AE-504

ANALYSIS OF EPR WITH LARGE QUADRUPOLE INTERACTION

Karl-Ake Thuomas

AB Atomenergi

Studsvik, Nyköping, Sweden

ABSTRACT

A method has been developed to analyze EPR spectra for the

case when the quadrupole coupling and the hyperfine coupling are of

comparable magnitudes but much smaller than the electronic Zeeman

term. A computer program which calculates the EPR spectrum for

a finite Gaussian or Lorentzian line width has been written. The pro-

gram is particularly suitable for cases with several interacting nuclei.

The method has been applied to confirm the planar structure

of .CHC12.

Ab initio UHF calculations have further confirmed this struc-

ture.

LIST OF CONTENTS

INTRODUCTION

GENERAL THEORY

PROG!1 AM ORGANIZATION

ANALYSIS OF SPECTRA

UHF CALCULATIONS

DISCLSSION

REFERENCES

LIST OF FIGURES

FIGURES

- i -

INTRODUCTION

Alkyl halides are generally assumed to react by dissociative

electron capture when exposed to ionizing radiation [ 1}. Recent

observations of the " CH^Cl radical in a single crystal of methyl

chloride [2], the • CHCK radical in a single crystal of dicloro-

methane f 3] and the • CC1, radical in a single crystal of trichloro-

acetaimide f 4) have shov.n that this reaction may not be dominant

in all matrices. ESR spectra of chloro radicals are often very comp-

lex, resulting largely from the chlorine nuclear quadrupole inter-

action which leads to additional transitions and to deviations from

the expectations of first order analysis. Analysis of such spectra

has been performed either by higher order perturbation theory or

by computer diagonalization of the full Hamiltonian. The first method

fails when the quadripole interaction is comparable to the hyperfine

interaction. The second method is time consuming when there are

several interacting nuclei. The dimension of the (complex) Hamil-

tonian mafrix increases by (21 + 1) for each nucleus of spin I. There

35 37are also two chlorine isotopes ( Cl, C1) and in most crystals

site splitting, except for special orientations of the magnetic field.

Our aim has been to c'evelop a method to analyze EPR spectra for the

case when the quatirupole coupling and the hyperfine coupling are of

comparable'rnagnitudes but much smaller than the electronic Zee-

man term. A computer program which calculates the EPR spectrum

for a finite Gaussian or Lorentzian line width has been written. The

program is particularly suitable for cases with several interacting

nuclei. The method haa been used to confirm the radical structure

in 1; radiated single crystals of dichloromethane [3] . Ab initio UHF

calculations have further confirmed this structurs.

- 2 -

GENERAL THEORY

In most cases ESR spectra of pari-jnagnetic systems with

S = 1/2 and single nucleus with I > 1 are described adequately in

terms of the spin Hamiltonian

H = H + H +

with Hg = 6 • S - ^ - B • i , Ha =1 • A - 5, ^ = - gN • BN • B • i • I

H = I • Q • I, where r is the Bohr magneton, •» the nuclear mag-q ~ I\

neton, g .̂ the nuclear moment. B and_l a*e the strength and the di-

rection of the static magnetic field respectively. S and_I are the

electronic and nuclear spin operators and g, ^ and Q are symmetric

tensors describing the anisotropic splitting factor in the ele^'ronic

Zeeman effect, the magnetic hyperfine coupling, and the coupling

of the electric quadrupole moment of the nucleus to the field of the

surrounding electrons.

Analysis of H has been carried out assuming H »

H + H, + H . A perturbation treatment may then be used.

The representation of the electronic Zeem.in Hamiltonian H is

diagonalized by the eigenfunction of S , which is the component of

S along the effective Zeeman field. The unit vector u is given by

(2)

i (3)

- 3 -

Using Eq. (2), H becomes

Hg = egBSu (4)

By introducing the unit vectorsj. andj, which are mutually per-

pendicular and also perpendicular to u, the effective hypérfine Ha-

miltonian is given by

H + Hb = (I_. A • u)Su + (I • A • V)S. + (I • A • j)S. -

- g N = N B ' i - i ( 5 )

If we retain only that part of S in H which lies along u, (5)

becomes

Ha + r^ = (I • A • u)Su - gN5NB -I- I (6)

With this approximation Eq. (1) becomes

H = BgBSu + (I • A . u)Su - gN8NB • I • I + 1 . Q • _I =

+ H, (7)

The off-diagonal elements of S in H lead to terms in the ener-

gies of the order (| <m|2 * Al1"'5"! /gSB)M. The zero-order ener-

gy of state (M, m) is E_(M, m) = $gBM. The first-order energy

correction, Ej(M, m), is found through a complete diagonalization

of the eigenvalue - eigenvector matrix for Hj. The matrix elements

of Ha are

- 4 -

<m!H !m> = — • V • ma g 7. (8)

i1 H ' m t 1> - —! I f l + 1) - m ( ma g • '

• 0 . 5(V + iVx - v (9)

where V = AV = A • g • l_

The matrix elements of H, areb

H, • m> = - b • m (10)

c m J H > m L 1 > = - [ p i + 1 ) - m ( m + 1 ) ] X'Z

0. 5(b 4 ib )x - y ' ( l i )

where b =

The matrix elenents of H areq

<m]H |m> = [Irn - 1(1 + 1)] • 0. 5 • Q (12)

<m|H |ir. ± i> = (2m + I)f(I + m

- 5 * ( Qxz

(13)

< m | H j m + 2> = f(I + m f

(14)

- 5 -

To first order the transition probability for (M, m) •—• (M - 1,

m* ) is given by

I - l<rM. mjaS • j | . B t • _lj j M - 1, m'>| 2 =

= B2Bj|G|2[S(S + 1) - (M - l ) M ] ! < m ! m ' > | 2 / 4 (15)

where

2B. and_l. are the strength and the direction of the oscillatory

magnetic field, respectively. The nuclear eigenstates of H. marked

by |m> and |m r > are mixings of nuclear spin states.

k k k k * k k

Using Eq. (17), I becomes

I« const. • E ajj1*^"1 (18)

provided that the intensity dependence due to g-factor anisotropy

can be neglected.

PROGRAM ORGANIZATION

In this section we shall briefly outline the organization of the

program.

In the first step the principal values of A, Q and g of a nucleus

are transformed to the laboratory system.

- 6 -

= 3 - ! . A p r i n c - z (19)

•where a is the direction cosine matrix exemplified in table 1. QPr l n c

and £ ' are treated in the same way.

In the second step the eigenvalue - eigenvector matrix for H.

is set up for a certain M-value. An extended Householder's method

[5] is used to reduce the complex matrix to upper Hessenberg form.

This procedure augments Householder's method by a diagonal unitary

similarity which causes the lower subdiagonal elements of the Hes-

senberg matrix to become real. The matrix is now real, symme-

tric and tridiagonal and the eigensystem [6, 7] can be found. Finally

the eigenvectors [5] of H. are found by transforming the eigenvec-

tors of the Hessenberg matrix. These eigenvalues and eigenvectors

(normalized) are saved. The H. matrix for other M-values is treated

in the same way.

In the third step the transition energies and probabilities are

calculated. For the transition (M, m) <—«(M - 1, m* ) we have

E(M, m) - E(M - I, m' ) = 0gB + Ej(M, m) -

- E,(M - 1, m») (20)

The probability for this transition ia given by Eq. (18). For sev-

eral interacting nuclei the steps are repeated.

Finally in the fourth step the EPR spectrum for a finite Gaus-

sian or Lorentzian line width is plotted. Our program can calculate

a variable number of superimposed spectra. We have tested it against

a program that makes a complete diagonalization of the Hamiltonian

matrix [s J . Spectra from these programs agreed very well.

- 7 -

ANALYSIS OF SPECTRA

EPR and ELDOR studies have shown that the • CHC1, radical is

planar. There are two sites. The radical planes are oriented parallel

to the z-axis and inclined^ 30° to the x-axis ^fig. t). We have tried

to confirm this model by simulation of the EPR spectra for some di-

rections of the magnetic field, namely, B ; ' x 'fig 2a), B/ y (fig 2b),

B / 'z. ffig 2c) and B /xy-plane (fig 2d) at an angle of 30 to the x-axis.

In fig 2a, 2b .ind 2c the spectra from radicals in the two sites

coincide. In fig 2d the spectra from the two sites are superimposed.

In all simulations the spectra of -CH^Cl , , .CH35ci37ci, -CH37C135C1

and • CH Cl_ were superimposed in a ratio determined by the iso-

topic abundance.

The principal values of the hyperfine and quadrupole tensors

of the Cl nucleus are smaller by a factor of 0.833 and 0.786 de-

pending, respectively, upon the ratio of the nuclear magnetic mo-

ments and the ratio of nuclear electric quadrupole moments. In all

figures the solid line gives the experimental spectrum.

The principal values of the chlorine and the proton hyperfine

couplings were varied starting with the values estimated previously.

The values in table 1 gave best agreement with the experimental

spectra. The quadrupole couplings found by Michaut and Ron c in [ 2]

in their analysis of ' CH-C1 spectra were used. Variation of the

magnitude of these couplings by +̂ 10 % strongly influences the width

of the spectra. The principal axes of the hyperfine and quadrupole

couplings are assumed to be oriented as indicated in fig 1. Ab initio

UHF calculations described below confirm the assumption made

about the directions of the principal axis. The coupling tensors

finally obtained are shown in table 1.

Uf IF C A LCU LATIONS

The calculations wore performed in a spin - unrestr icted

MO LCAO SCF approach, using Gaussian-type functions for the ex-

pansion of the molecular erbi ta ls . The basis set used for carbon

consisted (if seven s-type and thret» p-type functions. This was con-

tracted to four s-type and two p-type functions, or (7, 3) - • 4,2 >

in a common shorthand notation. A corresponding basis set used

for chlorin,- '= denoted (10, 6) •-« 5, ? > and for hydrogen (4) —- •' 2 >.

The orbital exponents and contraction coefficients were taken from

the l i terature f{), 10] . The orbital exponents uf hvrlrogen from ref. 10

were multiplied by a sealing f.ictur of \.Z^. The I'HF r*l<-ulations

were performed with the program system MOLECULE [ ' ' ] . The

spin densities at the nuclei were computed using a program based

on the single annihilation method f !.'] . This method removes the

major contaminating spin component, lu:rc S 3 fl, from the wave

function. The dipolar hyperfine and electric quadrupole couplings

were determined using a program written by Kortzeborn f H] . The

same integrals were evaluated as in the calculation of the electric

field gradient. For evaluation of the dipolar hyperfine interactions

the total charge density was replaced by the spin density.

A partial geometry optimization was made for the radicals

' Cf-LCl and • CHC1-. For both radicals the bond length d r „ was

assumed to be 1. 07 A. Fur ther the angle HCH in ' CH Cl and the

angle C1CC1 in • CHCL, was taken to be 120°. For • CH-C1 a C-Cl

bond length of 1.7 1 Å and an angle a between the C-Cl bond and the

plane H-C-H of 20 was found to minimize the total energy (E =

= - 497.44021 a. u). For • CHC1,, the optimized geometry gave a

total f-nrrgy of - 955. 35738 a. u. . H ... 1. 11 A and an angle •> be-

tween the C-H bond and the plane Cl-C-Cl of 30°.

The variation of the total electronic energy with the angle o for

•CHjCl is shown in fig. 3a and for • CHCL, in fig 3b. The curves show

shallow minima for this particular basis Bet. Tv e potential barrier

is only 0.0006 a.u. in • CHC1., and 0.0004 a.u. in • CH^Cl. In re-

cent ; 14 j nonempirical calculations of the ground-state energy of

the isoelectronic H^NO and H,CO" radicals Eilinger et al. found

that the potential barriers for inversion are dependent on the basis

sets used. Let us assume, however, that our calculated barriers are

approximately correct. The minima in fig. 3b represent the two "stable'

equilibrium positions of the carbon atom in the • CHC1., radical, sym-

metric with respect to the plane Cl-H-Cl (fig. 4). If d is the distance

from the equilibrium position to the symmetry plane, and x the in-

stantaneous coordinate of the carbon atom on the x-axis, the poten-

tial energy will resemble the energy given by a simple one-dimen-

sional double oscillator model [15] . A potential barrier prevents

classical oscillation between the equilibrium configurations (a) and

(b) in fig. 4, but quantal ba r r i e r penetration may produce strong os-

cillations. The ratio of the time during which the configurations (a)

and (b) change to the period of the harmonic oscillator is given

approximately by [ 15]

! a fe s 0 . 2 5 .

where htv is the energy of the harmonic oscillator, which is here

k • T. Vfl is the potential barrier between the equilibrium configu

- 10 -

-4ra t i ons (a) and ; ' ( / . FY. r T 77 K with * x - 2 .44 • 10 a . u . and

t, = 6. 2 • 1 0 " 1 1 so o wo find t . - 1 . 7 - 10" s e c . This shows thath ab

at l e a s t on the ESR t ime s c a l e the • CHC1 , can be a s s u m e d to be

p l a n a r , in a g r e e m e n t with the e x p e r i m e n t a l findings in ref. 3. The

- 12s a m e ana lys i s oi • CH.,C1 g ives t , = 4. 1 " 10 s e c .

L* t\ t)

The hyperfine coupling tensors of Cl and H after single anni-

hilation of the wave function are given in table 1. The effect of mole-

cular vibrations on the hyper fine couplings are not calculated. In

fig. 5a and 5b we show how the isotropic. couplings of C, H and "Cl in

•CHC1, and -CH^C!, after Amos and Snyder annihilation f 12] , vary

with the out-of-plane bending. The isotropic coupling of C increases

with the increasing s-character of the unpaired electron whe- the

radicals go from planar to pyramidal configuration.

The dipoie hyperlinc and quadrupole couplings of the planar

• CH?C1 are j,:.ven in table 2. The experimental values are those given

by ref. 2 for the not completely planar configuration, ry ~, 7 , As we

see, annihilation of the UHF wave function has little effect on the

dipoie couplings, in agreement with previous calculations nnn-ra-

dicals [16], The charge dependent one-electron properties, the

electric quadrupole couplings, are the same before and after spin

annihilation of the major contaminating spin component in the wave

function.

It is shown in table 3 that the dipolar hyperfinu and quadrupole

couplings are very little affected by bending out of the plraiar confl"^—

ration.

In all calculations the expectation value of S is very close to

3/4 after annihilation of the spin component S = 3/2 from the wave

function.

- 11

Ta hl»- 1

C o u p l i n g t e n s o r s for the Cl a n d i! n u c l e i in G a n d t h e g - t r n s o r for

t h e • CHC.l r a d i c a l . S i m u ! -in'! " ' I I F A A I a r e t h e v a l u e s o b t a i n e d

by s i m u l a t i o n of the s p e c t r a arui a f t e r a n n i h i l a t i o n of the

S 3 '?. c o m p o n e n t of the w a v e f - inc t ion , r c s p ' - c t i v c l v

T e n s o r P r i n c i p a l v a l u e s D i r e c t i o n c o e i n t - s wi th r e s p e c t tov y z

S i m u l (L 'HFAA) S i m u l f t ' H F A A ) S i m u l U H F A A t S i m u l ' U H F A A l

A ( * 5 C 1 ) - 5 . 8 (-2.6) 0 . 7 5 0 ' 0 . 7 6 5 ) 0 . 4 3 3 ( 0 . 4 0 6 ) 0 . 5 ' 0 . 5 )- 5 . 1 ( 0 . 9 ) 0 . 4 3 3 ( 0 . 4 0 6 ) 0 . 2 5 0 ( 0 . 2 5 0 ) - 0 . 8 6 6 ( - 0 . 7 6 5 )1 7 . 0 ( 1 3 . 6 ) - 0 . 5 ( - 0 . 5 1 0 . 8 6 6 ' ' 0 . 8 6 6 ) 0 . 0 ' 0 . 0 )

Q ( 7 ; 5 C 1 ) 3 . 8 f - 3 . 0 ) 0 . 7 5 0 ( 0 . 7 5 7 ) 0 . 4 3 3 iO.42O) 0 . 5 ( 0 . 5 )- 1 . 5 i - l . . 3 ) 0 . 4 3 3 ' 0 . 4 2 0 } 0 . 2 5 0 ; 0 . 2 5 9 ) - 0 . 8 6 6 ( - 0 . 7 5 7 )- 2 . 3 ( - 1 . 7 ) - 0 . 5 ( - 0 . 5 ) 0 . S 6 6 ( 0 . 8 6 6 ) 0 . 0 ' 0 . 0 )

A ( 3 5 C 1 ) - 5 . 8 ( - 2 . 8 ) - 0 . 7 5 0 ( - 0 . 7 6 5 ) - 0 . 4 3 3 ( - 0 . 4 3 3 ) 0 . 5 ( 0 . 5 )- 5 . 1 ( 0 . 9 ) - 0 . 4 3 3 ( - 0 . 4 0 6 ) - 0 . 2 5 0 ( - 0 . 2 5 0 ) - 0 . 8 6 6 ( - 0 . 7 6 5 )1 7 . 0 ( 1 3 . 6 ) 0 . 5 ( - 0 . 5 ) - 0 . 8 6 6 ; - 0 . 866) 0 . 0 ( 0 . 0 1

Q ( 3 5 C 1 . , ) 3 . 8 ( + 3 - ° > - 0 . 7 5 0 ( - 0 . 7 5 7 ) - 0 . 4 3 3 ' - O . 4 2 0 ) 0 . 5 ' 0 . 5 )- ' . 5 ( - l . V i - 0 . 4 3 3 f - 0 . 4 2 0 ) - 0 . 2 5 0 ( - 0 . 2 5 0 ) - 0 . 8 6 6 ( - 0 . 7 5 7 )- 2 . 3 ( - 1 . 7 ) 0 . 5 ' 0 . 5 ) - 0 . 8 6 6 ( - 0 . 8 6 6 ) 0 . 0 ( 0 . 0 )

A ( ! H ) - 7 . 5 ( 1 . 7 ) 0 . 0 ( 0 . 0 ) 0 . 0 ( 0 . 0 ) 1.0 ( 1 . 0 )( 0 . 5 ) 0 . 0 ( 0 . 0 )

0 . 8 6 6 ( 0 . 8 6 6 ) 0 . 0 ( 0 . 0 )

-7-31-18

2.2.2.

. 5

. 5

.0

Oil0100025

(1(-2(-1

.7)9.2)5.5)

0.00.866

-0. 5

0. 00.866-0.5

(0.(0.(-0.

0)866)5)

0.00. 50.866

0.00 . 50.866

g 2 .011 0 .0 0 . 0 1.0- '•- - -•- - - o . o

0.0

t >

The d i p o l e a n d q u a d r u p o l e c o u p l i n g s <>i 11st- p l a n a r • ( • ! ! , ( " I b r l o r e s p i n

a n n i h i l a t i o n ( U H F ' and a l t e r a n n i h i ' . i t t n n U H F A A nf

t h e S 5 •'Z c o m p o n e n t <if t h e w a v e f u n c t i o n (G)

N u c l e u s D i p o l a r c o u p l i n g s

• U H F A A ( U H F i UH

1 3 C 0 . 7 S 0 1 B :( 0 . 7 6 2 7 )

B 3 :

I H B , :

B , :

B 3 :

3 5ci

B 2 :

B , :

•"" A A

SO. 0

-,'. 4 . 9

- 2 - . 1

1 5 . 2

- 1 . 8

- 1 3 . 4

10. 4

- 3 . 8

- 6 . 6

(UHr

.'48.

• - 2 4

i - 2 4

(14.

i-2.

( - 1 2 .

( 9 .

( - 4 .

( - * .

)

5)

. t i

. 4 )

S i

0)

S)

8)

0)

8)

Electric quadrupole

UHFAA =

»c,

P 2 :

P 3 :

2 . 9

- 1 . 3

- 1 . 6

U H F

e x p

12.2

- 2 . 9

- 9 . 3

17.7

- 8 . 1

- 9 . 6

couplings

exp

3 . 8

-1.5

-2.3

Table 3

The dipole and quadrupole couplings of -CHC1, for the planar

(z - 0 ) and the bent configuration (n 30 ) after annihi-

lation of the S - 3/2 component of the wave function (G)

• Nucleus

13c

»H

35C1

B i

B 2

B 3

B l

B 2

B 3

B l

B 2

B 3

Dipolar

= 0°

: 54. 3

: - 27 . 3

: - 2 7 . 0

: 16. 0

: - 1 4 . 9

: - 1 . 1

: -6 .7

: -3 .0

: 9.7

couplings

o , 30°

50. '»

- 2 4 . 9

- 2 5 . 1

IS. 6

- 2 2 . 7

- 2 . 9

-6.4

-3 .6

10.0

Quadrupole

pr-P 2 :

P 3 :

-- 0"

3 . 0

- 1 . 3

-1 .7

couplings

, . 30°

3 .2

- 1 . 4

-1.8

DISCUSSION

Wr h.ive cornparod the experimental and theoretical spect .a of

•CHC1-, lor tour directions of the magnetic fit-Id and found gnofl ig-

reernent between cor responding spectra. In the experimental analysis

it w..s assumed that the dipole and quadrupole- couplings » e r e parallel

(fig 1). This assumption was confirmed by the simulated spectra and

the LJHF calculations (table 1). The planar configuration of the • CHC1,

radical was found experimentally and was assumed in the simulation

program. The UHF geometry optimization shows that the • CHC1, ra -

dical can be assumed to be planar. The configuration of 'CH7C1 can

also be assumed planar. This is contrary to the IN'DO calculations of

Biddle and Hudson F 17) . They find y = 25° for CH2C1 and a ~- 35° for

• CHC1,. Fig. 3a and 3b show shallow minima for o = 20 and o = 30°

•CH?C1 and • CHC1., respectively, but a precise determination of a

in these radicals seems to be somewhat speculative.

In a previous calculation f 18] we have found that the quatlrupole

couplings of first row atoms can be accurately predicted by the UHF

method. In this calculation the experimental and theoretical quadru-

pole couplings of Cl are also in good agreement.

It seems that the UHF method can give a good determination oi

the electric quadrupole couplings of first and second row atoms using

small basis sets.

The calculated dipolar couplings of Cl are not in good agreement

with the observed couplings.

i n

- 15 -

REFERENCES

t. BONIN, M. L. , IONIN, M. A. and WILLIAMS. F . (ESR studies oi gamma -irra,..ated cryetalline I-bromobutan-.J. Chem. Phys. 54(1971) p. 2641.

2. M1CHAUT. J. P. andRONCIN, J.ESR study of the CH2CI radical in a single crystal of CH,C1.Chem. Phys. Letters 12(1971) p. 95. ' 3

3. LUND, A. , GILLBRO. T. , FENG, D. F. and KEVAN, L. ,EPR and ELDOR studies of • CHCI2 in v-irradiated singlecrystal dichloromethane.Chem. Phys. 7( i975)p. 414.

4. KISPERT, L. D. and ROGERS, M. T. ,Thrichloromethyl and other radicals in irradiated single cry-stals of trichloroacetamide.J. Chem. Phys. 58(1973) p. 2065.

5. MUELLER, D. J. ,Householder's method for complex matrices and eigensystemsof hermitian matrices.Numerische Mathematik 8(1966) p. 72.

6. WILKINSON, J. H. ,Calculation of the eigenvalues of a symmetric tridiagonalmatrix by the method of bisection.Numerische Mathematik 4(1962) p. 362.

7. WILKINSON, J. H. ,Calculation of the eigenvectors of a symmetric tridiagonalmatrix by inverse iteration.Numerische Mathematik 4(1962) p. 368.

8. BYBERG, J. ,Private communication.

9. ROOS, B . , and SIEGBAHN, P . ,Gaussian basis sets for the first and second row atoms.Theoret. Chem. Acta 17(1970) p. 209.

10. HUZINAGA, S. ,Gaussian-type functions for polyatomic systems I.J. Chem. Phys. 42(1965) p. 1293.

11. ALMLÖF, J. ,in: Proceedings of the Second Seminar on ComputationalQuantum Chemistry, Strasbourg 1972 p. 14.

12. AMOS, T. andSNYDER, L. C . ,Unrestricted Hartree-Fock calculations I. An improved methodof computing spin properties.J. Chem. Phy». 41(1964) p. «773.

- !b -

13. KORTZEHORX, R. X. ,IBM report RJ^TT 1I>69>.

14. ELLJNGER, Y. . SUBRA. K. . RASSAT, A . . DOUADAY, J.and PERTHIER, G. .Nonempirual calculations of the conformation and hyperfinestructure ot the nitroxide and ketyl groups. Consequencesof out-of-plane bending on hyperfine intractions.J. Am. Chem. Soc. 97<1975)p. 476.

15. MERZBACHER, E. .Quantum Mechanics, John Wiley & Sons, Inc . , New Yorki%l p. " 3 .

16. ALMLÖF, J. , LUND, A . , and THUOMAS, K-A. ,Ab initio MO LCAO UHF calculations of magnetic hyperfineinteractions in ^- rad ica ls . Isotropic and anisotropic couplingsof -CH}, -N'H^, -C-,H5 and -N 2 Ht .Chem. Phys. 7(1975) p. 46^.

17. BIDDLES, I. and HUDSON, A . ,An 1NDO study of the hyperfine coupling constants and equi-librium geometries of some te t ra-a tomic radicals .Mol. Phvs. 25/1973) 707.

18. ALMLÖF, J. , LUND, A. and THUOMAS, K-A. ,Ab initio MO LCAO UHF calculations of magnetic hyperfineinteractions in r radicals , Isotropic and anisotropic couplingsof NO2 and COj.Chem. Phys. Letters 28('974) p. 179.

- 17 -

LIST OF FIGURES

Fig 1. Orientation of the -CHCl, radical with respect to the z-axis,the x-axis and the y-axis'! The directions of t'*.9 T»rinci~^l-rtK of the hrp«rfine -nc1 ".••.-r'rapole ooaplin,-^.

Fig 2. Experimental (polid line) and theoretical X-band EPR spectraof y-irradiated CH^Cl, at 77 K with the magnetic field direc-ted along

2a x-axis

2b y-axis

2c z-axis

2d xy-plane at an angle of 30 to the x-axis

Fig 3. Variation of the total electronic energy with the angle a

3a between the C-Cl bond and the plane H-C-H in • CH Cl

3b between the C-H bond and the plane Cl-C-CJ in 'CHCl,.

Fig 4. The equilibrium configurations (a) and (b) of • CHC1, withrespect to the plane Cl-H-Cl.

Fig 5. Variation of the isotropic coupling with the out-of-planebending

5a for I 3 C in-CH2C1 and .CHC12

5b for !H and 35C1 in • CH2C1 and • CHC12

a

Fig 1.

'-g 2a,

F i g 2b,

Fig 2c.

Fig 2d.

-955.350

g; -955.355

(O

- 955.3601-

-50 25 50

(degrees)

Fig 3a.

- -»4 -

-4974395-

(0

T>-497.4400h

-497.4405-

a( degrees)

Fig 3b.

o

Fig 4.

10 15 20

a (degrees)

25 30

Fig 5a.

20.0

15.0

oa*JL 10.0

AE:« kontorstryckenNyköping 197S

' H ( C H 2 C I )

XUCH2CI)

1 1 I

10 15 20

a (degrees)

Fig 5b.

25 30

LIST Or PU1ISHCD Al-RtPORTS Optical maoM calculations ol lost aaofrfor some rooeter moleiiols. By M. A.

1—44* | 1 M back n m earlier reports.)

Mt.

Ml.

441.

447.

451

4M.

*M.4*4.

454.

455

417.

451.

4M.

411.

4*1.

4(1.

470.

471.471.

471.

474.

47S.

47S.

477

471.

4».

4*1. Neutron elastic scattering1*71, I I p. Sw. er. It:-.

Wgh cycle fatigue crack r o w * , el two »trceniwa alley».1174. 3* p. Sw. cr. 21-

: Katterna crots socMoaoI. Ml p. To. er. »:-.

By V. S. Rao.

**1

**1

4*3.

4(7.

soc.

501.

sn.

so.5*4.

gamma ray cross sections for Ta. Ag, In and Au betweenM end ITS'keV. By J. Hellström and S. Beshei. 1*71. M p. Sw. cr. IS:-. *•»•Thermodvnemic.l properties of tho solidified rara gases. By I. Ebbsjé 107140 p. Sw. cr. IS:- . **>.reel neutron radiative caature cross sections far sama important stand»! d>from K kaV ta 1.S MeV. By J. Hallström 1*71. n p. Sw. cr. IS:-.A Gc (Li) ben hale probe lor in situ gamma ray spectremetry. By A. Leu-Bar end O. Lendatrom. 1*71. 2* p. Sw. cr. IS:-.Neutron inolanie scattering study el liquid organ. By K. Skold. J. M Rowe.0 . Ostrowski end P. 0 Randolph 1*71. 42 p. Sw. cr. IS:-. 40*.Personnel desimetry et Studsvik during 1(7*. By L. Hedlin and C O Wid.ll1*71. I p. Sw. cr. 15:-.On Hie action of o rotating magnetic tiald ea o conducting liquid. By EDahraerg. 1(71. M p. Sw. cr. IS:-.Lew grade beet from thermal electricity production. Quantity, worth andpossible utilisation in Sweden. By J. Christensen. 1*71. 103 p. Sw. cr. 15 -Personnel dosimolry at Sludsvik dunng 1071 By L. Hedlia end C.-O Widell1(71. t p. Sw. cr. 15:-.Deposition of oero»! particles in electrically charged membrane filter». ByL. Strom. 1(71. M p. Sw. cr. 15:-.Depth distribution studies of carbon in steel surfoces by means of chargedparticle eetivetion an.lv.is with an account o' hoot end diffusion effect» inthe lample. By D. Bruno. J. Lerenten end E. Witalis. 1*71. 41 p. Sw.cr. 1 5 -Fost neutron .l .sl.c scottering eiperiments. By M. Solarna. 1*71. 00 p. So.cr. IS:-.Progress report 1*71. Nuclear chemistry. 1*71. 11 p. Sw. cr. IS:-.Msasursmant of bane mineral content using radiation seurcas. An annotatedBibliography. By P. Schmoling. 1*71. 14 p. Sw. cr. IS:-.Msssimmonl ol bane m'neral content using radietion sources. An annotatedbibliography. Suppl. 1. By P. Schmeling. 7*74. M p. Sw. cr. JO -Long-term test ef self-powered detectors in HBWR. By M. Brakas. O. Strin-deheg and B. Sederlund. 14 p. 1*71. Sw. cr. IS:-.Measurement of the effective detevad ne-itron fraction in Uuee di««r»«tFR*-«ores. By L. Moberg end J. Kockum. 1(71. Sw. er. IS:-.Applications of megnetohydrodynamics in the metal industry. By T. Robinsen. J. Breun end SI Linder. 1(71. 41 p. Sw cr. 15 -Accuracy end precision studies ef a radiechemicol multielement me'.hodfor ectivetien analysis in the field of life sciences. By K Somsahl. 1(71» p. Sw. cr. IS:-.Temperature increments from deposits on hoot transfer surface»: the thermalresistivity and thermal conductivity ef >Hpo»its of magnetite, celcium hydro-sy apatite, humus and capper oiidas. By T. Keren end J. Arveaen. 1(71. Mp. Sw. cr. IS:-.loniietion of e high-pressure gas flow in o longitudinal discherge. By SPolmgren. 1*71. 10 p. Sw. cr. 15:-.The caustic stress corrosion crocking of elloyed steels - en electrochemi-eel study. By L. Dehl. T. Dahlgren end N. Lagmyr. 1(71. 41 p. Sw. cr. IS:-.Electredepesitien of "point" Cu'"l roentgen sources. By P. Beronius, B.Johansson end R. Sörcmark. 1(71. 11 p. Sw. cr. IS:-.A twin l»rge-«raa proportional How counter for the essay of plutonium inhuman lung». By R. C. Shemte. I. Nilsson and L. Lindgren. 1073. SO p. Sw.cr. IS:-.

404. Meosuraments and analysis e' gemma heating in the Rl core By R. Corls-sen end L. G. Larsson 1*71. 14 p. Sw. cr. IS:-.

4SS. Determination ef oiygen in tircaloy surfaces by means of eh.ro.od perticleactivation analysis. By J. Lorenion and D. Bruno. 1(71. I I p. Sw. cr. IS:-.

404. Neutron activation ol liquid »amplas at lew temperature in reactors withreference ta nucleer chemistry. By D. Bruno. 1(71. ( p. Sw. cr. IS:—.

417. Irradiation facilities far ceatcd perticle fuel testing in the Studsvik Rl re-actor. By S. Sandklef 1171. 2* p. Sw. cr. 20;-.

4*0. Neutron absorber techniques developed in the Studs vik Rl reactor By RB e * and S. SandkW. 1 t n . M p. Sw cr. » : - .

400 A radiechemicol machine for the analysis of Cd. Cr, Cu, Mo and Zn. By K.Sameohl, P. O. Wester, 0 . Blemavist. 1(71. 11 p. Sw. cr. 20 -Proton pulse »dialysis. By H. C. Christensen, O. Nilsson. T. Reitbergerand K.- i . Thuomas 1(71. 20 p. Sw. cr. » : - .Progress report 1(71. Nucleer chemistry. 1(71. M p. Sw. cr. » : - .An automatic sampling stallen far fission gas analysis. By S. Sandklef andP. Svensson. 1(71. SI p. Sw. cr. 1 * : - .Selective slap scanning: e simple moons of outometing the Philips diffrac-lometer for studies of line profiles and residual »Ires». By A. Brown endS. A, Llndh. 1(71. I t p. Sw. er. 20:-Radietien damage in CeP. end Be», investigated by the channeling tech-nique. By R. Hellberg end a . Skog 1(71. 1* p. Sw. cr. 20 -A survey ef applied instrument systems for use with light water reactorcontainments By H. Tuien-Meyer. 1(71. M p. Sw. er. 20:-.Eicitetlon functions for rherged particle induced reactions In light elementsel low pre|ectile energies. By J. Lorenien and D. Bruno, 1(71. 154 p. Sw.er. M: - .

. Stadia* of redoi equilibria el elevated temperatures 1. Oiide/eilde endeiide/metal couple» of Iran, nickel, soppor, »liver, mercury «nd antimony inequoain systems up to 1ft°C, By Karin Johansson, Kantin Johnsson andDerek Lewi». 1(71. 41 p. Sw. cr. 20;-.Irradiation facilities for LWR fuel testing in the Studsvik Rl reector. By S.Sendklef and H. Tameni. 1(71. I t p. Sw. er. » : - .Systematic» in the (p.in) and (P.p«n) reaction eras» sections. By L. Jeki1(71. 14 p. Sw. er. I t : - .

• Axial and transverse momentum balance in subchannel analysis By S. Z.Reuhanl. 1*71. I f p. Sw. cr. 20:-.

. Neutron Inelr tin scattering eross »actions in the enacgt range t ta 4.4MeV. MeoMrxment» and calculation». By M, A. Etomed. f t » . » p . Sw. er.

measurements ft 7,0 MeV. By M. A. Itemed.

4*1. Zeeplenklen in Tvlran 1M1-1tt>. By I . Almqulst. I t » , M p. Sw, er. » • - .414. Neutron radiography el the Studsvik R1-* reector. By I. (rwlafssen and I .

Sakelewskl 1(74. <4 p. Sw. er. » : - •

4*7. Studios o* turbulent flow parallel le o •Krellstrem. K74. I N p. Sw. cr. JO -A critical enerysi» of waa ring aapenaian toot en tircelay tiadetag IK. Pettersaon. 1*74. I p. Sw. cr. 20:-Bana mineral dewrminations. Piotoadma» ol the »ympaslum en bona »•mo-ral deleimlnaliana held in Stecfchelm-Studs.ik. Sweden, 17-1* may 1*74.

Val. 1. Ptesented papers, 1*74. 17» p. Sw. cr. IS—.Vat. 1. Presented paper» leant) and groan» discussion» 1(74. I N p. Swer. M — .v f ) l - #. U l U IV^fB^Ivy Oft w)#A9 HI#I^VV#Mt#f^Y wWBJ 4pg)o*aSna9wiBwTw^ Ml MaeW. g*W

A. Hersmea and M. Simpson 1*74. I l l p. Sw. cr. 20—The ovai pewei ramp fuel failure plui is i i run end its bum-up dapandante• need of systenMtic. ralevont end occurate irrediotion Investigations -Program proposal. By H Magard. 1*74 Sw. cr. 20—Phonon »nharmonicity of germanium in * » tomperalura range 10 0*0 IIBy O. Nolin ond G. Nilsson 1*74. IB p Sw. cr. 14):-.Harmonic tottice dynamics of germanium. By Q. Nalin. 1*74. n p.Sw cr. J * : - .Oiffusion of hydrogen in the -oh»»» of Pd-H srudiod by small e n g itransfer neutron scattering. By O. Nelin and K. SkWd. 1074 M p. Sw

opplicalioM in the Rl-roaclor, Studsvik. By

bate allay». By J v'ibergB.' Rahae.B. Rahao. 1*74. M p. Sw cr. M >Estimation al the rote of »onsititalian in nick1*74. 14 p. Sw. cr. J» -A hart-el^anslos in Sweden. By J. Ckristenaon. 1*74. tt p. Sw. cr. » : - .Effect of wall friction end verb» generation an radial void drstrikatiea - aWwelt-vertes effect. By Z Raahanl. 1*74. M p. Sw. cr. M-Tbe deposition kinetics of calcium hydroiy apatita an heat transfer tuHacesot bailing. By T. Kolon and R. Outla's ,<J" 1*74 M p. Sw. cr. M -

, BfffBJgfVlSf, |%. rWW&f%99Hr R. AtoVfoeTnaT.

*n . 1*74. I I p. Sw. cr. » : - .. Melon. 1*74. IS p. Sw. cr

in ilrconiuni alloys By O. Pstwaig, H.K. Narrgtrd. L-O. Jansson ond K. MelonX-ray el.ttic constants far cubic matariels. By K.

Electromagnetic screening and akin-current distribution with magnetic endnon-magnetic conductors. By E. Dahlberg 1174. 44 p. Sw. cr. oft—.Depth distribution studio, el carbon, oiygen end nitrogen in motel sur-

neutron apoctrometry. By. J. Larenien. 1(75. S4 p.fece» bySw. cr. 1A systemetic study of neutron inelastic scattering in the energy range 10to 4.S MeV. By E. Almon-Ramitrom 1*7» 10* p. Sw. cr. M r - ,Analysis of EPR with large quedrapele interaction. By K.-A. Thuomas 1075M p. Sw. cr. JO—

List of published AES-roparls (In Swedish)

Analysis by means ef gamma spoctrowMtry. By D. Bruna. 1(41. 10 p. Sw.er. I : - .Irradiation chengoa and neutron atrnaephera in raacter pressure veeeel»-•ome points of view. By M. Oroune». 1(JU. » p. Sw. cr. • : - ,Study of the elongation limit in mild »tool. By O. Östberg and R. Attar-mo. 1M3. 17 p. Sw. cr. I : - .Technical purchasing in the reactor field. By Erik Jamen. 1*41 04 p.Bw. er. I : - .Agaste nuclear power station. Slemmary af taehattal date, desertpttaa»,ate. far the renter. By B. llllleheok, 1M4. M l p. Sw ar. » : - .

f«H. n\ p. Sw. er. 15:-.

lection "point ef view. By StTa O. W. Bergström and Tar Wahlberg; i K r21 p. Sw. «r. I t : - .Uranium market, 1(71. M p. Sw. er. IS: ' .Redlegreohy day at Sludsvik, Tuesday 17 april 1(71. Arranged be AB Atom-energy, IVA's Committee far nondestructive tosling and TRC AB. 1*71.i n p. Sw, cr. I I : - .The supply of enriched uranium. By M. Mtrtairuen. I f » . M p. Sw. er. « : -tin studies ef eleetlc-lmuleted efectrie sable», tearing leed-ln wfres end j•wHch goer cubicles and floors. I t » . 117 p. Sw. er. M7-. ISevlet-Swedlsh »yrnpailmii an reoelor »efety prablems. Stadavrk, mareh t-tjIt».

•ort 1. Siradlsli aepara. 1*71. 1tt p. Sw. »r. » : -Port 1 Serial ptpm. I t » . 1 « p. Sw. »f. »>-.

Is^jfläMBjéBgjÉläajBäall mm£ ÉBea>taaiBa1wäll a^fsBVaaB^aTaa^ljassbSl afjHmBitJB tan^al1 vvrgVvnqTnvVvnvF gavreV (vaTVVOvVwrt B^^fg^aTvVvnpVorveVBr ^vfwrJtsT/ arraVgT

S. Sendtlrfwi. I t » . M p. Sw. »r. Mr- ,1 tJB^PIffav BaTaffVaTaTfV rrtavnV Wlv sVvonVrW V I ^

Pogo Print, Stockholm 1(71