting terms for

the cxnitributions from the 1s and 23 orbitals for 13c

and 1‘N. For the present it will be assumed that the odd

54
electron contribution to the isotropic splitting on 13C or
2
14N arises primarily from the l‘l’(0)|ZS term. For a Hartree

2s atomic orbital it has been calculated that the isotropic

. . 13 - 13 _
splitting from Y23( C) is Aisozs( C) — 1190 gauss (60,

61), and for 14m, A180 (14u) = 550 gauss (60,61). It is
28

possible to calculate the fractional 5 character by simply
dividing the observed isotropic splitting by the appropriate

calculated Hartree splitting. This is justified recalling

N

that Ytotal = E c. 01, where the ¢i are atomic orbitals,

and if the coefficient of ¢13 is assumed to be zero then

¢ becomes ¢25,and'flr:fractional 3 character for 13C will

K
be given by
Aiso
% (28)(13C) = If??? X 100 (53)

An analogous expression holds for the fractional 5 char-

acter for 14N.
In marked contrast to isotropic splittings from a
hydrogens which are nearly constant, isotropic splittings

from 13C and 1"‘N nuclei on which the odd electron is pri.-

marily localized have a wide range of different values as

seen in.Table X.

.For the case of nuclei further removed than the a,
posijzion it has been shown by McConnell (2) that the total
splithings are largely isotropic. Thus, the B-proton
spljthings are largely isotropic and are usually well de-

scribed by an expression of the form (2)

= 2
AiSO Bo + B2 C03 9 (59)

55

Table X. Representative 13C and 14N isotropic splittings.

 

 

 

 

Radical Aisoggauss) Reference
1@602" 167 78,114
19=CH(c00H)2 33 71,72
lqco3' 11.2 115
155cm, 37.7 24
141611(603") 13.5 58
14fi33+ 19.5 56,116
:1.‘1l1~m+ 16.0 55

(CH3)314fi 27.5 117

 

56
where the values Bo and B; are found by measuring the
splitting for more than one nucleus 6 to the site of the
odd electron. This can be done rather easily if the split-
tings arise from three different hydrogens in a non-rotating
methyl group or NH3 group but must be done by comparative
methods if this is not the case. In one radical,
(C03H)CH2-éH(C02H) (2), observed in irradiated succinic
acid, a comparison with the splittings from (CH3)zéOH radical
was made. The angle 9 in Equation 59 is the angle between
the axis of the orbital containing the odd electron and the
plane containing the B C-H or N-H bond on the adjacent
carbon or nitrogen (Figure 3). The isotropic splittings
for nuclei, even from several protons in a methyl group or
NH3 group,can be very different from one another if rotation
of the group is not free.

In general it is quite difficult to determine the ab-
solute signs of isotropic coupling constants. Recently
Fessenden (118) proposed a method whereby the relative
signs are determined by a detailed analysis of line posi-
tions. This involves an analysis of a system containing
art least two nuclei which give separate isotropic split-
‘tingsw. Fessenden utilized the fact that hyperfine split-
tings are quite sensitive to changes in sign if second-
order effects are included. The measurements were done
mostly on fluorine-containing radicals although it was pos-
sible: to make tentative determinations of the relative

signs cxf a~‘y§_6 protons in isoprOpyl radical. By this

57

 

 

Figure 3. Relationship of nucleus at a Bposition relative
to the odd electron orbital. A °C-CH fragment
is shown looking along the C-C bond with the

dotted line outlining the p” orbital of the odd
electron.

58
method the Hamiltonian matrix is set up and the isotropic
splittings calculated assuming various sign choices and the
effect observed of the choices on the second-order correc-
tions to the hyperfine splittings. AFessenden's calculations
are an extension of the method of Heller (119L'Who used a
similar procedure with a Hamiltonian including second-order
termq,varying one isotropic splitting holding the second
isotropic splitting constant. vThe computed spectra (119)
were then compared with the experimental ones for the sys—
tems R2HC-éHR (substituted ethyl radical), ch-éH-CHR (sub-
stituted allyl radical), and R213éH (substituted methyl.

radical) and the agreement was excellent.
2) Anisotropic Splittings

The energy corresponding to the anisotropic
contribution to the hyperfine coupling can be rewritten
from Equation (14) if the substitutions to transform to

polar coordinates are made as given in Equations 60—62:

x = R sin 9 cos ¢ (60)
y = R sin 6 sin ¢ (61)
z:

r cos 9 (62)

'where 9 is the angle between 2 and the direction 1R

(iJl the reference axis system), and ¢ is the angle from
x tx: the projection of R in the x—y plane. Substituting
these relationships in the matrix of Equation 14 and ex-

panding. the following simplified forms are obtained to

59

first-order:

_ R2 - 3x2
Axx - -969NBN <--——-R5 > (63)
= _ 3:;221
Ayy ngNBN < R5 > (64)
— R_2_:_§Z_2_
Azz - gBQNfiN < R5 > (65)
or Aii = c<3 cos2 9i“ 1)/R3>, where now Bi is the angle

between the principal axis, i, and the direction of R in

the principal-axis system.

It is possible to predict from this relationship the

anisotropic Splitting corresponding to a principal direction

and the relative signs of the various splittings. -If for

the moment the anisotropic splittings are considered to

arise from a hydrogen nucleus (I = 1/2) interacting with

an odd electron localized primarily in a 2p orbital on

carbon the principal directions are defined as 1) parallel

t1) the C-H bond, 2) parallel to the p orbital occupied

by the unpaired electron, and 3) perpendicular to the C-H
lxnud in the plane of the radical, as illustrated in Figure 4.

JNOw'from the above relationship the anisotropic split—

ting ,is proportional to (3 cos2 6 — 1)/R3. In Figures 5a-

5c each plane is divided into regions in which the term

(3 cos2 9 - 1) is positive or negative. This is accom-

plished by setting (1 - 3 cos2 9) = 0 from which is

6O

\
/

 

 

D
I
1.4

Figure 4. Principal directions of the hyperfine splitting
tensor or g tensor for an a proton.

.ucmEmmnm anon m How omumuumsHHfi cououm o no How Homswu msflamsoo
Hmaomflo on» no mmsHm> Hmmwocflnm may no moosuflcmma m>fiumamu cam mamam .m madmflm

// E \\
Q

IJH.ILHA\
\ A
\
\\\ L. III III
\ /

61
g
E

 

d
/
‘5

 

62
obtained 9 = 55°. The values along the principal axis are
determinedhby an examination of Figures 5a-5c.

It is assumed that the principal axis is always pointing
in the positive direction. The largest positive principal
value occurs in Figure 5a so that this direction corresponds
to the largest positive splitting value (along the C-H bond).
The largest negative Splitting value corresponds to Figure So
so that this is the direction perpendicular to the C-H bond
in the plane of the radical. Therefore Figure 5b corre-
sponds to a value intermediate between the other two coupling con-
stants since the restriction still exists that the trace of

the anisotropic splitting matrix, 5, must vanish.
III. Planaritygof Radicals

The 13C hyperfine splitting provides a good indication
of the geometry of a 7r-electron radical. The deviation
from planarity is easily calculated in the case of radicals
with the odd electron centered on carbon if the components
of the 13C tensor can be obtained. Karplus and Fraenkel
(120) considered the case of a carbon atom with sp2
hybridization. In the case of a planar radical the single
unpaired electron is considered to be in a 7r orbital and
all other electrons are paired in sigma atomic orbitals or
bonds . The isotropic 13C splitting has a significant
magnitude only if there is net unpaired spin density at the
nucleus which in turn must arise from some s character in

the odd-electron orbital. For a planar radical the odd

63
electron is in a w-orbital and therefore the isotropic value
would be expected to be small. AHowever, if the radical
is bent the amount of 3 character in the odd-electron
orbital will increase through hybridization. The devia-
tion of the 13C isotropic splitting in a bent radical
:from the 13C isotropic splitting in the case of planar
methyl radical is the basis for determining the extent of
bending of the radical out of the plane. For methyl radi-

cal the isotropic 13C splitting is described by

= 13 = .c C
ac Aiso) C) S +3QCH ,(66)

mfluere Sc is the contribution to the isotropic splitting
at: from 1s character on carbon and equals -12.7 gauss,
arui QC is the contribution from spin polarization by
time hydrogens attached to carbon and is equal to 18.85 gauss.
The theoretical calculation by Karplus and Fraenkel (120)
Yields ac = +43 .8 gauss in good agreement with the ex—
PeriJnental value of 41 i 3 gauss obtained by Cole et al.
(106) .

~2Karplus and Fraenkel (120) have also calculated the
13C: isotropic splitting as a function of 9 , the angle
bet“Ween the direction of the 7r- orbital and one of the CH
bonds in methyl radical, and deduce the following relation-
shis);

ac(9) = ac(0) + 1190 (2 tan2 6) (67)

where ac(0) is the measured isotropic 13C splitting value

for a given 6 and ac(0) is the isotropic value for

64
planar methyl radical. This equation has been applied in a
limited number of cases to determine 9 for substituted
methyl radicals and some of the results are given in Table XI.

Table XI. Deviation from planarity for some substituted
methyl radicals1

 

 

 

Radical (g::ss) 9 Reference
°CH3 41 i 3 .2 5° 121,24
-CF3 271.6 17.80 109
'CHFz 148.8 12.70 109
-CH3F 54.8 -1 5° 109
-CF3 270 17.80 74
-662c00‘ 145 12.50 122
°CF2COO- 73 8° 122
-CF2c00' 69 8° .122
~cr2coo' 70 8° 122
~cc13 90 8° 122
'CFHCONHZ 45 0° 74
°C(CH3)3 47 3.50 +

 

tHere a =‘Aiso (13C) is the isotropic 13C hyperfine
splittifig.

‘+This work.

EXPERIMENTAL
I. Analysis of ESR Data for_;rradiated Single Crystals

There are now numerous references which provide the
necessary background for carrying out ESR studies of ir—
radiated single crystals. An introductory book has been
written by Bersohn and Baird (123) which treats the subject
fairly simply. A more advanced text which has good sec-
tions dealing with organic radicals, and magnetic resonance
in general, has been written by Carrington and McLachlan
(100). Carrington and Mc Lachlan's book also is excellent
for a treatment of some of the experimental aspects in-
volved when studying irradiated single crystals. A recent
book by Ayscough (171) treats the theory and the experi-
mental aspects of ESR. Books which treat the theory of
resonance in some detail have been written by Slichter (82),
Pake (124), and Low (125). ‘

A good reference for the electronic aspects of ESR
spectrometers as well asva short discussion of irradiation
sources and dosages of irradiation is given in a recent
loook by Poole (126). Also useful in this respect are several
\fiarian (127, 128) manuals which accompany the spectrometer

systems. There are also numerous review articles which

65

 

providt

organl

“'1er u
v5).lCa
I

n :

d‘n

trys té

66
provide an introduction to ESR. A very useful review of
organic and inorganic radicals is given by Morton (61).
Whiffen (14) has a good introductory review which includes
a summary of the relevant theory involved.

Although a knowledge of X-ray structure determination
is not absolutely essential for aligning a crystal in the
magnetic field, X—ray methods provide the best way to
align crystals. The techniques involved are well known and
a good treatment of structure analysis is given in a recent
book by Stout and Jensen (129). Chapters 1-5 in this book
should be sufficient to acquaint one with the techniques
involved. A complete analysis is not required, only a
unit cell and space group determination and the location of
crystal axes. Although it is possible to get this informa—
tion from other methods such as optical crystallography,
.X—ray diffraction is by far the best procedure. For an
introduction to the general treatment of space groups and
optical crystallography Phillips'(130) book is very good.
.A more complete discussion of optical crystallography and
the use of a polarizing microscope is given in a book by
‘Hartshorne and Stuart (131). Optical methods are very use-
ful if the structure has already been determined, especially
if the crystallographic data have been reported by Groth

(132) who lists the interfacial angles for a large number

of crystals.

67

II. Spectrometer System

The spectrometer used operated in the X—band frequency
range (9'9.0 GHz) and was manufactured by Varian Associates,
Palo Alto, California. The system (model V-4502—04) con-
sisted of a 12-inch magnet which maintained a magnetic
field approximately equal to 3000 gauss. The field was
modulated with a 100 KHz crystal oscillator to improve the
signal—to-noise ratio. An added circuit permitted switch-
ing from first to second-derivative presentation; the latter
was normally used, since the positions of the lines could
be followed more easily. The signal from the detector was
fed into an oscilloscope or a Hewlett-Packard Model No.7000A XY—
Recorder the x axis of which was driven as a function of
magnetic field. The x axis (corresponding to the magnetic
field) was regulated by a Hall probe device so that linear-
ity was maintained when spectra were recorded.

The magnetic field was measured by means of a proton
Jnarginal oscillator (133). The frequency from this oscil-
lator was measured by a Hewlett-Packard Electronic Counter,
Model 524C. Provision was made so that a frequency mark
could be put on all spectra.

The Klystron frequency was measured with a Ts-148/UP
[1.5. Navy spectrum analyzer. The analyzer was tunable
cover a range from 9.0—9.5 GHz, but most of the time was
11sed at 9.2 GHz. The analyzer was usually accurate to 0.1
MHz and had been previously calibrated over the range

£9.0-9.5 GHz 80 that the correction could easily be made.

68

III. X-r§y_Structure Determination and Optical Crystal-
lography

Since the alignment of crystals is very important in
simplifying spectra, an explanation of the procedure used
needs to be made. If no report of the structure was avail-
able, it was necessary to do an x—ray determination to ob-
tain the space group, unit cell dimensions, and positions
of the crystal axes. It is usually preferable to use a
small crystal, 0.1 mm or less, for an X—ray analysis. How-
ever, it was found that it was possible to work with larger
crystals, up to 0.5 mm maximum length, if the exposure time
was increased. All determinations were done with unfiltered
Cu (1K0 = 1.542 8) radiation. The crystals were chosen
such that the crystal shape closely resembled those to be
used for ESR analysis. In this way the faces corresponding
to known directions of crystal axes could be used for align-
ment in the ESR cavity.

After a suitable crystal was found it was examined
under a polarizing microscope to ascertain whether it was
truly a single crystal. When a single crystal had been
found, it was mounted on a glass fiber 2" longYWhich was
attached to asxniometer head. The fiber was held in place
xwith Versene or some other type of putty-like material.
{The crystal was attached with Canada balsam or Duco cement.
:[f the crystal was air sensitive or hygroscopic, it was
xnecessary to seal off the crystal in a quartz capillary

tube similar to the ones used in powder diffraction analyses.

69

The goniometer head was then attached to the Weissen—
berg camera and oscillation pictures were taken according
to the procedures outlined in Stout and Jensen (129). The
oscillation range was 115° and two pictures were taken 90°
apart from one another on the scale of the Weissenberg
camera. The alignment of the crystal was corrected with
the arcs on the goniometer head and the correction was
usually 2° or less. If more correction was needed, it was
usually easier to realign the crystal on the head by moving
the fiber slightly.

-After the preliminary alignment axis had been measured,
the beam stop was replaced with a layer screen and a zero-
layer Weissenberg photo was taken. The range was usually
200° so that the complete reciprocal lattice could be taken
on a single piece of film. The zero—layer film was allowed
to expose for 5 or 6 hours. For most monoclinic organic
crystals encountered in this work, it was possible to choose
'the b axis as the alignment axis. The zero—layer film,
therefore, indicated the positions of the a and c*, or
a1* and c, axes and the angle B* between them. The re—
flxections on the zero—layer film were then indexed by plot—
th39 them on spherical coordinate graph paper using the
scxale 1 mm = 2° and the appropriate scale for zero-layer
iguiexing which is given in Buerger's (134) book. The posi-
‘ticnns of the axes were usually quite evident if the plot on

spherical coordinate paper was traced onto a plain sheet

of white paper.

70

Once the positions of the axes were found the goniometer
head was removed from the Weissenberg camera and mounted on
the precession camera. The scale reading corresponding to
the positions of the axes was set on the precession camera;
the precession range was set at u = 30°. The film was
allowed to expose for one hour. If the axes were indeed
present at the reSpective scale positions on the camera,
the resulting precession photograph showed the expected two-
fold symmetry along the b-axis. By this procedure it was
possible to identify positively the directions corresponding
to the crystal axes. Buerger (135) also has a book dealing
with the precession method which was quite useful.

The goniometer head was then remounted on the Weissen-
berg photos were taken. It was usually only necessary to
take a zero-layer, a one-layer and a two-layer photo. The
method for doing this is described in Stout and Jensen's
(129) book. The first and second-layer photos were then
indexed in the same manner as was used for the zero-layer
‘photo with a change in the scale according to Buerger (134).
In this way it was possible to make a Space group determina-
tion with enough reflections along each axis. If the pos-
silxility arose of more than one Space group corresponding
tx) the observed reflections it was necessary to measure the
number of molecules per unit cell by flotation methods.

The crystal was floated in a mixture of carbon tetrachloride
(d == 1.589) and heptane (d = 0.684). From the observed

density and molecular weight it was possible to determine

71
the number of molecules per unit all by the method given in
Stout and Jensen (129).

If the interfacial angles have been reported, in Groth's
(132) book for example, it is possible to determine the posi-
tions of the crystal axes with an optical goniometer. How-
ever, determination of the space group still requires an
X-ray analysis.

.For the case of a hexagonal crystal it was possible to
use the polarizing microscope to identify the position of
the c-axis. Both of the prisms were inserted and the
Bertrand lens was then put into position. ~The direction
of the c crystallographic axis was easily identified by
the interference fringes.

Although it is reported by Hartshorne and Stuart (131)
that interference fringes are also seen for biaxial crystals

it was not possible to detect these in the case of any of

the monoclinic crystals used.

IV. Materials
A. Acetamidine Hydrochloride

Crystals were grown from a saturated aqueous solution
cxf the reagent obtained from Eastman Organic Chemicals,
Rochester, N.Y. The crystals were extremely hygroscopic
and had to be kept in a desiccator when not in use. The
crystals had to be sealed in quartz capillary tubes to do

an.}c—ray analysis. The deuterated crystal was Obtained by

72
recrystallizing acetamidine hydrochloride three times from
99.84% D20 (Stohler Isotope Chemicals, Montreal, Quebec,

Canada).
B. Isobutyramide

Crystals were grown from a saturated aqueous solution
of the reagent obtained from Eastman Organic Chemicals,
Rochester, N.Y. The crystals did not appear to be hygro—
scopic to any appreciable degree and could be easily handled
while exposed to the air. Deuterated crystals were obtained

by recrystallizing isobutyramide from D20 three times.
C. Trimethylacetamide

Trimethylacetamide was prepared by M. T. Rogers from
pivalic acid. The crystals obtained were from a saturated
aqueous solution. The amide did not appear to be hygro-

scopic and could be easily handled.
D. Hydrazinium Dichloride

Hydrazinium dichloride single crystals were obtained
frtnn a saturated aqueous solution of the reagent from
Fisher Scientific Co., Fair Lawn, NJ. The crystals were

hygroscopic and had to be stored in a desiccator.
LE. Hydrazinium Difluoride

fiydrazinium difluoride was prepared by the method of

Kronberg and Harker (136) by neutralizing 49% HF solution

73
(J.T. Baker Chemical Co., Phillipsburg, N.J.) with 95%
hydrazine solution (Eastman Organic Chemicals, Rochester,
N.Y.) in a 2:1 mole ratio. The crystals are hygroscopic
according to Deeley and Richards (137) and were therefore
kept in a desiccator. The deuterated crystals were obtained

by recrystallizing hydrazinium difluoride three times from

D20 0
F. Hydrazinium Dibromide

Hydrazinium dibromide was prepared by neutralizing
48% HBr solution (Matheson, Coleman and Bell; Rutherford,
N.J.) with 95% hydrazine solution (Eastman Organic Chemicals,
Rochester, N.Y.) in a 2:1 mole ratio. The crystals were

extremely hygroscopic and had to be kept in a desiccator

when not in use.
V. Procedure
A. Crystal Growing

As was mentioned in the previous section all crystals
‘were obtained from aqueous solution by Slow evaporation.
The solutions were saturated by pumping carefully on them
in a vacuum desiccator until a slight precipitate formed.
It was possible to obtain good seed crystals by this method.
{rhese seeds were then used to obtain larger crystals from
-the saturated solutions.

The solutions were usually allowed to evaporate slowly

13y setting a beaker containing the solution on a shelf and

 

covering t‘.
appeared t
cater cont
these meth
crystals 0
in about t
pumping on

a desiccat

No t
The mCSt 4

The CrYSt.
Caps and
CCCtainin
the Ceflte
irradi at e
Ecssible
the Only
sincefltra
;t was me

.‘ufw A,

«q‘en

74
covering the beaker with a watch glass. If the solution
appeared to evaporate very slowly it was placed in a desic—
cator containing CaSO4 or some other desiccant. Using
these methods it was usually possible to obtain Single
crystals of the required dimensions, about 3 mm on an edge,
in about ten days. The crystals were then dried by either
pumping on them in a vacuum desiccator or putting them in

a desiccator containing CaSO4.
B. Radiation Procedure

Two types of radiation were used to produce radicals.
The most frequently used was the 6°Co y-ray source which
delivered a dose rate of 2 x 106 rad/hr, or Since 1 rad =
100 erg/gram the dose rate would be 2 x 108 erg/gram-hr.
The crystals were placed in 2-dram glass vials with screw
caps and these vials were then placed in a glass dewar flask
containing liquid nitrogen. The dewar flask was placed in
the center well of the irradiation source and the samples
irradiated for periods of from 3 to 10 hrs. It was usually
‘possible to detect radicals after 3 hrs irradiation and
the only effect of longer irradiations was to increase the
concentration of radicals present. In some cases, however,
it was necessary to irradiate longer than 3 hrs to obtain
sufficient concentration of radicals, especially in the
case of the hydrazinium compounds.

The other type of irradiation source available was a

:1 Mev G.E. Resonant Transformer which produced accelerated

 

 

‘4
raw 'fl

5:: '

electrox
2.97 x 1
cf 47 cr
insuffic
It was ;
time, us
than 8 1
fine crys

ticn am

~\'H as
'0
.v‘
:._*€
v" w
\1.
._ u
- v
5‘
1:11,,
‘ 1
‘7'
L4
. \
“:te
54
‘v‘ '54
on:

75
electrons. The dose rate available from the source was
2.97 x 106 rad/min or 2.97 x 108 erg/gram-min at a distance
of 47 cm from the tube window. This source was used when
insufficient radiation was obtained with the 6°CO source.
It was possible to irradiate for much shorter periods of
time, usually from 3 to 8 minutes. Radiation periods longer
than 8 minutes usually resulted in complete destruction of
the crystal; sometimes this occurred with even less radia-
tion and it was usually necessary to test the crystal with
differing amounts of radiation to determine the limit. The
crystals to be irradiated were placed in small sealed poly-
ethylene bags which were allowed to float on the surface
of liquid nitrogen in a stainless steel dewar flask during
the irradiation. If any difficulty was encountered keeping
the crystals floating, a small piece of styrofoam was placed
in the polyethylene bag to keep it afloat. It was very
important to keep the crystals floating near the surface,
since the crystals received very little radiation if they
sank even 1 cm below the surface. The amount of heating
of the crystal from the source while it was floating ap—
.peared neglibible. This was demonstrated in several instances
:in.which the same radicals were present after y-irradia-
'tion as after electron irradiation. The most conclusive
Erroof was with the V centers observed in this work. These
cxanters were stable over a very short temperature range,
usually -150° to -196°, and appeared in the electron ir—

readiated material in higher concentration than in y-irradi-

ated material .

76

C. .Mounting Crystals

It was necessary to keep the irradiated crystals at
liquid nitrogen temperature (77°K) in order to detect any
radicals which had formed at this temperature. A procedure
was devised for transferring the crystals to a crystal mount
allowing as little warm-up as possible. -When not in use
the crystals were kept at 77°K.

The irradiated crystals in glass vials or polyethylene
bags were transferred to a 100 x 50 crystallizing dish con-
taining liquid nitrogen. This dish was insulated by a
piece of Styrofoam which was hollowed out to accommodate
the dish. The vials or bags were opened in this dish and
the crystals allowed to float out into the liquid nitrogen.
The crystals were handled with forceps which had been pre-
cooled with liquid nitrogen.

The crystals were transferred with these forceps into
a small aluminum foil scoop containing liquid nitrogen.

The scoop containing the crystal under liquid nitrogen was
then moved to the crystal mount. The crystal mount consisted
of a 2 mm diameter glass rod 17 inches long. At one end was
attached a brass clip held by Pliobond cement. The other
end of the mount contained a circle of sponge rubber 1.5
inches in diameter and 3 inches thick. The mount is Shown
.in Figure 6. The clip end of the mount was kept cooled to
'77°K by placing it in a small pool of liquid nitrogen. AA

lpiece of Styrofoam which had been hollowed out for this

77

Foam.rubber
insert

 

 

2mm glass rod

Side view

 

Brass clip

 

Ffiigure 6. .Single crystal holder.

 

purpose w
transferr
into posi
forceps.
of liquid
Afte
to a dewa
T3102 Var
P310 Altc
9f glass
and attau
the dewar:
litrogm
Q‘GiCkly .
into the
the Spon.
in Place
as far (1
pessible
T0

Cagnetic

78
purpose was used. The scoop containing the crystal was
transferred to this pool and the crystal was then moved
into position under the brass clip with the aid of precooled
forceps. Figure 7 shows the crystal mount lying in the pool
of liquid nitrogen with the attached crystal.

After the crystal had been mounted it was transferred
to a dewar flask which was designed to fit into the ESR
TEloz Varian Multipurpose Cavity. (Varian Associates,

Palo Alto, California). The dewar container was constructed
of glass with the tip constructed of optical grade quartz
and attached to the glass by a graded seal. Figure 8 shows
the dewar container used. It was filled first with liquid
nitrogen and the crystal mount with crystal attached then
quickly transferred to it and the sponge rubber top squeezed
into the top of the dewar container. After several minutes
the sponge rubber circle froze and kept the crystal mount
in place. The brass clip containing the crystal was pushed
ras far down into the quartz tip of the dewar container as
gnossible to prevent bumping from the liquid nitrogen.

To measure the angle of rotation of the crystal in the
Inagnetic field, the dewar container was inserted in a plexi-
qglass platform which had been scored in degrees from 0° to
180°. The platform rested on the top of the magnet with
tflae dewar container inserted into the magnet pole gap which
cxontained the rectangular TE102 cavity. A pointer was
airtached to the dewar flask to simplify the recording of

arugle of rotation. The system is Shown in Figure 9.

79

mufl>mo mmm ou Hommcmuu How Hmoaon

Hmummno SH coussoa amumwuo mHmSHm .5 demHm

Mooan Emomonmum

h

 

 

 

«2 can an Hmummuo

 

 

 

80

[4+2 -4"—’l

g—mw—y

 

11 .2"

 

 

 

 

Pyrex—Vycor

graded seal \ a. -- n O .196”
/

419".

fig

 

 

 

 

 

 

0 .437" $4 It

Pi u
9 re 8 ~ Dewar container for ESR single crystal studies.

Pointer : f Plexiglas platform

  

 

 

 

 

 

 

 

 

 

 

LiqUid N2

 

 

 

 

 

 

 

H TE102 caVity
'. /
I
h '

I jr“—————‘Crystal

 

 

Figure
9- Apparatus for rotating Single crystals in the

magnetic field.

I
a.

e

n
O
.

bra

Ln.
~3L‘ld b

VL

I!
.55:

 

 

 

82

Spectra in one crystallographic plane could be taken
in this manner. »In order to obtain the Spectra in the other
two crystallographic planes, it was necessary to remove the
crystal from the brass clip on the crystal mount and remount
it repeating the above procedure.

There was no detectable background signal from the
brass clip, Pliobond cement or quartz dewar tip which inter-

ferred with signals from the radicals.

D. Rotation Spectra

Spectra were recorded at intervals of 10°, or more
often if the pattern was more complex. .It was necessary
to do a complete 180° rotation to obtain a complete set of
spectra in one crystallographic plane. AS stated above

it was considered easier to rotate the crystal in the fixed

external magnetic field, fizxt’ rather than to rotate the

magnet .

After a complete set of rotation Spectra were obtained
in three mutually perpendicular planes, the line separations
wvere measured as a function of 9, the angle of rotation in
the magnetic field. The hyperfine splittings were then
:fitted to either Equation 46 or 48 and the principal values
cxf the tensor obtained by diagonalization. A computer pro-
gram written by Lowell D. Kispert for this purpose was
used and a listing of this program is given in the Appendix.
The principal values of either the A" or 3' tensor

could be determined in this way.

83

E. Temperature Studies

If more than one type of radical was present after ir-
radiation at 77°K. it was desirable to study each radical
independently if possible. This could often be accomplished
by warming the crystal Slightly with different types of
slush baths. This was found to be a better method than
using the Varian V-4557 Variable Temperature Accessory
(Varian Associates, Palo Alto, California). By a judicious
choice of Slush baths it was possible to heat the crystal
enough to largely destroy one radical without allowing the
other radical to decay appreciably. A good listing of slush
baths providing a large range of temperatures has been given
by Rondeau (138).

The crystal was placed in a 2-dram glass vial with
screw cap and allowed to warm in the Slush bath for periods
of 15 seconds to 15 minutes. The crystals were then re-
lnounted at liquid nitrogen temperature (77°K) using the

‘procedure in Part D above.
VL Standard Samples and Conversion Factors

Occasionally the Spectrometer was checked with standard
asamples to determine if all systems were operating properly.

{Ehe standard samples used were:

Varian Pitch in KCl: g = 2.0028
1.99454 i 0.00005

Aqueous KZCr (CN ) 5no : g
A = 5.265 r 0.05 gauss.

 

 

 

sped

‘
ate:

"" h
‘Lacol
J

 

84
A list of conversion factors used in interpreting the

spectra iS given below:

0.714489 Ve (MHz/sec)

 

 

g = H(gausS) $68)

H(gauss) = 2.3487465 x 102 x vp (MHz/sec) (69)
0.714489 x Ve (MHz) at free spin

H(gauss) = 2.0023' (70)

A(gauss) = A (MHz/sec)/2.8026 [for g = 2.0023] (71)

A(gauss) = (1.0697 x 104) A (cm-1) (72)

where A is the measured hyperfine splitting, H is the
magnitude of the external field, Ve is the klystron

frequency in MHz and vp is the proton oscillator fre-

quency in MHz.

RESULTS
I. irradiated Acetamidine Hydrochloride

A. Crystal Structure

No X-ray crystallographic study of acetamidine hydro-
chloride had been previously reported. The identification
of the space group and unit cell dimensions was made ac-
cording to the method described in the Experimental section
and in Stout and Jensen's book (129). Oscillation and
Weissenberg photos Showed the crystal to be monoclinic
smith unit cell dimensions a = 7.25 R, b = 8.18 R, and c =
(4.54 X, B = 104°. The Weissenberg photos showed the pres-
ence of hkl reflections with no conditions; hk0, no
(nonditions; 001, l = 2n. This is consistent with space
(groups P21 or P21/m. The density of the crystal was
rmeasured with a mixture of carbon tetrachloride (p =
21.589 g/ml) and n—heptane (p = 0.684 g/ml). The experi-
mentally determined density was 1.210 g/ml in this mixture
vflhich gives 2.01 molecules per unit cell. This seems to
jJndicate the space group P21 rather than P21/m. The
cfloservation that a crystal of acetamidine hydrochloride
dipped in liquid N2 was attracted to the walls of a Silvered
dewar flask (piezoelectric effect) means no center of

85

 

 

 

syrue

red

I953

the
flea
DhOU

4

8X98

 

86
symmetry is present. This additional evidence lends support
to the choice of P21 as the correct space group and the
resultant ESR spectra tend to confirm this assignment.
-The crystals were easily aligned along the b axis and
the a and c* axes were chosen from the appearance of re-
flections along these axes from the zero-layer Weissenberg

photos. A drawing of the crystal and crystallographic

axes is Shown in Figure 10.

B. lgentification of Radicals Produced in Irradiated

Acetamidine Hydrochloride
1) Low-Temperature Radical - C12-

Single crystals of acetamidine hydrochloride were
y-irradiated with the 6°Co source for 3 hours at 77°K. The
crystals were then mounted, without warmup, according to
the procedure in the Experimental section. The three crys-
tallographic planes ab, bc*, ac* were chosen by reference
tx: the crystallographic axes presented in Figure 10 and the
<:rystals were rotated through 10° intervals in each plane.

Figure 11 shows the second-derivative spectrum of the
radical stable at 77°K taken with the magnetic field in
the ac* plane at 50° from a. As can be seen from

.Firrure 11 the Spectrum consists of seven basic groups of

lixues. The measured intensity ratios for the most prominent
lines (labeled 1 to 7) were 1:2:3:4.1:2.8:2:1. The Split-

tiru; between these main peaks at this orientation was 95.5

gauss.

 

 

 

IE

 

87

 

 

 

 

 

Figure 10. Crystallographic axes for acetamidine hydro-
chloride.

88

.wcmHm *0m 0;» Ga 0 Eoum com ma
«Ho mSHBOQm wofinoacoouomn enacHEmumom omumflomnua mo

m .xcss um

Al

Esuuommm mum

.HH masons

 

 

 

 

 

 

 

89

When the crystal was rotated 90° from the position in
Figure 11 a more complicated pattern resulted. Figure 12
Shows the Spectrum obtained with the magnetic field 40° from
c* in the ac* plane. The spectrum has become consider-
ably more compact, being only 285 gauss in total width com-
pared with a 551 gauss total width in Figure 11. Seven
main groups of lines are distinguishable but in this case
there are two sets of seven lines each, resulting from the
presence of two nonequivalent radicals at this position.
This nonequivalence is also present if the crystal is ex-
amined at 60° from a in the ac* plane as can be seen
from Figure 13.

Rotations in the ab and bc* planes similarly showed
the presence of 7 basic groups of lines with two nonequi-
valent radicals present at most orientations. -For rotations
in both the ab and bc* planes the two radicals present
Ibehaved differently than for the ac* plane where, as can
ibe seen from Figures 11 and 12, the angular dependence of
'therhyperfine splitting followed nearly the same pattern
for both radicals. The spectrum Shown in Figure 14 was ob-
tained with the magnetic field parallel to the b axis in
the ab plane and it can be seen that one radical exhibits
a rninimum hyperfine splitting at this position relative to
the hyperfine splitting of the second radical. A 90° rota-

‘ticui to place a parallel to the magnetic field in the ab

plane leads to the Spectrum Shown in Figure 15. The hyper-

fine splitting at H H a in the ab plane is again at a

 

 

 

90

 

 

Figure 12 .

 

 

 

 

»ESR spectrum of irradiated acetamidine hydro-

chloride Showing C12 at 77°K. - H> is 40
c* in the ac* plane.

from

 

91

« .mcmHm *Um may CH m Eonm com ma Am .Mabh um
I Ho mca3osm wcflHoHnoouoms msflofiemuwom Umumaomnua mo amnuowmm Mmm .mH madman

 

 

 

 

 

 

 

 

 

 

 

92

fllll
won

.wcmam Am may SH Q __4m nuHB luau mo Eduuommm mum. .wfi musmflm

93

.wsmHm Am

0;» an

6 __4m nuns

 

«Ho mo Ednuommm Mmm. .nH musmfim

 

 

 

mirr'r‘

94

minimum indicating that a maximum has occurred for the radi-
cal at a position somewhere between a and b.

In order to follow the hyperfine splitting in detail a
plot of the splitting, A, was made in the three crystallo-
graphic reference planes as a function of 9, the angle be-
tween the field direction and the respective crystallographic
axis. The lines of maximum intensity for the seven basic
groups of lines were followed in this manner and the re-
sults are given in Figures 16 to 18.

These plots were then used to fit the hyperfine Split-
ting to Equation (46) and the principal values obtained by
the diagonalization of the tensors according to the probedure
in the Theoretical section. The principal values for the
hyperfine tensor are given in Table XII with the direction
cosines to the principal-axis system.

The experimentally determhmfl hyperfine splittings and
the measured intensities from Figure 11 are consistent with
the presence of the radical anion C12_. The main lines in
Figure 11 upon which the hyperfine Splittings were based
are the lines belonging to the (3fCl-35Cl)- species. The
theoretical intensity ratios of 1:2:3:4:3:2:1 agree well
‘vith the experimentally measured ratios. The other lines in
the Spectrum of Figure 11 belong to the isotropic Species
(35Cl-37Cl)- and (37Cl-37Cl)-. A discussion of the rela-
‘tionship of these lines to those due to the 35c1—35c1 Species
.is given in Slichter's book (82) and will not be repeated
Inere but it Should be pointed out that using these arguments

alJ.1ines can be accounted for.

95

.mcmHm

owH own

___

*UQ

mg» SH SOHDMDOH mo mamcm.MM luau mo mcfluuflamm mcflmuwmmm

m
40:
ova omH ooH om

om ow n r_
____________ow_l_

lluo

al.0H
nu

Iluom

 

II oHH

.©H musmflm

Anmsmmv

96

.msmam

owH

_

 

*om

oma

 

mnu SH coflumuou mo mamsm_mw.ruav mo msfluuflamm mcflmummmm

m
5: .

ovH ONH OOH ow om ov ON o

_____.________ _J

.hH musmflm

OH

ON

on

o¢

on Ammsmmv

om
Oh
ow

cm

03

Can

 

Ill DON.

97

.mcmam no mnu SH coflumuon mo mamsm MM.INHU mo mGHUpHHmm mcfimummhm .wH mnsmflm

5: 5:

owH owe owu ONH OOH ow om ow o

_________._______.._r.r.

o

OH
ON
on

0%
on

cm
as
om
om
2:

o:

Ammsmmv

 

Table

Rad

cr1

 

 

 

a
Relat

98

 

 

 

 

 

 

 

Table XII. Principal hyperfine Splitting and g values
and their orientations for Clz- radical in
irradiated acetamidine hydrochloride.

. Principal Values . . . a
Radical (gauss) Direction Cos1nes

c1," AC1 103.1 0.01 0.99 -0.07

29.8 -0.52 0.07 0.85

10.0 0.85 0.03 0.52

Radical PrinCngl Values Direction Cosinesa
012' 2 .0437 0.08 0.18 0.98
2.0317 —0.97 —0.18 0.12

2.001 0.20 -0.96 0.16

 

aRelative to a,b,c* crystallographic axes.

99
Since anisotrOpy of the 3' tensor exists for C1; due
to an admixture of the fig excited state with the 09 \

ground state (82), the principal values of the 3' tensor

were also determined. ‘ThiS was accomplished by measuring

the angular variation of g as a function of 6 and diagon-

alizing in the usual manner. -The plots of angular variation

for g are given in Figures 19—21. Principal values of

the 3' tensor and the associated direction cosines are

given in Table XII. +
NH,
ll

2) High—Temperature Radical 'CHz‘C‘NHg

It was felt that perhaps other radicals might be

detected in addition to the radical C12- observed at 77°K.

In order to determine whether this was the case, a Single
crystal of acetamidine hydrochloride was electron irradiated
‘with the G.E. Resonant Transformer for 10 minutes at 77°K.
{The single crystal was then allowed to warm up using a liquid
.nitrogen-isopentane slush bath maintained at -150°. «The
(crystal was mounted periodically and a Spectrum recorded to

detect whether Clz- was still present as the crystal was

warmed. The presence of C12- hampered the identification

cxf any other radical due to the large number of lines.

After 1 hour at -150° the crystal was removed from the

slush bath and remounted in the crystal holder. It was

found after 1 hour that all C12- had disappeared and a new

radical was present. Figure 22 Shows a spectrum of the new

radical with the magnetic field 60° from b in the ab plane.

 

 

100

.msmam *on may CH luau Mom GOHDMMOH mo mamsm.MN m mo uoam

m
*0:
omH omfi ovfl om“ ooH om om ow

.Iuoooo.m
.ruomoo.m
loos. m
r.omHo.m
r.oomo.m

commo.m

oomo.N

a .l ammo. a

a l 83. a

I 03.0. N

.mH musmflm

 

 

101

.mcmHm *0m 9:» as :30 you soflumuou no 939» a 0 no uon .ON shaman
m
.5 : a __

owe or: ONH coH ow Mom ow ON 0

I} ommm. H
a II 0000. N
.I.. once. N
I oouo. N
In Omno. N
0 II GONG. N
I. omNo. N
I come. N

a
c I. ammo. N
Oooco. N

I. omvo.N

102

.mcmam 9m. 93 CH luau How coaumuou mo mamsm a m mo poem .fiN mnsmflm
m

m _ _ a _ _
owH owe ovH ONH cow ow 00 cc ON

o
__________________r_

loooo. N
Ilonoo. N
IIOOHO. N
lomHo.N

IIOONC. N

        

I ammo. m
Income. .5
l. ammo. m
cove. m
I. 33. a
.I come. a

II ammo. N

103

.wsmHm Am

0:9 :H

n 509m com

 

am

0 w.

nuns Hmonumu

«m2+
«marorumo

mo Eduuommm mmm

 

.NN musmam

 

 

 

\
n
i

r
‘-

N

(v

 

104
The appearance of the spectrum is a triplet of triplets

with intensity ratios of 1:2:1:2:4:2:1:2:1. The larger

triplet spacing is 20.2 gauss and the smaller 5.8 gauss as

indicated in Figure 22. As the crystal is rotated in the

ab plane a more complicated pattern appears at 50° and 70°

from b in the ab plane. Figure 23 Shows the pattern

with the magnetic field at 50°, which is identical to that

observed at 70°. This pattern consists of a quartet of ap-

proximately 1:1:1:1 intensity ratio with the Smaller Split—

ting of 5.8 gauss still present. Further rotation in the

ab plane gives a quartet of 1:1:1:1 intensity ratio at 100°

from .b as is seen in Figure 24. The smaller 5.8 gauss

splitting has been lost in the line width at 100° . The

spectrum simplifies further at 140° from b in the ab

plane where a triplet is observed. Figure 25 shows this

case with the splitting between these lines being 22.7 gauss.

The measured intensity ratio at this orientation is

1:1.7:1.2.

Spectra in the ac* and bc* planes Show similar

patterns to those observed in the ab plane. In the ac*

plane with H I] a an identical spectrum to that in

Figure 23 results. AS the crystal is rotated in the ac*

plane toward c* the pattern Simplifies to a triplet and

at 90° (H H c*) becomes Similar to Figure 25. Continued

rotation restores the spectrum of Figure 23 when H becomes

parallel to a. .In the bc* plane a triplet Similar to

Figure 25 is observed when H I] b , changing to the spectrum

 

 

105

.msmam Am m
N mm . 0H5 Hm
93 an a some com Am and: H863 «570: no no 23900 mmm mm

«mm
+

0 mN

w1::

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

106

5

a 609m 62: Am a»? H863

4-
‘-

0 mN

 

.msmam Am map
«szUIumw mo Ednuommm mum. .eN shaman
£2
+

 

107

qr

n Eoum

0 nN

 

5.? H6033

 

 

£2
+

 

.mcmHm Am

an...

uEZIUIumw mo Eduuommm mum .mN musmflm

 

108
of Figure 23 at 80° from b in the bc* plane. The spec—
trum of Figure 22 is observed at H II c* in the bc* plane.
Continuing the rotation in the bc* plane gives a quartet
similar to Figure 24 at 160° from b. This quartet reverts
to the triplet of Figure 25 when the field becomes parallel
to b in the bc* plane.

The larger hyperfine splitting of 20.2 gauss for the triplet
of triplets observed in Figure 22 can be interpreted as
arising from the interaction of the odd electron with two
equivalent protons, and smaller 5.8 gauss Splitting could
arise from interaction of the odd electron with a second
set of two equivalent protons. This would result in a
'triplet of triplets with intensity ratios 1:2:1:2:4:2:1.2:1
as observed, so the interpretation of the spectra using
these criteria was attempted. If the large 20.2 gauss
proton Splitting is attributed to two equivalent or- protons
tins pattern Should change to a quartet with two different

sgilittings, one larger and one smaller, if the protons be- ‘

cxmne nonequivalent. Such behavior is observed in Figure 23

“fluere the quartet is attributed to two different a proton

hyperfine Splittings, one of which has increased to 22.3

gauss and the second has decreased to 17.1 gauss. An even

larger splitting occurs for the field at 120° from b in

the ab plane where one measured or proton splitting becomes

31 .5 gauss .
Using the above arguments the angular variation of the

(1_£xroton lines was plotted in each of the ab, bc*, and c*a

"I

109
planes. These plots are presented in Figures 26-28. The
principal values for the a-proton hyperfine coupling tensor
were obtained using Equation (46). The values and direction
cosines for the two a-protons are given in Table XIII. The
isotropic values agree well with other a-proton splittings
reported in the literature (Table I). The principal values
are somewhat different from the normal -10, -20, -30 gauss
principal values expected for an a proton but the values do
appear reasonable for a-Splittings.

In order to confirm that the 5.8 gauss splitting in
Figure 22 belongs to the protons on the —NH2 group,the ESR
spectrum of a single crystal of acetamidine hydrochloride
in which deuterium had replaced hydrogen was analyzed. The
deuterated crystal was electron irradiated for 3 minutes at

77°K and then warmed to -125° for 1 hour to remove C12-.
+

NH2

IIt was found that 'CHz-E-NHZ radical was stable at -125°
and the higher temperature increased the rate of decay of
Clz'.

The deuterated crystals were not well formed but it
was possible to identify the b axis with certainty and
tinis allowed an analysis of spectra in the c*a plane.
With H H a in the ac* plane it was found that the Spec-
‘trrun of Figure 23 had changed so that now a quartet appeared
xvitfla intensity ratios 1:1:1:1 as is seen in Figure 29. On
rotation of the field in the c*a plane to H II c a trip-

let with intensity ratios of 1:2:1 was obtained (\Figure 30).

110

mcououm o How mmsfiuuflamm

OOH OOH OvH ONH

_______

b

 

.HMUHOMH «m21olumw CH

«an?
madmummms mo wcmam no on» SH coaumaum> Hmasmc< .ON musmam

5: 6:
OOH ow om Ofi ON O

___________I_

r0 .0.

.. 3

NH

.IIOH
Iluwfl

II ONAmmsmmv
0 4
II.NN

II.¢N
II.ON

O t 0 v QN

II.Om

6 o 0 6.1.2

111

 

h

in ”I

 

.HmoHoMH nszUIumU as

«34+

msououm;o How mOSHHUHHmm unflmummwn mo mamam *on on» CH Gofiumflum> Hmasms¢

0

*0: n:
om“ om“ ova omH ooH om om as on

O
_ _ _ _ _ _ _ _ _ _ _ _ ,e _ _ _ _ .14

II.NH

             

II.¢H
nl.®H

I|_mH

II.ON

|I_NN

.. c .m .r on

Il_vm

Ammsmov

.bN musmflm

 

112

.‘iu In

.HmoHomu «mZIOrmmU SH
: .

«92+
msououm.o How mmSHuuHHmm oSHMHmm>£ mo oSme *om may SH SoHumHMm> HmHSOSm .wN mnsmHm

®
a. : .5 :
owH OOH OVH ONH OOH ON OO O¢ ON O
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ I—
ll.NH
II.¢H
.... a. ...
a. .m 0. 1|.OH
3 G O Q 0 G 0 0 c OH Ammsmmv
8 c fl
. .. I. cm
a n. 0.,
.. o a o w. a o 0 e .I an
o . II VN
C J J A. .
c II ON

ll ON

Table XII]: .

Principal values of the hyperfine Splitting

113

tensor for the two nonequivalent a protons in

'CHz-C-NH2° radical. “

+NH2

 

 

 

 

 

 

Proton Principal Values Direction Cosines
{4(9auss)
1 -35.9 0.79 0.49 0.36
-23.1 -0.58 0.44 -0.68
- 7.5 -0.17 0.75 0.64
Aiso = -22.2
2 -36.2 0.06 0.92 0.38
-19.0 —0.61 0.34 -0.72
- 5.8 —0.79 -0.19 0.58
A = -20.3

iso

 

114

.mSmHm *Um
mnu SH m __Am. SUHB HMUHomu «mZIUIumw. omumumusmo mo Enuuommm mmm. .ON wusmHm

«my? .

1!-
‘b

0 mN

 

 

115

an

“WEI! . .ou‘r

*0 :Am 5:3 H863

 

0 MN

 

 

a .mSMHm *Um. may
manurumw omumumusoo mo ESHuommm Mum. .om musmHm

«32+

 

 

 

 

 

116

At no orientation in the c*a plane was any hyperfine struc-
ture detectable with a Splitting value near 5.8 gauss. This
provided conclusive proof that the smaller splitting results
from protons on the -NH2 group.

It was possible to obtain principal values of the tensor
for the —NH2 protons using Schonland's method (Equation 48).
It was not possible to plot these lines as was done pre-
viously Since at orientations where the splitting was small
it was lost in the linewidth of the lines from the a protons.
The maximum and minimum hyperfine Splitting and the angle
at which the maximum Splitting occurs, along with the princi-
pal values obtained, are given in Table XIV.

The hyperfine splitting values for the -NH2 protons
are in reasonable agreement with those reported recently
(139) for X-irradiated succinamide. Kashiwagi reports
.principal values of -1, -3 and -6 gauss for the -NH2 protons

O 0

ll
iJ1.H2N-C-CH2-CH-C-NH2 radical. This is reasonable agreement
smith the -1.7, —4.1, -6.4 gauss principal values reported
111 this case where the negative signs were selected to agree

with those reported by Kashiwagi.
II.. Irradiated Trimethylacetamide Single Crystal
.A. Crystal Structure

Ifio previous report of the unit cell and Space group of
trimethylacetamide could be found so that it was necessary

to determine these by the usual techniques. Weissenberg

 

 

 

 

117

Table XIV. Hyperfine splitting values for —NH2 protons in
'CHa‘C‘NHg radical

 

 

 

+ 2
ll Eu
Plane Amax Amin emax
(gauss) (gauss) (degrees)
ab 6.0 ‘3“ 0.0 150
bc* 6.3 2"0.0 100
c*a 6.0 9'0.0 80

 

 

 

Pr1nc1pal Values Direction Cosines

 

Radical (gauss)
+1532
.-CH2 -C-NH2 -6 .4 0 .83 -0 .42 0 .37
(*finaz Protons) -4.1 0.40 20.0 -0.91
-1.7 0.39 0.91 0.17
Aiso = -4.1

 

118

layer photos and Precession photos showed the unit cell to

be monoclinic with cell dimensions a — 12.84 R, b
10.27 X, c = 5.18 X, and B = 106°. Restrictions for re-

flections were 001, 1 = 2n; 0k0, k = 2n: hOl, 1 = 2n which

is consistent with the Spece group P21/c. The density of
the crystal was measured in a mixture of carbon tetrachlor-
ide (p = 1.589 g/ml) and n-heptane (p = 0.684) and the
value found was 1.056 g/ml. The calculated number of mole—
cules per unit cell using this density is 4.17 in good
agreement with the theoretical number for the Space group
P21/c, which is four.

The crystals grew as large hexagonal plates (Figure 31)

‘with the large face perpendicular to the a* axis. ~The

crystal was easily mounted with the long edge along b.
CH2 0

B. EfButyl Radical and CH3-C -'C-NH2 Radical at 77°K
.
Qfla

Single crystals of trimethylacetamide were y—irradiated
for 3 hours at 77°K and were then mounted without warmup
according to the usual procedure. According to previous
ESR studies of irradiated trimethylacetamide (140) the
radical observed at -140° is _t_-butyl radical.) The spectrum
frtnn‘gfbutyl radical would be expected to consist of ten
lines with intensity ratios of 1:9:36:84:126:126:84:36:9:1

assuming that the nine protons were coupled equivalently

to the odd electron.

119

 

———v——d\
\
\
\

\_--_. _._,..__._.

 

3%
\\

 

 

 

>———.

   

Figure 31. Crystallographic axes for trimethylacetamide.

120

The type of Spectrum observed at 77°K in y-irradiated
single crystals of trimethylacetamide is shown in Figure 32.
The magnetic field in Figure 32 is 60° from the b axis in
the a*b plane. ‘The presence of Efbutyl radical is evident
although only eight lines of the expected ten-line pattern
are seen. If it is assumed that these eight lines are the
central lines of a ten-line Spectrum the experimentally ob~
served intensity ratios (1:9:38:75:128:128:77:36:9:1) are
in reasonably good agreement with the theoretical values.
The hyperfine splitting at this orientation is 22.9 gauss.

In addition to the ten—line pattern attributed to the

.E—butyl radical a three-line pattern is also present.

.Figure 33 shows the Spectrum obtained when the magnetic

field is 30° from the axis c in the a*c plane. The in—

tensity'ratios at this position for the three-line pattern
are 1:1.9:1. The measured hyperfine splitting is 22.4 gauss.

in“; same three-line pattern is also evident in Figure 32

aliflnough the intensities are not as easily measured. This

CH2 0
I 0|

three-line pattern is attributed to the CH3-C - C-NHa
I .
CH3

radical for which coupling to two equivalent a-protons would

give rise to the triplet with 1:2:1 intensity ratios and

—22.4 gauss hyperfine splitting. Deuteration showed this

to In; the correct assignment since the Spectrum of ~CONH3

would be lost upon deuteration. The same spectrum was ob—

served after deuteration. The negative Sign is selected to

121

2

mm

Al

 

.mSMHm a*m 0:» SH 9 Eonm coo
.xobh um Hmummuo moHEmumUMHmnumEHnu omSMHomuuH mo Eduuommm Mum

 

w mN

 

.Nm mHsmHm

 

 

 

 

122

.wSMHm a*c onp SH 0 Eoum coo
mH m .Mobb um Hmummuo moHEmuoomHmsumEHHu omumHomHHH mo ESuuoomm mmm_ .mm musmHm

Al

 

 

 

0 mN J

 

 

 

 

 

 

 

 

 

 

123
agree with previously reported a- proton splittings but is
not determined in these experiments.

As the crystal was rotated in the a*b, a*c, and bc

planes a negligible amount of anisotropy was noted in the

spectrum of the g-butyl radical. At all positions in each

of the three crystallographic planes the hyperfine splitting

remained close to 22.9 gauss. Also in the case of the

CH3 0
I II
triplet Splitting from CH3-C - C-NHz no anisotropy was
I
CHa
detected indicating that this radical must be rapidly re-
orienting at 77°K.

The measured hyperfine splittings for both radicals
are presented in Table XV.

C. Temperature Studies

The single crystal of trimethylacetamide which had
been y-irradiated for 3 hours was first warmed to -80°

in a dry ice-acetone slush bath. The crystal was allowed

to warm for ten minutes at -80° and then remounted in the

crystal holder.

The spectrum of Figure 34 was recorded at 77°K after

warming. The magnetic field is parallel to the

c axis in
the a*c plane.

As can be seen from Figure 34 the ten—

line pattern attributed to E-butyl radical is still present

CH2 0
I II
while the three-line pattern attributed to CH3—C - C—NH2
I

CH3

 

 

124

 

Table XV. Hyperfine Splittings for radicals in irradiated
trimethylacetamide

 

 

F:
'.

 

 

Radical Hyperfine Splitting
(gauss)
H A = 22.9
9 3 H
CH3-C’
CH3 Az(13C) = 92.0
CH; 0
I II
CH3-C - C-NH2 AH = -22.4

CH3

 

125

. m|
.mSMHm 0*m 0:» SH 0 __Am oo
ou omEumz Hmumhuo onEmuoUMHmnumeHuu ooumHomHHH Sm mo Ennuommm Smm

w ON

 

 

 

 

 

 

 

 

 

 

 

 

.vm musmHm

 

126

radical has decreased in intensity. Figure 35 shows the
spectrum obtained 40° from c in the a*c plane. Only

eight lines of the expected ten—line pattern are evident

and the hyperfine splitting is 23 gauss. Spectra in the

other two planes also Show the pattern attributed to £-

butyl radical and resemble those obtained at -80° with

 

slightly less intensity.

D. 13C Splitting for .t-Butyl Radical

‘ I

A search was undertaken to attempt to detect the hyper-

fine splittings from.1.1% naturally abundant {3C in ir-
radiated trimethylacetamide crystals at 77°K. The crystal

was rotated in each of the three crystallographic planes

and first-derivative presentation of the spectra was used

so that the weak resonance from 13C

could be detected.

It was found that when the magnetic field was 10° from b

in the a*b plane, a weak line was observed 92 gauss from

the high field line of the E-butyl radical Spectrum. This
line was also observed 92 gauss from the low field line
when figxt was 10° from b in the a*b plane. This line
is attributed to the maximum 13C hyperfine Splitting in
g-butyl radical. The position of this line in relation to

the spectrum from E-butyl radical is shown in Figure 36.

Attempts to follow the 13C hyperfine Splitting as

the crystal was rotated proved fruitless so that the com-

plete tensor could not be evaluated. The results obtained
are presented in Table XV.

 

127

.mSmHm a*c may SH 0 Eoum cos mH Am .ooml ou
ooEHm3 Hmummuo moHEmuoomenumsHuu omumHomHHH So no Ennuommm Mmm

 

 

 

 

 

 

 

 

 

 

 

 

.mm mHSOHm

 

128

H = 3080 .35 G

 

 

H = 3392.48 G

 

I —”\r;
H—-)

 

‘

 

Figure 36. ESR first-derivative spectrum of irradiated tri-
ggthylacetamide crystal at 77°K Showing 13C lines.
H is 10° from b in the a*b plane.

129

III. -_]_:rradiated Isobutyramide Single Crystal

.A. Crystal Structure

IHamrick et al. (17) have reported that the unit cell

«of isobutyramide is monoclinic with a = 9.69 + 0.02 R,

b = 5.97 i 0.01 R, c = 10.11 a; 0.01 R and B =‘ 107.10 and

that the space group is P21/a with four molecules per

unit cell.

Rectangular plates grew easily from a saturated aqueous
solution. -It was found that the large rectangular face was
perpendicular to the c* axis while the long edge of the
plate was parallel to the b crystallographic axis. The
crystals were easily mounted using the a, b, and c* axes
as rotation axes. .A drawing of the crystal is given in

Figure 37.

B. Low—Temperature Radical CH—C-NH2
CH6

*

Single crystals of isobutyramide were y—irradiated for
5 hours at 77°K. The crystals were then mounted without
wammup in the usual manner. Spectra were recorded for every
10° rotation in each of the three crystallographic planes
ab, bc* and ac*.

When the crystal was rotated in the ab plane, the
spectrum in Figure 38 was obtained for the magnetic field
10° from b. The Spectrum consists of two sets of lines,

the first a four-line Spectrum with relative intensity ratios

 

130

 

 

 

 

 

""'WL"L

 

‘V
U"

 

 

 

 

 

Figure 37. Crystallographic axes for isobutyramide.

131

mH

Am

 

.mSMHm no on» SH n. Bonn oOH
.Mchb um Hmummuo ooHEmumusnomH ooumHomuuH mo Eduuommm mmm

 

 

 

.mm mHSOHm

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

132

of 1.1:3.3:3.2:1 as denoted in Figure 38 and with a hyper—

fine Splitting of 24.0 gauss. The remaining lines in the

0
CH3 . ll
spectrum are due to the radical >CH—C—NH2 which has
CH3

been reported previously (17). The four-line Spectrum has

' 0
(CH2 u
been assigned to the radical >CH-C-NH2 in which an
CH3

or- proton has been abstracted from the methyl group. The

experimental intensity ratio agrees well with the predicted
1:3:3:1 ratio for the equivalent Splitting by three protons.
The orientation in Figure 38 would thus correspond to equiva-
lent hyperfine Splitting by two a protons and one B proton.
The four-line Spectrum can be more easily seen in the

case of deuterated crystals in which deuterium has replaced
hydrogen in the -NH2 group. This can be seen from Figure 39

which is 10° from b in the ab plane. The spectrum now

has been simplified so that the doublet Splitting in

0
CH3 1:
;:C-C—NH2 radical has been eliminated. The doublet Split-
CH3

ting therefore presumably arose as a result of one of the

-NH2 protons giving a larger hyperfine Splitting than the
other -NH2 proton, the smaller being unobservable.

When the crystal was rotated in the bc* plane, the

spectrum of Figure 40 was obtained when H I] c* . Disre-

garding for the moment the lines belonging to

 

 

133

 

.mSmHm no man SH n Eonm eOH mH
.Mobb um kummuo moHEmumuSQomH omumuouswo ooSMHomHHH mo Esuuommm m

 

 

Am.
mm

.mm musmHm

 

 

 

 

 

 

 

 

 

 

 

 

134

.mSmHm *on on» SH “swam
. 0 v 0 o
oma muMHomuuH mo Esuuommm mmm O
*0 __Am .Xobb um Hmummuo moHEmumuSQ . o

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

135

CH3 0
. u
;:C-C-NH3 radical, it can be seen that a six-line Spec-

C33

trum remains as denoted in Figure 40. In the case of the

deuterated crystal the resultant spectrum is the same for

H [I c* in the bc* plane. A similar spectrum is obtained

for H [I c* in the ac* plane. The six-line Spectrum
can be interpreted as the equivalent coupling of two a pro-
tons and a further, but nonequivalent, splitting by a B

proton. The hyperfine splittings in this case would be

A = A = 20.5 auss and A = 13.6 auss.
01 02 g 5 g

In the ab crystallographic plane it was found that
a four-line spectrum resulted for all orientations of the

crystal in the magnetic field. This was demonstrated when

éHL (.3
the plot of the line positions was made for /CH-C-‘-NH2
CH3

radical in a deuterated crystal as is seen in Figure 41.

CH3 .9

The lines for >C-C-NH2
CH3

radical have been left out for

Simplification. The slight anisotropy of the outer lines
is thought to result from a slight misalignment of the crys—

tal in the magnetic field. It was also found that the spec-

tra were more easily resolved using deuterated crystals
than undeuterated ones because the hyperfine splitting from
-NH2 protons is removed in the deuterated crystals: the

deuteriumhhyperfine splittings are much smaller and are

lost in the line width.

136

.._.. 70°

 

h g, __ 900

 

" —- 120°
0 n __ 130°
. o __ 140°

0 —150°

9 — 160°

0 ———170°

 

" 0 ———180°

1 L 1

3250 3275 3300 3355
Gauss -—->

Figure 41. Angular plot of line positions for the
° 0
CH2

CH3/

II
\‘CH-C-NHZ radical in the ab plane.

 

137
Additional evidence for the equivalence of the a and
B protons in the ab plane was provided from variable tem—
perature studies using the Varian V-4557 variable tempera-

ture accessory. The crystal was mounted along both the a

' 0
CH2 "

and b crystallographic axes; the decay of ;:CH-C—NH2
CH3

lines was followed as a function of temperature as shown
in Figures 42 and 43. .It was found that only four lines
decayed at the same rate along either a or b indicating

that the a and B protons must be equivalent in the ab

plane.
CH2 9
When the decay of lines belong to :;CH-C—NH2 radi-
CH3
cal was studied as a function of temperature for H II c*,

it was found that Six lines could be attributed to the

- O
CH 3 u

:;CHEC-NH2 radical as Shown in Figure 44. -In all cases
(:H3

where variable temperature studies were done the lines he-

° 0
CH2 u
longing to >CH-C-‘NH2 radical have disappeared at -80°C
CH3 0
CH3 . u
leaving only those from the >C—C—NH2 radical.
CH3

The line positions found for the spectrum of the

(EH 9

2
’;}1:H-C-NH2 radical were plotted versus angle of orientation

CH3

.Figure 42.

138

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-160°c
-150°C
35 6'
“ —145°c

 

 

 

Variable temperature study of the spectrum of the

- 0
CH2\ u . . _>

CH-c-NH2 radical Wlth H || a.
CH;"

 

m
.4 'L—n

 

-130°c

 

 

 

 

 

—125°c

 

 

—120°c

-115°c

-110°c

igure 42. (Continued)

140

 

- 100°C

 

- 80°C

 

259

gure 42 . (Continued) .

141

_;=

 

-160°c

 

 

 

 

 

 

 

 

 

 

-150°c

ll

Figure 43. Variable temperature study of the spectrum of

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

- 0
CH2\ " _>
the CH-c—NH2 radical with H [I b.
/
c533

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

143

 

 

 

U ‘ -115°c

 

 

 

 

 

 

w W-

see—e

 

 

 

 

 

Figure 43. (Continued).

144

 

” R r n ; 25 G i

 

 

 

-160°c

MAM "1500C

 

 

 

 

 

 

 

 

 

 

o
-140 C

 

 

-130°c

-120°c

 

 

 

 

W
'WNV

 

-115°c

-100°c

Figure 44. Variable temperature study of the spectrum of the
' 0
CH2 " _>

‘CH—C-NHZ radical with H II c*.

C 3

Figure 44 . (Continued).

145

25G

 

-90°c

—80°c

 

146

6 in the bc* and ac*

planes also; these plots are

given in Figures 45 and 46.

In both the bc* and ac*

planes only Six lines were observed for most orientations.

The only exception to this was for H II b in the bc*

plane as mentioned previously. This is consistent with

equivalent Splitting by the two or- protons with an additional

different splitting by the

B proton. At no orientation

were eight lines present as would be true if the a :protons

had become non-equivalent. All measurements were done on

the Spectra of deuterated crystals for these plots.

-There is a certain amount of anisotropy in the case of

the hyperfine Splitting in any of the three crystallographic

planes. It was assumed that (11 - —

— a2 - B in the ab

plane: and (11 = (12 ¢ 6 in the bc* and ac* planes.

Since the amount of anisotropy was small, the hyperfine
splitting tensors were constructed according to Schonland's
method (Equation 48): the results are presented in Table XVI.

The reason for the apparent equivalence of o and 6 pro-

tons in the bc* and ac* planes and their equivalence

in the ab plane is not obvious but will be commented on

in the Conclusions. The Signs have been chosen to agree with

the values found for a and B proton splittings in pre-

vious investigations (Tables I and II).

0
CHK .
C. Radical Stable at Higher Temperatures C

£4512
cit-K

When the crystal was warmed to —80°, as Shown in the

variable temperature Spectra (Figures 42 to 44.) , a seven-line

147

—0° | [b
_100
—-20°
__300

___40°

1

—-60°

ET

 

—-—700
._80
———900 II c*
__100°
__110°

-——120

--130
—1400
——-150°

-—160°
—-——170°

 

——-180°

 

1 l 1 l

u I l l Gauss -*>
3250 3275 3300 3325

' 0
CH2 n
Figure 45. Plot of line positions for ;CH-C-*NH2
CH3
radical as a function of field orientation in

the bc* plane.

148

__ 100

 

l 1 l l
3250 3275 3300 3325 a

Figure 46. Plot of line positions for \CH-C-NHZ

radical as a function of field orientation in
the ac* plane.

Table XVI.

149

~Hyperfine splitting tensors for protons of the

H2_C.\ 9

H3C

/CH "C "NHQ

radical

 

 

 

Proton Principal Values Direction Cosines
(gauss)
o1 = Q2 -24.2 0.99 -0.11 3'0.0
-20.3 .2: 0.0 9' 0.0 1.0
-17.8 -0.11 -0.99 2'0.0
Aiso -20.8
B 22.8 0.98 —0.19 3'0.0
18.9 0.19 0.98 9"0.0
12.2 2’0.0 3'0.0 1.0
A = 18.0

iso

 

150

CH3 . 9

pattern attributed to )C-C-NHz _radical results. This
CH3
radical has previously been reported by. Hamricket al. (17)
in X-irradiated isobutyramide single crystals. '
The basic seven-line pattern was observed for all ori-
entations of the crystal in the magnetic field except
where H II b in the bc* and ab planes as is seen in
Figure 47. The measured splitting when H I] b was 4.6
gauss for the additional doublet fine structure which agrees
well with the 4.2 gauss splitting reported previously (17)
for one of the protons of the —NH2 group. The quintet pat-
tern for H I] c* , which arises from equivalent splitting
by the -‘NH2 protons and the amine group nitrogen, was also
observed and agrees with previous work (17) . The measured
hyperfine Splitting for H H c* was 2.5 gauss for the
quintet Splitting and the spectrum obtained when H H c* in
the ac* plane is Shown in Figure 48. The A." tensor for
the Six-equivalent Bw-methyl protons was constructed using
Schonland's method and the principal values obtained by the
usual procedure. Principal values for the hyperfine Split-

ting tensor and the associated direction cosines are given

in ~ Table XVII .

 

151

men 6H

kWh-.115...

firm

 

A.

‘D

0 mN

 

.-
5‘

fit. H863

 

 

 

 

 

 

 

 

 

 

«m2: 0... o/

O

 

 

m
\mmU

. «mo

 

 

 

 

 

 

 

 

 

.mSMHm no
0:» mo Ednuommm mmm.

.bv onsmHm

 

 

 

 

 

152

4r

*0m

0 mN

 

A.

 

 

 

0:» SH *0 __Am. nuHB HmoHomH umzrol

O

0’

m
\\30

«mo

 

 

.mSmHm
onu mo Eduuowmm Mum

.wv ousmHm

 

153

Table XVII. Hyperfine splitting tensor for methyl protons
CH3 . 9
in the ,)C-C-NH2 Radical.
CH3

 

 

Principal Values

 

pjgauss) Direction Cosines
23.0 0.00 0.91 0.40
21.7 0.00 -0.40 0.91
21.7 1.00 ~0.00 0.00

 

IV. Irradiated Single prstals of Hydrazinium.Dichloride

A. Crystal Structure

The crystal structure of hydrazinium dichloride has
been previously reported (14). The unit cell is cubic with
a = 7.89 R. The space group is Tg - Pa3 with four mole-
cules per unit cell.

.Crystals grew easily from aqueous solution and were

mounted along cubic axes with relative ease.

B. Presence of C12- at 77°K

 

Single crystals of hydrazinium dichloride were y—irradiL

ated for 3 hours at 77°K and then mounted without warm-up.

The crystal was rotated in the aa' plane. .When ngt
was 45° from the a axis in the aa' plane, the Spectrum
of Figure 49 was obtained. Although the Spectrum is compli-

cated, it was possible from the outermost low and high'field

154

.mSmHm .mm 0:» SH m Eoum omv

mH Am .Mobb um ooHHoHsoHo ESHSHNSHUNS owumHomHHH mo Eduuowmm mum, .mv mHSOHm

w on

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

155

lines to confirm the presence of C12_. -The hyperfine split-
ting at this orientation is 97.3 gauss which is in reasonable
agreement with reported maximum hyperfine Splittings for
Clz-. The measured 9 value was 2.0035 which is Slightly
larger than the expected 9 value at this position (where

A is a maximum). Rotation in the aa' plane again shows

a maximum hyperfine splitting of 96.4 gauss 135° from a

or 90° from the above orientation as shown ianigure 50.

These spectra indicate that the species C12- is pres-
ent and is oriented along (110) directions in the crystal.

It was not possible to analyze completely the hyperfine split-
ting tensor for C12- because the presence of a second un-
identified radical made the spectra complex and a complete
analysis impossible. This complexity is illustrated in Fig-
ure 51 which shows the spectrum obtained when the crystal

is rotated 45° from the position in Figure 49.

When the crystal was warmed, it was found that C12-
lines had almost disappeared by -80° and the spectrum of a
secxnrd radical predominated. Analysis of this second radi-
cal wms not possible due to the large number of molecules
per unit cell and the complexity of the spectra. Figure 52
Shows the Spectrum of the second radical at 45° from H II a-
111 the aa' plane. The second radical, previously discovered

by'Vflaiffen (142), remained even at room temperatures.

156

5....

Am

 

.mSmHm .mm 0:» SH m EOHH omMH
.Mobb um moHHoHSUHo ESHSHNmHoNS omSMHomHHH Ho Enuuommm Mmm, .om musmHm

0 On

 

 

 

.mSmHm .mm map SH w EOHM
com mH m .Mobb um moHHOHSUHo ESHSHNmHomn omSMHomuuH mo Esuuommm mmm. .Hm mHSmHm

Al

0 Oh

157

 

 

 

158

.mSmHm .mm 0:» SH m Eoum one mH Am

. om ou OSHEHSB Hmumm onHoHSUHo ESHSHNSHONS owumHomHHH mo Esuuommm Mmm
c I . .

0 on

 

 

 

 

 

 

.Nm oHSOHh

 

159

\L grradiated Single Crystals of Hydrazinium Dibromide

A. ACrystal.Structure

No crystallographic data for hydrazinium dibromide have

been previously reported. The space group and unit cell

dimensions were determined using the usual Weissenberg and
Precession method. X-ray photos Showed the unit cell to be
a = 3.86 X, b = 7.53 R, c = 10.28

001:

monoclinic with dimensions
R . and B - 94°. Systematic absences occur only for

l = 2n, consistent with space groups P21 or P21/m. *The

measured density in a mixture of methylene bromide (p):

2.495 g/ml) and carbon tetrachloride (p = 1.589 g/ml) gave

.2.144 g/ml. This yields a theoretical 1.98 molecules per

Lurit cell consistent with the Space group P21. The obser-

xnation that the crystal was attracted to the walls of a

Silvered dewar flask containing liquid nitrogen is further

evidence for the space group P21.

.A.drawing of the crystal Showing the location of the

a*, 13 and c crystal axes is given in Figure 53. The crys-

taJ.<grew so that the long edge was parallel to b.

:B. Brz- Radical in Crystals Irradiated at 77°K

ESingle crystals of hydrazinium dibromide were put in

glass vials and y—irradiated for periods of 5 to 10 hours

at 77°K. The crystals were then mounted, without warm-up,

in the single-crystal holder described previously.

160

 

 

 

 

 

 

Figure 53. Crystal axes for hydrazinium dibromide.

161
It was found that the spectrum of y—irradiated hydra-
zinium dibromide Single crystals at 77°K consisted of seven

basic groups of lines forming a septet with superhyperfine
structure on each line. The main lines of the septet had
relative intensity ratios nearly 1:2:3:4:3:2:1. -Figure 54
shows the Spectrum obtained after 5 hours of y-irradiation;

§:xt is 30° from b in the ho plane and the measured

hyperfine splitting at this orientation is 366 gauss.

-Each line of the septet is further split and it should

be noted that the outer lines are 1:2:1 triplets. The spec—

trum of Figure 54 was assigned to the radical anion Brz- in
which the odd electron interacts equally with the two Br
(I = 3/2) nuclei which couple together to give an effective

nuclear spin of three and hence the basic seven-line pattern

«observed. The 1:2:1 triplet structure of the outermost
lines results from the presence of two isotopes of bromine.
The outermost line of the triplet belongs to the radical

(813r - 31Br)- formed from two bromine nuclei of mass 81

(49.43% natural abundance). The next innermost line, which

is tnvice as intense, belongs to (79Br - slBr)- and

(313r — 79Br)-. Finally the last line of the triplet pat-

tern can be assigned to the radical anion ("Br - 79Br)-

formed with two 7(9Br nuclei (50.57% natural abundance).
These anion radicals have been observed previously and

are well characterized. For the space group P21 one would

expect two nonequivalent radicals per unit cell: this was

found to be the case for Brz- in NzHBBrz. The two radicals

162

6H

m

 

.mSmHm on may SH Q EOHM com
.Xobh um moHEounHo ESHSHNmuomn ovumHomnnH mo Enuuommm mum

 

.em mHSOHh

 

L

 

163
become equivalent at certain positions as the crystal is
rotated in the magnetic field. -Figure 55 shows the spec—
trum at the orientation where the minimum hyperfine split-
ting is encountered; 1fi2xt is 30° from c in the a*c
plane and the hyperfine splitting at this position is 128
gauss.

Principal values for the i' and 3' tensors were
computed using Schonland's method. The anisotropy was large
enough that the conventional curve fitting technique failed
to apply. The plots of hyperfine Splitting versus angle
of rotation are given in Figures 56 to 58: the plots of
g versus angle of rotation are given in Figures 59 to 61.

I\ compilation of the principal values for each tensor and

'cheir associated direction cosines is given in Table XVIII.

Table XVIII. Principal values of the hyperfine Splitting
tensor and g tensor for Bra in y—irradi—
ated hydrazinium dibromide.

 

 

 

Tensor Principal Values Direction Cosines
(gauss)
3' 415.6 0.75 0.64 0.16
243.5 -0.61 0.57 0.55
79.7 0.26 -0.51 0.82
3- 2.0635 0.40 0.08 -0.91
2.0471 -0.59 0.78 -0.19

1.9809 0.70 0.61 0.36

 

164

3

m

All

.mSmHm 0*m 0:» SH 0 Eoum com
.mobh um moHEoHQHo ESHSHNSHONS omumHomnuH Ho ESHuommm mmm

0 OOH

 

 

.mm mHSOHm

 

 

 

 

 

 

165

.mSmHm a*m

OmH OOH

msu SH SoHumuou mo onSm momnm>

m

.3:
ca” one ooH om

0:
N O
______I.

«Hm mo mSHuuHHmm mSHHHmmmm_ .Om musmHm

O 0 II OOH Ammsmmv

_Il OON

II.OOm

II oov

166

.mSmHm

on

0:» SH SOHumuon mo mHmSm mSmHm>

O
0.:

omH _ owfl _ owe omH ooH om

mum mo OSHuuHHmm oSHmHmmmm

0:
om ow on o

_ _ _ _ _ _ r4

II.OOH

 

.sn musmHm

Ammsmmv

167

OOH

 

0*m

0:» SH SOHumuou mo onSm mSmHm>

e
0:
cue oeH omH ooH om

_._ _ _ . r _ __

.mSmHm
«am no mSHuuHHmm oSHmummNm .wm musmHm

.m __
OO Ow ON O
_ _ . . _ _.rn
II. OOH
Ammsmmv
d
OON
OON

OOfi

168

.wSmHm 9*m

OOH OOH

was cH

OvH

 

ONH

How SoHumuoH mo mHmSm mSme> m mo uon .on musmHm

e

4m: a:

ooH om cm as ea c

__________r|r_e3o.N
Incomes
I my
.1.oomo.~
rr.ooeo.n
.r.oono.m

l\\.b

 

II.OOOO.N

 

169

5W9i'lit 1

.oSMHm

on may cH

 

ON

«Hm How SOHumuou mo mHmSm mSmHm> O no uon .OO musmHm

0:
o

_ l_

II.OmOO.N

0

ll OnHO. N

I ammo. a
11.8mmo.m
rr.cmvo.m
I. ammo. a

II. omOO. N

170

OOH

OOH

.wSmHm

OHH

0*m

ONH

mnu SH Innm Sow SoHumuou mo mHmSm mSmHm> O no uon
O
o: 4.:
OOH om OO ow ON

o
_____hv_._Uooma.H

,V

O I OOOO. H

o In OOOO. N
0 II

a l 83. N
0

II OONO. N

1| OONO. N

II OOHuO. N

I. OOOO. N

..I OOOO. N

.HO musmHm

171

C. Temperature Studies

When a crystal of y-irradiated hydrazinium dibromide
was allowed to warm to -160° it was found that the Spec-
trum due to Bra- had disappeared. The measurements were
done using the Varian V—4557 variable temperature dewar
insert, although essentially the same results could be ob-
tained by allowing the crystal to warm in an isopentane—

liquid nitrogen Slush bath at -155°.

 

The spectrum obtained consisted of a single line with
g = 2.0043 which ultimately disappeared as the temperature
was raised to -60°. No structure was noted on this line
'which would indicate any interaction with other magnetic
nuclei. In the absence of any other information this line
can be attributed to the formation of a peroxide radical at
—160° after Brz- has disappeared. Figure 62 shows the
first—derivative spectrum obtained with H ll‘c in the
a*c plane. .First-derivative presentation was necessary
since the concentration of radical was too low to obtain
second-derivative Spectra .

No other radical was observed after the decay of the

peroxide radical indicating that and radicals produced from

its decay are very unstalbe. No radicals stable at room

temperature are produced.

172

 

.mSmHm a*c 0:» SH 0 __ m noOOHI ou omEHMB

moHEounHo ESHSHNSHUNS oouMHUMHHH mo Esuuommm

O OO

 

 

 

mm w>Hum>HHmo umHHm

 

.mm musmHm

173

VI. Irradiated Hydrazinium Difluoride

A. Crystal Structure

Kronberg and Harker (136) report that hydrazinium di-

fluoride is hexagonal with unit cell dimensions a0 =
4.43 i 0.01 R and co = 14.37 i 0.02 R and Space group

ng - 2'35; the measured density of 1.46 g/ml gives three

molecules per unit cell.

Truncated hexahedra grew easily from a 1:2 molar mix-

ture of hydrazine hydrate and hydrofluoric acid. The large

hexagonal face was found to be perpendicular to the c

crystallographic axis in some cases. A drawing of the crys—

tal is given in Figure 63 Showing the more frequently en-

countered case where the c axis is perpendicular to one

(If the side faces. Because of the unique axis system en-

cyountered in hexagonal crystals, the reference axes chosen

were the c crystallographic axis and two others perpen-

dirnilar to c as defined in Figure 63.

B. Hydrogen Atoms Formed at 779K

.A Single crystal of hydrazinium difluoride was elec-

trtni irradiated with the G.E. Resonant Transformer for

eight minutes at 77°K according to the procedure outlined

in the Experimental section. The crystal was then mounted

and the ESR spectrum observed at 77°K.

when the crystal was mounted with .H H c, a doublet

appeared as shown in Figure 64. The separation between

 

174

L.
r

 

 

 

.l
I
I
I

/)—-———

/

/

_ ______(‘

/

b

 

 

Figure 63. Crystal reference axes for hydrazinium difluoride;
c .is the threefold axis.

175

 

 

.mSmHm on map SH
0 __Am .AumHnsoo Hmusov Eoum Smmouown on» no Eduuoomm on» OSHSOSm
Mebb.Mm moHSosHmHo ESHSHNmuoms omumHomuuH SOHDUOHO mo Esuuoomm Smm. .¢O ousmHm

 

O OO

 

 

\g.

 

 

 

176
these lines was found to be 508 gauss. AS the crystal was
rotated in the plane perpendicular to c, it was found that
the doublet hyperfine splitting remained essentially con-
§t9331339 equal to 508 gauss. This splitting is attributed
to the presence of hydrogen atoms trapped in the crystal.
In order to prove the existence of hydrogen atoms the hydra—
zinium difluoride was exchanged three times with D20. .Since
the magnetic moment of deuterium is 0.32 times the magnetic
moment of a proton, the hyperfine splitting for deuterium
atoms is only 15.4% of that for protons or about 78 gauss.
Figure 65 Shows the ESR Spectrum of a crystal of NgDst
'which had been y-irradiated for ten hours with H [I c in
the bc plane. The spectrum consists of a broad central
(peak with a line spaced equally on either side of the cen-
tral peak by 61 gauss. As the crystal is rotated in each of
the three reference planes ab, bc, and ac, the splitting
changes from a maximum of 61 gauss to a minimum of 55 gauss,
and.thus remains fairly isotropic. This splitting is prob-
rably due to deuterium atoms: however, the reason for the
‘perturbation from the theoretical value of 85 gauss is not
tinderstood. ~This effect was not noted in the case of hydro~

«gen.atoms where the isotropic splitting was always 508 gauss.

C. «Radical Pairs at 77°K

Single crystals of hydrazinium difluoride were y-ir-
radiated for ten hours at 77°K and were mounted without

warms-up in the usual manner. The spectrum was found to be

 

177

.0523 on 0:» SH 0 __ m, .Ouo SSH»; ommSmsoxm Soon mm:
SUHSB onHOSHmHo ESHSHNSHUNS omummmmunHr> «0 Met. um Esuuommm mum. .OO musmHh

w
.E-

GOO

 

 

 

 

178

very sensitive to the amount of microwave power used: it
was necessary to use 30 db attenuation of the high power
arm of the Varian microwave bridge to avoid saturation.
When the crystal was mounted in the bc plane with H I] c
the spectrum of Figure 66 was obtained. AS can be seen
from the spectrum, the pattern observed is quite complicated
but the outer lines in the central portion can be attributed
to the presence of a radical pair. This was confirmed by
the observation of a complex group of lines at g 3'4
(Fig. 67). The spectra are not well enough resolved even
with H I] c to permit identification of the species form-
ing the pair: when the field is rotated from H II c the
Signals from the pair rapidly become unobservable.

.The strong lines in the center of the Spectrum of Figure
66 are from a radical which is stable at higher temperatures.
By warming to -70° the radical pairs may be destroyed and
well-resolved spectra of the new radical obtained as dis-

cussed below.
D. The Radical at -70°

A Single crystal ofludrazinium difluoride,which had
been y-irradiated for ten hours, was allowed to warm to -70°
in a liquid nitrogen-acrylonitrile slush bath for three
minutes. It was found that the radical-pair Spectrum had
disappeared after this treatment; a much Simpler spectrum
was observed. Figure 68 shows the spectrum with Hlic in

the bc plane. The pattern is a septet of quintets with

179

L.

 

.HHmm HMUHomu m on
muSQHHuum mum mon some So mmSHH Sm>mm Houso one. .OSMHQ on map SH
_AmnuH3 Moth um moHHOSHHHo ESHSHNMHONS omumHomnqu> mo Enuuommm mum, .OO musmHm

O OO

 

 

 

 

 

 

 

 

 

 

 

 

 

180

.SoHuSHommH Hmuumn SSHB mmSHH v u 0 map An . u m um OUSSS
Iommn may on m>HumHmH mmSHH v n.O may no SOHuHmom Am “0 m_Am, SUHB Kath

um moHHOSHHHo ESHSHNmHoNS OOSMHomHHHI> mo Esuuommm Mum m>Hum>HHmo umHHm_

3V

TI.
0 ON

0 FF.waN H m

 

 

 

.bO OHSOHm

181

 

 

.cObI on omEHm3 moHSOSHHHo ESHSHNMHUNS ow

 

‘.

0 ON

 

 

 

 

 

 

 

 

 

 

 

 

 

.mSmHm on may SH 0 __
SSHomHHHI> mo ESHuommm m

 

 

 

 

 

 

 

 

 

 

mm
mm .OO musmHm

 

182

intensity ratios for the septet being nearly the binomial values
1:6: 15:20:15:6:1, while those for the quintet hyperfine are
approximately in the ratio 1:2:3:2:1. -The outer lines of
the quintet pattern are not visible on all the lines of the
septet due to overlap. This is indicated in Figure 68.

»The Spectrum of Figure 68 has been attributed to a radi—
cal with coupling to Six equivalent protons resulting in
the septet pattern. The quintet fine Structure on each
line of the septet is attributed to equivalent coupling by

two nitrogen nuclei (I = 2). The proton hyperfine

total
splitting for H II c (Figure 68) is 19.3 gauss and the
nitrogen splitting is 6.0 gauss. AS the crystal is rotated
in the ho plane toward the b-axis, the Spectrum of Figure
69 is observed when §:xt is 40° from .c. This pattern
can be again assigned to equivalent Splitting by six protons
with a smaller splitting by two equivalent nitrogen nuclei.
.The proton splitting at this orientation is 15.1 gauss; the
nitrogen splitting is 5.5 gauss as indicated in Figure 69.
As the crystal is rotated further in the bc plane, the
nitrogen and proton Splittings decrease. The spectrum of
Figure 69 appears again at 135°} and that of Figure 68 re-
appears for 9 = 180° (H II c).

In the ab plane (H J_c) the nitrogen splitting is
unobservable for all orientations. -The maximum proton
splitting occurs 30° from the a-axis and is 19.3 gauss.

This orientation is shown in Figure 70. The minimum proton

Splitting occurs when fi2xt is 120° from the a axis in the

183

. .OGMHQ 0Q 03“ CH U EOHM OOfi mH Am
.oObr ou omEHMB moHHOSHmHo ESHSHNmHomn UOSMHUMHHHI> mo Esuuommm mum. .OO OHSOHm

 

r R

0 ON

 

 

 

 

 

 

 

 

;

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

184

T

.Amem 0 on H.0SmHmv OSMHQ Am mnu SH mem m may ECHO com mH
con: 0» ooEHmz moHHosHmHo ESHSHNSHONS omumHomuHHa> mo Esuuowmm m

I.

0 ON

3
MM. .Ob wusmHm

 

 

185

ab plane and is estimated from the line width to be 12.6
gauss. -This orientation is shown in Figure 71.

In the ac plane the Spectrum of Figure 71 is shown
when H ||c , while that of Figure 69 appears when fi:xt
is 50° from the a axis. .Further rotation gives the septet
of quintets again at 90° from a in the ac plane (H II C).
Further rotation in the ac plane gives the Spectrum of )
Figure 69 when Hex is 109° from a in. the ac plane

t
resulting ultimately in the spectrum of Figure 71 for

H I] a.

The hyperfine Splittings for both nitrogen and hydrogen
‘were followed as the crystal was rotated in each of the
three reference planes. ~The angular variation was most
‘pronounced in the bc and ab planes in the case of the
laroton hyperfine splitting. The nitrogen splitting in the
ab plane (H l c) was assumed to be rather constant and
equal to 1.7 gauss for all crystal orientations. ~~ These
pilots are given in Figures 72 to 74. -The principal values
caf the nitrogen tensor were obtained by Schonland's method.
Enough points were available to permit a curve fit (Equa-
‘tixzn 46) for the proton hyperfine values. -The results of

these calculations are given in Table XIX.

The g value for the radical was found to change very
ljjztle and was 2.0035 1 0.0005 for all orientations in the
at). be and ac reference planes.

'Upon warming no other radical appeared, but it was:noted

‘true -70° radical was stable after being brought to room

186

.mSmHm no 0:» SH mem m was Eoum oONH mH m.

.oObr on omEHMB moHHOSHHHo ESHSHNMHUNS UOSMHOMHHHI> mo Eduuowmm mmw

 

.Hb musmHm

 

187

mSmHm no

OOH

.HmoHomH con: man How
on» SH OSHuuHHmm OSHHHOQNS Smmonomz on» no SOHSMHHM> HMHSOSO .Nb OHSOHm

O
Q m
OOH O¢H ONH OOH OO OO oe O

N O
____________.___J

N

Ammsmmv

'3 a.

 

188

 

.HSOHomu oObI map How OSMHQ on
on» SH OSHuuHHmm mSHmHmmmn Smmouomn OSm SOOOHUHS map mo SOHumHHm> HmHSOSO. .Ob OHSOHm

o
o n
OOH OOH ovH ONH OOH OO OO ow ON O
.___.____.________I_
N
0 II _v
00
II. O
II. O
Smmouqu
0 I1OHAmmSmmv
Sou0um0 O,
.II NH
vH
OH
OH
ON

 

NN

189

 

.HmoHomu cone 0:» How mSmHm om may SH.
mSHuuHHmm mSHOHmmmS SOOOHONS OSm SmmouuHS 0:» mo SoHumHHm> HMHSOSO. .vb OHSOHm

Smmonqu, 0

Sououm 0

 

ON

190

vTable XIX. Hyperfine splitting tensors for nitrogen and
hydrogen in the -70° radical.

 

 

Tensor

Principal values

Direction COSines

 

 

 

 

(gauss)

-18.4 -O.82 -0.21 0.54
-12.0 0.44 -0.82 0.36

A180 3 -17.2
AN 1.7 1.00 0.00 0.00
6.0 0.00 0.17 -0.98
1.5 0.00 0.98 0.17

A. = 3.1

180

 

temperature. No trace of

'was found above -80°.

the Spectrum from hydrogen atoms

When the deuterated hydraziniumcfifluoride crystal was

examined the Spectra were, as expected, relatively unresolved.

-Since the nitrogen Splitting is small all resolution was

lost. .The Spectrum of Figure 75 is the only exception and

inas obtained when the magnetic field was —10° from the c

axis in the ac plane.

At this position the nitrogen split-

ting is large enough to permit the resolution of some of

the deuterium lines. ”The separation of the lines on the

laigh-field Side of the central peak is 3.1 gauss.

'ThiS is

Fir-In...

191

 

.mSmHm on map SH mem u or» Eoum coHI mH Am

.xobh um moHHOSHOHo ESHSHNSHONS omumnmusmo OOUMHUSHHHI> mo ESHuommm MOO.

r p
a J

O OO

 

 

 

 

.Oh mnsmHm

192
close to the expected value of 3.5 gauss for the maximum
deuterium splitting which should be about 0.153 AH or
21.2 x 1,6.5= 3.3 gauss at this orientation.

CON CLUS IONS
I. Radicals in Irradiated Acetamidine Hydrochloride

A. C12" Radical in Irradiated Acetamidine Hydrochloride

 

Radical anions of the type X2-, where X iS‘a halogen
species have been known for some time among the products
of irradiated alkali halides (80,81). Their appearance in
irradiated organic crystals was not reported until recently
when Box gg_gl. (86) observed C12- in X-irradiated mono-
clinic glycine hydrochloride. The principal values of the
chlorine hyperfine Splitting tensor which he reports are
110.7 gauss, 42.5 gauss and 24.3 gauss, slightly higher than
the principal values of 103.1 gauss, 29.8 gauss, and 10.0
gauss observed in the present case. ~The values reported
by Ueda (85) (103.9, 32.1 and 12.1 gauss) in irradiated
hydroxylamine hydrochloride are in better agreement with
those found here. .The crystal environment of C12- in y-ir-
radiated NHaofiCl is such that each chlorine has three
nearest neighbor chlorines. The Cl-Cl distances calcu-
lated from the crystal structure of NH30HCl are Cll-Cla
(3.92 R), Cl1—Cl4 (4.90 R), Cll-Cla (4.17 8), while the dis—
tances from chlorine to other nuclei are much closer, QLQ.

Cll—N (3.16 R). These neighboring N, O and H atoms

193

194
could cause the distortion of the hyperfine tensor of C12-
from the expected axial symmetry. Although a detailed X-
ray analysis has not been done for acetamidine hydrochloride,
a distortion of the hyperfine tensor from axial symmetry
might be expected, depending on the relative positions of
the chlorine nuclei with respect to the neighboring nitrogen
and carbon nuclei, because of the low (monoclinic) sym—
metry. The Space group of acetamidine hydrochloride (P21)
does make such a distortion seem reasonable in light of the
results of Box (86) on glycine hydrochloride which is also
monoclinic (Space group P21/E).

Additional evidence for the asymmetry of the C12_ hyper-
fine tensor is supplied by a computer Simulation of C12-
assuming axial symmetry. The program, which was written
for the CDC 3600 computer, assumed axial symmetry for both
the K' and 3' tensors with All = 103.1 gauss, AJ.=
10.0 gauss, 9'] = 2.0437, and 91.: 2.0011 as determined
by the diagonalization procedure. The program was designed
to Simulate a powder pattern using Bleaney's equation (107)
(Equation 34). To obtain a spectrum to compare with this
computed one a sample of acetamidine hydrochloride which
had been y-irradiated for three hours at 77°K was examined.
The comparison is shown in Figure 76. It is quite evident
that the agreement is poor and that the hyperfine splitting
tensor for C12- is not axially symmetric.

It is evident from the direction cosines that the largest

principal value, 103.1 gauss, lies nearly along the b axis

195

.ESHuommm owusmeov on .Esuuowmm ow>nmmno Am

«move um Hmo3om moHHOHSUOHoms mSHoHEmuwom omumHomnuHI> mo Enuuommm OOH

 

 

 

 

 

 

 

 

 

.oe madman

196
which also corresponds to the minimum 9 value of 2.0011.
In glycine hydrochloride the maximum hyperfine Splitting
of 110.7 gauss lies nearly along the c axis which also cor—
responds to the direction of minimum 9, g = 1.999.

There have been other examples of irradiated hydro-
chloride salts of organic compounds reported in which no
trace of C12- was found, including irradiated guanine
hydrochloride dihydrate (51), L-leucine hydrochloride (143)

and L-lysine monohydrochloride dihydrate (31).

 

+
NHg

, n
B. CH3-C-NH3 Radical

 

The radical formed by the abstraction of an a-proton
from acetamidine hydrochloride probably arises by the fol-

lowing scheme:

 

+ +
NHg NH:
_ u . :1
C12 + CH3'C‘NH2 > H. + CH2”C"NH2 + C12 + e
+
NHg +NH:

‘H' + CH3-C-NH2

 

u
> H2 'l' 'CHz-C-NHZ

'Fhe C12- fragment formed at 77°K might be expected to lose
its extra electron, which is in a o antibonding orbital,

'but it.seems reasonable to assume that the Cl-Cl bond should
remain.intact, since it requires 57.1 kcal/mole to break
this bond. The energy for the decomposition of C12- to

(112 and an electron would then go to break a CH bond.
The C-H bond energy of 98.2 kcal/mole is large but could

be overcome by the ability of H' to abstract an

197

+NH2

a-hydrogen atom from a neighboring CH3-C-NH2 molecule to
form stable .H2. The gain in enthalpy of 103.2 kcal/mole
for H2 formation could account for the C-H bond breakage
+NH1

in the second step. The process for forming CH3-C-NH3'
radical appears therefore to involve a secondary radiative
attack by H'.

The principal values of the a proton hyperfine Split-

+NH2

ting tensor indicate that CH3-E-NH3 ' radical is a w-
electron radical with the odd electron in a p” orbital
on carbon; these are (-35.9, -23.1, -7.5 gauss) for H1
and (-36.2, —19.0, -5.8 gauss) for H2, which are charac-
teristic of the values obtained for a protons. .The iso-
tropic values for H1 (-22.2 gauss) and for H; (-20.3
gauss) are characteristic of isotropic splittings in which
carbon has induced a spin polarization of about -0.05 in
the hydrogen 1s orbital.

The anisotropic parts of the hyperfine tensor are
-13.7 gauss, -0.9 gauss and +14.7 gauss for proton H1 and
-15.9 gauss, +1.3 gauss, and +14.5 gauss for proton H2
in agreement with the anticipated axial symmetry of the
anisotropic components.

The amount of s character in the molecular orbital
containing the odd electron may be estimated by comparing

the isotropic proton splitting with the theoretical value

 

198

of 508 gauss for a pure ls orbital on hydrogen and is

found to be from 4.0 to 4.4%, in good agreement with the

5% delocalization predicted from spin polarization.
McConnell (144) proposed a relationship between iso-

tropic splitting and the spin density on carbon pc:

H
a = Op

6 c

(72)
where Q is -22.4 gauss, assuming Spin polarization of
-0.05. Using McConnell's relation and the ,Q value above
the Spin density on carbon in the radical from acetamidine
is 0.91. The odd electron density is therefore localized
on a 2p orbital on carbon to the extent of 91% and is
only 4.0 to 4.4% on each proton.

In agreement with the results for other w-electron
radicals, the most positive principal value is associated
with the direction parallel to the c—H bond. For this
direction the corresponding anisotropic values are 14.7
gauss for proton H1 and 14.5 gauss for proton H2. The
most negative principal values of the proton tensors are
associated with the directions perpendicular to the C-H
bond in the plane of the radical and these are -13.7 gauss
and —15.9 gauss for protons ‘H1 and H2, respectively.
The other values are associated with the directions parallel
to the p71’ orbital.

Using the direction cosines for the principal values
in the plane of the radical and along the C-H bonds it is

found that the angle between the two protons is 111°_36',

'-e'. ‘—

.3

199
which is not far from the normal tetrahedral angle for Sp3
hybridized bonds. Thus, it seems as if not much distortion
of this bond angle has resulted from the formation of the F-
radical. It would be necessary to obtain the 13C hyper-
fine Splitting in order to estimate the deviation from
planarity, if any, for the radical but the necessary hyper-
fine lines could not be observed.

The principal values of the hyperfine Splitting tensor
for the -NH2 protons are,as stated before in good agreement
with the values reported by Kashiwagi (139) for the radical
H3NOCCHZCHCONH3 in irradiated Single crystals of succin—
amide. The anisotropic contributions to the principal
values are -2.3 gauss, 0.0 gauss and 2.4 gauss. Since the
principal values were the same for both protons, the protons
are equivalent. The reason for the absence of any nitro—
gen hyperfine splitting is probably that the interaction,
which is a long-range one, is very small. Kashiwagi (139)
obserxed a nitrogen splitting with principal values of 5.3
gauss, 0.4 gauss and 0.2 gauss in the case of

o ., O-'
u . - u
HzN-C-CHZ-CH-C-NHZ radical.. Such an interaction would

surely be evident in the deuterated form but was not found.
II. Radicals in Irradiated Trimethylacetamide

A. t-Butyl Radical

 

The primary product of y—irradiation of trimethyl-

acetamide single crystals is the Efbutyl radical; this has

 

200

been previously detected in irradiated powders (140,142)
and in several liquids (48,147). The binomial intensity
distribution of 1:9:36:84:126:126:84:36:9:1 observed is
characteristic of equivalent hyperfine splitting by 9 pro-
tons. The B-proton splittings are isotropic as eXpected
from previous studies of this radical (Table II). The
proton hyperfine splitting, 22.9 gauss, is a reasonable
value for B-methyl protons (17,18,29,37,43). The equiva-
lence of the methyl protons implies rotation about the
C-CH3 bonds at 77°K. The tunnelling rate for the methyl
groups must be faster than 107 sec-1. Horsfield‘ggygl.
(36) explain the nonequivalence of the three -CH3 pro-
tons in the CH3-CH-COOH radical (from y-irradiated
l-a-alanine) as arising from lifting of the three-fold
degeneracy of the torsional energy levels. This could
result from a tunnel effect if the barrier to rotation
is small or from the hyperfine coupling itself. This im-
plies, in the case of CH3-CH-COOH, that the tunnelling
rate is Slower than 107 sec“1 if the methyl protons are
nonequivalent.

No noticeable effect occurs upon raising the tempera-
ture except that the lines sharpen somewhat, probably as a
result of decreased broadening from the lines of the

CH2 0

H3C-C -C-NH2 radical.
I
CH3

201

The positive Sign attributed to the B-proton Splitting
in the Efbutyl radical is in accord with the convention (61)
for such an assignment based on theoretical considerations
which allow mixing of the 2pz orbital on the a carbon with
a pseudo w System on the methyl group. Both molecular or-
bital (145) and valence bond (146) calculations predict
positive Spin density on the methyl protons resulting in

the positive sign for B—proton splittings.

CH3
I

B. 13c Splitting in nae—13c' .Radical
I
CH3

 

 

The maximum splitting from 13C for Efbutyl radical was
observed at 10° from b in the ab plane and was 92 gauss.
Since the complete tensor could not be obtained for 13C it
was not possible to measure the large anisotropy usually
, associated with 13C Splittings (Table 7).

It was possible to obtain an estimate of the deviation
from planarity of the radical by using the equation of
Karplus and Fraenkel (120) (Equation 67) along with the
anisotropic and isotropic carbon hyperfine splittings pre-
viously reported for methyl radical (24). The 13C tensor
is assumed to be axially symmetric and the isotropic Split—

ting for 13C may then be written
13 : 13 . -

‘where 2B0 = 45 gauss (24). Using these values .Aiso(13C)

47 gauss and 6, the deviation from planarity, is found

202
to be 6 = 3° 31'. This means that the radical has been
distorted from the planar arrangement of the methyl radical
to a conformation in which the C-C bonds are bent 3.5°
out of the plane. More drastic changes are noted in the
cases of 'CXa where X is a halogen atom (Table XI)
Since these substituents have more tendency to be repelled
by the electron Spin density in the odd electron p—orbital
on carbon.

Molecular orbital calculations (148,149) have been
previously done on some substituted methyl radicals. -The
list, however, does not include Efbutyl radical. .An
interesting method has been proposed recently by Pauling
(150) who uses electronegativities of groups attached to
the methyl carbon to calculate bond angles. Since the
electronegativity of -CH3 is essentially the same as that
of hydrogen the method would predict a planar radical.

CH3 0
C. H3C-C -C-NH2 Radical
'— an,

 

The presence of another radical which gives a three-
line spectrum with relative intensities 1:2:1 was also ob-
served at 77°K. This has been attributed to the presence

CH2 0
I II

of H3C—C - C-NH2 radical. The radical is apparently re-
CH3

orienting more rapidly than 107 sec.1 Since anisotropy

would be detected in the hyperfine Splitting otherwise (36).

203
The barrier to reorientation is probably less than 4-5 kcal
but it was not possible to measure the potential energy bar-
rier Since no line broadening was noted.

The hyperfine Splittings for the radical are consistent
with those observed for other w-electron radicals with the
electron primarily localized in 3 2p orbital on carbon.

The amount of Spin density on carbon using McConnell's re-
lation(144), AH = Qpc, and the measured isotropic splits
ting of -22.4 gauss gives PC = 1.00. .The actual spin
density is obviously somewhat less than this since there
must be some spin polarization for the proton hyperfine

interactions to be observed.

III. -Radicals in y-Irradiated Isobutyramide

 

° 0
CH2 u
A. >CH-C-‘NH2 Radical at 77°K
C33
CH2 9
The spectra obtained at 77°K for ’:fCH-C—NH2 indi—
CH3

cate that.the proton hyperfine Splittings for two a protons
rand a single B proton are approximately equal. Any inter-
action with the -NH3 protons was ruled out by the Spectra
from the deuterated crystal. In the case of the a protons
the anisotropy observed is small, —-17 .8 gauss to -24.2 gauss.
The apparent equivalence of the a proton splittings must

be a result of restricted motion about the CHz-CH bond
which could be of the order of 107 sec-1. If it happened

that the frequency of the reorientation coincided nearly

v’a'. '

204
with this value then a detectable amount of anisotropy, but
not the full anisotropy, might be observed. This contrasts
with a somewhat less restricted reorientation which was

CH2 0
I II

observed in the case of the CH3-C -C-NH2 radical found
I
CH3

in y—irradiated trimethylacetamide.

.The isotropic proton splitting for the a protons is in
the range usually found for such splittings (Table I).
Using McConnell's relation (144), AH = Qpc, the calculated
spin density on the a carbon is 0.93 with probable equal
spin densities on the a protons accounting for the remain-
ing spin density. The direction cosines indicate that the
principal values are oriented close to the crystallographic
axes. The proton anisotropic splitting of -3.4 gauss is
directed nearly along the a axis, the splitting of +0.5
gauss nearly along the c* axis, and the splitting +3.0
gauss nearly along the b axis.

'The expected cylindrical symmetry is present in the
anisotropic hyperfine splitting values as expected for o-
protons. The magnitudes are Slightly larger than those
reported for CH3 radical by Rogers and Kispert (24) where
rotation is occurring about the threefold symmetry axis.
The apparent equivalence of both o- and B-proton Split-
tings in the ab~plane is undoubtedly accidental.

The varoton splitting is somewhat more anisotrOpic

than the a splittings. Although this is usually not the

205
case when both a and B protons are present (Tables I and
II) the magnitude of the anisotropy for the B proton is
reasonable. Rowlands and Whiffen (151) observed a fairly

large anisotropy in the case of HOOC-CH-C-COOH, which had
an an
anisotropic Splittings of 7.8 gauss, 0.3 gauss, and -2.1
CH2 (3

I
gauss. In the case of CH3-CH - CéNHz the anisotropic ‘

splittings are 4.8 gauss, 0.9 gauss and -5.8 gauss. The

. ._-. -:-.r

isotropic value of 18.0 gauss is larger than the 10 gauss
splitting observed by Rowlands and.Whiffen (151). Other
examples of large B-proton anisotropy are reported for the

(DO)2-CH-CH-CH20D radical by Rao and Gordy (152) and for
NH; R '

the HOOCfCHeCH-COOH radical by Cook et al. (39).

The B-proton principal values are also oriented close
to crystal axes with the 22.8 gauss Splitting lying nearly
along the aoaxis, the 18.9 gauss splitting lying nearly
along the b~axis, and the 12.2 gauss splitting lying nearly
along the c*-axis. The configuration of the B proton is
apparently fixed by the interaction of the CH2—, H- and

O
-C-NH2 groups which are attached to the B carbon. .A similar

fixed configuration could also explain the large anisotropy
of the B-proton hyperfine splitting in HOOC-CH—C-COOH radical.
on an
The orientation of the B proton with respect to the
<orbita1 of the odd electron can be calculated using Equa-

tion 59, which relates the isotropic B-proton splitting to

206
the dihedral angle 6 and the constants Bo, Ba by the equa-
tion Aiso = Bo + 35 cos 6. Values of B0 and B2 have
been reported by Whiffen (153): for C-CH these are Bo =
3.6 gauss and B3 = 51.4 gauss. The measured isotropic
splitting of 18 gauss gives 6 = 93° which means that the
B-proton is oriented 93° from the plane containing the two
carbon atoms and the pr orbital on the a carbon. This
could explain the relatively high anisotropy of the B-pro-
ton splitting Since the other groups have to be oriented

at definite angles with respect to the oddaelectron orbital.

0
CH3\ . n
B. C-CeNH3 .Radical

c113/

 

The sec-butyl radical, which appears when y—irradiated
isobutyramide single crystals are warmed, has already been

previously investigated (17). When the crystal containing

on2 ‘3

“CH-C-NH2 radical was warmed to -80°, a spectrum of 7
CH3/
lines with relative intensity ratios of 1:6:15:20:15:6:1
appeared indicating that the new radical contains six
equivalent protons: the pattern and the observed hyperfine
Splittings (Table XVII) are incéeasonable agreement with
3 \

the reported values (17) for ‘/,C-C-NH2 radical (Table

CH3 '3

II).

_1' !I.Ln-3-.‘..F.-.fl

207
The mechanism for formation of the high temperature
radical probably involves abstraction of a proton from a
neutral isobutyramide molecule by the low temperature radi-

cal. This can be represented by the following scheme:

 

CH1‘ 9 CH3 9 CH1‘ 9 CH , 9
,,CH—c—NH2 + QFCH-CéNHa > ’,CH-C-NH2 + ’,C-C-NH2
~CH3 CH3 CH3 CH3

(1) (2) (1) (2)

IV. V-benters in y-Irradiated Hydrazinium Dihalides

 

A. ~Clz-Radical Anion in yflrradiated Hydrazinium
Dichloride

 

When a single crystal of hydrazinium dichloride was
y-irradiated at 77°K an extremely complicated Spectrum re-
sulted for a general orientation in the aa' plane. <It
was possible at certain orientations to observe a much
simpler spectrum and so confirm the presence of the C12-
radical anion previously identified in y-irradiated acet-
amidine hydrochloride. rThe outermost group of three lines
on either the high or low—field side of the spectrum is
associated with the three outer lines anticipated from the
istOpic species (35Cl-35Cl)- , (35cl—37cl)-, and (37cl-
37C1)-. '

The maximum hyperfine Splitting of 97.3 gauss is in
good agreement with previous reported maximum splittings

for C12_ in irradiated alkali halides (Table VIII). ~It

T“ ‘bu—Q ‘f
5 ‘ :

208
might be expected that the environment would be similar
Since the hydrazinium dichloride crystal structure has also
been reported to be cubic (141). The agreement for 9min
is not as good, perhaps because the crystal was aligned
slightly off a crystal axis. .It must be remembered that
the principal axes of the 3' and 5' tensors must be co-
incidental if principal values are to be measured directly
from the Spectra.

.The positions of maximum hyperfine Splitting for C12-
are 45° from the crystal axes indicating that the c12-
radical anions are oriented along face diagonals, (110), of
the unit cube. ~This is similar to the situation reported
in X-irradiated KCl crystals by Hayes and Nichols (154).
.The reported 9min = 2.0010 value in the case of irradiated
ZKCl (154) is also closer to the g = 2.0035 observed in y-

irradiated hydrazinium dichloride than the value for

9min

crystals where C12- is oriented parallel to a cube face.

B. Brz— Radical Anion in ydIrradiated Hydrazinium Di-

bromide

When hydrazinium dibromide single crystal was y—irradi-
eated at 77°K the spectrum of Bra- was detected. .There
luave been no reports of ‘Br2- in irradiated single crys-
txals belonging to the monoclinic system other than the
Liresent case. ~Nevertheless, it is possible to rationalize
tflae deviation from axial symmetry of the 3' and 3' tensor

Extincipal values on the same basis as was done for C12- in

209
a monoclinic crystal (86). .The environment of the Brz—
fragment is such that anisotropic interactions with nitrogen
may tend to distort the symmetry of the g and hyperfine
tensors from that observed in a cubic crystal.

A more plausible explanation is used to account for

the g' anisotropy. «The 9 value, it will be recalled,
is perturbed from the free Spin value of g = 2.0023
primarily by spin-orbit coupling. The spin-orbit coupling
is directly related to the electric fields in the crystal
and is determined by the spin-orbit coupling parameter, A.
Since the electric field environment in a monoclinic crys-
tal depends on direction, whereas it doesn't in a cubic
crystal, it should be expected that the g values would
be correspondingly affected. »They are altered as shown by
the unusually small maximum 9 value, 9 = 2.0635, found
'here: the minimum 9 value, 9 = 1.9809, is in considerably
ibetter agreement with the reported gmin values for cubic
crystals given in Table VIII.

The principal values of the hyperfine tensors lie
<:lose to crystallographic axes with the largest value of
4415.6 gauss lying nearly along the a* axis and the minimum
‘value of 79.7 gauss lying nearly along the c axis. Likewise
the minimum 9 value of g = 1.9809 lies along the a*--axis

arnd the maximum 9 value (2.0635) lies nearly along the

c- axis.

 

210

V. Radicals in y-Irradiated Hydrazinium.Difluoride

 

A. Trapped Hydrogen Atoms

When a y—irradiated crystal of hydrazinium difluoride
was examined at 77°K a doublet with 508 gauss Splitting was
observed. -The 9 value for the doublet was 9 = 2.0023.
These values are consistent with the formation of hydrogen [-
atoms in the irradiated crystal. -It was observed that the
508 gauss doublet was stable up to -80°. !

Although hydrogen atoms have been detected in numerous A
irradiated liquids (Table IX) the number of instances of
its presence in an irradiated crystal is small. -Recently
it was reported in y-irradiatedN2H4'HCl single crystal (99)
and it has been reported (as an impurity) in single crystals
of CaF2 (97) and in KCl crystals (155).

In hydrazinium difluoride the hydrogen atoms may be
trapped in the crystal lattice in the tetrahedral holes ad—
jacent to each nitrogen atom resulting from the cubic
closest packing (136) of the molecular layers. .Normally
these holes are partially filled by fluoride ions from
neighboring layers of molecules, but it has been reported
by Kronberg and Harker (136) that the distance from a
fluoride ion in the hole to the surrounding fluoride ions
forming the hole is 25% larger than is normally associated
\Nith the F-F contact distance. Thus, a small hydrogen

atom could be trapped in these tetrahedral holes.

211

The linewidth of the hydrogen atom resonance is about
40 gauss which is large compared with the narrow linewidth
associated with hydrogen atom resonances in liquids or in
other crystals. This broadening could be caused by inter-
actions with the adjacent nitrogen or fluorine nuclei or
both. Thus the observed peak is probably an envelope of
lines rather than a single absorption. However, it would
be necessary to do ENDOR experiments (electron-nuclear'

double resonance) to prove this. (Irradiated crystals of

 

N2D6C12 should give, by analogy, deuterium atoms and their
Spectrum would be a triplet with hyperfine splitting about
508 /6.5 or 78 gauss. Actually the outer lines in the Spec-
trum of N2D3C12 are separated by only 110—120 gauss and if
these arise from deuterium atoms there has been a very large
perturbation from the expected splitting; the reason for

this is not known.
B. Radical Pairs at 77°K

The nature of the radical pairs has not been determined
since it was not possible to obtain sufficiently well-re-
solved spectra over a range of orientations of the magnetic
field. A variety of radical pairs has been observed in

irradiated nitrogen compounds (Table XX).

C. The Radical at -70°

When the y-irradiated crystal of hydrazinium difluoride

vwas warmed to -70° for 3 minutes it was found that the

212

 

mOH oe.o «mo. .m dengue:
A Hwfla . NmzoummUo
cm no.5 HSHHEHanoV «OZOONOU. OUHEmumomouosHHOSoz
O0.0 Amsouomnva
mos mm.o Amuasosssoc .ooouooom oaos oaaoxo
. re o r oumusumHo
HOH H O .O m 0 0m mHHHuHSQUOUSIOSOSHSUOHomm
. n . r mumSOHmoum
owe a a .ozA move ooou rosHemeo H saHoom
s.v AHusmO
OOH H.O AENmV .OzmorvmoUIHo mEononuSOQOHOHSULm
O.b .
me m.m .oonmovormozom ostomHmHHSuoz
0.0
mnH m.e .ozmoumozom oasxomeu
0.0 . .
amH v.m .ozflnmovorohamovzom ostomHmHmnumsHo
moSwnmmmm Amy mHHmm HMUHomm, moSsomEoo
OUSMSmHO

 

mHHmm HMUHomm. .xx mHQmB

213

 

 

 

OOH O0.0 .Omzooumz monsmxoaohm
O O
\./ \+/
OOH mm.O ouo ouo OSm ouo ono 0oHHo>SSm 0H0Hmz
/ \ / \
UHU UHU
\ ,/ \ x
m m m m
bOH 0.0H rmomoo. mummHSmHom ESHmmmuom
OOH 0.0 nmoolo. OHSSOQHMUHNSOSQHQ
OOH 0.0 «Ammouvz. mSHNmuomsHmSmnmmuuma
vOH O zo«Asmovo. AmHHuuHSoumuSnomvaHnoum
OUSOHommm AMV mHHmm HMUHomm mOSsomEoo
OUSMHmHO

 

 

AomSSHuSoov .XN mHQme

214
spectrum attributed to the .radical pairs had vanished and
a much Simpler Spectrum nOW'WaS observed. This Spectrum
for H I] c is a septet of quintets, the relative intensi-
ties of the septet being nearly 1:6:15:20:15:6:1 while
the quintet intensity ratios are 1:2:3:2:1 (Figure 67).
This suggests that in the radical the odd electron inter-
acts with Six equivalent protons and two equivalent nitro-
gen atoms. The nitrogen anisotropic hyperfine tensor is
nearly axially symmetric if the Signs of the principal
values are all positive; the principal components of the
anisotropic hyperfine tensor would then be +2.9 gauss along
the c axis, -1.4 gauss along the a axis and —1.6 gauss
along the b axis.

The proton hyperfine values are in reasonable agree—
ment with those reported previously for protons attached
to nitrogen (Table IV). The value of -4.0 gauss is prim-
arily directed along the c axis, the value of -1.2 gauss
is associated with axis a and the value of +5.2 gauss is
associated with the b axis.

The spin density of the odd electron in the 23 or-
bital on nitrogen may be computed using the observed nitro—
gen isotropic splitting and the theoretical Spin density
(60,61) (550 gauss) for an electron in a 2S orbital, as-
suming that the contribution from the 1s orbital is
:negligible. Since the measured nitrogen isotropic split—

ting is 3.1 gauss the S Spin density is 3.1/550 = 0.0056

or only 0.56%.

 

.-
a
.I...

215

The nearly isotropic g tensor with g = 2.0035 i
0.0005 is similar to the results for NH3+ previously re-
ported (56); NH3+ was found to be rotating in the crystal
with principal g values of gaa = 2.0034 r 0.0003, gbb =
2.0034 i 0.0003, and gcc = 2.0032 i 0.0003.

Three possible radicals which would lead to the odd
electron interacting with Six equivalent protons and two
equivalent nitrogen atoms may be suggested but none provide
completely satisfactory explanations of all the data. (a)
Removing an electron from the hydrazinium ion N2H6++ would
give a radical cation N3H63+ with some of the properties
observed. However, the isotropic nitrogen hyperfine split-
ting for such a radical Should be rather larger than ob-
served Since the odd electron would be partly in a nitrogen
orbital with 25% S character. Also, it is rare to find
species in irradiated crystals formed by removing electrons
:from stable cations. (b) An electron could be added to
N2H6++ which would then have an electron over and above
'the number required to fill the stable orbitals. This
cxm11d be accommodated to form a three-electron bond between
tins nitrogen atoms, probably utilizing a 2p orbital on
each nitrogen with each set of protons then tending to be-
cxmne coplanar with the nitrogen to which they are attached.
This species would have a nearly isotropic proton Splitting,
as.<ibserved, but should have either a somewhat larger aniso-
tropic nitrogen splitting than found here (if the NH3

grrfilps are planar) or a much larger anisotropic nitrogen

 

, ...._—-r
Wad-mu. T‘r
I
,.

216
splitting (if the NH3 groups remain pyramidal). (c) A
third possibility is that an electron trapped in a fluoride
ion vacancy interacts with three protons and a nitrogen
atom from each of two N2H5++ ions in the lattice. ~Such
F-centers are well known but are not often stable to room
temperature, as is this radical, and are usually associated
with absorption bands in the visible region of the spec-
trum. Also, it is difficult to locate an electron such
that it would interact only with Six equivalent protons and
two equivalent nitrogen atoms since the holes it might be

expected to occupy would generally have larger coordination

numbers.
VI. Summary

The ESR Spectra of the radicals,produced in sit single
crystals by irradiation with X-rays and y-rays have been
obtained and analyzed. The Spectra have made it possible
to identify the radicals produced and, in several cases,
to discuss their structures. The systems studied and the
radicals found are:

+NH2
(1) The radicals C12— and °CH2—C‘NH2 in acet-

amidine hydrochloride.

CH3 (EH2 0
I I II
(2) The radicals CH3-C° and CH3-C -C-NH2 in
I I
trimethylacetamide. CH3 CH3

 

 

217

‘ 6Hz 9 CH3 . 9
(3) The radicals #:7CH-CSNH2 and ;>C-C-NH2
. . CH3 cm,

in isobutyramide.

(4) The radical c12’ in hydrazinium dichloride.

(5) The radical Bra. in hydrazinium dibromide.

(6) A radical pair and another radical, possibly N2H6+,
Showing coupling with two nitrogens and six protons in
hydrazinium difluoride.

These results Show the unusual stability at low tem-

 

peratures of the X2- radical ion in irradiated organic
ionic halides. The reactions of the radicals on warming
from 77°K to room temperature have also been studied and

the various stable radical Species identified.

REFERENCES

.3!

All. . 'J. .
i
.4.

 

 

10.

11.

12.
13.

14.

15.
16.

REFERENCES
H..M. McConnell and R. W. Fessenden, J. Chem. Phys.,
él, 1688 (1959).

C. Heller and H. M. McConnell, J. Chem. Phys., 22,
1535 (1960). _

D. Pooley and D. H..Whiffen, Mol. Phys., 3, 81 (1961).

A. Horsfield, J. R. Morton and D. H. Whiffen, Nature,
189, 481 (1961).

H. M. McConnell, C. Heller, T. Cole and R. W. Fessen-
den, J. Am. Chem. Soc., 22, 766 (1960).

J. R. Rowlands, J. Chem. Soc., 4264 (1961).

A. Horsfield, J. R. Morton and D. H. Whiffen, Mol.
Phys., 3, 169 (1961).

J. R. Morton and A. Horsfield, Mol. Phys., 3, 219 (1961).

N. M. Atherton and D. H. Whiffen, Mol. Phys., 2, 1
(1960).

N. M. Atherton and D. H. Whiffen, Mol. Phys., 2, 103
(1960).

.D. Pooley and D. H. Whiffen, Trans. Faraday Soc., 21,

1445 (1961).
I. Miyagawa and W. Gordy, J. Chem. Phys., 22, 255 (1960).

J.-R. Morton and A. Horsfield, J. Chem. Phys., 22,
1142 (1961).

D. H. Whiffen, "Free Radicals in Biological Systems,"
Academic Press, New York, 1961.

D. K. Ghosh and D. H. Whiffen, Mol. Phys., 2, 285 (1959).

I. Miyagawa, Y. Kurita and W. Gordy, J. Chem. Phys.,
§§, 1599 (1960).

218

 

17.

18.

19.

20.

21.
22.

23.

24.

25.
26.

27.

28.

29.

30.

31.

132.
:33.

34”

135.

-D. V. G. L. N. Rao and M. Katayama, J. Chem. Phys.,

219

P. J.-Hamrick, Jr., H. W. Shields and S. H. Parkey,
J. Am. Chem. Soc., 29, 5371 (1968).

Y. Shioji, S. K. Ohnishi and K. Nitta, J. Polymer Sci.,
Pt.-A., l, 3373 (1963).

R. J. Cook, J. R. Rowlands and D. H. Whiffen, Mol. Phys.,
2, 31 (1963).

A. Horsfield and J. R. Morton, Trans. Faraday Soc.,
a. 470 (1962).

Y. Kurita, J. Chem. Phys., 22, 560 (1962).

_31, 382 (1962).

H. N. Rexroad, Y. K. Hahn and.W. J. Temple, J. Chem. ‘
Phys., :12. 324 (1965). ,

M. T. Rogers and L. D. Kispert, J. Chem. Phys., 22,
221 (1967).

R. E. Bellis and S. Clough, Mol. Phys., 29, 33 (1965).

P. B. Ayscough anth..K.-Roy, Trans. Faraday Soc., pg,
582 (1968).

H. Ohigashi and Y..Kurita, Bull. Chem. Soc. Japan, 32,
275 (1968).

M. Kashiwagi, Nippon Kagaku Zasshi, 21, 1298 (1966).

P. B. Ayscough and A. K. Roy, Trans. Faraday Soc.,
22, 1106 (1967).

J. B. Cook, J. P. Elliott and S. J. Wyard, Mol. Phys.,
_1_2_, 185 (1967) .

M. Fujimoto, W; A. Seddon, and D. R. Smith, J. Chem.
Phys., fl, 3345 (1968).

D. G. Cadena and J. R. Rowlands, J. Chem. Soc., 488 (1968).

1W. Bernhard and W. Snipes, Proc. Natl. Acad. Sci. U.S.,

fl, 1038 (1968).

M. Iwasaki and K. Toriyama, J. Chem. Phys., 32,
4693 (1967).

H. C. Box, H. G.-Freund, and K. T. Lilga, J. Chem.
Phys., 32, 1471 (1965).

36.

37.

38.

39.

40.

41.

42.

43.
44.

45.

46.

47.
48.

49.

50.

51.

52.

53.

54.

220

A. Horsfield, J. R. Morton and D. H. Whiffen, Mol. Phys.,
3, 425 (1961).

A. Horsfield, J. R. Morton and D. H. Whiffen, Trans.
Faraday Soc., 21, 1657 (1961).

H. Shields ande.~Hamrick,. J. Chem. Phys., 21, 202
(1962).

R. J. Cook, J. R.-Rowlands, and D. H. Whiffen, J. Chem.
Soc., 3520 (1963).

Y. D. Tsvetkov, R. J. Cook,-J. R. Rowlands and D. H.
Whiffen. Trans. Faraday Soc., 22, 2213 (1963).

M. Kashiwagi, and Y. Kurita, J. Chem. Phys., 32, 1780
(1964).

Y. D. Tsvetkov, J. R. Rowlands, and D. H. Whiffen,
J. Chem. Soc., 810 (1964).

M. thimoto, J. Chem. Phys., 22, 846 (1963).

J.-R. Rowlands and D. H.-Whiffen, Mol. Phys., 3, 349
(1961).

Y. Kurita, Bull. Chem. Soc. Japan, 32, 94 (1967).

H. Shields, P. Hamrick, and D. DeLaigle, J. Chem. Phys.,
,3Q. 3649 (1967).

D. H. Whiffen, Pure Appl. Chem., 3, 185 (1962).

1R. W. Fessenden and R. H. Schuler, J. Chem. Phys., 22,

2147 (1963).

J. P. M. Bailey and R. M. Golding, Mol. Phys., 12, 49
(1967).

G. R. Underwood and R. S. Givens, J. Am. Chem. Soc.,
.29. 3713 (1968).

C. Alexander and W. Gordy, Proc. Natl. Acad. Sci. U.S.,
§§, 1279 (1967).

O. Edlund, A. Lund and R. Nilsson, J. Chem. Phys., 12,
749 (1968).

M. A. Collins and D. H. Whiffen,.Mol. Phys., 12, 317
(1966).

.K. N. Shrivastava and R. S. Anderson, J. Chem. Phys.,

éé, 4599 (1968).

 

55.
56.
57.
58.

59.

60.

61.

62.

63.

64.

65.
66.
67.

68.

69.

70.

71.
72.

73.
74»

'75.

'76.

221
J. R. Morton, J. Phys. Chem. Solids, 23, 209 (1963).

T. Cole, J. Chem. Phys., 22, 1169 (1961).
J. R. Rowlands and D. H. Whiffen, Nature, 193, 61 (1962).
J. R. Rowlands, Mol. Phys., 2, 565 (1962). 1

H. W. Shields, P. J. Hamrick and W. Redwine, J. Chem.
Phys., 22, 2510 (1967).

.E. Clementi, C. C. J. Roothaan and M. Yoshimine, Phys.

Rev., 127, 1618 (1962).
J. R. Morton, Chem. Rev., 22, 453 (1964). l

J. N. Herab and V. Galogaza, J. Chem. Phys., 22, 3101 a
(1969). E

D. Cordischi and R. DiBlasi, Can. J. Chem., 21, 2601
(1969).

A. Horsfield, J. R. Morton, J. R. Rowlands and D. H.
Whiffen, Mol. Phys., 2, 241 (1962).

J. H. Hadley, Bull. Am. Phys. Soc., _1, 315 (1966).

C. Chacaty and C. Rosilio, J. Chim. Phys., 22, 777 (1967).

-R. Blinc, M. Schara and S. Poberaj, J. Phys. Chem.

Solids, 23, 559 (1963).

J. R. Brailsford, J. R. Morton and L. E. Vannotti, J.
Chem. Phys., 22, 1051 (1969).

E. Gelerinter and R. H. Silsbee, J. Chem. Phys., 22,
1703 (1966).

P. L. Marinkas and R. H. Bartram, J. Chem. Phys., 22,
927 (1968).

T. Cole and C. Heller, J. Chem. Phys., 22, 1085 (1961).

H. M. McConnell and R. W. Fessenden, J. Chem. Phys.,
‘21, 1688 (1959).

J. R. Morton, J. Am. Chem. Soc., 22, 2325 (1964).

M. T. Rogers and L. D..Kispert, J. Chem. Phys., 22,
3193 (1967).

J. E. Bennett, B. Mile and A. Thomas, Trans. Faraday
Soc., 22, 263 (1967).

C. Corvaja, Trans. Faraday Soc., 22, 26 (1967).

77.

78.

79.

80.
81.

82.

83.

84.

85.

86.

87.

88.
89.

90.

91.

92.
93.

94.

95.

96.

97.

222

J. E. Bennett and L. H. Gale, Trans. Faraday Soc., 64,
1174 (1968). __-

D. W. Ovenall and D. H. Whiffen, Mol. Phys., 2, 135
(1961).

J. Sinclair and M. W. Hanna, J. Chem. Phys., 22, 2125
(1969).

W. Kanzig, Phys. Rev., 22, 1890 (1955).

T. G. Castner and W. Kénzig, J. Phys. Chem. Solids,
2, 178 (1957). p

C. P. Slichter, "Principles of Magnetic Resonance,"
Harper and Row, New York, 1963.

H. R. Zeller. L. Vannotti, and W. Kanzig, Phys. Kondens. E
Materie, 2, 133 (1964). ;.

 

F. W. Patten and M. J. Marrone, Phys. Rev., 142, 513
(1966).

H. J. Ueda, J. Chem. Phys., 21_, 285 (1964).

H. C. Box, E. E. Budzinski, and H. C. Freund, J. Chem.
Phys., 22, 2880 (1969).

E. Boesman and D. Schoemaker, J. Chem. Phys., 21,
671 (1962).

C. L. Marquardt, J. Chem. Phys., 22, 994 (1968).

J. W. Wilkins and J. R. Gabriel, Phys. Rev., 132, 1950
(1963).

D. Schoemaker, Phys. Rev., 149, 693 (1966).

L. S. Goldberg and M. L. Meistrich, Phys. Rev., 172,
877 (1968).

C. E. Bailey, Phys. Rev., 136, 1311 (1964).
J. Sierro, Phys. Rev., 138, 648 (1965).

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

T. Cole and J. T. Harding, J. Chem. Phys., 22, 993 (1958).

C. K. Jen, S. N. Foner, E. L. Cochran and V. A. Bowers,
Phys. Rev., 104, 846 (1956).

J. L. Hall and R. T. Schumacher, Phys. Rev., 127, 1892
(1962).

98.

99.

100.

101.

102.
103.

104.

105.

106.

107.
108.
109.

110.

111.

112.
113.

114.

115.

116.

117.

 

223

R. Livingston, H. Zeldes, and E. H. Taylor, Discussions
Faraday Soc., 22, 166 (1955).

A. G. Kotov and S. Y. Pshezhetskii, Zh. Fiz. Khim.,
22, 1920 (1964).

S. N. Foner, C. K. Jen, E. L. Cochran and V. A. Bowers,
J. Chem. Phys., §§, 351 (1958).

E. B. Rawson and R. Beringer, Phys. Rev., 22, 677
(1952).

C. L. Gardner, J. Chem. Phys., 22, 2991 (1967).
C. L. Gardner, J. Chem. Phys., 22, 5558 (1968).

N. Vanderkooi and J. S. Mac Kenzie, Advan. Chem. Ser.,
53.9.. 98 (1962) .

_ -‘-.“"‘.=-.'tzl

Ln... .- ~——
u

H. Eyring, J. Walter and G. E. Kimball, "Quantum Chem-
istryfl John Wiley and Sons, New York, 1944.

A. Carrington and A. D. Mc Lachlan, "Introduction to
Magnetic Resonance," Harper and Row, New York, 1967.

B. Bleaney, Phil. Mag., 22, 441 (1951).
G. Breit and I. I. Rabi, Phys. Rev., 22, 2082 (1931).

R. W. Fessenden and R. H. Schuler, J. Chem. Phys., 22,
2704 (1965).

J. Maruani, C. A. McDowell, H. Nakajima, and P.
Raghunathan, Mol. Phys., 22, 349 (1968).

D. S. Schonland, Proc. Phys. Soc._(London), 12, 788
(1959).

J. E. Nafe and E. B. Nelson, Phys. Rev., 12, 718 (1948).

H.-M. McConnell and H. H. Dearman, J. Chem. Phys., 22,
51 (1958).

J. E. Bennett, B. Mile, and A. Thomas, Trans. Faraday
Soc., 2;. 2357 (1965).

G. W. Chantry, A. Horsfield, J. R. Morton and D. H.
Whiffen, Mol. Phys., 2, 589 (1962).

J. G. Hyde and E. S. Freeman, J. Chem. Phys., 22,
1636 (1961).

G. Schoffa, J. Chem. Phys., 22, 908 (1964).

118.
119.

120.

121.

122.
123.

124.

125.

126.

127.

128.

129.

130.

131.

132.

133.
134.

135.

136.

224
R. W. Fessenden, J.-Mag.-Res., 2, 277 (1969).
H. C. Heller, J. Chem. Phys., 22, 2611 (1965).

M. Karplus and G. K. Fraenkel, J. Chem. Phys., 22, 1312,
(1961).

T. Cole, H. O Pritchard, N. R. Davidson and H. M. Mc-
Connell, Mol. Phys., 2, 406 (1958).

Unpublished data by M. T. Rogers and L. D. Kispert.

M. Bersohn and J. C. Baird, ”An Introduction to Electron
Parmagnetic Resonance," W. A. Benjamin, New York, 1962.

G. E. Pake, "Paramagnetic Resonance," W. A. Benjamin:
New York, 1962.

W. Low, "Paramagnetic Resonance in Solids," Academic
Press, New York, 1960.

C. P. Poole, "Electron Spin Resonance," John Wiley and
Sons, New York, 1967.

"V—4502 EPR Spectrometer System Manual," Varian Associ-
ates, Palo Alto, California.

"V-4503 EPR Spectrometer System Manual," Varian Associ-
ates, Palo Alto, California.

G. H. Stout and L. H. Jensen, "X-ray Structure Deter-
mination," Macmillan Co., New York, 1968.

F. C. Phillips, "An Introduction to Crystallography,"
John Wiley and Sons, New York, 1963.

N. H. Hartshorne and A. Stuart, "Practical Optical
Crystallography," American Elsevier Co., New York, 1964.

P. Groth, "Chemische Krystallographie," Vol. 3, Verlag
von Wilhelm Engelmann, Leipzig, 1910.

L. Buss and L. Bogart, Rev. Sci. Instr., 22, 204 (1960).

M. J. Buerger, "x-ray Crystallography," John Wiley and
Sons, New York, 1942.

M. J. Buerger, "The Precession Method in X-ray Crys-
tallography," John Wiley and Sons, New York, 1964.

M. L. Kronberg and D. Harker, J. Chem. Phys., 22, 309
(1942).

 

225

137. C. M. Deeley and R. E. Richards, Trans. Faraday Soc.,
.QQ. 560 (1954).

138. R. E. Rondeau, J. Chem. Eng. Data, 22, 94 (1966).
139. M. Kashiwagi, J. Chem. Phys., 22, 2823 (1966).

140. M. T. Rogers, 8. J. Bolte and P. S. Rao, J. Am. Chem.
Soc., 21, 1875 (1965).

141. J. Donohue and W. N. Lipscomb, J. Chem. Phys., 22,
115 (1947).

142. D. H. Whiffen. Unpublished data communicated by M. T.
Rogers.

143. G. Lassmann and W..Damerau, Biophysik, 2, 14 (1968).

144. H. M. McConnell and D. B. Chesnut, J. Chem. Phys., _2,
107 (1958).

145. D. B. Chesnut, J. Chem. Phys., 22, 43 (1958).
146. A. D. Mc Lachlan, Mol. Phys., 2, 233 (1958).

147. P. B. Ayscough and C. Thomson, Trans. Faraday Soc.,
22, 1477 (1962).

148. J. A. Pople and G. A. Segal, J. Chem. Phys., 22, 3289
(1966).

149. J. A. Pople, D. L. Beveridge and P. A. Dobosh, J. Chem.
Phys., 21, 2026 (1967).

150. L. Pauling, J. Chem. Phys., 22, 2767 (1969).

151. J. R. Rowlands and D. H. Whiffen, "Hyperfine Couplings,"
National Physical Laboratory, Teddington, 1961.

152. N. D. V. G. L. Rao and W. Gordy, J. Chem. Phys., 22,
764 (1961).

153. D. H. Whiffen, Colqu. Int. Centre Nat. Rech. Sci.,
No. 164, 169-175 (1967).

154” W. Hayes and G. M. Nichols, Phys. Rev., 117, 993 (1960).
155. J. M. Spaeth, J. Phys. Radium, 22, 146 (1967).
156. I. Barber, Phys. Stat.VSol., 22, 711 (1969).

1573 (a) Y. Kurita, J. Chem. Phys., 22, 3926 (1964); (b)
Nippon Kagaku Zasshi, 22, 833 (1964).

 

w a...» m ("I

L‘-

.2
1'

 

158.

159.

160.

161.

162.

163.

164.

165.

166.

167.

168.
169.

2170.

171.

226

Y. Kurita and M. Kashiwagi, J. Chem. Phys., 22, 1727
(1966).

M. Kashiwagi and Y. Kurita, J. Phys. Soc. Japan, 22,
558 (1966).

H. Hayashi, K. Itoh, and S. Nagakura, Bull. Chem. Soc.,
Japan, 22, 284 (1967).

H. Ohigashi and Y. Kurita, Bull. Chem. Soc. Japan, 22,
704 (1967).

G. C. Moulton, M. P. Cernansky and D. C. Straw, J.
Chem. Phys., gg, 4292 (1967).

W. Gordy and R. Morehouse, Phys. Rev., 151, 207 (1966). 1
a; P. D. Bartlett, Chem. Eng. News, 22, 106 (1966); A

b Y. S. Lebedev, Dokl. Akad.-Nauk SSSR. 171,.373;:
1966); (c) M. c. R. Symons, Nature, 213, 1226 (1967).

 

D. A. Wiersma and J. Kommandeur, Mol. Phys., 22, 241
(1967).

(a) A. Davis, J. H. Golden, J. A. McRae and M. c. R.
Symons, chem. Commun., 398 (1967); (b) J. A. Mc Rae
and M. C. R. Symons, J. Chem. Soc., 428 (1968).

(a) P. W; Atkins, M. C. R. Symons and P. A. Trevalion,
Proc. Chem. Soc., 222 (1963): (b) S. B. Barnes and
M. C. R. Symons, J. Chem. Soc., 66 (1966).

-M. Iwasaki and B. Eda, Chem. Phys. Letters, 2, 210 (1968).

K. Reiss and H. Shields, J. Chem. Phys., 22, 4368 (1969).

H. M. Mc Connell and J. Strathdee, Mol. Phys., 2, 129
(1959).

P. B. Ayscough} "Electron Spin Resonance in Chemistry,"
Methuen and Co. Ltd., London, 1967.

APPENDIX

1: ~.' .mlmhg
EL

APPENDIX

The following is a listing of the diagonalization pro-

gram used to obtain principal values and direction cosines

for the

600
610

1001
4010

1003
1000

1004
1005

1007
1009

1008
1010

"g":

or K'

PROGRAM DIAGON

DIMENSION A2(50
1DQ(3), AXY(14,4

FORMAT

(512)

3

tensors:

.THETA(50),AX(4
,Z(50,5),BB(3,3
READ 610,IG,IB,N,JVEC,MM

IF(IG) 1007,1007,1001
IG =IG-1
READ 4010,(ssc(J).J=1.3)
(3210.4)
READ 1003,GPL.THP,GM1N.MA.MB
(3F10.5,212)
PRINT 1000,MA,MB.GPL.THP.GMIN
FORMAT (212,6H PLANE,4HGPL=,312.5,4HTHP=,212.5,5HGMIN
1=,E12.5)
THP=0.0349065*THP
MA)*SSC(MA)

FORMAT

FORMAT

GPL2=GPL*GPL*SSC
ALP= (GPL2+GMIN2
BET= COSFETHP
GAM= SINF
Q(MA.MA)

9(-
THP)*
= ALP+BET

E

S

/2.0

BB(MB,MB) = ALP-BET
Q(MA.MB) = GAM
PRINT 1005,0(MA,MA),BB(MB,MB),Q(MA,MB)

FORMAT (//

1=,E15.5//)

Q 1,1

000
HODN
“CON

I
I
I

GO TO

Q
10234

é

E

3

1,1
2,2

3,3
.1)

 

+ BB
+ BB
+ BB

{

GPLZ-GMINZ
GPLZ-GMINZ

1,1
2,2
3,3

 

READ 1009,(Ax(J),J=1.3)
FORMAT(3F10.0)
DO 1022 I=1,3
READ 1008,SCAL.NP
FORMAT(F10.4,12)
READ 1010,(A2(IK).IK=1,NP)
FORMAT(8F10.0)
READ 1011,(THETA(NK).NK=1.NP)

227

3

 

(3:3

/2.0
(3:3

3

I

SINT

.ssc(3

(50),Q(3,3),V(3,3),

,5HGAA2=.EIS.5,3X,5HGBB2=,E15.5,3X,5HGAB2

1011

1014
1015

1020
1022

1023

1024

1026

2100

2190

2191
2195
2196
4000
5000

F0RMAT(16F5.0)

(DO 1020 J=1,NP

‘SINT(J)=SINF(THETA)(J))

1 EIGVAL(3)

228

B=0.0

A=0.0

Ax(4)=Ax(1)
fiéfifitfiifimézg

A2(J):A2(J)*A2(J)*SCAL*SCAL
THETA(J)=0.0349065*THETA(J)

 

z(J,I)=A2(J)-xx-COSF(THETA( ))*YY
B=E+2(J.I)*SINT(J) ~ -
.A=A+SINT(J)*SINT(J)
AXY(I,I+1)=B/A -

IB=IB-1
1,1 Ax 1
Ax 2
AX 3

AXY§1,2

 

 

me—‘m 0.:
. w

5.-

AXY 2,3
AXY 314
Q 1,2
Q 2,3
. ) 0 1.3

PRINT 1024.16.13
FORMAT (21HUNDIAGONALIZED MATRIx./.10HA RADICAL=,12.

 

000000000

wwNHNHwN
s s s ‘ ~ s s

HNHODOJNCON
II II II II II II II II

 

14H G =,12,///)

PRINT1026,((Q(I,J)'J=1,3).I=1.3)
FORMAT (5x.3(E14.5,2x)./)

CALL DIAG (Q.N.JVEC.V.DQ.MM)
PRINT 2100, (IB,(DQ(I),I=1,3))

FORMAT (//.3IHDIAGONALI2ED MATRIX RADICAL A =.12.
PRINT 2190, (IB,(DQ(I),I=1,3)
FORMAT(5HRADI=,12,48HEIGVAL(1 EIGVAL(2)

./,6x,3(E14.5))

 

DO 1 = ABSF DO 1
D0 2 = ABSF DO 2
DQ 3 = ABSF D0 3
V1 = SQRTF DO 1
V2 = SQRTF DO 2
V3 = SQRTF DQ 3

 

PRINT 2191,(v1,v2,v3)

FORMAT (3Hv1=,E14.5,2x,3Hv2=,E14.5,2x,3Hv3=.E14.5)
PRINT 2195

FORMAT (//.34HNORMALIZED EIGENVECTORS OF RADICAL./////)
PRINT 2196,((V(I.J).I = 1,3),J = 1,3)
FORMAT(3(E14.5,5X),//)

IF(IG) 4000,4000,1001

CONTINUE

IF(IB) 5000,5000,1007

CONTINUE

END

10

11
12
14

15
17

20

3O
40

45
60

70

148
150

151
160

152

154

155
170

153

200

11P)-Q(JP,JP))**2+4.0*Q(IP,JP)**2

1(IP.IP)—Q(JP,JP))**2+4.0*Q

229

SUBROUTINE DIAG(Q.N.JVEC.V.DQ.MM)
DIMENSION QEMM.MM).V(MM.MM).DQ(MM)
DIMENSION X 100),IH(100)
IF(JVEC)15,10,15

DO 14 I=1,N

DO 14 J=1,N

IF(I—J)12,11,12

v(I,J)=1.0

GO TO 14

V(I,J)=0.0

CONTINUE

M=O

MI=N~1

DO 30 I=1,MI

x(I)=0.0

MJ=I+1)

DO 30 JeMJ,N
IF(x(I)eABSF(Q(I,J)))20,20,30
x(I):AESF(Q(I.J))

IH(I)=J

CONTINUE

DO 70 I=1,MI

IFEI—1)60,60,45

IF XMAX-X(I))60,70,70

5

LI... A‘fi 1A.:

.XMAx=x(I)

IP=I
JP=IH(I)

CONTINUE

EPSI=1 .0E-8
IF(XMAXaEPSI)1000,1000,148

.M=M+1

IF(1(IP,IP)-Q(JP,JP))150,151.151
TANG=-2.0*Q(IP.JP)/(ABSF(Q(IP.IPg-Q(JP,JP))+SQRTF((Q(IP.

)
GO TO 160 ,
TANG= 2.0*Q(IP.JP)/(ABSF(Q(IP.IPg-Q(JP,JP))+SQRTF((Q
IP,JP **2)) ..
COSN=1.0/SQRTF(1.0+TANG**2)
SINE=TANG*COSN
QII=Q(IP.IP)
Q IP,IP =COSN**2*éQII+TANG*(2.0*Q(IP.JP)+TANG*Q(JP.JP)g;
Q JP.JP =COSN**2* Q(JP.JP)=TANG*(2}0*Q(IP.JP)-TANG*QII
Q IP,JP =0.0
IF(Q(IP,IP)-Q(JP,JP))152,153,153
TEMP=Q(IP.IP)
QEIP.IP =Q(JP.JP)
Q JP,JP =TEMP
IF(SINE 154,155,155
TEMP=COSN
GO TO 170
TEMP=-COSN
COSN=AESF(SINE)
SINE=TEMP
IFEI-IP3210,350,200
IF I-JP 210,350,210

 

 

210
230
240
250

300
320
350

370

380

390

400

420

430

440

450

480

490
500
510
530
540

550

1000
1002

230

IFEIHEIg-IPg230,240,230

IF IH I -JP 350,240,350

K=IH(I)

TEMP=Q(I.K)

0(I.K)=0.0

MJ=I+1

x(I)=0.0

DO 320 J=MJ.N
IF(XI)-ABSF(Q(I,J)))300,300,320
X(I)=ABSF(Q I.J))

IH(I)=J

CONTINUE

Q(I.K)=TEMP

CONTINUE

xéIPg=0.0

x JP =0.0

DO 530 I=1,N

IF(I-IP)370,530,420

TEMP=Q I.IP) '

Q(I.IP =COSN*TEMP+SINE*Q(I.JP)
IF(x(I -ABSF(Q(I,IP)))380,390,390
x(I):ABSF(Q(I.IP))

IH(I)=IP
Q(I.JPie-SINE*TEMP+COSN*Q(I.JP)
IF(x(I eABSF(Q(I.JP)))400,530,530
x(I):ABSF(Q(I.JP))

IH(I)=JP

GO TO 530

IF(I-JP)430,530,480

TEMP=Q(IP.I)
Q(IP,I)=COSN*TEMP+SINE*Q(I.JP)
IF(x(IP)-ABSF(Q(IP.I)))440,450,450
x(IP):ABSF(Q(IP.I))

IH(IP)=I ‘
Q(I.JP;=-SINE*TEMP+COSN*Q(I.JP)
IF(x(I —ABSF(Q(I.JP)))400,530,530
TEMP=Q(IP,I)
Q(IP.I)=COSN*TEMP+SINE*Q(JP.I)
IF(x(IP)-ABSF(Q(IP,I)))490,500,500
x(IP):ABSF(Q(IP.I))

IH(IP)=I
Q(JP.I)=-SINE*TEMP+COSN*Q(JP.I)
IF(x(JP)-ABSF(Q(JP,I)))510,530,530
x(JP)=AESF(Q(JP.I))

IH(JP)=I

CONTINUE

IF(JVEC)40,540,40

DO 550 I=1,N

TEMP=V(I.IP)

v I.IP)=COSN*TEMP+SINE)V(I.JP)

v I,JP)=-SINE*TEMP+COSN*V(I,JP)
GO TO 40

DQ(I)=Q(I.I)

END

_'m

“it

9.

10.

11.

12.
13.
14.

15.

231
The input for PROGRAM DIAGON is as follows:
IG - Integer nudber of 3' or i' tensors to be diago:
nalized by Schonland's method.

IB - Integer number of 3' or K' tensors to be diago-
nalized by curve fitting technique.

N - Dimension of the matrix to be diagonalized (equals
3‘in this case).

JVEC - Must be set equal to 0 if the eigenvectors are
to be printed out, or set equal to 1 if the eigen-
vectors are not to be printed out.

MM - A variable which must have the same dimensions as
N(equals 3).

SSC(J) - Scale factors for Schonland's method to convert
g or A values.

GLP - Maximum 9 or A value in each plane

'THP - Angle where maximum 9 or A value occurs (in

degrees).
GMIN - Minimum 9 or A value in a plane.

MA - Dummy variables to identify reference planes, e.g.

MB _ for 1-2 plane MA = 1, MB = 2.

AX(J) - Squares of the hyperfine Splittings along the
reference axes (in gauss’).

SCAL - Scale factor for converting mm or inches to gauss.
NP - Number of points to be used in the curve fit.
A2(IK) - Hyperfine splittings measured in mm or inches.

THETA(NK) - Angle corresponding to each A2(IK) in degrees.

The output for PROGRAM DIAGON is as follows:

V1,V2,V3-Eigenvalues of radical in gauss or eigenvalues of

3' tensor.
V(I,J) - Eigenvector elements.

This program was written in FORTRAN IV for use on a CDC
3600 computer.

I.
:3-

HT
I’_: ‘0‘
‘.