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Electron paramagnetic resonance studies of matrix isolated inorganic radicals Tait, John Charles 1974

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c  i  ELECTRON PARAMAGNETIC RESONANCE STUDIES OF MATRIX ISOLATED INORGANIC RADICALS  by  B.Sc,  JOHN CHARLES TAIT University of B r i t i s h Columbia, 1967  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY  In the Department of Chemistry  We accept t h i s thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA March, 1974  In  presenting  this  an a d v a n c e d  degree  the  shall  I  Library  further  for  agree  scholarly  by  his  of  this  written  thesis  in p a r t i a l  fulfilment  of  at  University  of  Columbia,  the  make  it  that permission  p u r p o s e s may  representatives. thesis  available  be g r a n t e d  It  f o r financial  is  by  the  gain  Columbia  shall  not  requirements  reference copying of  I  agree  and this  copying o r  be a l l o w e d  for that  study. thesis  Head o f my D e p a r t m e n t  understood that  of  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada  for  for extensive  permission.  Department  Date  freely  British  the  or  publication  without  my  - i -  Supervisor:  C. A. McDowell  ABSTRACT  The technique of electron paramagnetic resonance (EPR) has been used to investigate the e l e c t r o n i c structure and geometry of several small triatomic or tetraatomic r a d i c a l s which have been trapped at 4.2  K i n the i n e r t matrices of neon, argon or krypton.  The  EPR  spectra were analyzed by using an extensive computer simulation program based on a d e t a i l e d general spin Hamiltonian which includes the Zeeman, nuclear Zeeman, hyperfine and quadrupole i n t e r a c t i o n terms.  A general method for analyzing the EPR spectrum of a poly-  c r y s t a l l i n e sample has been discussed with p a r t i c u l a r emphasis being placed on systems for which the p r i n c i p a l axes of the e l e c t r o n i c g-tensor and hyperfine tensors are not coincident. The chloroperoxyl r a d i c a l  (C100)  was  previously studied i n  several polar environments and i n an argon matrix, but the parameters were somewhat i n disagreement.  EPR  A study of t h i s r a d i c a l ,  formed by the UV i r r a d i a t i o n of c h l o r i n e dioxide (CIG^) trapped i n an inert matrix was of  the EPR  undertaken with a view to improving  parameters.  were found to be  the accuracy  The e l e c t r o n i c g-tensor and hyperfine tensor  non-coincident.  The r a d i c a l species FSO has been produced by the far UV photolysis of  thionyl f l u o r i d e  (F2SO)  i n an argon matrix.  The spin Hamiltonian  parameters were obtained for this r a d i c a l and found s i m i l a r to the well known species F00.  to be remarkably  The hyperfine components  were interpreted i n a manner s i m i l a r to F00.  - ii -  The c h l o r o d i s u l f o n y l r a d i c a l  (C1SS)  was produced by the near UV  photolysis of the dichlorodisufane molecule C ^ C ^ )  i n an argon matrix.  The e l e c t r o n i c g-tensor, hyperfine coupling and quadrupole coupling constants were determined from comparison of the observed spectrum with the computer simulated spectrum.  To obtain good agreement, the p r i n c i p a l  axes of the hyperfine and quadrupole tensors had to be rotated by ^ 10° from those of the e l e c t r o n i c g-tensor. The r a d i c a l species  HSO2  and FSO^ were produced by the UV photolysis  of HI/S0 2 or t r i f l u o r o m e t h y l h y p o f l u o r i t e (CF 3 OF)/S0 2 mixtures i n the rare gas matrices.  The  FSO2  r a d i c a l was a l s o produced by the f a r UV  photolysis of s u l f u r y l f l u o r i d e (^SC^).  The EPR parameters were  determined assuming non-coincident axes f o r the hyperfine and e l e c t r o n i c g-tensors.  Another species was produced i n the r e a c t i o n of methyl  r a d i c a l s with SC>2 but the nature of the adduct i s uncertain. Chlorine dioxide (ClO^) was studied i n several i n e r t matrices and the spin Hamiltonian parameters were determined f o r each matrix. P a r t i a l o r i e n t a t i o n has been observed i n a l l the matrices.  The  preferred o r i e n t a t i o n i s with the plane of the r a d i c a l p a r a l l e l to the deposition surface.  The spectrum has been simulated using an  approximate d i s t r i b u t i o n function f o r the molecular o r i e n t a t i o n s . A second trapping s i t e has been observed on annealing the argon matrix. This s i t e exhibits s l i g h t l y d i f f e r e n t hyperfine and Zeeman i n t e r a c t i o n s and i s thought to mean that the s i t e i s a s u b s t i t u t i o n a l one.  The  matrix s h i f t s of the e l e c t r o n i c g-tensor and hyperfine tensor are discussed i n terras of the van der Waals and P a u l i i n t e r a c t i o n forces.  - iii  -  TABLE OF CONTENTS  Page ABSTRACT  i  LIST OF TABLES  vi  LIST OF FIGURES  v i i  ACKNOWLEDGEMENTS  x  CHAPTER ONE:  INTRODUCTION  CHAPTER TWO:  ELECTRON PARAMAGNETIC RESONANCE  2.1  The S p i n H a m i l t o n i a n 2.1.1 2.1.2 2.1.3 2.1.4  The The The The  E l e c t r o n i c Zeeman N u c l e a r Zeeman I n t e r a c t i o n Hyperfine Interaction Quadrupole I n t e r a c t i o n  1  6  6 6 8 9 10  2.2  Thermal E q u i l i b r i u m  14  2.3  Lineshape  17  2.4  S o l v i n g f o r t h e Resonance F i e l d s  19  2.5  Calculation of Transition P r o b a b i l i t i e s  21  CHAPTER THREE:  EXPERIMENTAL  28  3.1  The Spectrometer  28  3.2  Dewar System  30  3.3  I r r a d i a t i o n Sources  33  3.4  Vacuum System and Sample P r e p a r a t i o n  34  - ivPage 3.5  3.5.1 3.5.2  3.5.3 3.5.4 3.5.5  3.5.6 3.5.7 3.5.8 3.6  36  Sample Gases  Molecular  CHAPTER FOUR:  Chlorine Dioxide Dichlorodisulfane  36 36  (C10 ) (S C1 ) 2  2  2  T h i o n y l F l u o r i d e (SOF ) Sulfuryl Fluoride (S0 F ) T r i f l u o r o m e t h y l h y p o f l u o r i t e (CF3OF) Sulfur dioxide (S0 ) Hydrogen I o d i d e (HI) Neon, Argon, K r y p t o n 2  2  2  2  37 37  38  38 38 39 39  Orbital Calculations  40  EPR POWDER SPECTRA  4.1  A n a l y s i s of P o l y c r y s t a l l i n e Spectra  40  4.2  Non C o i n c i d e n t Spectra  46  4.3  Computer S i m u l a t i o n o f P o l y c r y s t a l l i n e S p e c t r a  55  CHAPTER FIVE:  MATRIX ISOLATION TECHNIQUES  59  g and A t e n s o r s  i n Polycrystalline  5.1  Matrix Isolation  5.2  Generation of Free R a d i c a l s  64  5.3  Matrix Effects  68  CHAPTER SIX:  49  INTERPRETATION OF THE HAMILTONIAN 73  PARAMETERS CHAPTER SEVEN:  CHLOROPEROXYL RADICAL, C100  85  7.1  Introduction  85  7.2  R e s u l t s and D i s c u s s i o n  87  7.3  I n t e r p r e t a t i o n of the Hamiltonian  Parameters  97  -  V  -  Page CHAPTER EIGHT: 8.1  FLUOROSULFINYL RADICAL, FSO  103  R e s u l t s and D i s c u s s i o n  CHAPTER NINE:  103  CHLORODISULFONYL RADICAL, C1SS  9.1  P h o t o l y s i s of S u l f u r Monochloride (S C1 )  115  9.2  R e s u l t s and D i s c u s s i o n  116  2  CHAPTER TEN:  RADICAL REACTIONS WITH S 0  2  130  2  10.1  Introduction  130  10.2  R e s u l t s and D i s c u s s i o n  132  10.2.1 10.2.2 10.2.3 CHAPTER ELEVEN:  R e a c t i o n o f H atoms w i t h S 0 R e a c t i o n o f F atoms w i t h S 0 Reaction of methyl r a d i c a l s w i t h S 0 2  2  CHLORINE DIOXIDE, C 1 0  2  2  132 146 157 160  11.1  Introduction  160  11.2  I n t e r p r e t a t i o n o f the S p e c t r a  161  11.3  The H a m i l t o n i a n  179  11.4  Matrix Effects  Parameters  183  REFERENCES  188  APPENDIX A  200  APPENDIX B  205  - v i-  LIST OF TABLES Page 4.1  EPR parameters chosen f o r F i g . 4.4  49  7.1  P r i n c i p a l components o f t h e s p i n H a m i l t o n i a n parameters f o r the C100 r a d i c a l  94  P r i n c i p a l components o f t h e s p i n H a m i l t o n i a n parameters f o r t h e FSO r a d i c a l  109  C a l c u l a t e d ( I N D 0 / 2 ) and p r e d i c t e d s p i n d e n s i t i e s f o r t h e FSO r a d i c a l  109  E x p e r i m e n t a l l y determined p r i n c i p a l v a l u e s o f t h e s p i n H a m i l t o n i a n parameters o f the S 2 C I r a d i c a l  125  Comparison o f e x p e r i m e n t a l and c a l c u l a t e d v a l u e s f o r t h e EPR spectrum o f t h e S 2 C I r a d i c a l i n argon  125  c a l c u l a t i o n of the c o u p l i n g constant i n CIS2  129  8.1  8.2  9.1 9.2 9.3  10.1  I N D 0 / 2 , CND0/2  10.4  quadrupole  2  radical  141  P r e d i c t e d a n i s o t r o p i c h y p e r f i n e t e n s o r components for  10.3  C1  P r i n c i p a l v a l u e s f o r t h e s p i n H a m i l t o n i a n parameters for the HS0  10.2  3 5  HS0  145  2  P r i n c i p a l components o f t h e s p i n H a m i l t o n i a n parameters f o r t h e FSO2 r a d i c a l  154  P r e d i c t e d a n i s o t r o p i c h y p e r f i n e components f o r the F S 0  2  radical  156  11.1  EPR parameters f o r c h l o r i n e d i o x i d e  176  11.2  Calculated hyperfine i n t e r a c t i o n data f o r c h l o r i n e d i o x i d e u s i n g IND0/2 method  182  - vii -  LIST OF FIGURES  Figure 2.1  Page H y p e r f i n e l e v e l s and t r a n s i t i o n s f o r an S = 1/2, I = 3/2 systems  13  2.2  Lineshapes  18  2.3  S p h e r i c a l p o l a r c o o r d i n a t e s of a) the magnetic f i e l d H i n the x,y,z m o l e c u l a r frame and b) the r . f . f i e l d H^ i n a z,p,Q frame  23  3.1  L i q u i d helium cryostat  31  4.1  A n g u l a r v a r i a t i o n of the h y p e r f i n e resonances i n the t h r e e p r i n c i p a l p l a n e s f o r a h y p o t h e t i c a l S = 1/2, I = 1/2 system  42  T h e o r e t i c a l and broadened EPR l i n e s h a p e s f o r a p o l y c r y s t a l l i n e sample. a) a b s o r p t i o n l i n e s h a p e b) f i r s t d e r i v a t i v e of the a b s o r p t i o n  44  R e l a t i o n o f the g and A t e n s o r s i n a h y p o t h e t i c a l case where the t e n s o r s a r e n o n - c o i n c i d e n t  47  A n g u l a r v a r i a t i o n of the h y p e r f i n e t r a n s i t i o n s f o r the h y p o t h e t i c a l case of an S = 1/2, I = 1/2 system where the g and A t e n s o r s a r e n o n - c o i n c i d e n t ( F i g . 4.3). Only Am-j- = 0 t r a n s i t i o n s a r e considered  48  E f f e c t of changing the s i g n of AA and/or Ag i n the system shown i n F i g . 4.4  53  E f f e c t of changing (f>, the angle between A g i n F i g . 4.3  54  4.2  4.3  4.4  4.5 4.6  commonly observed  i n EPR  spectra  and  X  x  7.1  Observed EPR  spectrum of the C100  argon m a t r i x a t 4.2  r a d i c a l i n an  K  88  7.2  A x i s system f o r the C100  radical  90  7.3  Computer s i m u l a t e d EPR spectrum of the C100 r a d i c a l assuming c o i n c i d e n t axes ( C 1 o n l y ) 35  92  - viii -  Figure 7.4  8.1 8.2  Page S i m u l a t e d EPR spectrum of the C100 r a d i c a l assuming the n o n - c o i n c i d e n t a x i s system o f F i g . 7.2 Observed EPR spectrum o f the FSO r a d i c a l i n an argon m a t r i x a t 4 . 2 K  96 105  Computer s i m u l a t e d EPR spectrum o f the FSO radical  108  8.3  M o l e c u l a r a x i s system f o r the FSO r a d i c a l  113  9.1  Observed EPR spectrum o f t h e S C 1 r a d i c a l i n an argon m a t r i x a t 4 . 2 K Computer s i m u l a t e d EPR spectrum o f the S 2 C I radical  123  R e l a t i o n o f the s p i n H a m i l t o n i a n parameters to the m o l e c u l a r axes i n t h e S C 1 r a d i c a l  124  Observed EPR spectrum o f the HSO2 i n a k r y p t o n m a t r i x a t 4.2 K  133  9.2  9.3  2  2  10.1  10.2 10.3  10.4  10.5  10.6  10.8  radical  R e l a t i o n o f t h e s p i n H a m i l t o n i a n parameters to the m o l e c u l a r axes i n the HSO2 r a d i c a l  135  Effect of rotating by 90°  137  t h e sample d e p o s i t i o n s u r f a c e  Computer s i m u l a t e d EPR spectrum o f the HSO2 r a d i c a l assuming the n o n - c o i n c i d e n t a x i s system of F i g . 10.2  140  Observed EPR spectrum o f the FSO2 r a d i c a l i n an argon m a t r i x a t 4.2 K (formed by r e a c t i n g f l u o r i n e atoms w i t h SO2)  148  Observed EPR spectrum o f the F S 0 r a d i c a l i n an argon m a t r i x a t 4.2 K (formed by the UV 2  photolysis  10.7  118  of F S 0 ) 2  2  149  R e l a t i o n o f t h e s p i n H a m i l t o n i a n parameters to the m o l e c u l a r axes i n the FSO2 r a d i c a l  152  Computer s i m u l a t e d spectrum o f the FSO2 r a d i c a l  153  - ix-  Figure 10.9  11.1  Page Observed EPR spectrum o f t h e r a d i c a l s p e c i e s formed on UV p h o t o l y s i s o f a CH3I/SO2/A mixture a t 4,2 K  158  E x p e r i m e n t a l EPR spectrum o f CIO 2 i n an argon m a t r i x a t 4 . 2 K. H i s p a r a l l e l t o the r o d face  162  E x p e r i m e n t a l EPR spectrum of CIO2 i n an argon matrix. H i s perpendicular t o the rod face  163  M o l e c u l a r a x i s system f o r CIO2 (x a x i s i s p e r p e n d i c u l a r t o the m o l e c u l a r p l a n e and H i s the f i e l d d i r e c t i o n )  165  D  11.2  q  11.3  11.4  11.5  11.6  11.7  E x p e r i m e n t a l EPR spectrum o f CIO2 c e n t r a l p o r t i o n of F i g . 11.2)  Q  (expanded 167  P l o t o f angle against f i e l d f o r t r a n s i t i o n s w h i c h have a p p r e c i a b l e i n t e n s i t y . Upper p l o t i s i n x,z p l a n e and lower i n x,y p l a n e . The numbers above the l i n e s denote t h e Am^. v a l u e s  169  Computer s i m u l a t e d EPR spectrum o f C 1 0 u s i n g a c o m p l e t e l y random d i s t r i b u t i o n f u n c t i o n  170  Computer s i m u l a t e d EPR spectrum o f CIO2 u s i n g a d i s t r i b u t i o n f u n c t i o n o f 1 - 0 . 3 cos0. H i s p a r a l l e l to the rod face  173  Computer s i m u l a t e d EPR spectrum o f C 1 0 (expanded p l o t o f c e n t r a l p o r t i o n of F i g . 1 1 . 7 )  174  Computer s i m u l a t e d EPR spectrum o f C 1 0 u s i n g a d i s t r i b u t i o n f u n c t i o n o f 1 - 0 . 3 cos8. H i s perpendicular t o the rod face  176  Observed EPR spectrum of CIO2 i n an argon m a t r i x a f t e r a n n e a l i n g . I and I I denote t h e two observed s i t e s  178  2  Q  11.8 11.9  2  2  Q  11.10  -  X  -  ACKNOWLEDGEMENTS  I would l i k e t o e x p r e s s my g r a t i t u d e t o P r o f e s s o r  C. A. McDowell  f o r h i s i n t e r e s t , guidance and s u p p o r t throughout a l l a s p e c t s o f this thesis. I am a l s o g r a t e f u l t o Dr. F. G. H e r r i n g discussions thesis.  f o r many h e l p f u l  on t h e t h e o r e t i c a l and i n t e r p r e t a t i o n a l a s p e c t s o f t h i s  I w i s h a l s o t o thank Dr. P. Raghunathan f o r h i s h e l p and  u s e f u l comments i n t h e p r e p a r a t i o n  o f s e v e r a l a s p e c t s o f t h i s work.  I n a d d i t i o n I w i s h t o e x t e n d my thanks t o D r . J . A. Hebden f o r p r o v i d i n g a c c e s s t o s e v e r a l o f t h e computer programs he has developed and f o r p e r m i t t i n g  t h e use o f h i s t h e o r e t i c a l c a l c u l a t i o n s  on t r a n s i t i o n p r o b a b i l i t i e s .  A s p e c i a l thanks a l s o t o Mr. T. Markus  and Mr. J . S a l l o s f o r t h e i r c o n t i n u e d c a r e o f t h e EPR s p e c t r o m e t e r ; t o o t h e r members o f t h i s l a b o r a t o r y and  f o r many h e l p f u l d i s c u s s i o n s ;  an e s p e c i a l thanks t o my w i f e f o r h e r p a t i e n c e  preparation.of  and h e l p i n t h e  the f i r s t d r a f t of t h i s t h e s i s .  I a l s o g r a t e f u l l y acknowledge t h e r e c e i p t o f a N a t i o n a l  Research  C o u n c i l o f Canada b u r s a r y and s c h o l a r s h i p and s e v e r a l a s s i s t a n t s h i p s from t h e Department o f C h e m i s t r y .  CHAPTER ONE  Introduction A l t h o u g h f r e e r a d i c a l s undoubtedly p a r t i c i p a t e d i n t h e r e a c t i o n s s t u d i e d by e a r l y c h e m i s t s , separate  t h e e x i s t e n c e of f r e e r a d i c a l s as a  e n t i t y was w i d e l y r e f u t e d even as l a t e as t h e 1930's.  of t h e f i r s t f r e e r a d i c a l s proved c a p a b l e o f independent was the t r i p h e n y l m e t h y l r a d i c a l d i s c o v e r e d by G o m b e r g .  One  existence Later,  (2) Paneth -et al_.  succeeded i n i d e n t i f y i n g t h e m e t h y l r a d i c a l formed  by h e a t i n g t e t r a m e t h y l l e a d . preserved  These r a d i c a l s c o u l d n o t , however, be  i n t h e f r e e s t a t e f o r any l e n g t h o f time because o f r a d i c a l  recombinations.  I t was n o t u n t i l t h e e a r l y 1940's t h a t Lewis and  (3) Lipkin  succeeded i n s t a b i l i z i n g a s e r i e s o f o r g a n i c f r e e r a d i c a l s  i n a r i g i d medium a t a low t e m p e r a t u r e . m o l e c u l e was d i s s o l v e d i n a m i x t u r e  I n t h e i r s t u d y , an o r g a n i c  o f o r g a n i c s o l v e n t s which formed  a c l e a r " g l a s s " when c o o l e d w i t h l i q u i d a i r . s o l u t i o n was then i r r a d i a t e d w i t h u l t r a - v i o l e t  The r e s u l t i n g f r o z e n (UV) l i g h t and a  h i g h l y c o l o r e d s o l u t i o n r e s u l t e d w h i c h was a s c r i b e d t o the f o r m a t i o n of e i t h e r a f r e e r a d i c a l o r the d i s s o c i a t i o n o f t h e o r g a n i c m o l e c u l e i n t o p o s i t i v e and n e g a t i v e  ions.  An o p t i c a l study o f t h e s e s p e c i e s  c o u l d then be performed a t t h e i r l e i s u r e s i n c e they were found t o  -  2 -  be almost i n d e f i n i t e l y s t a b l e i f kept f r o z e n .  T h i s then was t h e  i n t r o d u c t i o n of "matrix i s o l a t i o n " to preserve h i g h l y r e a c t i v e species i n a r e l a t i v e l y concentrated The  form.  t e c h n i q u e o f u s i n g e l e c t r o n paramagnetic resonance (EPR) (4)  to study f r e e r a d i c a l s was i n t r o d u c t e d by Z a v i o s k y l a t e r by Bleaney et_ al_. ^  .  i n 1945 and  I n i t i a l l y , o n l y t h e paramagnetic  t r a n s i t i o n m e t a l complexes were s t u d i e d because t h e s e n s i t i v i t y of t h e i n s t r u m e n t a t i o n was v e r y low and h i g h c o n c e n t r a t i o n s o f r a d i c a l c e n t e r s were n e c e s s a r y  t o be e a s i l y d e t e c t e d .  The EPR  study o f f r e e r a d i c a l s trapped i n a g l a s s y medium d i d n o t g a i n p o p u l a r i t y u n t i l t h e mid 1950's because o f t h e i r r e l a t i v e l y low c o n c e n t r a t i o n s and t h e c o m p l e x i t y o f t h e EPR spectrum o f a p o l y c r y s t a l l i n e sample.  F o r these r e a s o n s ,  the EPR s t u d i e s were m a i n l y  concerned w i t h r a d i c a l s formed by i r r a d i a t i o n damage i n s i n g l e c r y s t a l s o r o f t r a n s i t i o n m e t a l complexes s u b s t i t u t e d i n an a p p r o p r i a t e c r y s t a l host. The  study of a r a d i c a l c e n t e r which i s trapped i n a s i n g l e  c r y s t a l h o s t , w i l l i n h e r e n t l y p r o v i d e more i n f o r m a t i o n about t h e trapped s p e c i e s than w i l l a s i m i l a r study on t h e same s p e c i e s generated  i n a g l a s s y or p o l y c r y s t a l l i n e environment.  This i s  because i n a s i n g l e c r y s t a l ( w i t h o n l y one r a d i c a l s i t e ) , a l l o f the r a d i c a l c e n t e r s w i l l have t h e same o r i e n t a t i o n w i t h r e s p e c t t o the c r y s t a l a x i s .  I f the c r y s t a l i s then o r i e n t e d i n a magnetic  f i e l d , a l l o f these c e n t e r s w i l l have t h e same o r i e n t a t i o n w i t h r e s p e c t t o t h e magnetic f i e l d and w i l l t h e r e f o r e produce t h e same  - 3 -  E P R spectrum.  The  r e s u l t s of t h i s EPR  c r y s t a l l o g r a p h i c study  study combined w i t h an x - r a y  i s u s u a l l y s u f f i c i e n t to a l l o w the  EPR  parameters to be r e l a t e d t o the c r y s t a l l o g r a p h i c or perhaps the molecular  axes of the r a d i c a l .  T h i s assignment to the  molecular  axes i s not e a s i l y a c c o m p l i s h e d w i t h a p o l y c r y s t a l l i n e sample s i n c e the r a d i c a l c e n t e r s are g e n e r a l l y randomly o r i e n t e d .  The  single  c r y s t a l s t u d i e s are l i m i t e d however, because not a l l compounds can be grown as a s i n g l e c r y s t a l or s u b s t i t u t e d i n t o a s i n g l e c r y s t a l host. and  A p o l y c r y s t a l l i n e sample i s not l i m i t e d by these r e s t r i c t i o n s  the range of r a d i c a l s which can be s t u d i e d i n the s o l i d phase  by EPR  i s thus g r e a t l y extended.  E a r l i e r s t u d i e s of r a d i c a l s i n p o l y c r y s t a l l i n e media, were g e n e r a l l y c a r r i e d out i n f r o z e n o r g a n i c s o l v e n t s or some s u b s t r a t e w h i c h would form a g l a s s on f r e e z i n g and would not produce a r a d i c a l s p e c i e s i t s e l f when s u b j e c t e d m a t r i c e s however, p r o v i d e d  t o UV p h o t o l y s i s .  These t r a p p i n g  a h i g h l y p o l a r environment f o r the  r a d i c a l s , w h i c h c o n s e q u e n t l y r e s u l t e d i n an i n c r e a s e i n the spectral linewidth.  The  f o r s t u d y i n g the trapped l i q u i d nitrogen  EPR  temperatures which were commonly a v a i l a b l e s p e c i e s were g e n e r a l l y o n l y as low  (77 K ) , and  i n some c a s e s , t h i s was  as  insufficient  p r e v e n t random t u m b l i n g motions of the r a d i c a l s p e c i e s .  of u s i n g l i q u i d h e l i u m as a c o o l a n t  center.  (4.2 K) became  more f e a s i b l e , a w i d e r range of t r a p p i n g media were e x p l o r e d . r a r e g a s e s , neon, a r g o n , k r y p t o n and xenon have now  to  This led  t o a d e c r e a s e i n the s t r u c t u r a l i n f o r m a t i o n about the r a d i c a l When the t e c h n i q u e  trapped  The  been e x t e n s i v e l y  - 4 -  used as a t r a p p i n g m a t r i x because of t h e i r n o n - p o l a r t h e i r i n e r t n e s s toward r e a c t i o n w i t h the trapped g e n e r a l ease of The  character,  r a d i c a l s and  their  handling.  f i r s t r a d i c a l systems to be s t u d i e d i n the r a r e gas  were the atomic s p e c i e s ^  f o l l o w e d by the more complex  s p e c i e s of w h i c h a g r e a t number a r e now  reported40)^  matrices molecular  (There  have been s e v e r a l comprehensive r e v i e w s s p e c i f i c a l l y c o v e r i n g  species  (41-45) s t u d i e d i n a p o l y c r y s t a l l i n e medium b e i n g s t u d i e d , the c o m p l e x i t y  of the EPR  .)  With l a r g e r systems  s p e c t r a i n c r e a s e d and  this  prompted a g r e a t d e a l of t h e o r e t i c a l i n v e s t i g a t i o n i n t o the observed p o l y c r y s t a l l i n e lineshapes.  S u b s e q u e n t l y , a wide v a r i e t y of computer  programs were developed t o s i m u l a t e the observed s p e c t r a l p a t t e r n ^ ^ These computer programs were g e n e r a l l y s p e c i f i c t o the problem w h i c h was  c u r r e n t l y b e i n g i n v e s t i g a t e d and c o n s e q u e n t l y they c o u l d not  be  a p p l i e d to e x p l a i n a more complex spectrum. The  EPR  study  of f r e e r a d i c a l systems by m a t r i x i s o l a t i o n a t  temperatures has now  low  developed i n t o a most v a l u a b l e method of o b t a i n i n g  i n f o r m a t i o n about the e l e c t r o n i c s t r u c t u r e and g e o m e t r i c a l of those h i g h l y a c t i v e and  transient species.  configuration  W i t h the t e c h n o l o g i c a l  advances i n the i n s t r u m e n t a t i o n d u r i n g the l a s t two decades, the p r e c i s i o n of the s p i n H a m i l t o n i a n c r y s t a l l i n e EPR  study can i n c e r t a i n c i r c u m s t a n c e s ,  w h i c h can be a c h i e v e d  with a single c r y s t a l  In the work p r e s e n t e d new  parameters o b t a i n e d  from a p o l y -  now  rival  that  study.  h e r e , EPR w i l l be used to study  f r e e r a d i c a l systems i s o l a t e d i n the r a r e gas m a t r i c e s  several a t 4.2  K.  .  -  5  -  A b r i e f i n t r o d u c t i o n to the t h e o r y of EPR w i l l be g i v e n , w h i c h w i l l among o t h e r t h i n g s d e s c r i b e the o r i g i n of the parameters of the s p i n Hamiltonian.  T h i s i s f o l l o w e d by a d i s c u s s i o n of the t e c h n i q u e s  a n a l y s i n g t h e spectrum of a p o l y c r y s t a l l i n e sample.  of  S e v e r a l problems,  which can a r i s e i n the i n t e r p r e t a t i o n of the spectrum w i l l be d e s c r i b e d w i t h p a r t i c u l a r emphasis on systems whose s p i n H a m i l t o n i a n parameters a r e not d i r e c t e d a l o n g a common m o l e c u l a r a x i s system.  The d e t a i l s of  the computer program which was w r i t t e n t o s i m u l a t e a g e n e r a l powder spectrum f o r S = 1/2 The  systems, w i l l a l s o be  presented.  r a d i c a l s w h i c h a r e trapped i n an i n e r t m a t r i x w i l l  be  s l i g h t l y p e r t u r b e d by the m a t r i x atoms and t h i s w i l l appear as a s l i g h t change i n the l i n e p o s i t i o n s i n the EPR spectrum. t h e s e changes w i l l be c h a r a c t e r i s t i c of the m a t r i x .  In g e n e r a l ,  A discussion  of the causes and e f f e c t s of these p e r t u r b a t i o n s w i l l be g i v e n , based on the t h e o r y developed  f o r atomic s p e c i e s  .  The  techniques  of  m a t r i x i s o l a t i o n and methods of r a d i c a l p r o d u c t i o n w i l l a l s o be b r i e f l y mentioned. The remainder of t h i s work w i l l d e a l w i t h the of the EPR  s p e c t r a of s e v e r a l new  interpretation  r a d i c a l s p e c i e s w i t h the emphasis  b e i n g p l a c e d on the d e t e r m i n a t i o n of t h e i r s t r u c t u r e and configurations.  electronic  A study of a w e l l known s t a b l e f r e e r a d i c a l ,  CIC^  w i l l a l s o be p r e s e n t e d w i t h s p e c i a l c o n s i d e r a t i o n b e i n g g i v e n to s t u d y i n g the e f f e c t s of a change i n the m a t r i x on the EPR  parameters.  CHAPTER  Electron  Paramagnetic Resonance  2.1  Spin Hamiltonian  The  2.1.1  The E l e c t r o n i c Zeeman I f a magnetic d i p o l e ,  f i e l d H, b y  TWO  Interaction  u, i s p l a c e d i n a homogeneous magnetic  the c l a s s i c a l energy of i n t e r a c t i o n between them i s g i v e n  (67-70)  -M-H  and f o r an  [2.1]  electron  H = "g 6S  [2.2]  e  where g  - 2, 6 i s the Bohr magneton and S i s the s p i n  momentum o p e r a t o r r e p r e s e n t i n g the " e f f e c t i v e s p i n " . Hamiltonian describing  angular The magnetic  the e l e c t r o n i c Zeeman i n t e r a c t i o n i n t h i s  case i s then of the form  s  g SS-H e  [2.3]  - 7 -  I f t h e magnetic f i e l d d i r e c t i o n i s t a k e n t o d e f i n e t h e z a x i s i n a l a b o r a t o r y r e f e r e n c e frame the p r o j e c t i o n of S on H w i l l be S_ and z  the  energy of t h i s system i s then  E  where M  g  s  [2.4]  = g 8HM e s 6  i s t h e magnetic quantum number r e p r e s e n t i n g t h e v a l u e of S_ . z  The s p i n magnetic moment f o r an S = 1/2 system can thus be a l i g n e d e i t h e r p a r a l l e l or a n t i p a r a l l e l t o t h e magnetic f i e l d g i v i n g r i s e t o two s t a t e s of d i f f e r i n g energy w i t h magnitudes  +1/2 ggBH.  The  quantum o f energy n e c e s s a r y t o i n d u c e a t r a n s i t i o n o f t h e type s  = ±1 i s g i v e n by the resonance c o n d i t i o n  [2.5]  E = hv = g $H  where v i s t h e f r e q u e n c y of an o s c i l l a t o r y r . f . d i c u l a r t o t h e magnetic f i e l d  f i e l d a p p l i e d perpen-  H.  I t i s found i n t h e s o l i d s t a t e , t h a t t h e Zeeman i n t e r a c t i o n depends n o t o n l y on t h e a n g l e between t h e e f f e c t i v e s p i n v e c t o r S and t h e magnetic f i e l d b u t a l s o on t h e a n g l e t h a t H makes w i t h a m o l e c u l e based s e t of axes. the  This w i l l give r i s e to anisotropy i n  g f a c t o r and e q u a t i o n [2.5] can be more g e n e r a l l y w r i t t e n as  [2.6]  - 8 -  or more f u l l y  ^ x ^ y ' V / xx xy xz  =  g  g  g  £ £ g °yx °yy y z g g g ' zx z y z z &  6  where g i s a symmetric t e n s o r .  6  V  S ' *  [2.7] L  J  A s u i t a b l e r e f e r e n c e frame ( t h e  p r i n c i p a l frame) c a n always be chosen t o d i a g o n a l i z e t h e g t e n s o r w h i c h i s then r e p r e s e n t e d by i t s p r i n c i p a l g v a l u e s g » ^ y y ' 8 " xx  2.1.2  Z Z  The N u c l e a r Zeeman I n t e r a c t i o n I f t h e n u c l e u s a l s o possesses  a s p i n , an analogous e x p r e s s i o n  t o [2.2] can be w r i t t e n as  v = g 3 I -N N NS  P  L  [2.8] J  where g^ i s t h e n u c l e a r g f a c t o r , 3^ i s t h e n u c l e a r magneton and I i s t h e n u c l e a r s p i n a n g u l a r momentum v e c t o r . The H a m i l t o n i a n w h i c h r e p r e s e n t s t h e e l e c t r o n i c and n u c l e a r Zeeman c o n t r i b u t i o n i s then g i v e n by  \'l  ~  I  [2-9]  The a n i s o t r o p y i n t h e n u c l e a r g f a c t o r has been n e g l e c t e d h e r e as i t i s v e r y s m a l l and n o r m a l l y cannot be d e t e c t e d by EPR.  - 9 -  2.1.3  The H y p e r f i n e  Interaction  The e l e c t r o n a l s o i n d u c e s an e l e c t r i c f i e l d  a t t h e n u c l e u s and  i n t e r a c t s w i t h the n u c l e a r moment t o produce a d i p o l a r term i n t h e H a m i l t o n i a n .  interaction  T h i s o p e r a t o r can be w r i t t e n as  |kl 3 k( r  k  3(I.r )(S_ -r ) 5 r k  k  k  [2.10]  where 5 ( r ^ - r ^ ) i s z e r o u n l e s s t h e e l e c t r o n i s a t the n u c l e u s , r i s the v e c t o r c o n n e c t i n g the n u c l e a r and e l e c t r i c d i p o l e s and r i s the d i s t a n c e between them.  The f i r s t term v a n i s h e s f o r r > 0 and i s  r e f e r r e d t o as the i s o t r o p i c or Fermi c o n t a c t term and has a c o n t r i b u t i o n o n l y i f the e l e c t r o n has s - o r b i t a l c h a r a c t e r s i n c e the p- o r h i g h e r o r b i t a l s have nodes a t the n u c l e u s .  The second term i s t h e  a n i s o t r o p i c o r d i p o l a r i n t e r a c t i o n and v a n i s h e s a t r = 0.  This  term  w i l l c o n t r i b u t e then o n l y i f t h e e l e c t r o n has p- or h i g h e r  orbital  c h a r a c t e r and v a n i s h e s when the e l e c t r o n c l o u d i s s p h e r i c a l . The H a m i l t o n i a n f o r t h i s o p e r a t o r can be expressed  as  aS-I + S-T-I = §' i  [2.11]  A-  where a i s the energy of t h e c o n t a c t c o u p l i n g , T i s the magnetic d i p c l e t e n s o r and A i s the t o t a l h y p e r f i n e t e n s o r .  I n the EPR of s o l i d s , the  d i p o l e t e n s o r i s u s u a l l y the most i n t e r e s t i n g as i t determines the. a n i s o t r o p y of' the h y p e r f i n e t e n s o r .  The e v a l u a t i o n of t h i s term i s  - 10 -  i m p o r t a n t i n d e t e r m i n i n g the e l e c t r o n d i s t r i b u t i o n i n a m o l e c u l e w i l l be c o n s i d e r e d i n Chapter  The  2.1.4  and  Six.  Quadrupole I n t e r a c t i o n  For a n u c l e u s w h i c h has a s p i n I > 1/2,  a term a c c o u n t i n g f o r  t h e i n t e r a c t i o n between the n u c l e a r e l e c t r i c quadrupole  moment and  the g r a d i e n t of the e l e c t r i c f i e l d a t the n u c l e u s must be i n c l u d e d . The c l a s s i c a l i n t e r a c t i o n of a charge d i s t r i b u t i o n of d e n s i t y p w i t h (67) a p o t e n t i a l V, i s g i v e n by  [2.12]  I f t h i s e x p r e s s i o n i s expanded i n a T a y l o r s e r i e s about the o r i g i n , o n l y one term i n the e x p r e s s i o n , the quadrupole  term, i s of i n t e r e s t ,  a l l lower o r d e r p o l e s v a n i s h or do not c o n t r i b u t e and a l l h i g h e r order poles being n e g l i g i b l y s m a l l .  The  quadrupole  energy can  then  be w r i t t e n  [2.13]  where a,3  = x  v a3  3V 3a33  r = 0  [2.14]  - 11 -  w h i c h c a n be r e p r e s e n t e d as a quantum m e c h a n i c a l e x p r e s s i o n by r e p l a c i n g Q^g by Q  U  = ^  t h e quadrupole o p e r a t o r .  k k" a3 k  ( 3 a  3  6  r  )  [ 2  '  1 5 ]  where t h e summation runs over k n u c l e a r p a r t i c l e s and  - 1/6 E  ^  V  a g  Q  [2.16]  ag  ap E v a l u a t i n g t h e m a t r i x elements o f Q  by employing t h e W i g n e r - E c k a r t  theorem, Q „ becomes a6  e Q  _  I  1  i\ ( I I . + I . I ) - 6 I \2 a 3 3 a otg R  s  1(21-1)  a P  2  | )  [2.17]  and  = 6lT2W 5 a3{f  ^  V  ( I  a  a h  +  h  V "a/} &  [ 2  '  1 8 ]  where e i s t h e p r o t o n charge and Q i s t h e quadrupole moment o f t h e nucleus.  A s e t of p r i n c i p a l axes can be chosen w h i c h w i l l d i a g o n a l i z e  the H a m i l t o n i a n w i t h t h e V  <^&T  Q  =  ,^ 21(21-1)  O T <  Since the tensor V  as t h e p r i n c i p a l v a l u e s .  (v I + V I + V I > ( xx x yy y zz z ) 2  2  2  L  [2.19] J  i s t r a c e l e s s and symmetric, t h e H a m i l t o n i a n  can a l s o be d e s c r i b e d by two independent c o n s t a n t s QD and QE d e f i n e d by  - 12 / eQ \ 3 " \ 21(21-1) j' 2  n D Q D  . zz *  Q l 1  I eO, ) ^xx \2I(2I-1)| 2  V  r [ Z  '  Z U J  ,  and = QD(I  2 z  - (1/3)I ) + Q E ( I 2  2 x  - I  2 y  )  [2.21]  or e q u i v a l e n t l y t h e e f f e c t i v e s p i n H a m i l t o n i a n can be w r i t t e n i n t e n s o r form  <^=  I-Q-I  [2.22]  Thus t h e t o t a l s p i n H a m i l t o n i a n f o r an S = 1/2 system i s d e s c r i b e d by<  7 1 )  = e H-g-S + S-A-I + I - g - I - g B H - I e  N  N  [2.23]  The l a s t two terms a r e g e n e r a l l y s m a l l and u s u a l l y become s i g n i f i c a n t when one or more components of t h e h y p e r f i n e t e n s o r i s of t h e o r d e r of t h e n u c l e a r Zeeman s p l i t t i n g o r t h e quadrupole c o u p l i n g .  A  s c h e m a t i c energy l e v e l diagram f o r an S = 1/2, I = 3/2 case i s shown i n f i g . 2.1 where t h e c o n t r i b u t i o n s from each term i n t h e s p i n Hamiltonian  (not n e c e s s a r i l y t o s c a l e ) a r e r e p r e s e n t e d a t a s p e c i f i c  f i e l d H and f i e l d o r i e n t a t i o n 8,<j). a r e Am  g  = ±1, Am^. = 0.  The n o r m a l l y " a l l o w e d " EPR t r a n s i t i o n s  However, h i g h e r o r d e r " f o r b i d d e n " t r a n s i t i o n s  (Am^. = ±1, ±2) a r e a l s o p o s s i b l e .  These t r a n s i t i o n s u s u a l l y a r i s e  when t h e r e i s a n u c l e a r Zeeman quadrupole i n t e r a c t i o n of s u f f i c i e n t magnitude  t o promote m i x i n g between h y p e r f i n e l e v e l s o r i f t h e h y p e r -  f i n e anisotropy i s very l a r g e .  - 13  -  Arty  0  ±2  ±1  •+3/2  1/2  -1/2  <  -1/2  %  »  -3/2  >  -3/2  It  -1/2  -1/2  -1/2 - +  ^  = gpH-S Fig.  2.1  +  S-A-I  • I-Q-I  H y p e r f i n e l e v e l s and 1=3/2  system.  - 9 P H-I N  N  t r a n s i t i o n s f o r an  S =  1/2,  3/2  - 14 -  2.2  Thermal e q u i l i b r i u m T r a n s i t i o n s between e l e c t r o n i c l e v e l s as a l r e a d y mentioned, a r e  induced by a r a d i o f r e q u e n c y f i e l d , d i c u l a r l y t o t h e magnetic f i e l d .  ( u s u a l l y ^ 9GH ) a p p l i e d perpenz  I n o r d e r f o r a t r a n s i t i o n t o be  o b s e r v e d , t h e r e must be a p o p u l a t i o n d i f f e r e n c e between t h e upper and lower e l e c t r o n i c Zeeman l e v e l s .  F o r a system w h i c h i s i n t h e r m a l  e q u i l i b r i u m , t h e r a t i o of t h e number of s p i n s i n t h e lower s t a t e , N , t o t h o s e i n t h e upper s t a t e , N^, i s g i v e n by t h e Boltzmann law:  N ^  =  exp |g BH/kT|  [2.24]  e  b where k i s t h e Boltzmann c o n s t a n t . can be assumed t h a t g S H « k T . e  F o r t e m p e r a t u r e s above 1 K i t  Time-dependent  perturbation  shows t h a t t h e p r o b a b i l i t y , P, t h a t a time-dependent  theory  perturbation  V ( t ) w i l l cause a t r a n s i t i o n between t h e l e v e l s whose e n e r g i e s a r e E  a  and E , i s b  P  ab  =  rT l<aMb>| 6(E 2  a  - E  b  - hv)  [2.25]  The p o p u l a t i o n d i f f e r e n c e n, between t h e two l e v e l s i s  n = N - N, = n ( 0 ) exp (-2Pt) a b  where P = P ^ = P^a  a  n  [2.26]  d n ( 0 ) i s t h e p o p u l a t i o n d i f f e r e n c e a t t = 0.  The r a t e o f a b s o r p t i o n  of energy from t h e r . f . f i e l d  i s g i v e n by  (68)  - 15 -  §| dt  =  nP(E -E ) a b  [2.27]  However, these r e l a t i o n s i m p l y t h a t upon a p p l i c a t i o n of a p e r t u r b i n g field,  t h e s p i n p o p u l a t i o n s w i l l be i n i t i a l l y unbalanced b u t through  a b s o r p t i o n of energy, the p o p u l a t i o n d i f f e r e n c e , n, w i l l e x p o n e n t i a l l y decay u n t i l the p o p u l a t i o n s become e q u a l o r become " s a t u r a t e d " .  This  i m p l i e s t h a t the r a t e of a b s o r p t i o n w i l l a l s o d e c r e a s e c a u s i n g the resonance l i n e t o e v e n t u a l l y d i s a p p e a r . field,  I n t h e absence o f a magnetic  t h e s p i n p o p u l a t i o n s o f t h e two l e v e l s a r e e q u a l , s i n c e they  are degenerate.  Upon a p p l i c a t i o n of a magnetic f i e l d , the system  r e t u r n s t o t h e r m a l e q u i l i b r i u m and thus t h e r e must be a mechanism through w h i c h t h e s p i n s a r e a b l e t o i n t e r a c t w i t h t h e s u r r o u n d i n g s c a u s i n g the s p i n o r i e n t a t i o n t o change.  T h i s p r o c e s s i s termed s p i n -  l a t t i c e r e l a x a t i o n and i s c h a r a c t e r i z e d by T^,  the s p i n - l a t t i c e  r e l a x a t i o n time and i s r e p r e s e n t a t i v e of t h e time r e q u i r e d t o reestablish equilibrium. for  Equation  t h i s mechanism, t h e r e s u l t  [2.27] can be r e w r i t t e n t o account  being  [2.28]  The p r o b a b i l i t y P i s d i r e c t l y p r o p o r t i o n a l t o the square of the i n c i d e n t power and so t o a v o i d s a t u r a t i o n e f f e c t s i t i s b e s t t o work a t a lower i n c i d e n t power.  The p r o b a b i l i t y e q u a t i o n  [2.25]  shows t h a t a b s o r p t i o n w i l l take p l a c e o n l y when t h e 6 - f u n c t i o n c o n d i t i o n s a r e s a t i s f i e d and t h i s w i l l r e s u l t i n a 6 - f u n c t i o n  - 16 lineshape.  However, t h i s l i n e s h a p e i s not observed e x p e r i m e n t a l l y  because of mechanisms w h i c h broaden the 6 - f u n c t i o n t o a f i n i t e width. the  S i n c e the  line-  processes are r e s t o r i n g thermal e q u i l i b r i u m ,  p o p u l a t i o n of t h e Zeeman l e v e l s w i l l have a f i n i t e  lifetime  w h i c h w i l l r e s u l t i n a l i n e b r o a d e n i n g of the o r d e r of 1/T^.  Other  p r o c e s s e s a l s o o c c u r w h i c h have the e f f e c t of v a r y i n g the r e l a t i v e e n e r g i e s of the s p i n l e v e l s . of  T h i s can be caused by the f l u c t u a t i o n  the f i e l d a t the u n p a i r e d e l e c t r o n due t o the presence of l o c a l  magnetic n u c l e i or o t h e r u n p a i r e d e l e c t r o n s . the  T h i s p r o c e s s i s termed  s p i n - s p i n r e l a x a t i o n or " t r a n s v e r s e " r e l a x a t i o n mechanism.  Because the energy l e v e l s a r e no l o n g e r sharp but d i f f u s e , a band of  e n e r g i e s e x i s t s over w h i c h the t r a n s i t i o n s can o c c u r r e s u l t i n g  i n f u r t h e r l i n e broadening.  Thus  (which i s a l s o a f f e c t e d by  w i l l be i n v e r s e l y p r o p o r t i o n a l t o the l i n e w i d t h . are  T^)  These two p r o c e s s e s  by no means the o n l y mechanisms w h i c h c o n t r i b u t e to l i n e  broaden-  (72) ing.  Portis  g i v e s an account of s e v e r a l o t h e r l i n e b r o a d e n i n g  p r o c e s s e s w h i c h a r e termed homogeneous b r o a d e n i n g s i n c e the t h e r m a l e q u i l i b r i u m of the s p i n system i s p r e s e r v e d d u r i n g a t r a n s i t i o n and the  energy absorbed i s t r a n s m i t t e d to a l l the s p i n s i n the system.  They i n c l u d e a) i n t e r a c t i o n w i t h the r a d i a t i o n f i e l d , b) m o t i o n of c a r r i e r s i n the microwave f i e l d , c) d i f f u s i o n of e x c i t a t i o n through the  sample and d) m o t i o n a l l y narrowed  field.  f l u c t u a t i o n s i n the l o c a l  I n homogeneous b r o a d e n i n g (which does not m a i n t a i n the s p i n  system i n e q u i l i b r i u m ) i s r e p r e s e n t e d by such p r o c e s s e s as:  hyper-  f i n e i n t e r a c t i o n , a n i s o t r o p y b r o a d e n i n g , and i n h o m o g e n e i t i e s i n the a p p l i e d magnetic  field.  - 17 -  2.3  Llneshape A broadened l i n e s h a p e can be e x p r e s s e d e m p i r i c a l l y by a l i n e -  shape f u n c t i o n g ( H ) , w h i c h d e s c r i b e s t h e v a r i a t i o n of energy when the resonance c o n d i t i o n i s s a t i s f i e d .  absorption  The p r o b a b i l i t y of a  t r a n s i t i o n (eqn.[2.25]) c o n s e q u e n t l y becomes  P (H) = ^ a b  |<a|v|b>| g(H)  [2.29]  2  where g(H) s a t i s f i e s t h e n o r m a l i z a t i o n c o n d i t i o n V i s a perturbing p o t e n t i a l (the r . f . f i e l d  | °° g(H)dH = 1 and  i n t h i s case).  Iti s  e x p e r i m e n t a l l y observed t h a t t h e l i n e s h a p e f u n c t i o n s f a l l i n t o two main t y p e s .  In l i q u i d s , the Lorentz  l i n e s h a p e i s most commonly  observed  T  g(H) = — *  2  1 ^ =• 1 + T (H-H r 2 o  T  2  [2.30]  0  whereas i n s o l i d s , g a u s s i a n  g(H) =  ( a b s o r p t i o n mode)  Z  e x  P  lineshapes  ( 1 2 | ~ 2* 2 ^ T  H - H  o^  predominate  2) I ( a b s o r p t i o n mode) [2.31]  where H  o  i s t h e f i e l d of t h e c e n t r e o f resonance and H i s t h e v a r i a b l e  magnetic f i e l d . (AH  PP  S i n c e 1^ i s i n v e r s e l y p r o p o r t i o n a l t o the l i n e w i d t h ,  ) , and s i n c e i n EPR t h e d e r i v a t i v e of t h e a b s o r p t i o n c u r v e i s  most commonly seen, these l i n e s h a p e s can be w r i t t e n as  (73)  - 18 -  LORENTZIAN  absorption curve  Fig. 2 . 2  L i n e s h a p e s commonly observed i n EPR s p e c t r a  - 19 Lorentzian:  g'(H) =  2/3  AH  PP  (H-H  )  0  3AH  2  PP  + (H-H )  2  0  [2.32]  and g a u s s i a n :  g'(H)  -(H-H y  (H-H ) o /2TTAH  [2.33]  o  exp  2 H PP  PP  A comparison between these two l i n e s h a p e s i n t h e a b s o r p t i o n and d e r i v a t i v e mode i s shown i n f i g . 2.2.  2.4  S o l v i n g f o r t h e Resonance  Fields  The r e s o n a n t f i e l d s and t r a n s i t i o n p r o b a b i l i t i e s a r e c a l c u l a t e d from an e x a c t s o l u t i o n t o t h e g e n e r a l s p i n H a m i l t o n i a n (eqn. [ 2 . 2 3 ] ) . The b a s i s of t h e m e t h o d i s  to d i v i d e the s p i n Hamiltonian  into  f i e l d independent and f i e l d dependent terms as f o l l o w s :  [2.34]  where nuc  [2.35]  h.(B g-S - B e  N  nuc £  g  n k  k  and h i s t h e u n i t v e c t o r i n t h e d i r e c t i o n of t h e magnetic Then, f o r a g i v e n i n i t i a l guess (H  [2.36]  I )  field.  ) a t t h e t r u e resonance  field  - 20 -  (H  res  ) , t h e term (H -H ^)(^L^ i s t r e a t e d as a p e r t u r b a t i o n on t h e r e s st  preceding  terms.  The i n i t i a l guess H  p r e f e r a b l y w i t h i n 30% o f  (  i s n o n - c r i t i c a l , but i s  poor guess w i l l o n l y i n c r e a s e t h e  a  number of c y c l e s n e c e s s a r y t o converge t o H  r e s  )•  The m a t r i c e s o f  ^ ^ ^ a n d ^ ^ ^ HQ and H^ r e s p e c t i v e l y , a r e c o n s t r u c t e d 1  i n the  m , m_,...,m_ > b a s i s and t h e combined terms H - H H, a r e s I' I. =0 st=l k A  d i a g o n a l i z e d e x a c t l y t o p r o v i d e a s e t of u n p e r t u r b e d , z e r o t h e n e r g i e s and e i g e n v a l u e s .  A s e t of p e r t u r b a t i o n e n e r g i e s  can now  be w r i t t e n i n terms of the z e r o t h order wave f u n c t i o n s and w i t h ^ ^ ^ a c t i n g as t h e p e r t u r b i n g H a m i l t o n i a n complex degenerate p e r t u r b a t i o n p r o c e d u r e .  r e s  - H ) and t h a t g t  thus o b t a i n e d  < ; :  energies  i n a seventh order,  I t might be noted t h a t  t h i s procedure i s independent of t h e p e r t u r b a t i o n (H  order  coefficient  ^ ^ i s i t s e l f independent of f i e l d .  Having  a s e t of s e v e n t h order p e r t u r b a t i o n e n e r g i e s , a power  s e r i e s i n H and t h e s e e n e r g i e s  can be c o n s t r u c t e d  from t h e resonance  c o n d i t i o n as f o l l o w s :  hv =  £ H (E n^O i S n  ( n )  m  - E  m  ! ,) i S  [2.37]  ( n m  m  where hv i s t h e microwave quantum and E^ ^ n  m  p e r t u r b a t i o n energies  of the mm  are the  order  i s m  s t a t e s i n v o l v e d i n the t r a n s i t i o n .  T h i s power s e r i e s can be s o l v e d f o r H by t h e Newton-Raphson method, a s t a r t i n g v a l u e of H f o r t h e i t e r a t i v e procedure b e i n g o b t a i n e d r e v e r s i o n of t h e s e r i e s .  by  The s o l u t i o n t o t h i s power s e r i e s i s thus  the p e r t u r b a t i o n parameter (H -H .) and H i s extracted to res st res r  v  become the new s t a r t i n g guess H  fc  .  The e n t i r e p r o c e d u r e i s c y c l e d  u n t i l t h e s i x t h and s e v e n t h order terms i n t h e power s e r i e s i n H  - 21 -  c o n t r i b u t e l e s s than 10 ^cm  1  t o t h e energy l e v e l s i n v o l v e d i n t h e  -3 transition.  A t t h i s p o i n t the value H  i s a c c u r a t e t o 10  gauss,  res and convergence i s assumed.  I t i s g e n e r a l l y found t h a t w i t h a  j u d i c i o u s c h o i c e of H , convergence i s o b t a i n e d i n t h e f i r s t g t  cycle.  To o b t a i n t h e c o r r e c t wave f u n c t i o n s n e c e s s a r y f o r t h e c a l c u l a t i o n of t r a n s i t i o n p r o b a b i l i t i e s , the t e r m ^ ^ ^ -  H  g t  ^^  S ?  i s diagonalized  at H res 2.5  C a l c u l a t i o n of T r a n s i t i o n P r o b a b i l i t i e s To c a l c u l a t e t h e t r a n s i t i o n p r o b a b i l i t y f o r any resonance, i t i  i s necessary [2.25].  to evaluate the matrix expression  I.  12  ••|<a-|V|b>|  of eqn.  C o n s i d e r t h e case of a system w h i c h e x h i b i t s no h y p e r f i n e ,  n u c l e a r or f i n e s t r u c t u r e i n t e r a c t i o n .  The H a m i l t o n i a n i s g i v e n  by eqn. [2.6] and can be more e x p l i c i t l y w r i t t e n  as^^  3H-(g 1 S + g 1 S + g 1 S ) x x x °y y y °z z z  (/Is  [2.38]  &  where t h e p r i n c i p a l a x i s system has been chosen f o r t h e g t e n s o r and 1 ,1 ,1 a r e t h e d i r e c t i o n c o s i n e s between t h e magnetic - f i e l d H and x y z 6  t h e p r i n c i p a l axes x , y , z .  F o r any g e n e r a l o r i e n t a t i o n of H, t h e  a x i s system c a n be t r a n s f o r m e d  i n t o a r e p r e s e n t a t i o n which i s  d i a g o n a l i n a new s p i n  sens; 2, 2 ^ 2 2 2. 2 g = g l + g 1 + g l x x y y z z 2  where  6  &  [2.39]  - 22 -  A Hamiltonian  representation f o r the perturbing, l i n e a r l y  polarized  microwave f i e l d can be w r i t t e n as  ffi? Clsl  and  = H.coscot (g 1 S + g l ' s + g l ' s ) 1 °x x x °y y y °z z z  transforming  ^  i n t o t h e same a x i s system as t h e s p i n  = Hjcosut  2  § 1  2  °1  &  e,  2  + g g y z  The  ( S^ + g ^  g = 1/g \< gx°y V d 'xly -  where  L  9 ' (1  1 l') x y '  [2.41]  + zg gx ( lz' xl 2  J  Hamiltonian:  + g^)  &  [2.40]  2  e  1 l') z x  ,  [  1 - 1 1 ) } y z y z '  2  -  4  2  ]  s e l e c t i o n r u l e f o r magnetic d i p o l e t r a n s i t i o n s i s Am^ = ±1 a n d  thus t h e t r a n s i t i o n p r o b a b i l i t y f o r a t r a n s i t i o n w i l l be p r o p o r t i o n a l t o <m |^£jjm ±l>| g  g  coupling the m transitions  s  2  and c o n s e q u e n t l y S  s t a t e s and o n l y S  x  ' z  w i l l be i n e f f e c t i v e i n  and S  y  w i l l be e f f e c t i v e i n i n d u c i n g  ( i e . the components o f t h e r . f . f i e l d w h i c h a r e perpen-  d i c u l a r t o t h e magnetic  field).  T h i s r e p r e s e n t a t i o n i s n o t c o n v e n i e n t f o r computation and a more e a s i l y handled r e p r e s e n t a t i o n i s o b t a i n e d by t r a n s f o r m i n g t o spherical polar coordinates  ( f i g . 2.3). The d i r e c t i o n c o s i n e s o f  the magnetic f i e l d a r e e x p r e s s e d i n terms o f t h e p o l a r a n g l e s 0 and (j) and t h e d i r e c t i o n c o s i n e s o f t h e r . f . f i e l d i n t h e z, P, Q frame T  are expressed i n terms o f t h e p o l a r a n g l e s n, 8 . A new s e t o f  i  i  i  d i r e c t i o n cosines 1 , 1 , 1 can now be d e f i n e d i f t h e r . f . f i e l d x y z  - 23 -  Fig.  2.3  Spherical polar coordinates of a) the magnetic f i e l d H i n the x,y,z molecular frame and b) the r . f . f i e l d H-, i n a z,P,Q frame.  - 24 -  coordinates a r e transformed  I  1  T  cos <j> - cos r| s i n <b  = sin n sin 9  x  i  i = sin n sin 0  1 1  i n t o t h e x,y,z frame.  i  = s i n n cos  z  s i n <J> + cos n cos c|>  [2.43]  t  e  S u b s t i t u t i n g i n t o eqn. [ 2 . 4 2 ] , an e x p r e s s i o n i s o b t a i n e d w h i c h i s p r o p o r t i o n a l to the t r a n s i t i o n p r o b a b i l i t y .  2 Sl  =  1 / g  +  2  j  j x S  2  2  8  y 2 2 g {sin z 2 2  2 cos  .2  n sin 2  2 2 sin< >j y  1  n s i n (9 -9) [g 2  2  2 y  + g cos $] + cos n cos 9 [g x  + 2 sin sin  2 cos <(> +  2 2  g s i n <j>] x  n cos n s i n 4> cos <t>"  (9* - 9) cos 0 ( g  2 y  - g^)}  [2.44]  2 I t i s c l e a r from t h i s e x p r e s s i o n t h a t g^ if  w i l l have a maximum v a l u e  i s p e r p e n d i c u l a r t o t h e magnetic f i e l d , t h a t i s , when 0 -0 =  90°, w h i c h i s t h e normal case i n most EPR e x p e r i m e n t s .  For studies  on s i n g l e c r y s t a l s , n i s a known v a l u e , and f o r a r e c t a n g u l a r c a v i t y , n = 0 so  i s p a r a l l e l to the c r y s t a l a x i s of r o t a t i o n .  case when H i s p a r a l l e l t o t h e x m o l e c u l a r  For the  a x i s (0 = 90°, <j> = 0°)  - 25 -  the  transition probability i s proportional  i s p a r a l l e l to the y molecular a x i s  2  to  .  However when H  (9 = 90°, <j> = 90°) t h e t r a n s i t i o n  2 probability i s proportional anisotropic  t o g^ .  Thus i n cases where a h i g h l y  g tensor i s present, the o r i e n t a t i o n  must be known i n o r d e r t o p r e d i c t  the correct  of the r . f . vector  i n t e n s i t y of a  transition. In t h e case of a p o l y c r y s t a l l i n e sample, a l l v a l u e s o f n w i l l t When 0 - 0 = 90°, t h e r e w i l l be an ensemble i n such a manner, t h a t even though H may mag  be e q u a l l y p r o b a b l e . of m o l e c u l e s o r i e n t e d  be a l o n g t h e same d i r e c t i o n i n each, t h e r e w i l l be a random d i s t r i b u t i o n of o r i e n t a t i o n s For  of t h e p l a n e p e r p e n d i c u l a r t o t h i s d i r e c t i o n .  example i f H i s p a r a l l e l t o t h e z a x i s , t h e r . f . v e c t o r can l i e  anywhere i n t h e x, y p l a n e g i v i n g r i s e t o t r a n s i t i o n p r o b a b i l i t i e s 2.2 2 2 p r o p o r t i o n a l t o g s i n n + g cos n. x y Thus n can range from 0 -»• TT f o r any g i v e n 0 and <j> and t h e r . f . v e c t o r i n the p o l y c r y s t a l l i n e case w i l l " s e e " an e f f e c t i v e g v a l u e . To account f o r t h i s when c a l c u l a t i n g p o l y c r y s t a l l i n e t r a n s i t i o n s , an 2 average must be t a k e n over a l l v a l u e s of n by i n t e g r a t i n g g^ as y " g ^ dn/2ir. T h i s i n t e g r a l i s e a s i l y computed and has t h e v a l u e of 2Tr  2  i a m u l t i p l i c a t i v e constant, the r e s u l t f o r 0  2 g  l  T =  g  2 2 x y ^ g  S  2  + g Z  g  X  n  2 ® 2  +  g  2 2 y z ^ -"" ^ g  s  n  2 +  c o s  2 2 2 {cos c|> + cos 9 s i n  - 0 = 90° b e i n g  2 9  c o s  2 ^  ~12/g 2  _J  [2.45]  Thus t h e t r a n s i t i o n p r o b a b i l i t y f o r a p o l y c r y s t a l l i n e sample i s now dependent o n l y upon t h e p o l a r a n g l e s 9 and <f> of t h e magnetic  field.  - 26 -  T h i s of course i s a v e r y s i m p l e case i n which t h e r e i s no h y p e r f i n e or n u c l e a r i n t e r a c t i o n . interactions  I n most cases however, these  w i l l be p r e s e n t and the g e n e r a l form f o r  t r a n s i t i o n p r o b a b i l i t i e s becomes more complex. b a s i s v e c t o r s , {<j>(m . m s i  calculating  F o r a g i v e n s e t of  ) } , the s t a t e v e c t o r il> can be I p n (7174) expressed as a l i n e a r c o m b i n a t i o n of t h e s e v e c t o r s . ' -S ^  p  .1  = m^ =S m S =1, s IT 1 1 T  T  ,...ni  ,n m =1 ^ ' I n n G  T  m  s  m  iI '•••  m  n» ) ^ g ^ x  '.•••m n ) I  k  I  I  [2.46]  where G i s a complex m a t r i x of m i x i n g c o e f f i c i e n t s o b t a i n e d from diagonalization  the  of the s p i n H a m i l t o n i a n (eqn. [2.23]). a t a p a r t i c u l a r  resonant f i e l d .  The most g e n e r a l t r a n s i t i o n p r o b a b i l i t y  can be  expressed a s  [2.47]  where u i s a s e t of d i r e c t i o n c o s i n e s of t h e r . f . f i e l d  i n the molecular  a x i s system.  of p o l y -  To adapt t h i s e q u a t i o n t o the c a l c u l a t i o n  c r y s t a l l i n e t r a n s i t i o n p r o b a b i l i t i e s , t h r e e assumptions  w i l l be made.  i 1.  H^ i s always p e r p e n d i c u l a r t o H ( ( 6  2.  The p r i n c i p a l a x i s system i s always the d i a g o n a l g-frame.  3.  g^ i s i s o t r o p i c .  Expanding I ,I  -0)=  [2.47] i n terms of the s p i n o p e r a t i o n s S ,  the t r a n s i t i o n p r o b a b i l i t y  +  becomes  90°).  S , S^, l  +  ,  - 27 -  T  ab  • iKi  W  s  +  +  s  _  )  _ V ^ j l ( I I . - ) ' B J x i i i=l < ,  V y  +  +  +  +  (  s  +  l ' ( I yy  +  -  s  _  )  +  - I . - ) 1 ii  ' A  2  +  2 l ' l  (| | z z ( b 1T V  e  [2.48]  I f t h e o p e r a t o r s a r e e v a l u a t e d and t h e e x p r e s s i o n s f o r t h e d i r e c t i o n c o s i n e s (eqn. [2.43]) a r e s u b s t i t u t e d an e x p r e s s i o n e q u i v a l e n t t o eqn.  [2.44] c a n be o b t a i n e d on a v e r a g i n g o v e r a l l v a l u e s of n.  2 2 2 2 2 T , = A. ( s i n 6 c o s d> + s i n <J>) + A ( c o s 8 sin2((>) + A _ ( s i n 8 c o s t ) ) ) ab 1 2. 5 1  1  1  0  2 i 2 2 ' 2 ' + A ^ ( s i n 9 s i n <j) + c o s (j>) + A ^ ( s i n 2 8 sincj>) + A ^ ( c o s 8 )  [2.49]  where t h e A^ a r e a s e t of complex c o e f f i c i e n t s w h i c h a r e dependent on t h e e l e c t r o n i c and n u c l e a r g-values and t h e c o e f f i c i e n t s G i n eqn.  [2.46].  I t may be noted t h a t t h i s e x p r e s s i o n i s dependent  i o n l y on t h e p o l a r a n g l e s o f the magnetic f i e l d more f u l l y A  1  - A  A  (8  = 8 + 90°).  A  d e r i v e d e x p r e s s i o n i s g i v e n i n Appendix A w i t h t h e v a l u e s  more f u l l y  expanded.  CHAPTER THREE  Experimental 3.1  The Spectrometer An X-band, super-heterodyne s p e c t r o m e t e r was used f o r t h e  d e t e c t i o n o f t h e EPR. s i g n a l s .  The s p e c t r o m e t e r was c o n s t r u c t e d  by t h e U.B.C. C h e m i s t r y Department E l e c t r o n i c s Shop, from commerc i a l l y a v a i l a b l e components.  I t was based on a d e s i g n developed  l a r g e l y by P r o f e s s o r J . B. Farmer o f t h i s U n i v e r s i t y .  The two  microwave s o u r c e s were V a r i a n type V153C k l y s t r o n s which were t u n e a b l e from about 8.5 GHz t o 9.8 GHz. 716-E k l y s t r o n power s u p p l y was used.  A H e w l e t t - P a c k a r d (HP) The microwaves were c a r r i e d  t o t h e EPR c a v i t y through s t a n d a r d waveguide components.  Because  of t h e low f r e q u e n c y s e n s i t i v i t y o f t h e microwave system, a l l waveguide components were s e c u r e l y b r a c e d t o a p l a t f o r m mounted on the magnet yoke.  A f o u r - p o r t c i r c u l a t o r was used t o d i r e c t t h e  microwaves r e f l e c t e d from t h e resonance c a v i t y t o t h e d e t e c t o r . Microwave A s s o c i a t e s 1N23G d i o d e s were used f o r d e t e c t i o n and were mounted i n an LEL XBH-2 i n t e r m e d i a t e f r e q u e n c y ( i . f . ) m i x e r preamplifier.  A second k l y s t r o n , o p e r a t i n g a t f r e q u e n c y o f 28 MHz  - 29 -  above o r below the f r e q u e n c y o f t h e f i r s t k l y s t r o n , t r a n s m i t t e d t o the second p o r t o f t h e i . f . m i x e r p r e a m p l i f i e r .  The two s i g n a l s  were mixed w i t h t h e r e s u l t a n t 28 MHz s i g n a l c o n t a i n i n g t h e EPR s i g n a l and t h i s was f u r t h e r a m p l i f i e d by a m o d i f i e d two s t a g e i . f . amplifier  (LEL model I F 30B 5 0 ) .  The a m p l i f i e d s i g n a l was then  passed t o a phase s e n s i t i v e d e t e c t o r ( l o c k - i n a m p l i f i e r ) whose c o n s t r u c t i o n was based on an E.M.C. - RJB l o c k - i n a m p l i f i e r .  The  EPR s i g n a l was then d i s p l a y e d on a Moseley 7005B x-y r e c o r d e r o r a Moseley 680 s t r i p c h a r t r e c o r d e r .  The f i r s t k l y s t r o n was s t a b i l i z e d  by an a u t o m a t i c f r e q u e n c y c o n t r o l (AFC) u n i t whose c o n s t r u c t i o n was based on a V a r i a n V4500-10 AFC c i r c u i t . k l y s t r o n was a l l o w e d t o d r i f t preamplifier  The f r e q u e n c y o f the second  s i n c e the band w i d t h o f t h e i . f .  (^ 3 MHz a t 28 MHz) was s u f f i c i e n t t o a l l o w f o r minor  v a r i a t i o n s i n the r e l a t i v e f r e q u e n c i e s o f t h e two k l y s t r o n s . The magnetic f i e l d was s u p p l i e d by a V a r i a n V3400-A 9" magnet, powered by a V a r i a n V-FR2501 Mark I I f i e l d i a l .  The f i e l d  modulation  c o i l s were mounted on the p o l e p i e c e s o f the magnet t o e l i m i n a t e mechanical v i b r a t i o n s of the c a v i t y . was  The f i e l d m o d u l a t i o n f r e q u e n c y  108 Hz and was s u p p l i e d by a HP model 200-J a u d i o o s c i l l a t o r  whose output was a m p l i f i e d by a Bogen MBT-60W audio a m p l i f i e r .  The  low m o d u l a t i o n f r e q u e n c y i s n e c e s s a r y s i n c e the m o d u l a t i o n must p e n e t r a t e t h e t h i c k w a l l s o f the m e t a l c r y o s t a t .  The h i g h e s t f r e q u e n c y  t h a t c o u l d be used w i t h o u t a s i g n i f i c a n t l o s s o f m o d u l a t i o n a m p l i t u d e was ^ 300 Hz. The a u d i o o s c i l l a t o r a l s o s u p p l i e d the r e f e r e n c e s i g n a l f o r the l o c k - i n a m p l i f i e r .  The EPR s i g n a l s were d i s p l a y e d  i n t h e f i r s t d e r i v a t i v e o f t h e a b s o r p t i o n mode.  - 30 -  A HP 431-C  power meter was  used t o measure the i n c i d e n t m i c r o -  wave power of the p r i m a r y k l y s t r o n . about • 1 mW  T y p i c a l power l e v e l s were  and were always below 2 mW.  The microwave f r e q u e n c y  was measured w i t h a HP 5245-L f r e q u e n c y c o u n t e r equipped w i t h a HP 5255-A f r e q u e n c y c o n v e r t e r t o cover the range 8.5 GHz HGz.  The magnetic  to  f i e l d was measured by an e x c e p t i o n a l l y  12.8  stable  magnetometer c o n s t r u c t e d by the U.B.C. C h e m i s t r y Department E l e c t r o n i c s Shop.  To measure the f i e l d as c l o s e as p o s s i b l e t o the c e n t e r of  the magnet p o l e p i e c e s , a t h i n magnetometer probe was c o n s t r u c t e d w h i c h covered the f i e l d r e g i o n from 2500 Gauss to 5600 Gauss.  A  V a r i a n C-1024 time a v e r a g i n g computer was used i n s e v e r a l e x p e r i ments t o enhance weak t r a n s i t i o n s observed i n s e v e r a l s p e c t r a . The microwave resonance c a v i t y i s a s t a n d a r d r e c t a n g u l a r c a v i t y o p e r a t i n g i n the TE^.^ ° d e .  Wide s l i t s were c u t i n the end  m  plate  of the c a v i t y t o p e r m i t the i n s i t u UV i r r a d i a t i o n of the sample w h i c h was  d e p o s i t e d on a c e n t r a l l y mounted, f l a t copper r o d .  These  s l i t s d i d not s i g n i f i c a n t l y a f f e c t the s e n s i t i v i t y of the c a v i t y .  3.2  Dewar System The m e t a l , r o t a t a b l e l i q u i d h e l i u m c r y o s t a t i s shown i n F i g . 3.1.  I t i s b a s i c a l l y s i m i l a r i n d e s i g n t o the c r y o s t a t s of o t h e r workers (7,34,76)^  ^  o  p  r e v e n t  t a e  i  o  w  f r e q u e n c y m e c h a n i c a l v i b r a t i o n of the  c a v i t y system, the t a i l of the i n n e r l i q u i d h e l i u m dewar was w i t h a T e f l o n s p a c e r which was b r a c e d a g a i n s t the r i g i d n i t r o g e n s h i e l d w i t h a minimum of c o n t a c t p o i n t s .  fitted  liquid  The heat c o n d u c t i o n  to the h e l i u m dewar through t h i s s p a c e r r e s u l t e d i n a s l i g h t i n c r e a s e  - 31  -  Mixed Gas  F i g . 3.1  L i q u i d helium  cryostat.  (Sample)  - 32 -  in  t h e b o i l - o f f r a t e o f t h e l i q u i d h e l i u m b u t t h i s was more than  compensated  f o r by a s i g n i f i c a n t i n c r e a s e i n t h e s i g n a l t o n o i s e  r a t i o o f t h e EPR s i g n a l s .  The dewar was evacuated through an o i l  d i f f u s i o n pump, backed by a h i g h speed Welch vacuum pump. p r e s s u r e s i n t h e dewar system were ^ 5 x 10  7  Typical  mmHg-. .  The EPR c a v i t y was i n d i r e c t c o n t a c t w i t h t h e t a i l o f t h e l i q u i d h e l i u m dewar.  A thin walled, stainless steel  connected t h e c a v i t y t o t h e e x t e r n a l waveguide  waveguide  system.  The sample  d e p o s i t i o n s u r f a c e c o n s i s t e d o f a t h i n , f l a t copper r o d which was mounted i n t h e c e n t e r o f t h e c a v i t y and connected d i r e c t l y t o t h e t a i l o f t h e h e l i u m dewar. to  The t a i l o f t h e dewar was c o n s t r u c t e d  a l l o w t h e r o d t o be r o t a t e d w h i l e t h e c a v i t y c o u l d remain f i x e d .  The sample gas was s p r a y e d onto t h e f l a t s u r f a c e o f t h e l i q u i d h e l i u m c o o l e d copper r o d by u s i n g a t h i n S u p r a s i l q u a r t z n o z z l e w i t h a f i n e o r i f i c e , which p r o j e c t e d i n t o t h e bottom o f t h e c a v i t y . The bottom o f t h e n o z z l e was connected t o an o u t e r s p r a y l i n e w h i c h was connected t o t h e sample v e s s e l .  The sample gas f l o w r a t e was  c o n t r o l l e d by a T e f l o n n e e d l e v a l v e s t o p c o c k such t h a t t h e t o t a l p r e s s u r e i n t h e s p r a y l i n e d i d n o t exceed .1 mmHg (as measured by a thermocouple gauge).  A t t h i s spray r a t e , the pressure i n the  dewar d i d n o t r i s e above 2 x 10 ^ mmHg. The h e l i u m c r y o s t a t o u t l e t was connected by vacuum t u b i n g t o a h e a t exchanger c o n s i s t i n g o f a c o i l e d copper tube immersed i n a water bath.  The o u t l e t from t h e h e a t exchange was connected t o a  h i g h speed Welch D u o - s e a l vacuum pump whose exhaust was connected  - 33 -  to a helium recovery l i n e .  For most e x p e r i m e n t s ,  of l i q u i d h e l i u m a t S.T.P. (4.2 K) was  used.  the  temperature  For s e v e r a l e x p e r i -  ments, the vapour p r e s s u r e above the l i q u i d h e l i u m was pumping t o about 40 mmHg w h i c h corresponds l i q u i d h e l i u m of 2.2  K.  reduced  t o a temperature  T h i s t e c h n i q u e was  by  of the  used i n an attempt  to  i n c r e a s e the s i g n a l to n o i s e r a t i o but no a p p r e c i a b l e enhancement c o u l d be d e t e c t e d .  3.3  I r r a d i a t i o n Sources For most of the p h o t o l y s i s e x p e r i m e n t s ,  lamp (500W PEK) was  used.  a h i g h p r e s s u r e mercury  T h i s lamp has an almost c o n t i n u o u s  out-  o  put of l i g h t e x t e n d i n g from about 3000 A i n t o the i n f r a - r e d . decrease  the warming of the d e p o s i t e d sample gas due  To  to IR h e a t i n g ,  s e v e r a l f i l t e r i n g systems were t r i e d but they were u n s u c c e s s f u l i n p r e v e n t i n g t h e warming of the sample. were thus r e q u i r e d to m i n i m i z e  Short i r r a d i a t i o n p e r i o d s  t h i s warming.  For samples r e q u i r i n g a h i g h e r energy to d i s s o c i a t e i n t o fragments,  radical  a low p r e s s u r e mercury lamp w i t h a maximum i n t e n s i t y a t  about 2537 1. and 1849 k was  used.  T h i s lamp c o n s i s t e d of a s e a l e d  q u a r t z tube c o i l w i t h a s m a l l drop of mercury added.  Discharge  p l a t e s were s e a l e d i n t o t h e ends of the q u a r t z tube and these were connected  to a h i g h v o l t a g e DC  source.  For h i g h e r e n e r g i e s , gas resonance lamps were used. two t y p e s ; a s e a l e d lamp or a f l o w d i s c h a r g e lamp.  These were  The s e a l e d lamp  c o n s i s t e d of a s t r a i g h t q u a r t z tube f i t t e d w i t h a s i d e arm t h a t would  - 34 -  be immersed i n a CC^/acetone s l u s h b a t h w h i c h was n e c e s s a r y t o remove any t r a c e s o f m o i s t u r e o r i m p u r i t i e s .  The lamp was f i l l e d  t o a p r e s s u r e o f about 1 mm w i t h e i t h e r argon o r k r y p t o n whose resonance l i n e s a r e a t (1067 A; 1048 A) and (1236 A; and 1165 X) respectively.  One end o f t h e q u a r t z tube w a s . f i t t e d w i t h a L i F  window w h i c h was p o l i s h e d f l a t .  The lamp was then mounted d i r e c t l y  on t h e dewar i n p l a c e o f t h e q u a r t z window.  The gas was d i s c h a r g e d  i n a microwave f i e l d from a c y l i n d r i c a l c a v i t y powered by a Raytheon CMD-4 microtherm  microwave g e n e r a t o r o p e r a t i n g a t 2.45 GHz.  The f l o w d i s c h a r g e lamp was c o n s t r u c t e d i n a manner s i m i l a r t o t h e above s e a l e d lamp, except t h a t i t was connected  t o a vacuum pump.  Hydrogen gas was mixed w i t h a stream o f h e l i u m gas which s e r v e d as a dilutent.  The gas f l o w r a t e s were a d j u s t e d u n t i l a f a i n t p i n k  glow appeared when t h e system was d i s c h a r g e d w i t h a microwave generator.  Because o f t h e h i g h i n t e n s i t y o f t h e hydrogen l i n e  (1216 A) and t h e h i g h energy i n v o l v e d , t h e i r r a d i a t i o n times t o produce a r e a s o n a b l e EPR s i g n a l were v e r y s h o r t . t i o n o f l i g h t s o u r c e s can be found i n C a l v e r t and  3.4  A further descripP i t t s .  Vacuum System and Sample P r e p a r a t i o n The gas samples used i n t h i s study were h a n d l e d  i n a pyrex  g l a s s vacuum system c o n s t r u c t e d by t h e U.B.C. Chemistry G l a s s Blowing Shop.  Department  To reduce t h e l i k e l i h o o d o f c o n t a m i n a t i o n  from  vacuum g r e a s e , h i g h vacuum T e f l o n s t o p c o c k s w i t h V i t o n "0" r i n g s were used.  Wherever a greased vacuum j o i n t was n e c e s s a r y , a f l u o r o -  - 35 -  carbon grease ( F l u o r o l u b e ) was used.  T h i s was n e c e s s a r y because  s e v e r a l o f t h e gases h a n d l e d r e a c t e d v i o l e n t l y w i t h h y d r o c a r b o n greases.  The vacuum m a n i f o l d was degassed w i t h a h e a t i n g tape  w h i c h c o u l d be heated t o 400 K i f n e c e s s a r y .  The m a n i f o l d was  heated between sample p r e p a r a t i o n s t o p r e v e n t t h e a d s o r p t i o n o f sample gases on t h e w a l l s o f t h e vacuum l i n e w h i c h might c o n t a m i n a t e subsequent samples.  Pumping o f t h e vacuum system was through a  Veeco o i l d i f f u s i o n pump backed by a Welch D u o - s e a l vacuum pump. P r e s s u r e s were measured by an NRC t y p e 401 i o n gauge o r an NRC type 531 thermocouple used i n c o n j u n c t i o n w i t h an NRC type 531 detector.  Gas p r e s s u r e s i n t h e vacuum system d u r i n g sample p r e -  p a r a t i o n were 10 ^ - 10 ^ mmHg.  P r e s s u r e s above 1 mmHg were  measured w i t h a gas s p i r a l gauge r a t h e r than a mercury  manometer  t o p r e v e n t t h e i n t r o d u c t i o n o f mercury vapour i n t o t h e sample. The e n t i r e vacuum system was mounted i n a fume cupboard  because  of t h e t o x i c i t y o f t h e sample gases. The v e s s e l c o n t a i n i n g t h e sample was u s u a l l y a 500 ml o r 1 l i t e r blackened bulb f i t t e d w i t h a Teflon stopcock.  The volumes  of t h e vacuum m a n i f o l d and t h e sample b u l b s were r o u g h t l y  calibrated  t o a l l o w t h e r a t i o s o f p r e s s u r e s o f t h e d i l u t e n t gas and sample gas t o be c a l c u l a t e d .  The sample gases were p r e p a r e d about one hour  b e f o r e t h e experiment t o a l l o w complete m i x i n g o f t h e c o n s t i t u e n t gases.  - 36 -  3.5  Sample Gases  3.5.1  C h l o r i n e D i o x i d e (C1C> ) 2  The c h l o r i n e d i o x i d e used was k i n d l y s u p p l i e d by Dr. F. Aubke of t h i s U n i v e r s i t y .  The method o f p r e p a r a t i o n i s t h e well-known  r e a c t i o n of potassium chorate w i t h o x a l i c a c i d i n a concentrated (78 ) s u l f u r i c acid solution  . The r e a c t i o n i s  2KC10,. + 2H„S0. + H„C 0.-2H 0 •i 2 4 2 2 4 2 o  2C10  o  o  L  + 2 C 0 + 4H„0 + 2KHS0, 2 2 4 o  The C l O ^ and CO^ e v o l v e d was passed over a ?2°5 d r y i n g tube and t h e CO2 can be f r a c t i o n a t e d from t h e CIC^ by t r a p t o t r a p  distillation  from a d r y i c e c o o l e d t r a p (195 K) t o a l i q u i d n i t r o g e n c o o l e d t r a p (77 K ) .  Extreme c a r e was e x e r c i s e d i n h a n d l i n g t h i s compound as i t (78)  has been found t o e x p l de f o r no o b v i o u s r e a s o n  . A l l joints  on t h e vacuum apparatus were greased w i t h F l u o r o l u b e and room l i g h t s were t u r n e d o f f when t h e sample was p r e p a r e d s i n c e CIC^ w i l l on i l l u m i n a t i o n . a T e f l o n stopcock.  decompose  The p u r i f i e d CIG^ was s t o r e d i n a g l a s s tube w i t h The sample tube was k e p t a t 195 K i n a d r y i c e /  t r i c h l o r o e t h y l e n e b a t h and kept away from room l i g h t .  The CIC^ was  found t o be i n d e f i n i t e l y s t a b l e a t t h i s temperature b u t was p u r i f i e d t o remove any p o s s i b l e d e c o m p o s i t i o n p r o d u c t s i m m e d i a t e l y p r i o r t o use. 3.5.2  Dichlorodisulfane Commercially a v a i l a b l e  House.  (S2CI2) S2CI2  The sample was a r e d d i s h  was purchased from B r i t i s h Drug orange i n d i c a t i n g t h e p r e s e n c e  - 37 -  of  SCI2  and  impurities.  The S ^ C ^ was d i s t i l l e d a t a t m o s p h e r i c  t h e r e s u l t i n g l i q u i d was f u r t h e r p u r i f i e d by t r a p t o t r a p vacuum  distillation.  The  S  2  C  1  2  w  a  s  Pl  a c e  d  i  n  a  c o l d t r a p a t 209 K  l i q u i d n i t r o g e n s l u s h ) and vacuum d i s t i l l e d (Toluene/liquid ^  slush).  t o 177 K  This p u r i f i c a t i o n process  The p u r i f i e d sample was s t o r e d i n a d r y i c e /  t r i c h l o r o e t h y l e n e bath (195 K ) .  The p u r i f i c a t i o n p r o c e d u r e was  r e p e a t e d p r i o r t o each e x p e r i m e n t . K (Chloroform/liquid ^  3.5.3  of 2 ^ 2  The vapour p r e s s u r e  S  s l u s h ) was used i n p r e p a r i n g  a  t  t h e sample.  T h i o n y l f l u o r i d e (SOF,,) The  was  t o a trap cooled  r e p e a t e d s e v e r a l times w i t h t h e f i n a l p r o d u c t b e i n g a c l e a r  yellow solution.  209  (Chloroform/  The r e s u l t i n g s o l i d was pumped t o remove  a l l traces of higher b o i l i n g i m p u r i t i e s . was  pressure  t h i o n y l f l u o r i d e was purchased from P i e r c e Chemicals and  > 99% pure.  The  SOF2  was passed through a c o l d t r a p a t 177 K  ( t o l u e n e / l i q u i d n i t r o g e n s l u s h ) and condensed i n a c o l d t r a p a t 144  K (n-pentane/liquid  nitrogen slush).  The s o l i d sample was pumped  -4 to 10 177  mmHg a t t h i s temperature.  The vapour p r e s s u r e  of  at  SOF2  K was used t o p r e p a r e t h e sample.  3.5.4  Sulfuryl fluoride ( S O ^ ) The  s u l f u r y l f l u o r i d e was purchased from Matheson C h e m i c a l s .  A l t h o u g h s t a t e d t o be 99.5% impurity.  pure, the  S  ° 2  F  2  c  o  n  t  a  i  n  e  d  S  0  F  2  a  s  a  n  T h i s i m p u r i t y c o u l d n o t be e a s i l y removed by t r a p t o t r a p  distillation  due t o t h e s m a l l d i f f e r e n c e i n t h e i r b o i l i n g p o i n t s .  - 38 -  The m i x t u r e was passed through a c o l d t r a p a t 177 K and trapped i n a c o l d t r a p a t 144 K.  The f r o z e n gas was pumped u n t i l a p r e s s u r e  -4 of 10 177  mmHg was reached.  of t h e l i q u i d a t  K was used t o p r e p a r e t h e sample.  3.5.5  T r i f l u o r o m e t h y l h y p o f l u o r i t e (CF^OF) The  The  The vapour p r e s s u r e  CF^OF was purchased from PCR Chemicals and was 75% p u r e .  i m p u r i t i e s were CG^, CF^, S i F ^ and C G ^ .  by s u i t a b l e d i s t i l l a t i o n t e c h n i q u e s . b o i l i n g p o i n t above l i q u i d n i t r o g e n  These c o u l d be removed  A l l t h e i m p u r i t i e s have a (77 K ) . The gas was condensed  i n a l i q u i d n i t r o g e n t r a p and l i g h t l y pumped.  The vapour  pressure  of CFgOF a t l i q u i d n i t r o g e n temperatures was used t o p r e p a r e t h e sample.  Sample p r e p a r a t i o n was done i n a darkened room t o a v o i d  d e c o m p o s i t i o n o f t h e CF^OF.  3.5.6  Sulfur dioxide ( S O j The  SC>2 was o b t a i n e d  was 99.9%.  from Matheson Gas P r o d u c t s .  The p u r i t y  The SG^ was condensed a t 195 K and pumped t o remove any  t r a c e s of oxygen.  The vapour o f SO^ as i t melted was used i n t h e  sample p r e p a r a t i o n .  3.5.7  Hydrogen I o d i d e ( H I ) ) The  HI was purchased from Matheson Gas P r o d u c t s .  products H  2  and  The d e c o m p o s i t i o n  were removed by s u c c e s s i v e d i s t i l l a t i o n u n t i l t h e  condensed gas was c o l o r l e s s .  The vapour p r e s s u r e  o f HI a t 227 K  ( c h l o r o b e n z e n e / l i q u i d n i t r o g e n s l u s h ) was used i n t h e sample p r e p a r a t i o n .  - 39 -  3.5.8  Neon, Argon, K r y p t o n The r a r e gases used were Matheson r e s e a r c h grade and were  used w i t h o u t f u r t h e r  3.6  purification.  Molecular Orbital Calculations In t h i s work t h e LCAO-MO-SCF c a l c u l a t i o n s were performed  u s i n g two m o l e c u l a r o r b i t a l c a l c u l a t i o n programs.  QCPE program  (79) #,141 was used f o r t h e CND0/2  , open s h e l l c a l c u l a t i o n s on  r a d i c a l s c o n t a i n i n g second row elements. t o s-, p-, and d- S l a t e r type o r b i t a l s .  The b a s i s s e t was l i m i t e d T h i s program,  however,  was n o t p a r a m e t e r i z e d t o p e r f o r m IND0/2 c a l c u l a t i o n s on m o l e c u l e s c o n t a i n i n g second row elements.  Instead, the I N D 0 / 2 ^ ^  calcula-  t i o n s were performed u s i n g a program d e v e l o p e d by D r . F. G. H e r r i n g (81) of t h i s U n i v e r s i t y . The b a s i s s e t was l i m i t e d t o s- and pS l a t e r type o r b i t a l s . The IND0/2 p a r a m e t e r i z a t i o n used f o r t h e (82 ) second row elements i s t h a t o f Benson and Hudson while the (83) p a r a m e t e r i z a t i o n of S a n t r y was used f o r t h e CND0/2 c a l c u l a t i o n s .  CHAPTER FOUR  EPR Powder S p e c t r a 4.1  A n a l y s i s of P o l y c r y s t a l l i n e Spectra C o n s i d e r t h e h y p o t h e t i c a l , s i n g l e c r y s t a l case o f a p a r a -  magnetic m o l e c u l e which has orthorhombic  symmetry and one n u c l e u s w i  a n u c l e a r s p i n I = 1/2 and one u n p a i r e d e l e c t r o n (S = 1/2).  When  the f i e l d i s o r i e n t e d a l o n g a p a r t i c u l a r d i r e c t i o n 6, <> t with r e s p e c t t o t h e m o l e c u l a r axes ( c f . f i g . 2.3a) an energy  level  system s i m i l a r t o t h a t i n f i g . 2.1 w i l l r e s u l t ( t h e t o t a l number of energy  l e v e l s w i l l be (2S+1)(21+1) = 4 i n t h i s c a s e ) .  When  the magnetic f i e l d i s swept a t a c o n s t a n t microwave f r e q u e n c y , two types o f t r a n s i t i o n s may be observed c o r r e s p o n d i n g t o Am^. = 0, ±1. The Am  = ±1 t r a n s i t i o n s a r e " f o r b i d d e n " and g e n e r a l l y  a r e much l e s s i n t e n s e than t h e Am^. = 0 t r a n s i t i o n s .  I f an a n g u l a r  dependence study o f t h e f i e l d p o s i t i o n s i s c a r r i e d out by r o t a t i n g t h e sample about a m o l e c u l a r a x i s , a p l o t such as f i g . 4.1 w i l l r e s u l t when 9 i s p l o t t e d v s H. indicate  The numbers above t h e c u r v e s  t h e Am^ = 0, ±1 t r a n s i t i o n s .  When t h e magnetic f i e l d i s  p a r a l l e l t o t h e m o l e c u l a r a x e s , a unique s e t o f parameters c a n r e a d i l y be e s t a b l i s h e d f o r t h e g and A t e n s o r s .  I n most m o l e c u l e s ,  the g and A t e n s o r s w i l l be c o i n c i d e n t and t h e s p i n H a m i l t o n i a n  - 41 -  parameters w i l l be d e f i n e d i n t h e d i a g o n a l , m o l e c u l a r frame. the  If  o r i e n t a t i o n o f the m o l e c u l e w i t h i n t h e c r y s t a l s t r u c t u r e i s  known, t h e t e n s o r can be a s s i g n e d t o s p e c i f i c d i r e c t i o n s i n t h e molecule. When a s i n g l e c r y s t a l c o n t a i n i n g a paramagnetic c e n t e r i s ground t o a f i n e powder, o r a s o l u t i o n of a paramagnetic c e n t e r i s f r o z e n o r formed i n a g l a s s y o r condensed m a t r i x , i t i s t o be expected t h a t a l l o r i e n t a t i o n s o f t h e m o l e c u l a r axes o f t h e c e n t e r w i l l be e q u a l l y p r o b a b l e .  Thus when t h e magnetic f i e l d  i s swept,  each m i c r o - c r y s t a l l i t e w i l l e x h i b i t i t s own p a r t i c u l a r s e t o f " s i n g l e c r y s t a l " resonances.  The a b s o r p t i o n spectrum w i l l thus  c o n s i s t o f the sum of a l l such resonances and w i l l extend from some H . t o some H as g i v e n i n f i g . 4.1. min max  The d i f f e r e n t i a l  p r o b a b i l i t y dP(H) t h a t a resonance w i l l o c c u r i n a p a r t i c u l a r c r y s t a l l i t e between t h e f i e l d s H and H + dH i s p r o p o r t i o n a l t o the  s o l i d a n g l e o f d5(9,(J>) f o r w h i c h the r e s o n a n t f i e l d  this interval  lies i n  ( i e . t h e m o l e c u l e s a r e o r i e n t e d between 6 and 6 +  d9, cj) and <J) + dd>  w i t h r e s p e c t t o t h e magnetic f i e l d )  .  The  2 a r e a o f a c i r c u l a r element o f a r e a about t h e z a x i s i s 2-nv • sin  0d9d<j>  and hence t h e s o l i d a n g l e i t subtends i s t h e r a t i o o f  t h i s area t o the s u r f a c e area of the sphere. d£(9,<l>) = 1/2 s i n 6d9d<j) = -1/2 dcos0d<j>  since the d i f f e r e n t i a l p r o b a b i l i t y i s p r o p o r t i o n a l to t h i s a n g l e , t h e shape o f t h e powder spectrum can be d e s c r i b e d by  [4.1]  solid  Fig.  4.1  A n g u l a r v a r i a t i o n of the h y p e r f i n e resonances i n the t h r e e p r i n c i p a l p l a n e s f o r a h y p o t h e t i c a l S = 1/2, I = 1/2 system.  -  dP  iy dH  This  43 -  (dH/dcos9d(j))  --  a  [4.2]  1  e x p r e s s i o n c a n be e v a l u a t e d n u m e r i c a l l y and t h e computer  p r o g r a m w h i c h was d e v e l o p e d  to perform  this w i l l  be d i s c u s s e d  later. The of  powder  l i n e s h a p e i s t h e r e f o r e dependent  change o f f i e l d  change  position  i n molecular  resonance  peaks  rate  orientation  .  o f change  i s least  molecular  axis.  different  orientations  resonant  line  orientations,  Although  large.  expected  Thus that  corresponding The  o n l y where  a t f i g . 4.1,  i t c a n be seen  when t h e f i e l d  i s oriented  t h e r e a r e many m o l e c u l e s  will  change l e a s t  and as a r e s u l t  whose o r i e n t a t i o n  occur  f o r these  these molecules  will  that  f o r the simple  there w i l l  case  o f change,  under  Am^  the three molecular  and G a u s s i a n  broadened  i s small, the molecular contribute those  this  case  = 0  Fig.  4.2b i s t h e d e r i v a t i v e  representation.  w h i c h a r e g i v e n i n f i g . 4.2b, h a v e b e e n single  crystal  assignment  ( f i g . 4.1).  i t is  transitions  axes.  powder l i n e s h a p e  i s r e p r e s e n t e d i n f i g . 4.2a w h e r e A _ „  a r e v a l u e s o f t h e h y p e r f i n e and g t e n s o r a l o n g  molecules  dH/dcos9dcj),  i for  i and g  the molecular  The p r i n c i p a l  taken d i r e c t l y I n most  a  slightly  consideration,  be s i x c h a r a c t e r i s t i c  to H being along  delta-function  the rate  than  that  near  with  rate  to the absorption i n t e n s i t y i s such,  a  Experimentally, the  i n a r e g i o n where t h i s  positions  more s i g n i f i c a n t l y  is  Looking  transition with  dH/dcos6d<)>.  i n a powder s p e c t r u m  (dH/dcos6dct>) -* 0 this  of a p a r t i c u l a r  upon t h e r a t e  cases,  axes.  values,  from t h e however,  Fig.  4.2  T h e o r e t i c a l and broadened EPR l i n e s h a p e s f o r a p o l y c r y s t a l l i n e sample, a) a b s o r p t i o n l i n e s h a p e b) f i r s t d e r i v a t i v e of the absorption.  -  45  -  the s i n g l e c r y s t a l d a t a a r e not a v a i l a b l e and the p r i n c i p a l  values  must be a s s i g n e d from the p o l y c r y s t a l l i n e spectrum a l o n e . p r e s e n t s a much more d i f f i c u l t  This  t a s k s i n c e the assignment of  the  l i n e p o s i t i o n s i n a powder spectrum t o a p r i n c i p a l a x i s i s ambiguous s i n c e one  cannot " p a i r " the l i n e s w i t h o u t a d d i t i o n a l i n f o r m a t i o n .  Thus the l i n e assignment 12'; 23';  31' c o u l d j u s t as e a s i l y have  been chosen f o r the p r i n c i p a l v a l u e s , and any l i n e s h a p e s i m u l a t i o n of the Am^. = 0 t r a n s i t i o n s , u s i n g these parameters would g i v e r e s u l t s i d e n t i c a l t o the " c o r r e c t " assignment.  In a l l , there are  s i x p o s s i b l e c h o i c e s f o r assignment of the p r i n c i p a l v a l u e s .  Most  of these c h o i c e s w i l l u s u a l l y l e a d to u n r e a l i s t i c t e n s o r v a l u e s for  the s p e c i e s i n v o l v e d and to d i f f e r e n t i a t e between the  remaining  c h o i c e s , the s p e c t r a l a n a l y s i s must be coupled w i t h t h e o r e t i c a l e s t i m a t e s of g - s h i f t s and h y p e r f i n e c o u p l i n g s , and even s o , s t i l l l e a v e the a x i s and  t e n s o r assignment u n c e r t a i n .  may  There a r e  c e r t a i n i n s t a n c e s , however, where an unambiguous assignment of t e n s o r v a l u e s and d i r e c t i o n s can be made.  I f the n u c l e a r Zeeman  i n t e r a c t i o n i s s u f f i c i e n t l y s t r o n g to a l l o w m i x i n g of the h y p e r f i n e l e v e l s , the " f o r b i d d e n " t r a n s i t i o n s Am^. = ±1 may  be  observable,  the l i n e p o s i t i o n s g i v i n g the e x t r a i n f o r m a t i o n f o r " p a i r i n g " powder l i n e s .  I n o t h e r c a s e s , i t may  the  be p o s s i b l e t o s u b s t i t u t e  the magnetic n u c l e u s w i t h an i s o t o p e of d i f f e r e n t n u c l e a r s p i n , where the assignment i s o f t e n s i m p l i f i e d by knowing the new positions.  line  I f t h i s i s not f e a s i b l e , r e p e a t i n g the experiment a t a  h i g h e r microwave frequency may  a i d the assignment, s i n c e the h y p e r -  f i n e terms a r e independent of magnetic f i e l d s t r e n g t h w h i l e  the  - 46 -  Zeeman terms a r e f i e l d dependent.  The components of the t e n s o r  can then be a s s i g n e d from the g - s h i f t s between the two f r e q u e n c i e s . In the case of a system which has i n t e g r a l n u c l e a r s p i n , the p r i n c i p a l g values are immediately t r a n s i t i o n s i n the 1 = 0 ,  g i v e n by the f i e l d p o s i t i o n s of the Am^ m a n i f o l d and the o n l y r e m a i n i n g t a s k i s  to a s s i g n the p r i n c i p a l v a l u e s to d i r e c t i o n s i n the O c c a s i o n a l l y , w i t h molecules  molecule.  t r a p p e d i n r a r e gas m a t r i c e s a t 4.2°K, (19 33 34  the phenomenon of p a r t i a l o r i e n t a t i o n i s o b s e r v a b l e . In  = 0  t h i s i n s t a n c e , a t l e a s t one p r i n c i p a l v a l u e can be  '  '  '  assigned  s i m p l y by o b s e r v i n g the r e l a t i v e changes i n l i n e i n t e n s i t i e s the sample i s r o t a t e d through 90°  40)  as  i n the magnetic f i e l d - those  l i n e s w h i c h change i n t e n s i t y i n the same manner a r e c h a r a c t e r i s t i c of a p a r t i c u l a r m o l e c u l a r 4.2  Non-coincident  direction.  g and A Tensors i n P o l y c r y s t a l l i n e  Spectra  I t has become e v i d e n t through the c o u r s e of the work p r e s e n t e d here, that a d d i t i o n a l d i f f i c u l t i e s  can a r i s e i n i n t e r p r e t i n g  p o l y c r y s t a l l i n e s p e c t r a when a l a r g e quadrupole  term i s p r e s e n t  o r when a m o l e c u l e has a v e r y low symmetry (eg. C ) and the g and A t e n s o r s are not p a r a l l e l .  A study has been c a r r i e d out f o r  the l a t t e r case on a h y p o t h e t i c a l system (S = 1/2,  I = 1/2)  has orthorhombic  The g and  symmetry i n the g and A t e n s o r s .  t e n s o r d i r e c t i o n s have been chosen such t h a t they have one  which A  tensor  d i r e c t i o n i n common (z a x i s ) and the A t e n s o r has been r o t a t e d about t h i s a x i s by 20°  from the g t e n s o r frame as shown i n f i g .  4.3.  - 47  A '9 Z  Fig.  In  4.3  -  Z  R e l a t i o n of the p r i n c i p a l axes of the g and A t e n s o r s .  the a n a l y s i s of t h i s system, o n l y the Am^  considered.  = 0 t r a n s i t i o n s were  In the examples chosen, g , g , g , A and A have x y z x z  been chosen t o have c o n s t a n t v a l u e s w h i l e A . was a l l o w e d to change y i t s v a l u e a c c o r d i n g to the f o l l o w i n g scheme. The d i f f e r e n c e between g  and x  g  was  chosen to be Ag = .0024 (^4  0  mAg  (Ag i s expressed  and  8.  The  anisotropy  then chosen such  i s the governing  t e n s o r a n i s o t r o p y (Ag)  .5,. 1, 2,  4  the case where the A t e n s o r  term to the case i n which the g  i s dominant.  H p l o t f o r these cases and T a b l e 4.1 g t e n s o r frame was  t h a t AA = A -A = x y  i n gauss u n i t s ) where m = .25,  cases range then, from (AA)  ; z  Ag (gauss) = h v / 3 (g.,-g„)) A was °1 2 y 0  gauss a t 9 GH  y  F i g . 4.4  the v a l u e s chosen.  The  chosen as the r e f e r e n c e frame so the f i e l d  will  be p a r a l l e l to the p r i n c i p a l g  lists  r e p r e s e n t s the < > t vs.  a x i s a t <J> = 0° and x  <j> = 90° w h i l e i t i s p a r a l l e l  to the p r i n c i p a l A  g  a x i s at y  a x i s at cj> =  20°  - 48 -  3350  3360  F i g . 4.4  3370 H (gauss)  3380  3390  3350  3360  3370 H (gauss)  3380  3390  A n g u l a r v a r i a t i o n of t h e h y p e r f i n e t r a n s i t i o n s f o r the h y p o t h e t i c a l case o f an S = 1/2, I = 1/2 system where the g and A t e n s o r s a r e n o n - c o i n c i d e n t ( F i g . 4.3). Only Am =0 t r a n s i t i o n s a r e c o n s i d e r e d .  - 49 -  and Ay a x i s a t c|> = 110°  ( t h e a n g l e s a t w h i c h the f i e l d  i s parallel  to the A frame a r e marked by two h o r i z o n t a l l i n e s on each  curve).  TABLE 4.1 EPR parameters chosen f o r f i g . 4.4  A (gauss) y  g  39.0  0.25  38.0  0.5  36.0  1.0  32.0  2.0  24.0  4.0  8.0  8.0  = 2.0064, g  x A  m(AA = m,  X  = 2.0040, g = 2.0020, y z = 4 0 . 0 gauss, A = 8 0 . 0 gauss z  From the p r e v i o u s d i s c u s s i o n on i n t e r p r e t a t i o n o f p o l y c r y s t a l l i n e spectra,  i t i s expected t h a t powder l i n e s w i l l appear a t t h e p o i n t s  where t h e magnetic f i e l d i s d i r e c t e d a l o n g a m o l e c u l a r o r t e n s o r axis.  I n t h i s c a s e , i t i s not c l e a r w h i c h t e n s o r a x i s w i l l r e s u l t  i n a minimum change i n dH/dcos8dcf) o r i f the f i e l d  i s necessarily  p a r a l l e l t o e i t h e r the g or A a x i s when the r a t e reaches i t s minimum or s t a t i o n a r y v a l u e w i t h r e s p e c t t o a change i n o r i e n t a t i o n .  This  -  i s c e r t a i n l y the case here,  50 -  as can be seen from f i g .  4.4 which  shows the angles a t which a minimum or maximum f i e l d p o s i t i o n i s reached  f o r each m^. l i n e .  These p o i n t s correspond  to a s t a t i o n a r y  v a l u e f o r the f i e l d and w i l l g i v e r i s e t o a powder peak a t t h i s position.  I t i s observed  t h a t as the d i f f e r e n c e between the A  v a l u e s i n c r e a s e s , the angles  a t which a powder peak appears w i l l  approach the case where the f i e l d t e n s o r axes (AA>8Ag).  i s o r i e n t e d p a r a l l e l t o the A  As the A t e n s o r a n i s o t r o p y i s decreased t o  the p o i n t where i t i s l e s s than the g a n i s o t r o p y , the s t a t i o n a r y p o i n t s approach the case c o r r e s p o n d i n g to the g tensor axes.  to H b e i n g a l i g n e d p a r a l l e l  The i m p l i c a t i o n s of t h i s a r e t h a t when the  A tensor a n i s o t r o p y i s much g r e a t e r than the g t e n s o r  anisotropy  (AA>8Ag), the s e p a r a t i o n between t h e powder peaks w i l l  represent  the t r u e A v a l u e s b u t w i l l g i v e o n l y the g v a l u e s along the A t e n s o r axes ( i e . the g v a l u e s i n the A frame).  The g v a l u e s ,  d i a g o n a l i n t h e i r own frame a r e not i n t e r p r e t a b l e from the powder spectrum i n t h i s case.  I f the A tensor a n i s o t r o p y i s much l e s s  than the g tensor a n i s o t r o p y the powder peak s e p a r a t i o n i s r e p r e s e n t a t i v e of the h y p e r f i n e t e n s o r v a l u e i n the g frame and w i l l g i v e the t r u e g v a l u e .  The i n f o r m a t i o n p r e s e n t  spectrum of t h i s type does not c o n t a i n s u f f i c i e n t determine the d i a g o n a l components o f both the angle between the two t e n s o r s . cussed  i n a powder  i n f o r m a t i o n to  t e n s o r s as w e l l as  I f , as i n the p r e v i o u s l y d i s -  example, some f o r b i d d e n t r a n s i t i o n s a r e o b s e r v a b l e ,  they  may p r o v i d e s u f f i c i e n t i n f o r m a t i o n to determine the angle between  - 51 -  the t e n s o r axes.  Also, i f isotopic substitution i s possible with  an i s o t o p e of i n t e g r a l s p i n , the 1 = 0  powder m a n i f o l d w i l l  the f i e l d p o s i t i o n s of H p a r a l l e l t o the g t e n s o r a x e s ^ ^ s h o u l d then g i v e t h e e x t r a i n f o r m a t i o n n e c e s s a r y  give and  t o determine  the angle between t e n s o r s , p r o v i d e d t h a t the case does n o t f a l l i n t o t h e c a t e g o r y where t h e powder p a t t e r n i s a l r e a d y governed by H b e i n g p a r a l l e l t o the g t e n s o r axes (AA<.5Ag). In  the case where the A t e n s o r a n i s o t r o p y i s o f t h e o r d e r o f  the g t e n s o r a n i s o t r o p y (l£m£2) s p e c i a l c a r e must be taken i n a t t e m p t i n g t o e x t r a c t t h e t e n s o r v a l u e s s i n c e the l i n e s i n the powder spectrum cannot s i m p l y be " p a i r e d " . occur at a d i f f e r e n t angular  The s t a t i o n a r y p o i n t s  orientation. (2  In  the case where a d d i t i o n a l t r a n s i t i o n s a r e n o t o b s e r v a b l e  o r i s o t o p i c s u b s t i t u t i o n i s n o t f e a s i b l e , t h e spectrum can be a n a l y z e d by p e r f o r m i n g t h e INDO o r CNDO c a l c u l a t i o n on the system for  d i f f e r e n t assumed m o l e c u l a r geometries  energy i s a c h i e v e d .  Having  u n t i l a minimum t o t a l  i n t h a t way e s t i m a t e d the bond a n g l e  i t i s then p o s s i b l e t o a c h i e v e a f i t t o t h e powder spectrum. Geometries chos en by t h i s method cannot be expected  t o be more  a c c u r a t e than about ±5°. The g e n e r a l o b s e r v a t i o n s made i n t h i s s e c t i o n a r e expected t o h o l d r e g a r d l e s s of the magnitudes of A and g o r the a n g l e o f rotation.  As the a n g l e o f r o t a t i o n i s d e c r e a s e d ,  of the e f f e c t s i s expected  to decrease.  t h e magnitude  The e f f e c t o f changing  the s i g n of Ag and AA ( i e . the r e l a t i v e magnitude of g  and g  or  - 52 -  A X and Ay ) i s shown i n f i g° . 4.5.  The o n l y change observed J O  i s that  the maxima and minima f o r each l i n e have s h i f t e d by 90° o r t h e high f i e l d ambiguity f i g . 4.5.  and low f i e l d t r a n s i t i o n s have exchanged r o l e s .  The  i n c h o o s i n g t h e x and y a x i s i s a l s o i l l u s t r a t e d by The c h o i c e o f axes f o r cases 1 and 3 ( o r cases 2 and  4) would b o t h r e s u l t i n i d e n t i c a l p o l y c r y s t a l l i n e s i m u l a t i o n s , the s t a t i o n a r y f i e l d v a l u e s o c c u r r i n g a t t h e same a n g l e s i n b o t h cases. expected  The g e n e r a l o b s e r v a t i o n s made i n t h i s s e c t i o n a r e a l s o t o h o l d , r e g a r d l e s s of the angle of r o t a t i o n .  I f the  a n g l e o f r o t a t i o n i s i n c r e a s e d , t h e l a r g e r w i l l have t o be t h e d i f f e r e n c e between AA and Ag b e f o r e t h e f i e l d  i s aligned along  the A o r g axes ( i e . m must be >> 8 o r << .25).  The converse  i s o f c o u r s e t r u e when t h e a n g l e between t h e t e n s o r s i s reduced. T h i s i s i l l u s t r a t e d f o r t h e case o f m = 4 and m = .5 f o r <{> = 40° and 10° i n f i g . 4.6. and minima do for  I t can be seen t h a t f o r <j> = 40°, t h e maxima  not correspond  <j) = 10° t h e f i e l d  to H along a tensor a x i s , w h i l e  i s o r i e n t e d a l o n g t h e g t e n s o r axes f o r  m = .5 and i s much c l o s e r t o b e i n g o r i e n t e d a l o n g t h e A t e n s o r axes w i t h m = 4 than i s t h e c o r r e s p o n d i n g cf> = 40° case. G o l d i n g and T e n n a n t ^ ^ have r e c e n t l y made a study o f t h i s e f f e c t on ESR s p e c t r a .  I n the t e s t case which they have chosen t o  i l l u s t r a t e t h e e f f e c t o f n o n - c o l i n e a r i t y o f Zeeman and h y p e r f i n e t e n s o r s on p o l y c r y s t a l l i n e s p e c t r a , t h e r e l a t i v e magnitudes o f t h e a x i a l Zeeman and h y p e r f i n e t e n s o r s remained c o n s t a n t w h i l e the a n g l e s o f r o t a t i o n were changed.  ( I n t h e i r c a s e , t h e r e was  no r e s t r i c t i o n on h a v i n g one common a x i s . )  They have n o t attempted,  however, t o i n t e r p r e t t h e r e s u l t s i n t h e l i g h t o f t h e r o t a t i o n  -  F i g . 4.5  53  -  E f f e c t of changing the s i g n of AA and/or Ag i n the system shown i n F i g . 4 . 4 .  -  55  -  a n g l e s o r t e n s o r magnitudes and have n o t i l l u s t r a t e d how one can b e g i n t o i n t e r p r e t powder s p e c t r a w h i c h f a l l i n t o t h i s c l a s s b u t o n l y warn t h a t h y p e r f i n e e s t i m a t e s from t h e s e type o f s p e c t r a c o u l d be e r r o n e o u s . I t i s f e l t t h a t t h e a n a l y s i s c a r r i e d o u t h e r e s h o u l d form a r e a s o n a b l e framework  from w h i c h a system w i t h n o n - c o i n c i d e n t  Zeeman and h y p e r f i n e t e n s o r s can be a n a l y z e d .  4.3  Computer s i m u l a t i o n o f p o l y c r y s t a l l i n e s p e c t r a There a r e a number o f computer programs a v a i l a b l e w h i c h w i l l  •  i +  i  . I T  (51,53,54,56,58,60,65,85)  simulate p o l y c r y s t a l l i n e spectra of  . Many  t h e s e c o n t a i n such s e v e r e r e s t r i c t i o n s as t o t h e type o f system  which may be s t u d i e d , ( a x i a l symmetry, second o r d e r p e r t u r b a t i o n c a l c u l a t i o n s , absence o f q u a d r u p o l e , p a r a l l e l t e n s o r a x e s , e t c . ) t h a t a program was developed which c o u l d be c o m p l e t e l y g e n e r a l and h a n d l e v i r t u a l l y any s p i n H a m i l t o n i a n ( w i t h t h e e x c e p t i o n o f s p i n m u l t i p l e t s t a t e s where S > 1 / 2 ) . I f the H a m i l t o n i a n c a n be w r i t t e n i n a c l o s e d form ( f o r example, a x i a l symmetry and a l l f i e l d p o s i t i o n s c o r r e c t t o second o r d e r i n h y p e r f i n e i n t e r a c t i o n ) the e x p r e s s i o n [ 4 . 2 ] can be e v a l u a t e d d i r e c t l y s i m p l y by d i f f e r e n t i a t i n g the c l o s e d form f o r the of  resonance l i n e p o s i t i o n s ^ ' . 2  However, a n a l y t i c a l  evaluation  t h i s e x p r e s s i o n from the e x a c t resonance c o n d i t i o n o f eqn.  [2.23]  i s n o t f e a s i b l e f o r o r t h o r h o m b i c symmetry s i n c e a c l o s e d form f o r the  d i f f e r e n t i a l i s not possible.  A computer program was thus  - 56  -  developed t o n u m e r i c a l l y e v a l u a t e the l i n e s h a p e f u n c t i o n f o r the c a s e of o r t h o r h o m b i c symmetry.  For cases of h i g h e r symmetry s e v e r a l  o p t i o n s a r e a v a i l a b l e w h i c h can c o n s i d e r a b l y reduce the c o m p u t a t i o n time.  The  general spin Hamiltonian  (eqn.  [2.23]) i s s o l v e d e x a c t l y  by the method p r e v i o u s l y d e s c r i b e d f o r the resonance f i e l d s of each c o n t r i b u t i n g m^  space t r a n s i t i o n a t a s p e c i f i c f i e l d o r i e n t a t i o n ,  6, <j> w i t h r e s p e c t t o t h e p r i n c i p a l g t e n s o r frame.  The  o r i e n t a t i o n s a r e chosen f o r an e q u a l i n t e r v a l s p a c i n g g r i d c o v e r i n g a cos 6 - <j> space. o n l y the cos 0 space (0 < cos 6<1)  t o form a  For the case of a x i a l symmetry need be spanned.  For  i f o n l y one  p r i n c i p a l a x i s i s common to a l l t e n s o r s , i t i s  chosen as the z a x i s and (0<<f)<Tr) i n o r d e r The  cases  (0<CJXTT/2) ,  w i t h lower symmetry, the <j> space must a l s o be c o v e r e d and  field  the <j> space must then cover  the  region  to account f o r a l l p o s s i b l e r e s o n a n c e s .  r e s u l t i n g m a t r i x of resonance f i e l d s H ( 8 a n d  transition  p r o b a b i l i t i e s T(0,<j>) a r e then t r a n s f e r r e d t o a l i n e s h a p e s i m u l a t i o n program where they are s u b j e c t e d routine.  T h i s r o u t i n e assumes t h a t the r e s o n a n t f i e l d s  smoothly w i t h any dH/dcos0d<j>  to a p o l y n o m i a l i n t e r p o l a t i o n  change i n the f i e l d  vary  o r i e n t a t i o n d0dc|> ( i e .  i s a w e l l behaved f u n c t i o n w h i c h e x h i b i t s no  dis-  c o n t i n u i t i e s ) and a l s o t h a t the t r a n s i t i o n p r o b a b i l i t i e s behave i n a s i m i l a r manner.  The  o r i g i n a l m a t r i x of H w h i c h may  contain  as few as 80 c a l c u l a t e d p o i n t s , i s expanded over cos 0 and cj> (86) u s i n g Newton's d i v i d e d d i f f e r e n c e i n t e r p o l a t i n g p o l y n o m i a l with a polynomial w h i c h may  degree of not l e s s than seven.  be as l a r g e as 180 x.180  The  final  matrix,  w i l l c o n t a i n a g r i d of over  32,000 p o i n t s .  T h i s c o r r e s p o n d s to an a n g u l a r s e p a r a t i o n between  p o i n t s i n the <}> space of .5 degrees and .3° near 0 = 90°.  The  i n a s i m i l a r manner and s t r u c t e d as an  from 6° near 0 = 0°  to  t r a n s i t i o n p r o b a b i l i t i e s are i n t e r p o l a t e d the r e s u l t i n g m a t r i c e s H and T a r e con-  (n x 2) " p a i r e d " v e c t o r , the f i r s t p a r t c o n t a i n i n g  the f i e l d p o s i t i o n and  the l a t t e r p a r t i t s i n t e n s i t y .  i s then n u m e r i c a l l y s o r t e d " p a i r w i s e " i n t o a s c e n d i n g the f i e l d p o s i t i o n s , the r e s u l t b e i n g a h i s t o g r a m  This vector sequence over  or  6-lineshape,  s t i c k r e p r e s e n t a t i o n of the powder spectrum f o r a p a r t i c u l a r |m ,m >-*-|-m ,m  1  > transition.  or L o r e n t z i a n l i n e s h a p e o f  A normalized  d e r i v a t i v e gaussian  a p p r o p r i a t e l i n e w i d t h and  i s then c o n s t r u c t e d about each f i e l d p o s i t i o n and  these  intensity lineshapes  envelopes summed to g i v e the powder l i n e s h a p e envelope of transition.  one  T h i s p r o c e d u r e i s then r e p e a t e d w i t h the next t r a n s i t i o n ,  the r e s u l t i n g envelope b e i n g c o r r e c t l y p o s i t i o n e d and the p r e v i o u s t r a n s i t i o n e n v e l o p e .  summed w i t h  I f i s o t o p i c s p e c i e s are  or i f secondary s p e c i e s a r e t o be o v e r l a p p e d ,  present  the e n t i r e p r o c e d u r e  i s repeated w i t h the t r a n s i t i o n p r o b a b i l i t i e s of the a p p r o p r i a t e l y o v e r l a p p i n g s p e c i e s s c a l e d t o g i v e the c o r r e c t o v e r a l l  intensity  ratio.  intensities  The v e c t o r s c o n t a i n i n g the f i e l d p o s i t i o n s and  as the t o t a l l i n e s h a p e a r e then p l o t t e d f o r comparison w i t h e x p e r i mental spectra. The  program as w r i t t e n does have a minor l i m i t a t i o n .  method of u s i n g a cos 6 m a n i f o l d over 9 may  i n s t e a d of e q u a l  not be g e n e r a l l y a p p l i c a b l e .  The  The  divisions  use of a cos 9  s p a c i n g i s p a r t i c u l a r l y u s e f u l when l a r g e q u a d r a p o l a r  couplings  -  58 -  a r e p r e s e n t o r s t r o n g a n g u l a r anomalies a r e e v i d e n t .  In both cases,  t h e s e a r e expected t o have t h e i r l a r g e s t e f f e c t when 6 > 6 0 ° ^ ^ . Due t o t h e cos 0 s p a c i n g , the r e g i o n where 0 > 60° w i l l have a much h i g h e r d e n s i t y o f c a l c u l a t e d p o i n t s than 0 < 60° and t h e f i e l d v s . a n g l e c u r v e s i n t h i s r e g i o n ( 0 > 60°) w i l l be b e t t e r d e s c r i b e d than they would, had an e q u a l i n t e r v a l s p a c i n g over 0 been chosen. There may however be cases where t h e r e g i o n near 8 = 0 ° s h o u l d be d e s c r i b e d more a c c u r a t e l y b e f o r e t h e i n t e r p o l a t i o n p r o c e d u r e .  In  t h i s case t h e l i n e s h a p e f u n c t i o n w i l l have t o be d e s c r i b e d by , s i n 8d8dcb ,„ , ., . ., . „ , -, , g(v)dH = — dH and an e q u a l i n t e r v a l s p a c i n g over 8 s h o u l d s 1TT  an  be chosen and t h e l i n e s h a p e m u l t i p l i e d by s i n 8. T h i s was n o t c o n s i d e r e d n e c e s s a r y f o r any o f the cases s t u d i e d h e r e .  CHAPTER FIVE  M a t r i x I s o l a t i o n Techniques 5.1  Matrix  Isolation  Chemical r e a c t i o n s i n v o l v i n g r a d i c a l intermediates u s u a l l y occur r a p i d l y and f o l l o w a m u l t i - p a t h r e a c t i o n scheme so t h a t t h e i n t e r m e d i a t e s p e c i e s i n v o l v e d can sometimes o n l y be i n f e r r e d from an a n a l y s i s o f t h e f i n a l p r o d u c t s .  To study and i d e n t i f y  l i v e d r a d i c a l s p e c i e s , one must imploy a t e c h n i q u e  short  t h a t i s capable  of i m m o b i l i z i n g t h e t r a n s i e n t s p e c i e s and p r e v e n t i n g f u r t h e r r e a c t i o n thus a l l o w i n g i t s c o n c e n t r a t i o n t o r i s e t o a l e v e l where i t can e a s i l y be d e t e c t e d . Pulse r a d i o l y s i s  (87)  (88) and f l a s h p h o t o l y s i s have been  employed t o i n c r e a s e t h e c o n c e n t r a t i o n o f r a d i c a l s p e c i e s f o r a short time.  R a d i c a l s p e c i e s can a l s o be formed by X - r a y , gamma  or u l t r a - v i o l e t i r r a d i a t i o n o f s i n g l e c r y s t a l s o r a s i n g l e c r y s t a l h o s t , doped w i t h the p r e c u r s o r s p e c i e s o f i n t e r e s t .  Radicals  s t u d i e d by t h i s method a r e commonly s t a b l e f o r o n l y s h o r t  periods  of time (hours t o weeks) a t room temperature and must be kept a t low temperatures i f decay i s t o be i n h i b i t e d .  X- o r gamma  i r r a d i a t i o n however i s n o n - s e l e c t i v e , due t o the h i g h  energies  i n v o l v e d and a v a r i e t y o f r a d i c a l fragments i s l i k e l y t o r e s u l t  -  60  -  on i r r a d i a t i o n and c r y s t a l s a r e u s u a l l y a l l o w e d t o " a n n e a l " a t room temperature t o a l l o w the more h i g h l y r e a c t i v e r a d i c a l s t o recombine i n o r d e r t h a t the more s t a b l e s p e c i e s may be s t u d i e d . The method commonly used and w h i c h w i l l be d i s c u s s e d i n some d e t a i l i s m a t r i x i s o l a t i o n , where the r a d i c a l s p e c i e s i s trapped at a low temperature, or " i n e r t " m a t r i x .  as a d i l u t e component i n a n o n - r e a c t i v e  There a r e a number o f c r i t e r i a w h i c h s h o u l d  be c o n s i d e r e d when c h o o s i n g most i m p o r t a n t  the m a t r i x m a t e r i a l .  The f i r s t , and  f a c t o r i s the " i n e r t n e s s " o f t h e m a t r i x .  Radical  i n t e r m e d i a t e s a r e u s u a l l y h i g h l y r e a c t i v e and a h o s t must be chosen w h i c h w i l l p r e v e n t r a d i c a l t e r m i n a t i o n . as f l u o r o c a r b o n s , h y d r o c a r b o n s and  S u b s t r a t e s such  s h o u l d be used w i t h some  c a u t i o n , s i n c e when r a d i c a l s a r e formed i n s i t u , they possess a c o n s i d e r a b l e amount o f energy which may be enough t o r e a c t w i t h the m a t r i x r e s u l t i n g i n atom a b s t r a c t i o n o r a d d i t i o n t o t h e matrix material.  In a d d i t i o n to n o n - r e a c t i v i t y , i t i s u s u a l l y  p r e f e r a b l e t o use a m a t r i x which i s s u i t a b l y t r a n s p a r e n t . f r e e r a d i c a l s a r e generated u l t r a - v i o l e t region.  Many  by i r r a d i a t i o n i n the near o r f a r  The m a t r i x s h o u l d not absorb o r be d i s -  s o c i a t e d by t h e i r r a d i a t i o n s o u r c e i n t h e wavelength r e g i o n where p h o t o l y s i s of the r a d i c a l p r e c u r s o r o c c u r s .  I t i s , however,  o c c a s i o n a l l y u s e f u l t o use t h e i n e r t m a t r i x as a p h o t o s e n s i t i z e r i n p r o m o t i n g the d i s s o c i a t i o n o f a trapped p a r e n t m o l e c u l e a r a d i c a l component.  F o r example, when u s i n g a k r y p t o n  into  matrix  w i t h a k r y p t o n resonance lamp, the f o l l o w i n g r e a c t i o n path i s possible.  - 61 -  Kr  +• (Kr lamp)  K r * + RY  K r + R- + Y-  Mercury can a l s o be c o - d e p o s i t e d w i t h the sample and a Hg resonance lamp used as the p h o t o c h e m i c a l s o u r c e f o r t h e p h o t o s e n s i t i z e d decomposition of the r a d i c a l precursor. Once t h e r a d i c a l s p e c i e s has been t r a p p e d and condensed from the gas phase o r formed i n s i t u , t h e r e i s t h e p o s s i b i l i t y of r a d i c a l r e c o m b i n a t i o n r e s u l t i n g from t h e r e a c t i o n between n e i g h b o u r i n g r a d i c a l p a i r s o r from d i f f u s i o n o f t h e r a d i c a l fragment through the m a t r i x u n t i l i t c o l l i d e s w i t h a n o t h e r fragment.  The former can be p r e v e n t e d by i n s u r i n g t h a t t h e  radical:matrix ratio i s quite small.  R a d i c a l : m a t r i x mole  r a t i o s i n excess of 1:50 a r e u s u a l l y s u f f i c i e n t t o p r e v e n t n e i g h b o u r i n g p a i r s from r e c o m b i n i n g and a l s o i s o l a t e t h e r a d i c a l s from one a n o t h e r t o a s u f f i c i e n t degree t h a t i n t e r m o l e c u l a r spin interactions are n e g l i g i b l e .  The l a t t e r f a c t o r can be  i n h i b i t e d by c h o o s i n g a m a t r i x which has a r i g i d c r y s t a l a t t h e condensed  temperature.  spin-  structure  T h i s i s u s u a l l y t h e case i f the  temperature o f t h e m a t r i x i s w e l l below 1/3 i t s m e l t i n g p o i n t , and almost always t r u e a t 4.2°K.  I t has been shown  that  d i f f u s i o n o f m o l e c u l a r s p e c i e s w i t h l e s s than 10 atoms w i l l o c c u r i n a m a t r i x i f t h e temperature o f the m a t r i x r i s e s t o w i t h i n .4 t o .6 o f t h e m e l t i n g p o i n t , T^, o f t h e m a t r i x .  I f the matrix  does n o t have an o r d e r e d c r y s t a l s t r u c t u r e b u t c o n s i s t s o f l a t t i c e d e f e c t s and m i c r o c r y s t a l l i t e s m a t r i x i s condensed  (which i s u s u a l l y t h e case i f the  a t a temperature much below one h a l f i t s  - 62 -  m e l t i n g p o i n t ) the temperature may  be lowered  range over w h i c h d i f f u s i o n  t o .1 t o .4 T,,.  t r o l l e d d i f f u s i o n may  occurs  In c e r t a i n c a s e s , however, con-  be v a l u a b l e .  I f the m a t r i x i s a l l o w e d to  warm s l i g h t l y and then r e c o o l e d ( a n n e a l i n g ) then l a t t i c e f e c t i o n s around the r a d i c a l t r a p p i n g s i t e may  be removed r e s u l t i n g  i n a more symmetric environment about the r a d i c a l .  This w i l l also  g e n e r a l l y reduce the number of t r a p p i n g s i t e s which may c o n s i d e r a b l y s i m p l i f y i n g the EPR  spectra.  imper-  be  present,  Moreover, i f two  have managed t o occupy a d j a c e n t t r a p p i n g s i t e s , they may  radicals  be a l l o w e d  t o e i t h e r recombine o r d i f f u s e a p a r t , b o t h r e s u l t i n g i n the r e d u c t i o n of l i n e b r o a d e n i n g  due  to s p i n - s p i n i n t e r a c t i o n s .  r a r e gases from argon to xenon a r e a l l e a s i l y annealed  The  (argon i s  r i g i d below 20°K but becomes s o f t and a l l o w s d i f f u s i o n a t 30°K), but neon, due  t o i t s low m e l t i n g p o i n t , i s e x t r e m e l y d i f f i c u l t  a n n e a l and i s u s u a l l y v a p o u r i z e d when t h i s i s attempted.  The  c r y s t a l s t r u c t u r e s h o u l d a l s o be compact enough t o p r e v e n t l a t e r a l motions w i t h i n the m a t r i x .  to  any  S i n c e one i s u s u a l l y t r y i n g  t o o b t a i n i n f o r m a t i o n r e g a r d i n g the a n i s o t r o p i c t e n s o r components o f the s p i n H a m i l t o n i a n , the t r a p p i n g s i t e s s h o u l d a l s o be s m a l l enough t o p r e v e n t t u m b l i n g motions of the r a d i c a l s p e c i e s .  The  most commonly used m a t r i c e s , which conform to the above p r e f e r r e d c o n d i t i o n s , a r e those of the r a r e gas elements,  N  2  and  CO,,.  There are s e v e r a l o t h e r f a c t o r s w h i c h s h o u l d a l s o be sidered.  In most c a s e s , the sample i s d e p o s i t e d from the  phase onto a c o o l e d s u r f a c e (see e x p e r i m e n t a l s e c t i o n ) .  congas It i s  d e s i r a b l e then to choose a m a t r i x which has a h i g h vapour p r e s s u r e  - 63 -  to e n a b l e t h e sample t o be e a s i l y p r e p a r e d and e v e n l y mixed w i t h the r a d i c a l p r e c u r s o r .  I t s h o u l d a l s o have a f a i r l y low m e l t i n g  p o i n t so t h a t i t i s n o t condensed p r e m a t u r e l y  i n t h e spray n o z z l e .  (The r a d i c a l p r e c u r s o r s h o u l d a l s o have a h i g h vapour p r e s s u r e (54) for  the same r e a s o n s , a l t h o u g h t h i s i s n o t s t r i c t l y  necessary)  Once t h e m i x t u r e i s condensed, i t s h o u l d have a v e r y low vapour -4 pressure  (10  deposition. of 10 ^  T o r r ) so t h a t t h e sample i s n o t pumped o f f a f t e r The i n e r t gases A r , K r , and Xe have vapour p r e s s u r e s  T o r r a t 20°K w h i l e Ne reaches  t h i s vapour p r e s s u r e a t  5°K making i t one o f the more d i f f i c u l t m a t r i c e s t o u s e . The m a t r i x s h o u l d a l s o have a r e a s o n a b l e t h e r m a l c o n d u c t i v i t y t o e f f e c t i v e l y t r a n s f e r heat from t h e condensing  gas f o r m i n g t h e  new l a y e r t o t h e s u r f a c e o f t h e s u p p o r t i n g m a t e r i a l , thus m i n i m i z i n g t h e amount o f " b o i l - o f f " due t o t h e i m p i n g i n g warm gas. As p r e v i o u s l y mentioned, when a r a d i c a l i s formed i n s i t u by p h o t o l y s i s , a l o c a l h e a t i n g w i l l o c c u r as t h e p a r e n t m o l e c u l e  fragments.  The  r a p i d t r a n s f e r o f excess energy t o t h e m a t r i x w i l l thus a l s o be an i m p o r t a n t f a c t o r i n s t a b i l i z i n g t h e fragment as w i l l t h e r a t e a t w h i c h t h e fragments can d i f f u s e away from each o t h e r b e f o r e recombination occurs.  The l o c a l h e a t i n g may h e l p i n s o f t e n i n g t h e  m a t r i x enough t o a l l o w l i m i t e d d i f f u s i o n t o o c c u r . I t i s a l s o d e s i r a b l e t o choose a m a t r i x which has no magnetic nuclei.  A m a t r i x such as xenon i s n o t o f t e n used because i t has 129 131  two abundant i s o t o p e s 3/2 r e s p e c t i v e l y .  Xe  a n  d  ^  e  w i t h n u c l e a r s p i n s 1/2 and  The c l o s e p r o x i m i t y o f t h e r a d i c a l s p e c i e s and  - 64  -  m a t r i x atoms w i l l a l l o w s u b s t a n t i a l magnetic i n t e r a c t i o n between them, i n t r o d u c i n g s u p e r h y p e r f i n e  i n t e r a c t i o n or l i n e b r o a d e n i n g  (8) o f the r a d i c a l spectrum.  The most advantageous r e a s o n f o r  u s i n g an i n e r t s u b s t r a t e i s to reduce m a t r i x p e r t u r b a t i o n s the r a d i c a l .  on  S i n c e the r a r e gases a r e c l o s e d s h e l l atoms and have  v e r y low l a t t i c e e n e r g i e s , i n t e r a c t i o n s are expected to be m i n i m a l and d a t a from a " g a s - l i k e " environment can be r e a d i l y M a t r i x e f f e c t s , although  obtained.  s m a l l , a r e p r e s e n t and u s u a l l y can  d e t e c t e d by s m a l l p e r t u r b a t i o n s on the s p i n H a m i l t o n i a n  be  in  EPR.  These e f f e c t s w i l l be d i s c u s s e d i n a f o l l o w i n g s e c t i o n . 5.2  Generation  of Free R a d i c a l s  There i s a wide v a r i e t y of methods used i n the p r o d u c t i o n free r a d i c a l species.  Some s p e c i e s a r e n a t u r a l l y paramagnetic  of and  (34) r e q u i r e o n l y warming of t h e i r dimers (NO.-,, NF  2  ( C 1 0 ) i n o r d e r to be s t u d i e d by m a t r i x i s o l a t i o n . 2  ) or d i l u t i o n In these  cases,  i t has been e x p e r i m e n t a l l y found t h a t r a d i c a l : m a t r i x mole r a t i o s i n excess of 1:2500 a r e n e c e s s a r y and  to avoid s p i n - s p i n i n t e r a c t i o n  the r e s u l t i n g l i n e s h a p e b r o a d e n i n g . To produce t r a n s i e n t s p e c i e s , a method must be employed w h i c h  w i l l cause a parent m o l e c u l e to be fragmented or e n a b l e i t to be a t t a c k e d by a n o t h e r atomic or m o l e c u l a r  free radical.  There are  two g e n e r a l c a t e g o r i e s i n t o w h i c h the f o r m a t i o n of r a d i c a l can be d i v i d e d :  a) those formed i n the gas phase and  trapped w i t h a m a t r i x onto a c o l d s u r f a c e , and b) those in  situ.  species  subsequently generated  -  65  -  In the f i r s t c a s e , a t e c h n i q u e commonly employed i s t h a t o f -, i j . . p y r o l y s i s or t h e r m a l d e c o m p o s i t i o n ,  , . (23,54,90,91) w e l t n e r e_t a l .  I7  have used t h i s t e c h n i q u e to g r e a t advantage t o s t u d y a v a r i e t y of t r a n s i t i o n and heavy m e t a l complexes.  The p a r e n t complex i s p l a c e d  i n a f u r n a c e and heated t o temperatures > 800°K i n vacuo a t which time the r a d i c a l vapour i s d i f f u s e d a l o n g w i t h the m a t r i x onto a cold surface. t h i s method.  Gas phase r e a c t i o n s can a l s o be a c c o m p l i s h e d  by  A pure m e t a l i s heated i n the same manner and a l l o w e d  t o r e a c t w i t h atomic o r m o l e c u l a r s p e c i e s such as F, 0, H, generated i n a second  furnace.  The r e s u l t i n g MX  OH  r a d i c a l species (27)  i s then t r a p p e d i n a c a r r i e r m a t r i x .  Gordy e_t al_.  have used  the t e c h n i q u e of gamma r a d i o l y s i s t o produce r a d i c a l s from the Group IV and V h y d r i d e s .  T h i s t e c h n i q u e however i s not  always  s e l e c t i v e and the p o s s i b i l i t y of e x c e s s i v e f r a g m e n t a t i o n or i o n formation e x i s t s . The s t u d y of a n i o n s such as CO2 CgHg  ,  ,  2 6 '  (95) have a l s o been s t u d i e d by the t e c h n i q u e of m a t r i x  i s o l a t i o n through d e p o s i t i o n of a s m a l l amount of sodium vapour i n a m a t r i x c o n s i s t i n g of pure s u b s t r a t e . Upon u l t r a - v i o l e t i r r a d i a t i o n o f the m i x t u r e i n s i t u the i o n i c s p e c i e s a r e The a l k a l i m e t a l elements  can a l s o be used to generate  from an o r g a n i c h a l i d e by the r e a c t i o n RX + Na-  *-'NaX + R*  formed.  radicals  - 66 -  R a d i c a l s p e c i e s can a l s o be produced by p a s s i n g a sample m i x t u r e through a microwave d i s c h a r g e immediately  p r i o r to d e p o s i t i o n .  This  t e c h n i q u e i s a g a i n r e l a t i v e l y u n s e l e c t i v e and u n c o n t r o l l e d fragment a t i o n u s u a l l y r e s u l t s .with the l a r g e r m o l e c u l e s . a l s o has the d i s a d v a n t a g e  The  technique  t h a t s m a l l amounts of i m p u r i t i e s , p a r t i c u l a r l y  o r g a n i c t r a c e s , w i l l a l s o be d i s s o c i a t e d and produce an background of methyl or hydrogen atom s p e c i e s . t h a t no m a t t e r how  annoying  I t i s g e n e r a l l y found  s t r i n g e n t the p u r i f i c a t i o n procedures  are, small  amounts of these r a d i c a l s p e r s i s t w i t h t h i s method of g e n e r a t i o n . Another f r u i t f u l method of r a d i c a l g e n e r a t i o n i s t h a t of p h o t o l y s i s i n the near or f a r u l t r a - v i o l e t .  The advantage of p h o t o l y s i s  i s t h a t the w a v e l e n g t h of i r r a d i a t i o n i s v a r i a b l e and thus i s more s e l e c t i v e towards d i s s o c i a t i o n than o t h e r methods.  High  pressure  mercury resonance lamps emit s t r o n g l y i n the near u l t r a - v i o l e t have a v i r t u a l continuum above 2500 A at red  the most i n t e n s e l i n e b e i n g  3650 A but t h e i r main d i s a d v a n t a g e b e i n g a h i g h output o f irradiation.  and  infra-  V a r i o u s f i l t e r s can be employed i f i t i s d e s i r e d  to work w i t h a narrow band w i d t h . lamp i s l i m i t e d below 2600 A.  The u s e f u l n e s s of the h i g h  pressure  I f a low p r e s s u r e mercury lamp i s  employed, the r e g i o n from 1800 A t o 3000 A i s a c c e s s i b l e b e i n g u s u a l l y by the type of window employed on the dewar.  limited  For the h i g h  o r low p r e s s u r e mercury lamp, a q u a r t z window i s u s u a l l y used w h i c h has a c u t o f f below about 1800 A.  Below t h i s p o i n t a L i F window can  be used w i t h a v a r i e t y of resonance lamps which have h i g h o  i n the f a r u l t r a - v i o l e t below 2000 A.  outputs  The gas resonance lamps of  - 67 -  hydrogen and xenon have i n t e n s e bands a t 1215 A and a t 1295 A:1470 A respectively.  I f s t i l l g r e a t e r e n e r g i e s a r e r e q u i r e d an argon  lamp can be used  (1048 A:1066 A) o r even a h e l i u m resonance  resonance  lamp  (548 I) a l t h o u g h i n the l a t t e r case a s p e c i a l aluminum window must be employed. The d i s a d v a n t a g e s of the p h o t o l y s i s method i s a g e n e r a l l y  low  y i e l d of r a d i c a l s , and t y p i c a l l y l o n g i r r a d i a t i o n times r a n g i n g from 1/4  - 2 h r . i n o r d e r t o a c h i e v e a r e a s o n a b l e l e v e l of r a d i c a l c o n c e n t r a -  tion.  The reasons f o r t h i s a r e t w o f o l d .  L i g h t s c a t t e r i n g by  the  m a t r i x (and l i g h t a b s o r p t i o n i n the f a r u l t r a - v i o l e t ) tend to reduce the quantum y i e l d . duction.  The "cage e f f e c t " w i l l a l s o reduce r a d i c a l p r o -  When a m o l e c u l e i s d i s s o c i a t e d , the s u r r o u n d i n g case of  m a t r i x w i l l tend to h o l d the fragments time to a l l o w t h e i r r e c o m b i n a t i o n . of  removing  t o g e t h e r f o r a l o n g enough  A l s o , i f the m a t r i x i s c a p a b l e  t h e e x c i t a t i o n energy of a m o l e c u l e r a p i d l y enough,  f r a g m e n t a t i o n w i l l indeed be i n h i b i t e d .  I f the r a d i c a l formed has  a s p e c i a l s t a b i l i t y l i t t l e r e c o m b i n a t i o n w i l l o c c u r and the "cage e f f e c t " w i l l be u n i m p o r t a n t .  T h i s method w i l l be used here t o g e n e r a t e  most of the f r e e r a d i c a l s s t u d i e d . I t i s i n t e r e s t i n g t o n o t e t h a t s e v e r a l t h e o r e t i c a l papers have appeared  d i s c u s s i n g the c o n c e n t r a t i o n of r a d i c a l s t h a t can be t r a p p e d  i n an i n e r t m a t r i x .  Golden  has d e r i v e d a s t a t i s t i c a l model o f  the s t a b i l i z a t i o n p r o c e s s and c o n c l u d e s t h a t the r a d i c a l c o n c e n t r a t i o n condensing from the gas phase i s about 10-14%.  Jackson  and  (97) Montroll  had a l s o a r r i v e d a t t h i s f i g u r e as a l i m i t i n g v a l u e f o r  the c o n c e n t r a t i o n . However f o r systems s t u d i e d by t h i s method, the  - 68 maximum c o n c e n t r a t i o n thus f a r o b t a i n e d i s l e s s than  2%^^. _g  However t h e lower l i m i t d e t e c t a b l e by EPR i s o f t h e o r d e r o f 10 molar so t h i s does n o t become a s e r i o u s i n h i b i t i n g  factor.  There a r e two b a s i c t e c h n i q u e s now commonly used f o r d e p o s i t i n g t h e m i x t u r e on the c o l d s u r f a c e .  The most o f t e n used i s t h a t  of slow spray on (SSO) i n which t h e gas i s d e p o s i t e d i n a s t r e a m over p e r i o d s o f an hour o r l o n g e r .  T h i s method i s g e n e r a l l y  b e l i e v e d t o i s o l a t e the s p e c i e s v e r y e f f e c t i v e l y . IR s p e c t r o s c o p i s t s > 1 0 0 )  ^ave h s  o  w  n  continuous  Recently  that pulsed matrix  isolation  (PMI) where t h e gas d e p o s i t e d i n s h o r t , h i g h p r e s s u r e p u l s e s can be e q u a l l y e f f e c t i v e i f n o t more so i n i s o l a t i n g t r a p p e d The d e p o s i t e d m a t r i x was observed  t o be more t r a n s p a r e n t when the  p u l s e d m a t r i x t e c h n i q u e was employed r a t h e r than t h e slow method.  species.  spray  A second advantage o f PMI i s t h a t s m a l l amounts of  i m p u r i t i e s r e s u l t i n g from apparatus  l e a k s w i l l be much l e s s  i m p o r t a n t w i t h PMI s i n c e the time o f d e p o s i t i o n i s r e d u c e d .  5.3  Matrix Effects Although  the r a r e gas m a t r i c e s p r o v i d e a non p o l a r environment,  the m a t r i x c r y s t a l f i e l d s have been shown t o p e r t u r b t h e trapped . (8-10,13,14,66) species .  ™ . _ . , „. The t h e o r y o f m a t r i x p e r t u r b a t i o n s i n ( 66")  EPR has been developed  by A d r i a n  f o r hydrogen atoms s t a b i l i z e d  i n the r a r e gas m a t r i c e s and has been extended t o s e m i - q u a n t i t a t i v e l y e x p l a i n m a t r i x s h i f t s on n i t r o g e n atoms (13) and s e v e r a l group VA atoms  .  ' ,  a l k a l i atoms  A s e m i - q u a l i t a t i v e explanation of  m a t r i x s h i f t s has been g i v e n f o r copper, s i l v e r and g o l d atoms  - 69 j , _ . (14) t r a p p e d xn t h e r a r e gas m a t r i c e s The e s t i m a t i o n o f h y p e r f i n e s h i f t s and Zeeman s h i f t s i n t h e EPR spectrum o f these atoms has been shown i n most cases t o agree q u i t e c l o s e l y w i t h the e x p e r i m e n t a l l y observed  shifts.  There a r e ,  however, s e v e r a l d i s c r e p a n c i e s w h i c h the t h e o r y can n o t s a t i s (9) f a c t o r i l y e x p l a i n i n s e v e r a l o f t h e a l k a l i atoms p r o b a b l y due t o the a p p r o x i m a t i o n s  .  This i s  used and the r e l a t i v e  difficulty  i n e s t i m a t i n g t h e e f f e c t s o f t h e van der Waals and P a u l i f o r c e s . As t h e t h e o r y has n o t been extended t o c o v e r m o l e c u l a r  trapped  s p e i c e s , a b r i e f q u a l i t a t i v e d e s c r i p t i o n o f the t h e o r y of m a t r i x s h i f t s w i l l be p r e s e n t e d h e r e w h i c h can then be a p p l i e d t o e x p l a i n t r e n d s i n m a t r i x s h i f t s on paramagnetic m o l e c u l a r s p e c i e s . understanding  An  o f these e f f e c t s becomes i m p o r t a n t i n the i n t e r p r e -  t a t i o n o f the c o m p l i c a t e d powder s p e c t r a t h a t may a r i s e due t o these  effects. The m a t r i x atoms can cause p e r t u r b a t i o n s i n the t r a p p e d  i n s e v e r a l ways.  species  The m a t r i x f i e l d w i l l tend t o a l t e r t h e s p i n  d e n s i t y a t the magnetic n u c l e u s , r e s u l t i n g i n a change i n t h e h y p e r f i n e s t r u c t u r e s p l i t t i n g c o n s t a n t s from the " f r e e g a s " v a l u e . f i e l d w i l l a l s o a l t e r the Zeeman c o u p l i n g due t o s p i n - o r b i t a c t i o n s of t h e u n p a i r e d e l e c t r o n w i t h the m a t r i x atoms.  This  inter-  The  magnitude of the s h i f t s observed w i l l depend on how c l o s e l y t h e m a t r i x atoms a r e packed around the t r a p p e d s p e c i e s and a l s o on t h e type of m a t r i x atom.  The r a r e gases have a l l been shown t o  c r y s t a l l i z e i n a f a c e - c e n t e r e d c u b i c s t r u c t u r e ^ " ^ " ^ and i f one assumes p e r f e c t o r d e r w i t h i n a c r y s t a l l i t e  ( i e . no l a t t i c e d e f e c t s ) ,  - 70 -  the trapped  s p e c i e s , depending on i t s s i z e , can occupy t h r e e  i n the l a t t i c e ;  the i n t e r s t i t i a l  sites  s i t e s can be e i t h e r t e t r a h e d r a l  or o c t a h e d r a l w i t h c o o r d i n a t i o n numbers of 4 and 6 r e s p e c t i v e l y or the s i t e can be s u b s t i t u t i o n a l , whose c o o r d i n a t i o n number i s 12.  The  i n t e r n u c l e a r s e p a r a t i o n between the trapped  the n e a r e s t n e i g h b o u r i n g  species  m a t r i x atoms w i l l be d i f f e r e n t — t h e  t e t r a h e d r a l environment has  the l e a s t f r e e space and  thus w i l l  have the h i g h e s t o v e r l a p between the charge c l o u d s on the and  trapped  and  matrix  s p e c i e s , w h i l e the s u b s t i t u t i o n a l s i t e s w i l l have the  most f r e e space and c o n s e q u e n t l y l e s s o v e r l a p .  I t can thus be  c o n c l u d e d a t t h i s p o i n t t h a t s p e c i e s w h i c h are trapped  in tetra-  h e d r a l s i t e s can be expected to e x h i b i t the l a r g e s t m a t r i x from the f r e e gas v a l u e and  shift  these s h i f t s would be expected to  d e c r e a s e i n the o c t a h e d r a l and  substitutionalsites.  atomic s p e c i e s , t h e s e e x p e c t a t i o n s have been confirmed  With with  the the  ( 8 ) o b s e r v a t i o n of a l l t h r e e t r a p p i n g s i t e s the most s e n s i t i v e to any any  .  The  cramped s i t e s  are  changes i n the l o c a l environment where  change i n the n e a r e s t n e i g h b o u r d i s t a n c e causes a  corresponding  change i n the h y p e r f i n e s p l i t t i n g s , and w i l l thus l i k e l y e x h i b i t temperature dependence e f f e c t s . environment w i l l l i k e l y remains now The  A l s o , any  l a r g e d i s o r d e r i n the  r e s u l t i n severe l i n e broadening.  It  t o e x p l a i n the cause of t h e s e s h i f t s .  i n t e r a c t i o n s w h i c h are n e c e s s a r y t o c o n s i d e r are the  Van  der Waals f o r c e s and P a u l i e x c l u s i o n f o r c e s which are l o n g range, a t t r a c t i v e f o r c e s and s h o r t range, r e p u l s i v e f o r c e s r e s p e c t i v e l y . Depending on the i n t e r m o l e c u l a r d i s t a n c e s , the two  forces w i l l  tend  - 71 -  t o compete, t h e former p r e d o m i n a t i n g i n t h e r e l a t i v e l y open, s u b s t i t u t i o n a l s i t e s w h i l e t h e l a t t e r w i l l predominate i n the cramped o c t a h e d r a l  or t e t r a h e d r a l  sites.  The v a n d e r Waals i n t e r a c t i o n i s an e l e c t r o s t a t i c : , i n t e r a c t i o n between two i n s t a n t a n e o u s e l e c t r o n d i p o l e moments, one o f t h e trapped r a d i c a l and t h e o t h e r on t h e m a t r i x p a r t i c l e , so t h a t as the p a r t i c l e s a r e brought t o g e t h e r a n e t a t t r a c t i v e f o r c e r e s u l t s . I t has been s h o w n ^ ^ t h a t f o r atoms, t h e r e s u l t o f t h i s  inter-  a c t i o n i s t o cause a s l i g h t e l e c t r o n i c c l o u d e x p a n s i o n i n t h e two p a r t i c l e s , w h i c h has t h e e f f e c t o f r e d u c i n g  t h e i n t e r a c t i o n between  the e l e c t r o n and t h e n u c l e u s , w h i c h i n t u r n r e s u l t s i n an o v e r a l l decrease i n the hyperfine i n t e r a c t i o n . When the i n t e r n u c l e a r s e p a r a t i o n becomes s u f f i c i e n t l y the e l e c t r o n charge c l o u d s o f t h e t r a p p e d s p e c i e s atoms w i l l o v e r l a p  substantially.  small,  and t h e m a t r i x  The exchange o r P a u l i e x c l u s i o n  f o r c e s w i l l n o t p e r m i t two e l e c t r o n s o f t h e same s p i n t o occupy t h e same r e g i o n o f space.  The m a t r i x  o r b i t a l whose s p i n i s t h e same as  the u n p a i r e d e l e c t r o n on the trapped s p e c i e s w i l l c o n t r a c t as w i l l  slightly  t h a t o f the u n p a i r e d e l e c t r o n i n o r d e r t o reduce t h e o v e r l a p .  T h i s c o n t r a c t i o n r e s u l t s i n an i n c r e a s e the n u c l e u s o f t h e t r a p p e d s p e c i e s hyperfine  interaction.  i n t h e charge d e n s i t y a t  and w i l l tend t o i n c r e a s e t h e  The c o n t r a c t i o n o f t h e m a t r i x  orbital  will  r e s u l t i n a n e t s p i n unbalance as o n l y t h a t o r b i t a l o f t h e same s p i n as t h e u n p a i r e d e l e c t r o n c o n t r a c t s .  S i n c e t h e r a r e gas m a t r i c e s  used f o r t r a p p i n g have a complete o u t e r p- s h e l l , i t w i l l be t h i s s h e l l which c o n t r a c t s  and t h i s w i l l r e s u l t i n an a n i s o t r o p i c magnetic  - 72 -  h y p e r f i n e i n t e r a c t i o n between the unbalanced p- e l e c t r o n s and the matrix nuclei.  T h i s w i l l u s u a l l y have t h e e f f e c t o f l i n e broaden-  i n g o f the EPR powder spectrum.  S i n c e the u n p a i r e d e l e c t r o n moves  i n a p- o r b i t a l on the m a t r i x atom, t h e r e w i l l be a s p i n - o r b i t , i n t e r a c t i o n which can l e a d t o a s h i f t i n the e l e c t r o n i c g - f a c t o r . I f t h e t r a p p e d s p e c i e s has i t s u n p a i r e d e l e c t r o n i n an o u t e r ps h e l l , i t w i l l a l s o e x p e r i e n c e a g - s h i f t from t h e " f r e e - g a s " v a l u e due to t h e change i n charge d e n s i t y i n t h i s o r b i t a l .  The c o m p e t i t i o n  between these two s h i f t s w i l l be t h e o v e r a l l g - s h i f t observed.  (The  o v e r a l l h y p e r f i n e s h i f t w i l l be the sum o f t h e two opposing v a n der Waals and P a u l i f o r c e s w h i l e t h e g - s h i f t s a r e due p r e d o m i n a n t l y  to  the s h o r t range P a u l i f o r c e s . ) In t h e case of the atomic s p e c i e s , the w a v e f u n c t i o n s  and the  average e x c i t a t i o n e n e r g i e s o f the atoms were o b t a i n a b l e and e x p r e s s i o n s f o r the h y p e r f i n e and g - s h i f t s c o u l d be d e r i v e d from a p e r t u r b a t i o n treatment estimated.  and the expected  I n the case o f a m o l e c u l a r  t a t i v e a s p e c t s o f t h i s treatment  s h i f t s roughly  s p e c i e s however, the q u a n t i -  are not a p p l i c a b l e but the  q u a l i t a t i v e a s p e c t s can be used t o e x p l a i n the s h i f t s i n these species.  CHAPTER SIX  I n t e r p r e t a t i o n of t h e H a m i l t o n i a n Parameters The i n t e r p r e t a t i o n o f t h e H a m i l t o n i a n parameters o f t h e r a d i c a l s of t h e type ABC o r ABG^ can g e n e r a l l y be based on a v e r y s i m p l e model and  t h e r e s u l t s a c h i e v e d w i l l u s u a l l y be s a t i s f a c t o r y .  In the  a n a l y s i s w h i c h w i l l be f o l l o w e d h e r e , c e n t r e A w i l l have a n u c l e a r s p i n I > 0 w h i l e t h e r e m a i n i n g c e n t e r s w i l l have 1 = 0 .  S i n c e many  of t h e arguments used a r e common t o t h e s e s p e c i e s , a b r i e f  treat-  ment of t h e methods used i n t h e i r i n t e r p r e t a t i o n w i l l be g i v e n .  Since  o n l y non p l a n a r ABO^ systems w i l l be c o n s i d e r e d , t h e s e s p e c i e s b e l o n g to  the C  g  symmetry c l a s s p o s s e s s i n g o n l y a p l a n e of symmetry.  Due t o  t h i s l i m i t e d symmetry, t h e ground s t a t e s o f t h e s e r a d i c a l s can be 2  e x p r e s s e d as e i t h e r  A", where t h e u n p a i r e d e l e c t r o n i s d e l o c a l i z e d  i n a p 7 r - o r b i t a l network p e r p e n d i c u l a r t o t h e symmetry p l a n e and i s 2  a n t i s y m m e t r i c w i t h r e s p e c t t o r e f l e c t i o n i n t h e symmetry p l a n e , o r  .  A  where t h e e l e c t r o n i s c o n f i n e d t o m o l e c u l a r o r b i t a l s which a r e symmetric w i t h r e s p e c t t o r e f l e c t i o n i n t h e m o l e c u l a r symmetry p l a n e . The t o t a l wave f u n c t i o n f o r a r a d i c a l can be w r i t t e n as  * = IW  2  •••• W n l  - 74 -  where <|>  i s t h e odd e l e c t r o n o r b i t a l and t h e symmetry o f t h e wave  f u n c t i o n s h o u l d be determined by t h i s o r b i t a l .  The o r b i t a l d> can n  be e x p r e s s e d as a l i n e a r c o m b i n a t i o n of atomic o r b i t a l s on each nucleus.  2 A' s t a t e t h e s e w i l l be  For a  <j> = C n  and f o r a  + cx + c + C + x s x px z pz s s A  A  A  B  x  X  X  [6.1]  2 A" s t a t e  |> = C  A X  + C  y py  n  + . . .  E X A  where t h e C's a r e t h e c o e f f i c i e n t s each c e n t e r .  [6.2]  y py  A  of t h e atomic o r b i t a l s x on  The a x i s system i s d e f i n e d as f o l l o w s :  the x a x i s  i s p e r p e n d i c u l a r t o the A-B bond and i n the m o l e c u l a r symmetry plane  y i s p e r p e n d i c u l a r t o t h e m o l e c u l a r symmetry p l a n e and z  i s p a r a l l e l t o the A-B bond.  The d i p o l a r o p e r a t o r i n e q u a t i o n  [2.10]  (102) can be w r i t t e n i n the form  6 ap  = (3r. r - r 6 J r l a 13 1 aB 2  1  [6.3]  5  Q  where a,3 = x , y , z . The a n i s o t r o p i c h y p e r f i n e c o u p l i n g c o n s t a n t T (103) w r i t t e n as  T  a3  = g  eWN  S  "7 a3 S l 6  Q  ( r  ) d T  can then be  - 75 -  where Q ( r ) / S i s a normalized spin density function which can g  1  be  expressed i n terms of the expansion c o e f f i c i e n t s of the atomic orbitals,  Q (r )/S = E E C c\ b i p q p q p  In t h i s expression,  (r)/(r) q  a r e s t r i c t e d wave function has been used  where the spins of the doubly occupied molecular o r b i t a l s exactly cancel and the only term contributing to the spin density matrix i s then the spin i n the odd electron m.o.  orbitals.  Thus T „ can ag  be expressed as  T  a3  =  g  e%Wp q E  Consider now  C  p q C  < X  P ^  1  ° a • *p  ( r )  >  B  the contributions to the anisotropic  hyperfine  2  tensor or a " a - r a d i c a l " ( A' ground s t a t e ) . the ground state wave function „ T  ag  A 2 A  V  =  + c < B  2  x  |2A  ,A  XP l0 g| X x  a  X Pr  x' a g  B  1  > +  using  [6.1]  J . 2 A X  |0 J xp x > + A  B  P  Expanding [6.6]  C  z  <  ."A ,A pJ.O | X  o  B  , X P  .k Z  k A > + 2 C  ,:A x  ,A xpjoj  V<z xp* z | 0agJ • p z> ...  + ^A^xi^i V  B  A  1  +  B  X  +  ^ V»,i^iV - • • +  [6  The f i r s t three terms are the one center i n t e g r a l contributions and for most molecules t h i s i s the dominant term since the dipole  7!  X P  Z  - 76 -  3 o p e r a t o r has a 1/r dependence and t h e c o n t r i b u t i o n s w i l l be dominated by i t s own environment.  The f o l l o w i n g two terms a r e t h e two c e n t e r  i n t e g r a l c o n t r i b u t i o n s from t h e n e i g h b o u r i n g n u c l e u s t o t h e a n i s o t r o p y  i at  c e n t e r A.  These i n t e g r a l s c a n be e v a l u a t e d by t h e method o f  McConnel and S t r a t h d e e ^ ' ^  as c o r r e c t e d by P i t z e r e t a l . ^^^^.  These f u n c t i o n s ( i n c l u d i n g t h e c o n t r i b u t i o n s from i n t e g r a l s o f t h e Ai~A i B type <xs 0 [ x p which have been n e g l e c t e d h e r e ) a r e t a b u l a t e d f o r >  0  ot p  a S l a t e r 2p o r b i t a l on c e n t e r B by B a r f i e l d .  The c o n t r i b u t i o n s  from a S l a t e r 3p o r b i t a l have been d e r i v e d and a r e g i v e n i n Appendix B.  The l a s t two terms r e p r e s e n t t h e o v e r l a p i n t e g r a l c o n t r i b u t i o n  and can be approximated u s i n g t h e method o f M u l l i k e n ^ ^ ^ where  <  VcKel  where S  *V  ~~  h  s  ™  (  <  *?xl V  *V  +  <  XPX I *P » B  [ 6  X  -  8 ]  i s t h e v a l u e o f t h e o v e r l a p i n t e g r a l and can be e v a l u a t e d  XX  by M u l l i k e n ' s m e t h o d ^ ^ ^ ^ . F o r t h e case where A i s a hydrogen, t h e one c e n t e r  integrals  w i l l n o t c o n t r i b u t e t o t h e a n i s o t r o p y and the main c o n t r i b u t i o n s w i l l come from t h e two c e n t e r i n t e g r a l s and w i l l g e n e r a l l y have t h e form (-a, -g, 6) where |a|<JB|<|6| f o r t h e p - o r b i t a l on B p e r p e n d i c u l a r to  t h e H-B bond  (  p  ) and (-a', -a', 6') where |a'| =  Js|s'|  f  o  r  the  H-B bond p - o r b i t a l on B. For t h e case where A i s n o t hydrogen, and t h e r e f o r e has p - o r b i t a l s , the a n i s o t r o p i c c o n t r i b u t i o n s w i l l be dominated by t h e asymmetric  - 77 -  s p i n d i s t r i b u t i o n i n the p - o r b i t a l on c e n t e r A. c e n t e r c o n t r i b u t i o n d e s c r i b e d above.  T h i s i s the  one  ( I t s h o u l d be noted h e r e t h a t  the P y - o r b i t a l s w i l l have l i t t l e c o n t r i b u t i o n t o the a n i s o t r o p y and w i l l be n e g l e c t e d .  A l s o i n the argument f o r a " o - r a d i c a l "  e f f e c t of s p i n p o l a r i z a t i o n w i l l a l s o be The  the  neglected.)  t o t a l c o n t r i b u t i o n from the one c e n t e r terms on A t o the  a n i s o t r o p i c t e n s o r can be w r i t t e n as  %  T  2c  X  T  2 2 - c x z  y T z  where  - c  0  =  3/2c  X  c  z  3/2c  0 2 X  - c 0  2 z  X  c  z  0  B  [6.9] o  - c  2  x  4.  9  + 2c  2  z  i s the a n i s o t r o p i c h y p e r f i n e o f an e l e c t r o n i n a p - o r b i t a l  on c e n t e r A and T i s the observed  a n i s o t r o p i c hyperfine tensor.  The  2 2 - c )B can then be equated t o the term T and x z o y 2 2 thus c can be expressed as a f u n c t i o n of c . I f the o r i e n t a t i o n x z  c e n t r a l term (-c  of one component of the a n i s o t r o p i c t e n s o r can be e s t a b l i s h e d , o n l y one c h o i c e f o r the o r i e n t a t i o n of the o t h e r two components w i l l  be  2  2 and c^ a r e p o s i t i v e . The 2x2 s e c u l a r determinant 2 2 can then be s o l v e d f o r c and c w h i c h w i l l be r e p r e s e n t a t i v e o f the x z compatible  since c  x  s p i n d e n s i t y i n the r e s p e c t i v e o r b i t a l s .  T h i s a n a l y s i s always r e q u i r e s  t h a t the h y p e r f i n e component whose a b s o l u t e v a l u e i s i n t e r m e d i a t e between the o t h e r components, w i l l l i e p e r p e n d i c u l a r to the symmetry plane.  Of c o u r s e i f t h i s approach proves t o be i n a d e q u a t e ,  the  con-  - 78 -  t r i b u t i o n s from t h e two c e n t e r i n t e g r a l s o f t h e type <p |o B  |p >  A  B  Bi"A i A and o v e r l a p i n t e g r a l s o f t h e type <p 0 „ p > must be c o n s i d e r e d . p ' aB v r  The one c e n t e r c o n t r i b u t i o n f o r a " i T - r a d i c a l " i s t r e a t e d i n a s i m i l a r manner except t h a t t h e ground s t a t e i s now c o n s i d e r e d as a  2 A" s t a t e and t h e expansion  Tag =  A 2 A i A iA cy < Xyp' 0 p ag x y n  A r  of T  >  +  o 1 A t  [6.6] becomes  , B Z B l^AiB cy < xy p' a0g . h yp > + ... A t  1  + 2 c c < |0 | > + ... y y ^ y l ag' y A  B  A  A  [6.10]  B  X P  X P  r  r  where t h e f i r s t i n t e g r a l i s t h e one c e n t e r c o n t r i b u t i o n , t h e second i n t e g r a l i s t h e two c e n t e r i n t e g r a l and t h e t h i r d i s t h e o v e r l a p integral. to  F o r t h e case where A i s hydrogen, t h e o n l y c o n t r i b u t i o n  t h e a n i s o t r o p y a r i s e s from t h e two c e n t e r terms.  t i o n w i l l be o f t h e form  This c o n t r i b u -  .(-g,-a,-<5) where |a|<|g|<|6|.  The one c e n t e r treatment  f o r a non-hydrogen c o n t a i n i n g T r - t y p e " M  2 r a d i c a l ( A " ) , i s e s s e n t i a l l y s i m i l a r t o t h a t o f a a r a d i c a l , and i n t h i s case s p i n p o l a r i z a t i o n o f t h e AB bond by s p i n d e n s i t y i n the A and B o r b i t a l s must be c o n s i d e r e d .  I n t h i s case, the a n i s o -  t r o p i c h y p e r f i n e t e n s o r c a n be r e p r e s e n t e d as t h e sum o f two a x i a l t e n s o r s , one o r i e n t e d a l o n g t h e ir o r b i t a l (y) and one o r i e n t e d a l o n g the bond d i r e c t i o n ( z ) .  The s p i n d e n s i t y i n t h e p o r b i t a l on A  s h o u l d be p o s i t i v e w h i l e t h e s p i n d e n s i t y i n t h e P ( o 0 o r b i t a l z  s h o u l d be n e g a t i v e s i n c e p o s i t i v e s p i n d e n s i t y i n t h e B o r b i t a l induce AB bond.  will  a s l i g h t p o s i t i v e s p i n i n the p^ o r b i t a l on B f o r m i n g t h e T h i s s h o u l d tend t o i n d u c e a s l i g h t n e g a t i v e s p i n d e n s i t y  - 79  i n the bond p be w r i t t e n  o r b i t a l on A.  z  -  The  one  + c j .  2  then  y  2  z  0  2c  [6.11]  + c y  z -c  y  2 y  c o n t r i b u t i o n s can  as  -c  where c  center  2c z  2 and  c^ are r e p r e s e n t a t i v e  respective p o r b i t a l s . o r i e n t a t i o n of one  of the s p i n d e n s i t i e s i n the  Here a g a i n a c h o i c e must be made as to  component of the h y p e r f i n e  tensor  on the r e l a t i v e magnitudes of the g v a l u e s ) and 2 2 e q u a t i o n s may  be s o l v e d  for c  y  and  c^.  p i c t u r e would i n c l u d e the c o n t r i b u t i o n s from two  center  simultaneous  a more a c c u r a t e  center  I n any attempt t o e x p l a i n the g v a l u e s of a "TT" r a d i c a l , a one  (perhaps based  then two  As b e f o r e ,  the  terms.  or "a  type"  type argument i s a l s o u s u a l l y s u f f i c i e n t .  A  q u a n t i t a t i v e e s t i m a t e of the s h i f t s i n the g f a c t o r from f r e e s p i n g  e  will  r e q u i r e a c c u r a t e w a v e f u n c t i o n s f o r the ground and  s t a t e s and states. and  a good e s t i m a t e of the energy d i f f e r e n c e between t h e s e  These q u a n t i t i e s are r a r e l y b o t h a v a i l a b l e f o r most systems  o n l y a q u a l i t a t i v e e s t i m a t e can be made.  factor  excited  (Ag^g  where a,3  The  s h i f t i n the g  = x,y,z) i s caused by the i n t e r a c t i o n of  e x c i t e d s t a t e s w i t h the ground s t a t e through the phenomenon of o r b i t coupling.  spin  To f i r s t o r d e r i n energy, the s h i f t i n the g v a l u e  - 80 -  i s zero, i e . g = g .  By u t i l i z i n g f i r s t o r d e r p e r t u r b a t i o n t h e o r y ,  g  a m o d i f i e d wave f u n c t i o n which i n c l u d e s t h e a d m i x t u r e o r e x c i t e d s t a t e s c a n be w r i t t e n as  |<P±> = | >±> + + ^ V  <n £L-S Y ±> m - g — : |n> n m  [6.12]  g  where m i s t h e ground s t a t e , n i s t h e t o t a l w a v e f u n c t i o n  of the  e x c i t e d s t a t e , L i s t h e a n g u l a r momentum o p e r a t o r and £ i s t h e s p i n o r b i t coupling constant.  The t r u e magnetic H a m i l t o n i a n f o r t h e  magnetic i n t e r a c t i o n c a n be w r i t t e n as  mag  = 3H-L + g BH-S e  [6.13]  and t h e t o t a l g t e n s o r i s then d e s c r i b e d by  g =  < f ±  l^l l g  y ± >  t - *] 6  1  I f t h i s i s s o l v e d ^ ^ 7 ) ^ t h e e x p r e s s i o n f o r t h e g f a c t o r c a n be (108,109) w r i t t e n as  8  aB  =  8  e  (  1 +  A  »aB  )  m-1 <m|^|n><n| ZLg'? |m> Ag „ = / aB /-i E. - E i=l l m t  where  &  J  n <m | E L * | n><n | V* E. - E J=m+1 2 m  [6.15]  |m>  - 81 -  The sum over t runs over a l l atoms i n t h e m o l e c u l e and t o a f i r s t approximation  ^ o p e r a t e o n l y on those o r b i t a l s c e n t e r e d on t .  I t s h o u l d be noted h e r e t h a t a l l e x c i t e d s t a t e s w i l l have an energy g r e a t e r than t h e ground s t a t e and thus t h e energy w i l l always be p o s i t i v e .  differences  The f i r s t term c o r r e s p o n d s t o an e x c i t a t i o n  from a doubly o c c u p i e d o r b i t a l t o t h e s i n g l y o c c u p i e d o r b i t a l and the second term c o r r e s p o n d s t o an e x c i t a t i o n from t h e s i n g l y o c c u p i e d o r b i t a l to a v i r t u a l state.  This represents a p o s i t i v e c o n t r i b u t i o n  t o t h e g s h i f t from t h e f i r s t term and a n e g a t i v e c o n t r i b u t i o n from the second  term.  E x p r e s s i o n s can now be w r i t t e n f o r t h e g s h i f t i n t h e t h r e e p r i n c i p a l d i r e c t i o n s and symmetry arguments can be used t o s i m p l i f y the e x p r e s s i o n f o r t h e g s h i f t .  I n o r d e r f o r Ag t o be non z e r o , t h e  product of the i r r e d u c i b l e r e p r e s e n t a t i o n s T of the e x c i t e d  state  T and t h e ground s t a t e Y must be c o n t a i n e d i n TL^, t h e i r r e d u c i b l e n m a r e p r e s e n t a t i o n of t h e o r b i t a l a n g u l a r momentum o p e r a t o r .  The o r b i t a l  a n g u l a r momentum o p e r a t o r has t h e e f f e c t o f r o t a t i n g an o r b i t a l 90° about  and t h i s i s e q u i v a l e n t t o t h e symmetry o p e r a t o r R^.  the symmetry t a b l e f o r C , L S  and L X  t r a n s f o r m as A " and w i l l  From thus  z  connect o n l y those e x c i t e d and ground s t a t e s whose symmetries a r e different. £  i s expected.  <A'|L |A'> i y'  ^ 0 and a s h i f t  x, z F o r a "a r a d i c a l " t h e ground s t a t e i s A ' and 1  from g  IA'>  F o r a "TT" o r " a " r a d i c a l , <A"|L  must be e v a l u a t e d .  1  S i n c e t h e A ' s t a t e can be w r i t t e n  as a l i n e a r c o m b i n a t i o n o f p and p atomic o r b i t a l s and L p > = *x *z y'*x - | i p >; L |p > = | i p >, t h e i n t e g r a l w i l l have a non z e r o v a l u e , z y z x  - 82  -  However, f o r a ir r a d i c a l whose ground s t a t e i s A",  the m o l e c u l a r  o r b i t a l s a r e composed of l i n e a r c o m b i n a t i o n s  orbitals,  L y  of p  y  but  |p > = 0 so t h e r e w i l l be no s h i f t i n the g f a c t o r i n t h i s y  d i r e c t i o n from the one c e n t e r c o n t r i b u t i o n s . As was  the case i n the c a l c u l a t i o n of the a n i s o t r o p i c h y p e r -  f i n e c o u p l i n g , two c e n t e r terms may  a l s o be i n c l u d e d i n the g s h i f t .  These terms w i l l have the same form as e q u a t i o n [6.15] except L*" now  o p e r a t e s on the c e n t e r a d j a c e n t to the t as  that  w e l l .  I t s h o u l d be p o i n t e d out t h a t t h e s e arguments a r e o c c a s i o n a l l y not s u f f i c i e n t to account tensor s h i f t .  f o r the observed  h y p e r f i n e tensor or g  To i l l u s t r a t e , two w e l l known examples can  a n a l y s e d by t h i s method.  The H00  r a d i c a l » H - ) which has been 2  e s t a b l i s h e d as a TI r a d i c a l from a c c u r a t e LCAO - MO i n c l u d i n g c o n f i g u r a t i o n i n t e r a c t i o n (CI) t h a t cannot be r e a s o n a b l y accounted from t h e c e n t r a l oxygen a l o n e .  be  ^ h  a s  - SCF a  calculations  hyperfine tensor  f o r by the two c e n t e r c o n t r i b u t i o n s  The f o r m of t h e two c e n t e r i n t e g r a l  r e q u i r e s the s m a l l e s t h y p e r f i n e v a l u e to l i e p a r a l l e l to the TT o r b i t a l whereas the observed  tensor value along t h i s d i r e c t i o n i s i n fact  i n t e r m e d i a t e ( i n a b s o l u t e v a l u e ) between the x and z components. There a r e thus o t h e r terms w h i c h must c o n t r i b u t e to g i v e the t e n s o r i t s o v e r a l l shape.  The g t e n s o r , i s a l s o not s t r a i g h t f o r w a r d .  The  g t e n s o r t h e o r y j u s t d i s c u s s e d , p r e d i c t s a s h i f t of z e r o f o r the i r , (y) d i r e c t i o n .  The a c t u a l g t e n s o r i s (2.0353, 2.0042, 2.0086) and  f o r the y d i r e c t i o n t h i s r e p r e s e n t s a f a i r l y s t r o n g p o s i t i v e g s h i f t  - 83 -  o f +.0019.  The  one c e n t e r a p p r o x i m a t i o n  i s inadequate  t i o n s from the two c e n t e r terms i n the g s h i f t must be  and c o n t r i b u considered.  (26) A more ambiguous case i s the F00 r a d i c a l w i d e l y i n t e r p r e t e d as a i r a d i c a l . MO  - SCF  w h i c h has been  A r e c e n t n o n - e m p i r i c a l LCAO -  c a l c u l a t i o n ^ " * " ^ has r e p o r t e d t h a t the ground s t a t e i s 1  2 A'  ( i e . the u n p a i r e d e l e c t r o n r e s i d e s i n a symmetric "a  orbital").  R e i n t e r p r e t a t i o n of the h y p e r f i n e t e n s o r as a a r a d i c a l can  be  c a r r i e d out u s i n g e q u a t i o n  be  [6.9].  The h y p e r f i n e t e n s o r can  l a r g e l y accounted f o r by the one c e n t e r a p p r o x i m a t i o n c e n t e r c o n t r i b u t i o n s as c a l c u l a t e d i n Appendix  B  (the  two  are r e l a t i v e l y  s m a l l ) and g i v e as c o e f f i c i e n t s to the wave f u n c t i o n | c | =  .18  x  and  | c | = .29 and the square of these c o e f f i c i e n t s i s z  e q u i v a l e n t t o the s p i n d e n s i t y i n these p o r b i t a l s .  approximately  This a n a l y s i s  w i l l not change the r e p o r t e d o r i e n t a t i o n of the h y p e r f i n e t e n s o r and i s c o n s i s t e n t i n t h a t i n most a r a d i c a l s of t h i s t y p e ,  the  c l o s e s t v a l u e I s t o f r e e s p i n g i s l o c a t e d i n the m o l e c u l a r plane  ( i n t h i s case Ag^ = -.0001).  c o u p l i n g must now  The  symmetry  small isotropic hyperfine  be e x p l a i n e d by e i t h e r a v e r y s m a l l c o n t r i b u t i o n  from the f l u o r i n e 2s o r b i t a l where the b u l k of the s p i n d e n s i t y would be on the t e r m i n a l oxygen atom, or by p o s t u l a t i n g the c a n c e l l a t i o n of the F e r m i c o n t a c t term by the induced s p i n p o l a r i z a t i o n of the i n n e r I s o r b i t a l on f l u o r i n e by the o u t e r 2s The  orbital.  i n t e r p r e t a t i o n as a ir r a d i c a l , r e q u i r e s an u n u s u a l l y h i g h  s p i n p o l a r i z a t i o n of the h a l o g e n bond by the odd e l e c t r o n , c e n t r a l oxygen o r b i t a l to account f o r the l a r g e h y p e r f i n e c o u p l i n g i n t h i s  - 84  direction.  -  T h i s a n a l y s i s w i l l a l s o r e q u i r e t h a t the g f a c t o r  perpendicular  to the m o l e c u l a r  p l a n e i s not the g f a c t o r w i t h  s m a l l e s t s h i f t g = (2.0022, 2.0008, 2.0080).  The  small  the  hyperfine  c o u p l i n g i s c o n s i s t e n t w i t h the TT r a d i c a l i n t e r p r e t a t i o n . T h i s would seem t o i n d i c a t e t h a t i n c e r t a i n c a s e s , of EPR  a l o n e may  not be s u f f i c i e n t to d i s t i n g u i s h between a TI  a type r a d i c a l and MO  the r e s u l t s  t h a t a d d i t i o n a l i n f o r m a t i o n such as non  and  empirical  c a l c u l a t i o n s or the i n t e r p r e t a t i o n of the e l e c t r o n i c s p e c t r a  are n e c e s s a r y t o determine the ground s t a t e .  CHAPTER SEVEN  C h l o r o p e r o x y l R a d i c a l , C100 7.1  Introduction The c h l o r o p e r o x y l r a d i c a l (C100) was f i r s t proposed  i n t e r m e d i a t e i n the gas-phase p h o t o l y s i s o f C l and 2  as an  0^^^  The e x i s t e n c e o f C100 was a g a i n supported i n an i n v e s t i g a t i o n o f the mechanism o f t h e h a l o g e n monoxide f o r m a t i o n . and P i m e n t e l i n an IR s t u d y ( H ^ ) ^  n  a  v  e  suggested  that the species  formed i n t h e UV i r r a d i a t i o n o f trapped ClO^, was C100. and S c h w a g e r h a v e Cl at  i n an 0  2  4 K.  C100  2  Rochkind  Arkell  r e p o r t e d t h e IR s t u d y o f t h e p h o t o l y s i s o f  m a t r i x and a l s o on C 1 0 p h o t o l y z e d i n an argon m a t r i x 2  They p r e s e n t e d t h e f i r s t c o n c l u s i v e e v i d e n c e t h a t t h e  r a d i c a l was formed as an i n t e r m e d i a t e i n these two p r o c e s s e s .  Subsequent c a l c u l a t i o n s o f t h e f o r c e c o n s t a n t s and i s o t o p i c c i e s u s i n g assumed m o l e c u l a r s t r u c t u r a l parameters  frequen-  l e d to excellent  agreement w i t h t h e e x p e r i m e n t a l l y measured v a l u e s , c o n f i r m i n g t h a t the r a d i c a l s p e c i e s was C100.  F u r t h e r e v i d e n c e was p r e s e n t e d when  the UV spectrum was o b s e r v e d a n d  molecular modulation  kinetic  (122) s t u d i e s i n t h e UV and IR were  performed  The e l e c t r o n paramagnetic  resonance  (EPR) d e t e c t i o n o f t h i s  s p e c i e s went m i s a s s i g n e d f o r s e v e r a l y e a r s as the CIO s p e c i e s  (123,124)  - 86 -  (123 Eachus e_t al.  126) '  r e a s s i g n e d the r a d i c a l as C100 from o b s e r v a -  t i o n s o f the decay and r e g r o w t h o f paramagnetic s p e c i e s i n t h e p h o t o l y s i s of KCIO^ c r y s t a l s , and r e e v a l u a t i o n o f e a r l i e r powder (123) r e s u l t s on the p h o t o l y s i s o f CIG^ i n R^SO^ . The s i m i l a r i t i e s between the h y p e r f i n e and Zeeman t e n s o r s i n t h i s s p e c i e s and t h a t (26) i n F00  and o t h e r 19 e l e c t r o n r a d i c a l s was used as f u r t h e r (35)  e v i d e n c e f o r t h i s assignment.  Recently, Adrian et a l .  observed  the EPR of the C100 r a d i c a l produced by the p h o t o l y s i s o f a C l /  n  2  m i x t u r e i n argon a t 4 K.  2  They were a b l e t o o b t a i n from the powder  spectrum not o n l y t h e Zeeman and h y p e r f i n e t e n s o r s b u t a l s o the n u c l e a r quadrupole t e n s o r as had Byberg i n h i s s t u d i e s on y „ n m c r y s t-a li s ( > . ET?a r li i*e r w o r ki e r s (123,125,126) . i r r a dA- i a t* e dA KCIO^ had, 1 2 4  n e g l e c t e d the i n c l u s i o n o f t h e n u c l e a r quadrupole term, w h i c h has now been shown t o make a s i g n i f i c a n t c o n t r i b u t i o n . The a c c u r a c y of A d r i a n ' s assignment was l i m i t e d by a r e l a t i v e l y broad s p e c t r a l l i n e w i d t h and by the presence o f a s e t o f s t r o n g l y o v e r l a p p i n g near g = 2.  lines  The l a r g e n u c l e a r quadrupole term a l s o caused s e v e r a l  t r a n s i t i o n s t o o v e r l a p i n a 1:2:1 t r i p l e t whose o u t e r components c o u l d n o t be i d e n t i f i e d r e s u l t i n g i n an i n d e f i n i t e assignment o f the parameters f o r the t e n s o r i n t h i s d i r e c t i o n .  In the present  s t u d y , t h e powder EPR of the C100 r a d i c a l produced by the UV p h o t o l y s i s of CIG^ i n r a r e gas m a t r i c e s a t 4 K w i l l be r e e v a l u a t e d i n o r d e r to improve t h e a c c u r a c y o f t h e s p i n H a m i l t o n i a n  parameters.  The EPR parameters were determined from a c o m b i n a t i o n o f l e a s t squares f i t t i n g o f l i n e p o s i t i o n s and l i n e s h a p e s i m u l a t i o n .  - 87 -  7.2  R e s u l t s and D i s c u s s i o n A m i x t u r e o f CIC^  was  irradiated  i n the CIC^  i n an argon o r k r y p t o n m a t r i x  w i t h a h i g h p r e s s u r e mercury lamp.  (R:M^1:3000)  A gradual  decrease  EPR a b s o r p t i o n l i n e s was observed a l o n g w i t h the  eventual  b u i l d u p o f a secondary s p e c i e s  ( F i g . 7.1).  The s t r o n g l i n e from CIO2 a t  ^ 3335 G, c o u l d never be c o m p l e t e l y b l e a c h e d c o u l d be reduced i n i n t e n s i t y  out.by i r r a d i a t i o n  u n t i l i t contributed only  to the spectrum o f the secondary s p e c i e s .  A less  but  insignificantly  i n t e n s e mercury  i r r a d i a t i o n s o u r c e u s i n g a monochrometer t o s e l e c t an i r r a d i a t i o n o  l i n e a l s o produced the s p e c i e s s t a r t i n g to a b s o r b .  Although  a t ^ 4350 A where ClO^  the CIO2 was p a r t i a l l y o r i e n t e d b e f o r e  the secondary s p e c i e s was not p a r t i a l l y o r i e n t e d . to warm t o the s u b l i m a t i o n p o i n t d i d not p e r m i t  the g - v a l u e were not  irradiation  A l l o w i n g the sample  i s o t r o p i c motion of  the new s p e c i e s and thus the i s o t r o p i c v a l u e o f the c o u p l i n g and  begins  constant  obtained.  On comparison o f the observed spectrum w i t h t h a t o f e a r l i e r w o r k e r s , the s p e c i e s was i d e n t i f i e d as the c h l o r o p e r o x y l (C100)  radical  and measurements o f the l a r g e s t component o f the h y p e r f i n e  t e n s o r c o u p l i n g c o n s t a n t and g - v a l u e , agree f a v o u r a b l y w i t h e a r l i e r (35,123-126) „ , . . ,. . , „. , assignments . However, the h i g h f i e l d p o r t i o n o f t h e fc  spectrum i s c o m p l i c a t e d by a l a r g e n u c l e a r q u a d r u p o l e i n t e r C35 X2A) action  '  . The assignment o f the h y p e r f i n e , Zeeman and quadrupole  t e n s o r v a l u e s f o r t h i s r e g i o n was accomplished the s i n g l e c r y s t a l r e s u l t s  by B y b e r g f r o m  and an assignment o f the r e l a t i v e  signs  of the h y p e r f i n e and quadrupole t e n s o r s was made f o r a l l t e n s o r  - 88 -  Fig.  7.1  Observed EPR spectrum of the C100 r a d i c a l i n an argon m a t r i x a t 4.2 K.  - 89 -  components except the l a r g e s t h y p e r f i n e c o n s t a n t  (A^ i n our a x i s  system) and t h e s i g n of t h i s component was a s s i g n e d by Byberg t o  (35) be t e n t a t i v e l y p o s i t i v e .  A d r i a n e_t al_.  a s s i g n e d the components  from t h e C100 s p e c i e s i s o l a t e d i n argon a t 4.2 K, however they d i d not d e t e r m i n e t h e s i g n o f the h y p e r f i n e c o u p l i n g c o n s t a n t s .  The  a n a l y s i s o f the powder spectrum i s v e r y d i f f i c u l t because of the  37 s t r o n g o v e r l a p o f l i n e s and the presence of the  CI i s o t o p e w h i c h  has a s l i g h t l y s m a l l e r h y p e r f i n e and quadrupole c o u p l i n g . et  a l . analysed  Adrian  the powder spectrum on the b a s i s t h a t "each component  o f an ESR h y p e r f i n e c o u p l i n g m u l t i p l e t y e i l d s t h r e e ' l i n e s ' i n a powder ESR spectrum...  The low f i e l d  l i n e resembles an a b s o r p t i o n  l i n e ; t h e m i d d l e l i n e resembles the f i r s t d e r i v a t i v e of an a b s o r p t i o n l i n e ; and the h i g h f i e l d  l i n e resembles an a b s o r p t i o n l i n e whose  s i g n i s o p p o s i t e to t h a t o f t h e low f i e l d l i n e . "  However, as w i l l  be seen s h o r t l y , t h i s method of a n a l y s i s , w h i l e a c c e p t a b l e f o r w e l l r e s o l v e d h y p e r f i n e components o r p r e l i m i n a r y assignments o f l i n e components, can l e a d t o erroneous assignments o f l i n e p o s i t i o n s when l i n e s of t h e above t h r e e t y p e s o v e r l a p s t r o n g l y o r where "anomalous" t r a n s i t i o n s c o n t r i b u t e t o t h e spectrum and i n p a r t i c u l a r can be m i s l e a d i n g i n cases where the l i n e p o s i t i o n s a r e i n f l u e n c e d by a l a r g e quadrupole c o u p l i n g c o n s t a n t . The assignment of the magnitude o f the Zeeman, h y p e r f i n e and quadrupole t e n s o r s i n t h i s work i s based on the agreement between the s i m u l a t e d and observed spectrum.  I f , as i n p r e v i o u s s t u d i e s ,  the p r i n c i p a l d i r e c t i o n s of a l l t h r e e t e n s o r s a r e assumed c o i n c i d e n t ,  - 90 -  the  q u e s t i o n o f m o l e c u l a r a x i s assignment does n o t a r i s e when t h e  parameters a r e chosen t o s i m u l a t e the spectrum. axis  The C l - 0 bond  ( F i g . 7.2) i s chosen as t h e z p r i n c i p a l d i r e c t i o n  v e n i e n c e i n t h e s i m u l a t i o n method.  f o r con-  This d i r e c t i o n should define  the p r i n c i p a l d i r e c t i o n o f t h e quadrupole t e n s o r * " ^ Q D ,  which  12  s h o u l d e x h i b i t near a x i a l o r a x i a l symmetry about t h i s The l a r g e s t  direction.  component o f the h y p e r f i n e t e n s o r s h o u l d a l s o l i e a l o n g  t h i s a x i s s i n c e the s e p a r a t i o n s between t h e m^. components no s i g n i f i c a n t q u a d r u p o l a r s h i f t .  exhibit  T h i s i s expected f o r t h e case  where a h y p e r f i n e component i s p a r a l l e l t o t h e p r i n c i p a l quadrupole direction  (cf S2CI).  ( I t may a l s o i n d i c a t e  a v e r y s m a l l quadrupole  i n t e r a c t i o n b u t as w i l l be seen t h i s i s c l e a r l y n o t t h e c a s e . ) W i t h t h e s e a s s u m p t i o n s , t h e i n i t i a l v a l u e s f o r t h e p r i n c i p a l components o f the t e n s o r s were chosen u s i n g Byberg's s i g n c o n v e n t i o n , and t h e powder spectrum was s i m u l a t e d .  Fig.  7.2  A x i s system f o r t h e C 1 0 0 r a d i c a l .  - 91 -  The l i n e p o s i t i o n s of the s i m u l a t e d powder spectrum were measured and compared w i t h t h e c a l c u l a t e d f i e l d v s . a n g l e p l o t s o f l i n e p o s i t i o n s t o determine  the t r a n s i t i o n s w h i c h produce the powder l i n e s .  T h i s assignment was then used as the b a s i s f o r a l e a s t squares procedure  which determined  the a c t u a l spectrum.  fitting  the b e s t s e t o f t e n s o r v a l u e s which f i t  A f t e r s e v e r a l t r i a l and e r r o r f i t s a r e a s o n a b l e  s i m u l a t i o n was o b t a i n e d , b u t the i n t e n s i t i e s o f s e v e r a l t r a n s i t i o n s were anomalously h i g h . Exact agreement between the e x p e r i m e n t a l and s i m u l a t e d  intensities  i s n o t expected due t o t h e r e l a t i v e l y l a r g e dependence o f the s p e c t r a l i n t e n s i t i e s on temperature,  a change o f a few degrees i n c r e a s i n g the  i n t e n s i t y of the component a t 3390 G as w e l l as a l t e r i n g o t h e r intensities.  line  D i f f e r e n t e x p e r i m e n t a l c o n d i t i o n s such as r a d i c a l : m a t r i x  r a t i o s f o r t h e CIG^ p a r e n t m o l e c u l e , s p r a y r a t e and degree o f r e s o l u t i o n i n the CIG^ p r e c u r s o r a l s o appear t o a l t e r the observed The s i m u l a t i o n was f i t t h e n , t o t h e observed  intensities.  s p e c t r a w h i c h most  con-  s i s t e n t l y showed the i n t e n s i t i e s r e p r e s e n t e d i n F i g . 7.1 over s e v e r a l s e t s of e x p e r i m e n t s .  The s t r o n g o v e r l a p p i n g o f l i n e s i n the x,y  t r a n s i t i o n r e g i o n , p r e c l u d e d any d e t e r m i n a t i o n o f the magnitude o f the a x i a l component o f the quadrupole  t e n s o r (QE) as the o b s e r v a b l e  l i n e s i n t h i s r e g i o n were r e l a t i v e l y i n s e n s i t i v e t o t h i s v a l u e . v a l u e o f QE = 0 was chosen because i t has been shown t o be l e s s than .2 G ^  1 2 4  \ w h i c h i s about t h e l i m i t of the a c c u r a c y of the  experimental data.  The s i m u l a t i o n u s i n g t h e parameters f o r the  p a r a l l e l a x i s system i n T a b l e 7.1 i s shown i n F i g . 7.3.  A  Fig.  7.3  Computer s i m u l a t e d EPR spectrum of the C100 assuming c o i n c i d e n t axes. ( ^C1 o n l y ) 3  radical  - 93 -  At t h i s p o i n t i t was a n t i c i p a t e d t h a t t h e t h r e e p r i n c i p a l t e n s o r s may n o t be p a r a l l e l .  The h y p e r f i n e and quadrupole  tensors  s h o u l d have t h e i r p r i n c i p a l component axes p a r a l l e l s i n c e they s h o u l d b o t h be dominated by t h e CIO bond.  The g t e n s o r axes  however, may be governed more by t h e 0-0 bond and thus tend t o a l i g n i t s e l f towards t h i s bond. determined  The bond a n g l e i n C100 has been  f a i r l y r e l i a b l y by IR a n a l y s i s t o be 110° w h i c h  would suggest  an a n g l e o f from 0° - 20° f o r t h e a n g l e between t h e  g and A o r Q t e n s o r s i n t h e m o l e c u l a r p l a n e o f p l a n e axes must be c o i n c i d e n t ) . to w h i c h component axis.  (by symmetry, t h e o u t  A c h o i c e must now be made as  (x o r y ) i s t o be d i r e c t e d a l o n g t h e common  S i m u l a t i o n s f o r each c h o i c e were computed f o r an a n g l e o f  r o t a t i o n o f 5° and i t was i m m e d i a t e l y  apparent  t h a t when t h e l o w e s t  g-value component was d i r e c t e d a l o n g t h e x m o l e c u l a r a x i s ( i e . the a x i s p e r p e n d i c u l a r t o t h e C10 bond and i n t h e C100 p l a n e ) l a r g e changes i n t h e s p e c t r a l i n t e n s i t i e s and l i n e p o s i t i o n s o f t h e h i g h f i e l d components w h i c h c o r r e s p o n d  t o t h i s d i r e c t i o n were  observed.  I f t h i s component i s d i r e c t e d a l o n g t h e a x i s p e r p e n d i c u l a r t o t h e m o l e c u l a r p l a n e , q u i t e r e a s o n a b l e s p e c t r a r e s u l t e d when t h e a n g l e between t h e t e n s o r s was w i t h i n t h e range 0° - 10° and above t h i s range s e r i o u s d i s c r e p a n c i e s between the a c t u a l and s i m u l a t e d s p e c t r a line positions resulted. By v a r y i n g t h e angle between t h e t e n s o r s and p e r f o r m i n g a l e a s t squares  a n a l y s i s , t h e parameters i n T a b l e 7.1 were c a l c u l a t e d f o r a  r o t a t i o n a n g l e o f 5°. The main e f f e c t o f r o t a t i o n i s t o reduce t h e  TABLE 7.1 P r i n c i p a l Components o f the S p i n H a m i l t o n i a n Parameters f o r the C100 R a d i c a l .  H y p e r f i n e components  Quadrupole components  (cm" xl0 ) 1  8  x  y  g  z  A  (cm xl0 )  4  A  - 1  4  A  QD  QE  —  —  KCIO, 4  ±.1  KCIO. 4 (c) Argon  1.9983  2.0017  2.0130  4.9  6.7  z .14.0  1.9965  2.0035  2.0100  +4.3  +1.9  (±)16.8  ±6.8  1.9915  1.9987  2.0100  5.3  3.0  16.7  8.7  0.  1.9989  1.9883  2.0078  +3.7  +4.6  ±17.4  ±8.7  0.  Argon  1.9984  1.9883  2.0078  +3.7  +4.6  ±17.2  ±8.7  0.  Argon  8  X  y  ±.0002  ±.2  ±.2  (a)  R e f . (126)  (b)  R e f . (124)  (c)  R e f . (35)  (d)  T h i s work - a l l t e n s o r axes p a r a l l e l .  (e)  T h i s work - g t e n s o r r o t a t e d by 5° from A and Q t e n s o r frame.  ( a )  ( b )  - 95 -  i n t e n s i t y of t h e l i n e a t 3390 G t o a v a l u e more i n a c c o r d w i t h t h e experimental i n t e n s i t y  ( F i g . 7.4).  A l t e r i n g the s i g n of  from Byberg's p o s t u l a t e d p o s i t i v e  value  to a n e g a t i v e v a l u e had no o b s e r v a b l e e f f e c t on t h e s i m u l a t e d powder spectrum.  The " a l l o w e d " l i n e p o s i t i o n s ( i e . t h e most i n t e n s e l i n e s )  c o r r e s p o n d i n g t o H//x unaltered.  remained u n s h i f t e d and t h e i n t e n s i t i e s  S h i f t s were observed  i n the c a l c u l a t e d l i n e p o s i t i o n s  o f t h e " f o r b i d d e n " t r a n s i t i o n s , o f c o u r s e , b u t the i n t e n s i t i e s o f these t r a n s i t i o n s a r e t o o low t o c o n t r i b u t e t o the powder spectrum. R e v e r s i n g t h e r e l a t i v e s i g n o f t h e quadrupole  c o u p l i n g t e n s o r however  had a d e t r i m e n t a l e f f e c t on the spectrum, attempts simulated l i n e s to correspond  t o t h e observed  u n s u c c e s s f u l and a l l l e a s t squares RMS e r r o r s .  to s h i f t the  l i n e p o s i t i o n s were  f i t t i n g procedures  produced h i g h  I t i s reasonably c e r t a i n then, t h a t the r e l a t i v e s i g n s  chosen a r e c o r r e c t f o r QD and A , A . x y  The s i g n o f A  i s s t i l l somez  what u n c e r t a i n . I t i s u n f o r t u n a t e t h a t t h e i s o t r o p i c spectrum o f C100 c o u l d n o t be o b t a i n e d s i n c e t h i s would remove t h e a m b i g u i t y o f t h e r e l a t i v e s i g n choice f o r the h y p e r f i n e tensor. The m i s l e a d i n g method o f a s s i g n i n g l i n e s t o one o f t h e t h r e e " l i n e shapes" d i s c u s s e d e a r l i e r c a n be i l l u s t r a t e d h e r e .  The two  l i n e s marked by arrows i n F i g . 7.1 were a s s i g n e d i n c o r r e c t l y by A d r i a n e t a l . s i n c e a l i n e i n t e n s i t y of 1:2:1 was expected  where  the i n c r e a s e d i n t e n s i t y o f t h e c e n t e r component was presumed t o be from an o v e r l a p o f t h e m^. = l / 2 ; - l / 2 l i n e s due t o t h e quadrupole coupling decreasing t h e i r spacing.  When the l i n e s h a p e i s s i m u l a t e d ,  Fig.  7.4  S i m u l a t e d EPR spectrum of the C100 r a d i c a l assuming the n o n - c o i n c i d e n t a x i s system of F i g . 7 . 2 .  - 97 -  however t h i s l i n e i s e n t i r e l y m i s s i n g from t h e powder p a t t e r n due to f o r t u i t o u s " c a n c e l l i n g " o f these two t r a n s i t i o n s ' i n t e n s i t i e s . W i t h t h e t r a n s i t i o n s due t o H a l i g n e d an i n c r e a s e d appear w i t h  along the x p r i n c i p a l a x i s ,  c e n t r a l component was s i m i l a r l y p r e d i c t e d  but d i d not  t h a t i n t e n s i t y i n t h e a c t u a l spectrum, a g a i n because  of f o r t u i t o u s " c a n c e l l i n g " .  However t h e c o u p l i n g s i n t h i s d i r e c t i o n  are i n l i t t l e e r r o r due t o t h e o b s e r v a t i o n o f o t h e r t r a n s i t i o n s which defined  7.3  this  Interpretation  coupling.  o f t h e H a m i l t o n i a n Parameters  In a l l p r e v i o u s s t u d i e s , i t has been assumed t h a t r a d i c a l s o f the t y p e X00 were IT type r a d i c a l s where t h e u n p a i r e d resides  electron  i n a m o l e c u l a r o r b i t a l composed o f p type o r b i t a l s perpen-  d i c u l a r t o the molecular plane.  T h i s has been l a r g e l y  substantiated  (111 112) f o r H00  '  where a c c u r a t e m o l e c u l a r o r b i t a l c a l c u l a t i o n s have  been p e r f o r m e d ^ l " ^ .  i  na  n  attempt t o p r e d i c t t h e ground s t a t e o f  the C100 r a d i c a l from CNDO/2 and INDO methods a v a i l a b l e , s e v e r e d i f f i c u l t i e s were encountered i n t h e h a n d l i n g o f near d e g e n e r a c i e s 2 of t h e f i l l e d v a l e n c e o r b i t a l s , CNDO/2 p r e d i c t i n g an A' ground 2 s t a t e w h i l e INDO p r e d i c t s a  A" ground s t a t e .  the s p i n d e n s i t i e s and wave f u n c t i o n s and  For t h i s reason,  were c o n s i d e r e d  c o u l d n e i t h e r be used f o r a t h e o r e t i c a l e s t i m a t i o n  unreliable of the  a n i s o t r o p i c hyperfine tensor nor i n p r e d i c t i n g g tensor s h i f t s . (128^ A" ground s t a t e . Walsh's c o r r e l a t i o n diagram f o r an ABC system would p r e d i c t a 2  - 98 -  R e c e n t l y , a non e m p i r i c a l LCAO - MO - SCF c a l c u l a t i o n on b o t h C100 and F00 i n t h e i r e q u i l i b r i u m g e o m e t r y h a s been performed and a d i s c r e p a n c y as t o t h e ground s t a t e o f these  radicals  2 now e x i s t s .  I t was shown t h a t these two s p e c i e s a r e b o t h o f  A  1  symmetry i n t h e ground s t a t e ( i e . the u n p a i r e d e l e c t r o n i s i n a a type o r b i t a l i n t h e m o l e c u l a r  plane).  The i m p l i c a t i o n o f t h i s  c a l c u l a t i o n i s m a n i f o l d and s e r i o u s problems a r e posed i n attempti n g t o i n t e r p r e t t h e h y p e r f i n e t e n s o r and t h e g - s h i f t s . I f , as i n a l l p r e v i o u s work, t h e r a d i c a l i s assumed t o have a TT ground s t a t e , t h e t h e o r e t i c a l a n a l y s i s f o r a "ir r a d i c a l " p r e d i c t s t h a t t h e g t e n s o r component l y i n g a l o n g t h e d i r e c t i o n p e r p e n d i c u l a r t o the m o l e c u l a r  p l a n e would be c l o s e t o f r e e s p i n  ( g ) and t h a t t h i s d i r e c t i o n would a l s o e x h i b i t t h e l a r g e s t h y p e r g  f i n e coupling constant.  S i n c e , as p r e v i o u s l y mentioned, the  quadrupole e f f e c t s on the l a r g e s t h y p e r f i n e component a r e n e g l i g i b l e , t h i s component cannot l i e p e r p e n d i c u l a r t o t h e maximum quadrupole component (QD). The quadrupole c o u p l i n g t e n s o r expected dominated by t h e CIO bond and QD s h o u l d l i e a l o n g t h i s and  t o be direction  t h e h y p e r f i n e component a s s i g n e d k^ s h o u l d a l s o be o r i e n t e d  along t h i s d i r e c t i o n . of the r e m a i n i n g  I t now remains f o r us t o a s s i g n t h e d i r e c t i o n s  two h y p e r f i n e components and t h i s cannot be done  on t h e b a s i s o f t h e g - s h i f t s s i n c e n e i t h e r g t e n s o r component can be c o n s i d e r e d t o be c l o s e t o g . g  To account f o r t h e l a r g e h y p e r f i n e  component a l o n g t h e bond, a l a r g e s p i n p o l a r i z a t i o n o f t h e CIO bond must be i n t r o d u c e d as was done w i t h F00  .  F o l l o w i n g t h i s method  - 99 -  of a n a l y s i s , the a n i s o t r o p i c p a r t of the h y p e r f i n e t e n s o r i s (±6.78, -4 ±7.58, +14.37) x 10  -1 cm  .  The  a x i s assignment of the x and  t e n s o r components i s ambiguous a t t h i s p o i n t . be r e s o l v e d i n t o the sum  This tensor  can  of two a x i a l t e n s o r s , one a x i a l about the  y d i r e c t i o n and the o t h e r about the z d i r e c t i o n S i n c e the s p i n d e n s i t y i n the TT o r b i t a l a l o n g p and  y  the s p i n d e n s i t y i n the p  (Eqn. y  [6.11]).  s h o u l d be  positive  o r b i t a l on c h l o r i n e s h o u l d be  z  negative,  the o n l y s i g n c h o i c e and a x i s assignment c o m p a t i b l e w i t h t h i s c h o i c e , is for A  z  t o be n e g a t i v e and f o r the s m a l l e s t h y p e r f i n e component t o  be o r i e n t e d a l o n g the x a x i s . 6.8  T  7.05  -.25  XX  T  7.6  =  =  +  .5  7.05  yy T  -14.4  -.25  -14.10  zz [7.1]  Note t h a t t h i s w i l l a l s o r e q u i r e  t o be n e g a t i v e .  This a n a l y s i s  then p r e d i c t s t h a t the s m a l l e s t g t e n s o r component w i l l l i e a l o n g the y d i r e c t i o n  (g  y  = 1.9883).  T h i s i s c o n s i s t e n t w i t h the a s s i g n -  ment of the n o n - c o l i n e a r t e n s o r a n a l y s i s p r e v i o u s l y d e s c r i b e d t h i s cannot be c o n s t r u e d as s u p p o r t i n g e v i d e n c e f o r the c o l i n e a r i t y of the t e n s o r s . to  although  non-  This large negative g - s h i f t perpendicular  the m o l e c u l a r p l a n e cannot be r a t i o n a l i z e d on the b a s i s of the  one  - 100  -  c e n t e r g t e n s o r t h e o r y f o r a "ir r a d i c a l " and i t seems n e c e s s a r y  to  c o n s i d e r the c o n t r i b u t i o n s from the two c e n t e r terms. 2 As mentioned e a r l i e r , a this radical.  A' ground s t a t e has been proposed f o r  I f t h i s ground s t a t e i s assumed, the a n i s o t r o p i c  h y p e r f i n e c o u p l i n g t e n s o r can be i n t e r p r e t e d u s i n g the o u t l i n e d i n Chapter S i x f o r a-type r a d i c a l s . t i o n of the a-bond, which was  necessary  The  approximation  large spin polariza-  i n the i r - r a d i c a l  i s not r e q u i r e d i n a a-type r a d i c a l i n t e r p r e t a t i o n .  interpretation,  U s i n g Eqn.  and assuming t h a t the s p i n d e n s i t y i n the a bond i s now  [6.9]  positive,  the  approximate s p i n d e n s i t i e s i n the p - and p - o r b i t a l s on the c h l o r i n e c e n t e r a r e p^ = .006;  p  z  - .12.  I n t h i s a n a l y s i s , the assignment of  the x and y components of the a n i s o t r o p i c h y p e r f i n e c o u p l i n g t e n s o r i s also unequivocal,  w i t h the h y p e r f i n e t e n s o r component of  inter-  m e d i a t e a b s o l u t e magnitude ( A ) o r i e n t e d p e r p e n d i c u l a r to the y  molecular plane.  T h i s i s a l s o c o n s i s t e n t w i t h the i n t e r p r e t a t i o n  of n o n - c o l i n e a r axes s i n c e t h i s would r e q u i r e the y- component of the g t e n s o r bond and  (g  y  = 1.9983) to be o r i e n t e d p e r p e n d i c u l a r to the C l - 0  i n the plane of the  radical. -4  The s m a l l i s o t r o p i c h y p e r f i n e c o u p l i n g (±3 x 10  -1 cm  ) i s not  g e n e r a l l y found i n a r a d i c a l s and a l a r g e s p i n p o l a r i z a t i o n of i n n e r I s - 2s o r b i t a l s on CI would be n e c e s s a r y c o n t a c t term i n the 3s o r b i t a l . e l e c t r o n i s expected i t may  the  to c a n c e l the F e r m i  A l t e r n a t i v e l y , s i n c e the  unpaired  to r e s i d e l a r g e l y on the t e r m i n a l oxygen atom,  be t h a t t h e r e i s v e r y l i t t l e s p i n d e n s i t y d e l o c a l i z e d i n t o  the c h l o r i n e s - o r b i t a l s . The  i n t e r p r e t a t i o n o f the h y p e r f i n e and g t e n s o r i n t h i s  i s ambiguous and no c l e a r c h o i c e as to the ground s t a t e of the  radical radical  - 101 -  can be made on the b a s i s o f these r e s u l t s .  The d e t e r m i n a t i o n o f  i s o t r o p i c c o u p l i n g c o n s t a n t would c e r t a i n l y remove any a m b i g u i t y of t h e c h o i c e o f r e l a t i v e s i g n s b u t t h i s would s t i l l n o t r e s o l v e the ground s t a t e dilemma and t h i s c h o i c e may n o t be p o s s i b l e from EPR r e s u l t s a l o n e .  T h i s d e c i s i o n would be h e l p e d by a more a c c u r a t e  LCAO - MO - SCF c a l c u l a t i o n o f t h e r e l a t i v e e n e r g i e s o f t h e ground s t a t e and l o w e s t e x c i t e d s t a t e s as a f u n c t i o n o f g e o m e t r i c l conf i g u r a t i o n and s h o u l d i n c l u d e c o n f i g u r a t i o n i n t e r a c t i o n i n o r d e r to g i v e a good.estimate  o f t h e s p i n d e n s i t i e s and wave f u n c t i o n s  of the ground s t a t e . A t t h i s p o i n t i t may be o f i n t e r e s t t o c o n s i d e r the of f o r m i n g the  C100  r a d i c a l from the s y m m e t r i c a l  CIO2  process  radical.  A r k e l l and S c h w a g e r ^ ^ have proposed a mechanism w h i c h  first  1 2  i n v o l v e s t h e f o r m a t i o n o f a p a r t i a l 0 - 0 bond and a compressed C 1 0 0 bond a n g l e .  A s l i g h t r o t a t i o n o f the m o l e c u l e would a l l o w t h e  bond a n g l e t o i n c r e a s e t o a t t a i n a more s t a b l e s t r u c t u r e .  This  c o n v e r s i o n i s l i k e l y t o be enhanced by t h e "cage e f f e c t " w h i c h would r e s t r i c t a l l t h r e e atoms t o a c o n f i n e d  space.  T h i s p r o c e s s most l i k e l y i n v o l v e s an e x c i t e d s t a t e o f  CIO2  o  and s i n c e r e l a t i v e l y l i t t l e energy i s r e q u i r e d (hv ^ 4000 A) t h e e x c i t e d s t a t e l i e s v e r y c l o s e t o the ground s t a t e o f C 1 0 . I t 2  - 102  has been observed C100  -  i n y i r r a d i a t e d c r y s t a l s of K C I O ^  v  t h a t  r a d i c a l i s formed w i t h about 75% y i e l d , i f the ClO^  formed a r e i r r a d i a t e d w i t h UV l i g h t . to s t a n d a t 295 K the CIC^ m o l e c u l e yield.  centers  I f the c r y s t a l i s a l l o w e d i s reformed w i t h about  70%  The c o n v e r s i o n between these two isomers i s thus o n l y  i n h i b i t e d by a t h e r m a l  barrier.  the  CHAPTER EIGHT  Fluorosulfinyl Radical, 8.1  R e s u l t s and  FSO  Discussion  I t would appear t h a t the p h o t o d i s s o c i a t i o n of t h i o n y l f l u o r i d e (SG^)  (129) Donovan e_t al_.  has not been s t u d i e d .  s t u d i e d the UV p h o t o l y s i s of t h i o n y l c h l o r i d e .  and  Okabe  (130)  have  Donovan e_t a l . found  t h a t p h o t o d i s s o c i a t i o n i n v o l v e s the f i s s i o n of one s u l f u r - c h l o r i n e bond l e a v i n g an e n e r g i z e d  C1S0  r a d i c a l w h i c h may  d i s s o c i a t i o n t o y i e l d another c h l o r i n e atom and  undergo f u r t h e r the SO r a d i c a l i f  the C 1 S 0 i s not s t a b i l i z e d by c o l l i s i o n a l d e a c t i v a t i o n .  It is  thought t h a t t h i o n y l f l u o r i d e might a l s o undergo the same type of photodissociation. Thionyl f l u o r i d e , matrix  (R:M  was  (F2SO)  - .1mm:20mm) and  or a f t e r d e p o s i t i o n w i t h UV  d i l u t e d i n an argon or  the m i x t u r e was  photolyzed  krypton e i t h e r during  s o u r c e s of v a r y i n g wave l e n g t h s .  of the m i x t u r e w i t h the r e l a t i v e l y low energy, h i g h p r e s s u r e lamp f a i l e d t o produce any such as a low p r e s s u r e v  signals.  mercury lamp ( A  hydrogen resonance lamp (^ EPR  EPR  max  ~ 1215  spectrum r e s u l t e d , which was  due  When a h i g h e r  max  - 2537 A;  Photolysis mercury  energy s o u r c e  1849  A) or a  A) was  used, a r e a s o n a b l y  to two  overlapping r a d i c a l  intense  - 104 -  species.  One o f these s p e c i e s  i s the m e t h y l r a d i c a l whose EPR  spectrum has been s t u d i e d i n t h e i n e r t m a t r i c e s ^ ' .  The f o r m a t i o n  of t h i s s p e c i e s i s due almost c e r t a i n l y t o t r a c e i m p u r i t i e s i n t r o duced d u r i n g  t h e sample p r e p a r a t i o n  appeared when samples o t h e r  than  s i n c e these s i g n a l s i n v a r i a b l y  F2SO  resonance lamps o r t h e low p r e s s u r e  were p h o t o l y z e d  mercury lamp.  w i t h the gas  Stringent  p u r i f i c a t i o n p r o c e d u r e s i n c l u d i n g vacuum d i s t i l l a t i o n o f t h e t h i o n l y f l u o r i d e , b a k i n g the vacuum m a n i f o l d passing  the m a t r i x  f o r s e v e r a l days a t 80°C and  gases through a l i q u i d n i t r o g e n t r a p , f a i l e d t o  remove a l l t r a c e s o f t h e i m p u r i t y , a l t h o u g h t h e i n t e n s i t y o f t h e i m p u r i t y s i g n a l s were s i g n i f i c a n t l y reduced i n i n t e n s i t y i n comparison w i t h t h e second r a d i c a l s p e c i e s .  The spectrum of t h i o n y l f l u o r i d e  i n an argon m a t r i x i s shown i n F i g . 8.1. S i n c e t h e S-Obond i n  F2SO  i s l i k e l y t o be much s t r o n g e r  than  the S-F bond, p h o t o l y s i s w i l l most p r o b a b l y r e s u l t i n t h e l o s s o f a f l u o r i n e atom t o g i v e t h e a s y m m e t r i c a l r a d i c a l FSO w h i c h  should  (128) be b e n t , s i n c e i t i s a n i n e t e e n  electron radical  .  T h i s proposed  d e c o m p o s i t i o n p r o d u c t i s the o n l y one w h i c h i s c o n s i s t e n t w i t h t h e observed EPR spectrum.  I f more than one f l u o r i n e  i n the r a d i c a l , a much more c o m p l i c a t e d  were  contained  spectrum would r e s u l t due  t o t h e i n t e r a c t i o n o f two n u c l e i w i t h n u c l e a r  spin 1 = 1 / 2 .  A  l i n e a r r a d i c a l would a l s o r e s u l t i n a spectrum w h i c h e x h i b i t e d  axial  symmetry.  likely  Rearrangement t o t h e i s o m e r , FOS, i s n o t c o n s i d e r e d  s i n c e t h i s would p l a c e a l a r g e s p i n d e n s i t y on a t e r m i n a l s u l f u r atom (131-133) and t h i s u s u a l l y r e s u l t s i n l a r g e g - s h i f t s . Additional  - 105 -  Fig.  8.1  Observed EPR spectrum of the FSO r a d i c a l i n an argon m a t r i x a t 4.2 K.  - 106 -  support for the structure FSO,  comes from comparison of the  observed  ( 26)  spectrum with that of the F00 r a d i c a l i n an argon matrix  .  The  species FSO i s valence i s o e l e c t r o n i c with F00 and spin density d i s t r i b u t i o n s would not be expected  to be greatly d i f f e r e n t .  hyperfine tensors should then be s i m i l a r .  The  The g tensor values would  be quite d i f f e r e n t , however, because of the larger spin-orbit coupling constant for a sulfur atom.  Because of these observations, i t i s  considered that the most l i k e l y conformation  for the r a d i c a l species  i s FSO and the remaining analysis of the spectrum w i l l be based on this structure. The observed powder spectrum has several rather intense signals (26) at the center of the spectrum similar to those seen i n F00 Because of the rather large magnetic moment of a f l u o r i n e nucleus, there w i l l be a s i g n i f i c a n t contribution to the t o t a l spin Hamiltonian from the nuclear Zeeman term.  This term, while not affecting the  allowed transitions i n a f i r s t order approximation, i n the l i n e positions of Am^ "forbidden".  w i l l cause s h i f t s  = ± 1 transitions which are normally  The resonance f i e l d s of these "forbidden" transitions  w i l l be i n a region between the "allowed" t r a n s i t i o n s .  If the  i n t e n s i t i e s of these transitions i s large enough, to allow their detection, they provide the necessary information to determine the l i n e pairing of the allowed t r a n s i t i o n s .  The forbidden transitions  can also be used to determine the r e l a t i v e signs of the hyperfine tensor components.  If the powder lineshape i s simulated with d i f f e r e n t  choices for the r e l a t i v e signs, only one should agree with the lineshape.  observed  - 107 -  U s i n g t h e above g u i d e l i n e s , t h e observed analyzed.  spectrum can be  The two outermost l i n e s can be a s s i g n e d t o one p r i n c i p a l  a x i s s i n c e no f o r b i d d e n t r a n s i t i o n s a r e observed any o t h e r l i n e p a i r i n g scheme.  I f another  near t h e c e n t e r of  l i n e p a i r were chosen,  c o n s i d e r a b l y l a r g e r g - f a c t o r s h i f t s would r e s u l t and t h i s i s n o t expected remaining  from m o l e c u l e s  o f t h i s type.  The l i n e p a i r i n g of t h e  two h y p e r f i n e m u l t i p l e t s i s n o t c l e a r .  But t h i s can be  r e s o l v e d by comparing a computer s i m u l a t e d spectrum w i t h t h e observed spectrum. The H a m i l t o n i a n used t o d e s c r i b e t h i s system i s t h a t g i v e n i n Eqn.  [2.23] ( w i t h o u t the quadrupole t e r m ) .  I n i t i a l guesses were  taken f o r t h e h y p e r f i n e and g t e n s o r v a l u e s and t h e p o l y c r y s t a l l i n e l i n e s h a p e was s i m u l a t e d .  S e v e r a l l i n e p a i r i n g schemes were chosen  and a l l b u t one produced f o r b i d d e n t r a n s i t i o n s w h i c h d i d n o t correspond w i t h t h e observed  line positions.  Having determined the l i n e  pairing,  the parameters were a l t e r e d by t r i a l and e r r o r u n t i l a r e a s o n a b l e f i t was a c h i e v e d w i t h t h e a l l o w e d l i n e p o s i t i o n s .  The l i n e s h a p e was  then s i m u l a t e d w i t h t h e f o u r p o s s i b l e r e l a t i v e s i g n c o m b i n a t i o n s the h y p e r f i n e t e n s o r .  Only one s i g n c o m b i n a t i o n  l i n e s h a p e ( F i g . 8.2).  To f a c i l i t a t e t h e comparison o f t h e s i m u l a t e d  and observed  reproduced  of  t h e observed  s p e c t r a , t h e l i n e p o s i t i o n s of the CH^ r a d i c a l were a l s o  c a l c u l a t e d and added t o the s i m u l a t i o n f o r FSO.  The e x p e r i m e n t a l l y  determined g t e n s o r and h y p e r f i n e t e n s o r v a l u e s a r e g i v e n i n T a b l e 8.1. The observed  v a l u e s f o r F00 a r e a l s o g i v e n f o r comparison.  F i g . 8.2  Computer s i m u l a t e d EPR spectrum of the FSO r a d i c a l .  - 109 -  TABLE 8.1 P r i n c i p a l components o f t h e s p i n H a m i l t o n i a n EPR parameters f o r t h e FSO r a d i c a l .  S  l  g  2  g  3  l  A  2 3 -1 4 (cm x l O ) A  A  2.0011  2.0037  2.0019  +94.1  -37.9  -14.6  (-.0002)  (-.0002)  (-.0002)  (±.2)  (-.2)  (-.5)  2.0080  2.0008  2.0022  +96.2  ±47.1  ±13.1  The p r i n c i p a l d i r e c t i o n s a r e d e f i n e d i n F i g . 3.  TABLE 8.2 Calculated  (IND0/2) and p r e d i c t e d s p i n d e n s i t i e s f o r t h e FSO r a d i c a l  3p  z  3p y  .13  .24  r  2p  z  2p y  2p -3p y y  2p - 3 ^ z p^  -.023  .005  -.01  -.035  -.062  .013  -  -  INDO/2 predicted.  (F00  ( 2 6 )  )  -  110  -  I t s h o u l d be mentioned t h a t t h i s a n a l y s i s assumes t h a t the g and A t e n s o r s i n FSO  are p a r a l l e l .  Because of the l a r g e a n i s o t r o p y  i n the A. t e n s o r , the allowed powder l i n e p o s i t i o n s w i l l to  the f i e l d o r i e n t e d a l o n g the p r i n c i p a l A axes and  w i l l be n o n d i a g o n a l  correspond  the g t e n s o r  when measured i n the A t e n s o r frame.  Since  g t e n s o r a n i s o t r o p y i s v e r y s m a l l , the o f f d i a g o n a l components be n e g l i g i b l e and  the will  the g and A t e n s o r axes can be assumed to be  coincident. The  r e l a t i o n of the p r i n c i p a l axes of the h y p e r f i n e and  t e n s o r components to the m o l e c u l a r the p o l y c r y s t a l l i n e spectrum  axes cannot  alone.  be determined  g from  To make t h i s assignment, a  comparison w i t h t h e o r e t i c a l e s t i m a t e s of these q u a n t i t i e s i s n e c e s s a r y . U n f o r t u n a t e l y , the a c c u r a t e LCAO-MO-SCF c a l c u l a t i o n s needed f o r e v a l u a t i n g these v a l u e s are not a v a i l a b l e f o r the r a d i c a l s p e c i e s FSO  and  a more approximate MO  been shown used  v  '  '  ' t h a t CNDO/2 or INDO MO  f o r o b t a i n i n g a reasonable  molecules.  of  and FSO.  S-0 bond l e n g t h s  c a l c u l a t i o n s can  from  assumed angles of the FSO  be  e s t i m a t e of the geometry of s m a l l  the parent compound  can be used  bond angles and  radical  F2SO,  i n determining  M o l e c u l a r o r b i t a l c a l c u l a t i o n s were performed  energy was  I t has  I f i t i s assumed t h a t the bond l e n g t h s i n the  do not change s i g n i f i c a n t l y F-S  c a l c u l a t i o n must be used.  the known  the geometry  with various  a minimum i n the  total  f o r the case w i t h an angle of 1 2 0 ° .  reached  Both the CNDO/2 and  INDO c a l c u l a t i o n s p r e d i c t  t h a t FSO  should  2  be a "TT r a d i c a l "  ( A" ground s t a t e ) .  This i s also consistent with  - I l l-  Walsh's c o r r e l a t i o n diagrams f o r n i n e t e e n  electron radicals 2  I t should F00  be  r e c a l l e d here t h a t the assumed  r a d i c a l i s somewhat q u e s t i o n a b l e  have a A'  ground s t a t e .  2  between the FSO be d o u b t f u l .  and  The  F00  (Chapter  radicals,  i n t e r p r e t a t i o n which w i l l be I t should  g^ and  to the m o l e c u l a r  to the m o l e c u l a r  may  also  be noted t h a t an  equally  ground s t a t e .  plane w i l l have a  D e r i v a t i o n s from g plane  can be  along  g  caused by  to be  orbitals  lie  bond  the CIO  and  no  agreement w i t h component was  Seven).  the assignment i n F00 assigned  to the F-0  the  perpendicul unpaired  a x i s assignment  the assignment must tensor.  t h a t the l a r g e s t h y p e r f i n e  (Chapter  c l o s e to  through s p i n p o l a r i z a t i o n  based on a q u a l i t a t i v e a n a l y s i s of the h y p e r f i n e radical,  smallest  the i n t r o d u c t i o n of  the b a s i s of the g - v a l u e s ,  found i n the C100  to a s s i g n  the  the d i r e c t i o n  Because of the s m a l l g - s h i f t s observed f o r FSO, can be made on  value  I t i s tempting then,  %^ c o u l d a l s o be c o n s i d e r e d  e l e c t r o n d e n s i t y i n t o the i n plane  It  be  was  component must  This i s i n q u a l i t a t i v e  where the l a r g e s t h y p e r f i n e  bond d i r e c t i o n .  s i m i l a r i t y between the t o t a l h y p e r f i n e FSO,  similarities  component g^ to t h i s d i r e c t i o n s i n c e i t has  free spin value.  along  i n fact  followed here w i l l  for a " a "  c l o s e to t h a t f o r the f r e e e l e c t r o n .  g - s h i f t but  may  the  been p r e v i o u s l y mentioned t h a t the g - f a c t o r which i s  oriented perpendicular  the t e n s o r  S i x ) and  the ground s t a t e of FSO  p l a u s i b l e i n t e r p r e t a t i o n can be g i v e n I t has  ground s t a t e of  Because of the s t r o n g  is a 'V-radical.  assume t h a t FSO  A"  tensor  i t i s thought t h a t the l a r g e s t h y p e r f i n e  i n F00  Because of and  the  that i n  c o u p l i n g i n FSO  should  - 112 -  a l s o l i e a l o n g the F-S bond.  With t h i s assignment, t h e m o l e c u l a r  d i r e c t i o n s o f t h e r e m a i n i n g two p r i n c i p a l axes can be a s s i g n e d . R e t u r n i n g t o the a n a l y s i s o f t h e h y p e r f i n e  tensor  for a "IT radical"  g i v e n i n Chapter S i x , t h e a n i s o t r o p i c p a r t o f t h e h y p e r f i n e  tensor  can be e x p r e s s e d as two a x i a l c o n t r i b u t i o n s , one from t h e p ^ - o r b i t a l and  a n o t h e r from t h e p ^ - o r b i t a l a l o n g t h e F-S bond (Eqn. [ 6 . 1 1 ] ) . The  a x i s system chosen p l a c e s T  a l o n g t h e F-S bond, T zz ° yy t o the m o l e c u l a r p l a n e , and T normal t o t h e FS bond J  perpendicular  XX  but  i n t h e m o l e c u l a r p l a n e ( F i g . 8.3).  I n t h i s a n a l y s i s , the same  arguments t h a t were used t o a n a l y s e t h e a n i s o t r o p i c h y p e r f i n e of t h e F00 r a d i c a l w i l l be employed.  tensor  I t w i l l be r e c a l l e d t h a t t h e  s p i n d e n s i t y i n the p^ (TT) o r b i t a l , was t a k e n t o be p o s i t i v e w h i l e the s p i n d e n s i t y i n t h e p  z  (a) o r b i t a l was t a k e n t o be n e g a t i v e due  t o t h e s p i n p o l a r i z a t i o n o f t h e F-0 bond by t h e i r odd e l e c t r o n on the c e n t r a l oxygen.  U s i n g these p r e d i c t i o n s f o r t h e s i g n s o f t h e  s p i n d e n s i t i e s i n FSO, and h a v i n g a l r e a d y  e s t a b l i s h e d t h a t t h e maximum  h y p e r f i n e component c o r r e s p o n d s t o ^ , the assignment o f t h e t e n s o r components T and T can be made as f o l l o w s : xx yy z z  r  T  ~-l.ll'  "28.46"  " 36.23"  XX  T  =  51.77  =  15.54  +  36.23  yy T _  zz  -7.77  -80.23  -  -4 x 10 cm  -72.46  -  T h i s assignment a l s o p r e d i c t s t h a t t h e s i g n o f t h e i s o t r o p i c h y p e r fine coupling  -4 -1 c o n s t a n t i s n e g a t i v e (-13.9 x 10 cm ) .  T h i s was a l s o  - 113 -  F i g . 8.3  M o l e c u l a r a x i s system f o r the FSO r a d i c a l .  - 114 -  found t o be t h e case i n FOCT  '  .  The s p i n d e n s i t i e s i n the 2p- and 2p- o r b i t a l s on f l u o r i n e c a n y z be e s t i m a t e d from these two a x i a l t e n s o r s t o be p = .013 and y = -.062.  These v a l u e s can be compared w i t h t h e s p i n  densities  from an INDO/2 c a l c u l a t i o n on t h e FSO r a d i c a l ( T a b l e 8.2). As has been p r e v i o u s l y mentioned, t h i s a n a l y s i s does n o t account f o r the d i p o l a r o r o v e r l a p c o n t r i b u t i o n t o t h e a n i s o t r o p i c h y p e r f i n e coupling.  These c o n t r i b u t i o n s  can be e s t i m a t e d by c o n s i d e r i n g t h e  one c e n t e r , two c e n t e r and o v e r l a p i n t e g r a l s g i v e n i n Appendix B. U s i n g t h e INDO/2 s p i n d e n s i t i e s g i v e n i n Table 8.2, t h e c a l c u l a t e d -4 -1 a n i s o t r o p i c h y p e r f i n e t e n s o r i s (8.7, 15.2, -23.9) x 10 Although  t h e n u m e r i c a l agreement w i t h t h e observed  poor ( a l l v a l u e s b e i n g lower than t h e observed  cm  tensor i s very  v a l u e s by a f a c t o r  of about 3.6) t h e shape and r e l a t i v e s i g n s o f t h e t e n s o r a r e c o r r e c t .  CHAPTER NINE  C h l o r o d i s u l f o n y l R a d i c a l , C1SS 9•1  P h o t o l y s i s of s u l f u r m o n o c h l o r i d e  (S^Cl^)  The i d e n t i f i c a t i o n o f t h e t r a n s i e n t s p e c i e s and p r o d u c t s formed i n the p h o t o l y s i s o f s u l f u r c o n t a i n i n g compounds has been the s u b j e c t The y  of many s p e c t r o s c o p i c s t u d i e s i n the l a s t few decades.  r a d i o l y s i s of s u l f u r c o n t a i n i n g amino a c i d s has been found t o g i v e r i s e t o r a d i c a l s where t h e u n p a i r e d sulfur a t o m  ( 1 3 1  '  1 3 8  '  1 3 9 )  .  e l e c t r o n i s l o c a l i z e d on a  The p h o t o l y s i s o f a l k y l t h i o l s  y i e l d s p r i m a r i l y r a d i c a l s of the type RS of H S 2  ' 1^0) h - Q W  e  (RSH)  photolysis  and d i s u l f a n e (^S,,) g i v e the HS- and HSS* r a d i c a l r e s p e c t i v e l y  (132) A l l of these r a d i c a l s have an EPR spectrum w h i c h i s v e r y s i m i l a r , b e i n g dominated by a s t r o n g p o s i t i v e g s h i f t and d i s p l a y i n g l i t t l e o r no h y p e r f i n e c o u p l i n g w h i c h i s r e c o g n i z e d  as b e i n g  c h a r a c t e r i s t i c o f t h i s type of r a d i c a l where a l a r g e f r a c t i o n of the t o t a l s p i n d e n s i t y i s l o c a l i z e d on a t e r m i n a l s u l f u r atom. The c h l o r o d i s u l f a n y l r a d i c a l (C1SS) has been p o s t u l a t e d as an i n t e r m e d i a t e by Johnson and S e t s e r ^ ^ " ^ who s t u d i e d the i n f r a r e d 1  chemiluminescence from t h e r e a c t i o n o f hydrogen atoms w i t h s u l f u r monochloride ( S ^ C ^ ) .  T h i s r a d i c a l has a l s o been suggested t o be o  r e s p o n s i b l e f o r a t r a n s i e n t band s t r u c t u r e a t 2974 - 3390 A i n the  - 116 -  f l a s h p h o t o l y s i s o f S C1_ by Donovan e_t a l .  (142)  0  process  i n the p h o t o l y t i c d e c o m p o s i t i o n  The  primary  has been suggested t o be  the h o m o l y t i c  f i s s i o n o f the C1S-SC1 bond f o l l o w e d by r a d i c a l a t t a c k  on the parent  species  hv  (l)  s ci  (2)  CIS- + S C 1  2  2  2  *•  2C1S-  2  I n v i e w o f these p r o p o s a l s , i t i s thought t h a t m a t r i x  isolation  would p r o v i d e an e x c e l l e n t means o f i s o l a t i n g and i d e n t i f y i n g t h e r a d i c a l s p e c i e s formed i n the p h o t o l y t i c d e c o m p o s i t i o n  9.2  of  S2CI2.  R e s u l t s and D i s c u s s i o n S u l f u r monochloride  (S2CI2)  was d i l u t e d w i t h one o f the  three  r a r e gas m a t r i c e s , neon, argon o r k r y p t o n t o a c o n c e n t r a t i o n o f R:M ,1mm:20mm.  The sample was i r r a d i a t e d d u r i n g d e p o s i t i o n , w i t h a h i g h  p r e s s u r e mercury lamp and EPR s i g n a l s were produced w i t h i n a s h o r t p e r i o d o f time (^ 10 m i n ) .  I t was found t h a t t h i s method produced  the b e s t y i e l d o f the r a d i c a l , w h i l e d e p o s i t i o n o f the sample f o l l o w e d by UV i r r a d i a t i o n produced somewhat l e s s i n t e n s e s i g n a l s .  Gradual  warming o f the m a t r i x had no e f f e c t on the spectrum, p r o d u c i n g a g r a d u a l d e c r e a s e i n the o v e r a l l i n t e n s i t y .  only  The sample was checked  f o r p a r t i a l o r i e n t a t i o n by r o t a t i n g the d e p o s i t i o n s u r f a c e through 90° but no changes i n the l i n e i n t e n s i t i e s were o b s e r v e d .  Upon  - 117 -  examining t h e t a r g e t r o d a f t e r t h e experiment, formed on the copper s u r f a c e .  a b l a c k d e p o s i t had  A s u s p i c i o n arose that the r a d i c a l s  formed d u r i n g t h e i n i t i a l i r r a d i a t i o n were r e a c t i n g w i t h t h e copper s u r f a c e and were c o n t r i b u t i n g t o the EPR spectrum.  This s u s p i c i o n  was q u i c k l y d i s p e l l e d when i d e n t i c a l r e s u l t s were o b t a i n e d w i t h a s i l v e r plated target surface. 9.1.  A t y p i c a l spectrum i s shown i n F i g .  The f o u r c l o s e l y spaced low f i e l d l i n e s a r e expected  for a  c h l o r i n e c o n t a i n i n g s p e c i e s s i n c e the n u c l e a r s p i n o f c h l o r i n e i s 3/2.  The r e l a t i v e l y s m a l l c o u p l i n g s a r e i n d i c a t i v e o f a c h l o r i n e  with a small spin density (cf.  C100).  The h i g h f i e l d  transitions  a r e o b v i o u s l y n o t due t o a s i m p l e c h l o r i n e h y p e r f i n e i n t e r a c t i o n s i n c e a t l e a s t seven t r a n s i t i o n s a r e observed.  The wide s p a c i n g  o f the h y p e r f i n e components i s a l s o i n d i c a t i v e o f a v e r y s t r o n g g tensor anisotropy.  Before attempting  t o determine the s p i n  Hamiltonian parameters, the p o s s i b l e decomposition CI2S2  products of  are considered. S2CI2  has an S-S bond and a s t r u c t u r e s i m i l a r t o ^ C ^ . The  most l i k e l y i n i t i a l d e c o m p o s i t i o n  products are  C1SS*  and CIS* formed  by the h o m o l y t i c c l e a v a g e o f t h e S - C l and S-S bond r e s p e c t i v e l y . Two f a c t o r s a r e i n f a v o u r o f t h e former p r o c e s s .  Were t h e S-S bond  b r o k e n , t h i s would l e a d t o t h e d i a t o m i c s p e c i e s CIS- w h i c h , i n t h e n e g l i g i b l e c r y s t a l f i e l d o f an i n e r t m a t r i x , would e x h i b i t  axial  symmetry which i s c l e a r l y n o t c o m p a t i b l e w i t h t h e observed  spectrum.  A l s o , i f t h e bond e n e r g i e s i n CF^SSCF^ a r e c o n s i d e r e d ^"^"^ , t h e C-S bond has a bond energy o f 2 . 0 eV. as compared t o 3 . 9 eV f o r t h e  - 118 -  Fig.  9.1  Observed EPR spectrum of the m a t r i x a t 4.2 K.  S2CI  r a d i c a l i n an argon  -  SS bond.  I t i s expected  119 -  t h a t C1^2  w  i H be q u i t e s i m i l a r i n t h i s  r e s p e c t and the S-S bond s h o u l d then remain i n t a c t and f i s s i o n o f the C l - S bond would o c c u r . by Donovan e_t al_.  w  T h i s c o n t r a d i c t s the p r o c e s s  h o propose an SCI i n t e r m e d i a t e w h i c h sub-  s e q u e n t l y a b s t r a c t s a c h l o r i n e atom from the p a r e n t SCI2  and C 1 S S .  suggested  S2CI2  t o form  T h i s p r o c e s s i s not c o n s i d e r e d l i k e l y h e r e because  of the low c o n c e n t r a t i o n of ^ C ^ and the r e l a t i v e l y s h o r t f l i g h t p a t h between the s p r a y o r i f i c e and the copper t a r g e t  5mm).  Subsequent r e a c t i o n i n the s o l i d phase i s a l s o c o n s i d e r e d  unlikely.  There does however appear t o be a broad u n d e r l y i n g resonance i n t h e spectrum which may be due t o i m p u r i t i e s i n the  It i s  S2CI2.  r e a s o n a b l y c e r t a i n t h e n , t h a t the s p e c i e s can be a s s i g n e d t h e structure C1SS. In s u l f u r c o n t a i n i n g s p e c i e s o f t h i s t y p e , the h i g h l y a n i s o t r o p i c g t e n s o r dominates the s p e c t r a l p a t t e r n and w i t h many s m a l l c h l o r i n e c o n t a i n i n g r a d i c a l s , t h e r e i s u s u a l l y found t o be a (35) s u b s t a n t i a l quadrupole  c o u p l i n g ( c f . CIG^,  t h i s r a d i c a l s h o u l d be no e x c e p t i o n .  C100, C1C0  ) and  Indeed, i f an attempt  t o f i t the spectrum w i t h o n l y the Zeeman and h y p e r f i n e  i s made  parameters,  the agreement i s v e r y poor i n the h i g h f i e l d p o r t i o n o f the spectrum where even i n c l u s i o n of the n u c l e a r Zeeman terms cannot account the observed  seven l i n e p a t t e r n .  i n c l u d i n g quadrupole  for  The s p i n H a m i l t o n i a n f o r the system  i s g i v e n by Eqn.  [2.23].  I f the m a t r i x elements  of t h i s H a m i l t o n i a n a r e c o n s i d e r e d , i t becomes c l e a r t h a t the  quadrupole  term QD has i t s maximum e f f e c t on those h y p e r f i n e components w h i c h  - 120 -  are  o r t h o g o n a l t o t h e d i r e c t i o n o f QD.  The i n c l u s i o n o f t h e  quadrupole term w i l l a l t e r t h e expected f o u r l i n e p a t t e r n o f a s p i n 3/2 n u c l e u s t o an e x t e n t depending on t h e r e l a t i v e magnitudes o f A and Q.  A g r a p h i c i l l u s t r a t i o n o f t h i s i s g i v e n by B l e a n e y ^ ^ . 7  I t i s c l e a r from t h e appearance o f t h e spectrum i n F i g . 9.1 t h a t t h e low f i e l d l i n e s appear r e l a t i v e l y u n a f f e c t e d by t h e quadrupole s i n c e they a r e almost e q u a l l y spaced and o f n e a r l y e q u a l intensity. the  A g a i n , t h e m a t r i x elements o f t h e H a m i l t o n i a n show t h a t  h y p e r f i n e component p a r a l l e l t o t h e maximum quadrupole c o u p l i n g  s h o u l d be a f f e c t e d t h e l e a s t by the q u a d r u p o l e .  Now the quadrupole  c o u p l i n g t e n s o r s h o u l d be dominated by the d i r e c t i o n o f t h e CIO bond^ to  1 2 7  ^ and i t i s f o r t h i s r e a s o n t h a t t h i s d i r e c t i o n i s a s s i g n e d  t h e component e x h i b i t i n g t h e maximum g s h i f t .  With t h i s  assignment s e v e r a l guesses were made a t t h e magnitudes and Q t e n s o r s (which a r e i n i t i a l l y  initial  o f t h e g, A  assumed t o have c o l i n e a r  axes)  and t h e powder l i n e s h a p e was s i m u l a t e d u s i n g these parameters. Through t r i a l and e r r o r v a r i a t i o n , a r e a s o n a b l e f i t t o t h e observed spectrum was o b t a i n e d .  T h i s f i t was then r e f i n e d u s i n g a l e a s t  squares f i t t i n g p r o c e d u r e on t h e o b s e r v a b l e t r a n s i t i o n s . r e f i n e d f i t was o b t a i n e d , the n a t u r a l abundance.  When t h e  37, C I i s o t o p e was superimposed  i n the 37  T h i s s i m u l a t i o n p r e d i c t e d peaks due t o t h e C I  i s o t o p e t o l i e between l i n e s G and H, H and I and L and M i n F i g . 9.1. In  an attempt t o d e t e c t t h e s e t r a n s i t i o n s , t h e r e g i o n was scanned  155 t i m e s , w i t h t h e r e s u l t s o f each scan b e i n g accumulated by a time a v e r a g i n g computer.  The r e s u l t s of t h i s scan a r e shown i n t h e  - 121 -  inset  t o F i g . 9.L  A weak t r a n s i t i o n i s d i s c e r n i b l e  between l i n e s and  H and L and M b u t the resonance between H and I i s l o s t i n t h e t a i l of the l a t t e r ' s  resonance. (144)  Beagley  e_t a_l  have determined  the s t r u c t u r e o f  e l e c t r o n d i f f r a c t i o n and the C1SS bond a n g l e was found  CI2S2  by  t o be 108.2°.  I f i t i s assumed t h a t the bond a n g l e does n o t change a p p r e c i a b l y on r a d i c a l f o r m a t i o n , the r a d i c a l w i l l have a s t r o n g l y bent  structure.  In t h i s case the A and Q t e n s o r s can be assumed t o have t h e i r  tensor  axes p a r a l l e l and have the CIS bond as one p r i n c i p a l d i r e c t i o n . g t e n s o r , however, may be more determined  The  by the S-S bond and may  tend t o have one p r i n c i p a l d i r e c t i o n d e f i n e d by t h i s bond.  From t h e  l i m i t e d symmetry of C1SS, the d i r e c t i o n p e r p e n d i c u l a r t o t h e m o l e c u l a r p l a n e must n e c e s s a r i l y be common f o r one component o f t h e t h r e e tensors. to t h i s  I t must be d e c i d e d then which component s h o u l d be a s s i g n e d direction.  S i n c e one g t e n s o r component was found t o l i e v e r y c l o s e t o f r e e s p i n w h i l e the o t h e r two t e n s o r components were s t r o n g l y s h i f t e d d o w n f i e l d , i t i s r e a s o n a b l e t o s u s p e c t t h a t C1SS i s a "TT t y p e " radical.  This,  c o u p l e d w i t h the f a c t t h a t the maximum h y p e r f i n e  component i s a l s o a l o n g t h i s d i r e c t i o n and t h a t t h e r e i s a s m a l l i s o t r o p i c c o u p l i n g , i s f a i r l y s t r o n g e v i d e n c e t h a t t h i s i s the case. The assignment of t h e t e n s o r components t o t h e m o l e c u l a r axes o f C1SS i s as f o l l o w s :  the component e x h i b i t i n g  the minimum g - s h i f t i s  p e r p e n d i c u l a r t o the r a d i c a l p l a n e ( y ) ; the i n t e r m e d i a t e g s h i f t i s i n the p l a n e o f the r a d i c a l and a p p r o x i m a t e l y p e r p e n d i c u l a r t o t h e  - 122 -  CIS bond ( x ) ; t h e component w i t h t h e maximum g s h i f t i s p a r a l l e l to  t h e CIS bond ( z ) . W i t h t h i s assignment  t h e n , t h e a n g l e between  the g and A/Q t e n s o r s i n the p l a n e o f the r a d i c a l was v a r i e d w h i l e u s i n g the l e a s t squares a n a l y s i s t o f i t t h e observed l i n e p o s i t i o n s . A t an a n g l e o f about 10° between these t e n s o r d i r e c t i o n s t h e b e s t f i t between observed and c a l c u l a t e d l i n e p o s i t i o n s was a c h i e v e d . T h i s i s i n r e a s o n a b l e agreement w i t h t h e CNDO/2 and INDO/2 c a l c u l a t i o n s which p r e d i c t a bond a n g l e o f about 100°. parameters  The r e s u l t i n g  ( d i a g o n a l i n t h e i r own frame) a r e compiled i n T a b l e 9.1  and t h e s i m u l a t e d spectrum i s shown i n F i g . 9.2. The a x i s i s d e s c r i b e d i n F i g . 9.3. the s i m u l a t e d  system  The l i n e p o s i t i o n s were measured from  spectrum and the r e s u l t s a r e g i v e n i n T a b l e 9.2.  The agreement i s seen t o be b e t t e r than .4 gauss.  The o n l y  d i s c r e p a n c y between t h e observed and c a l c u l a t e d spectrum i s t h a t the i n t e n s i t i e s o f t h e l i n e s on t h e h i g h f i e l d s i d e o f t h e sharp c e n t r a l t r a n s i t i o n a r e n o t e x a c t l y reproduced.  This r e s u l t i s  n o t r e a d i l y e x p l a i n e d s i n c e t h e i n t e n s i t y p a t t e r n o f the low f i e l d components i s w e l l  reproduced.  S i n c e s e v e r a l " f o r b i d d e n " t r a n s i t i o n s were observed i n t h e h i g h f i e l d p o r t i o n o f t h e spectrum, and the two c e n t r a l sharp l i n e s have a d i s t i n c t "break", t h e s e f e a t u r e s were used as a c r i t e r i o n for  d e t e r m i n i n g t h e r e l a t i v e s i g n s g i v e n i n T a b l e 9.1. S i m u l a t i o n s  w i t h r e l a t i v e s i g n s o t h e r than those shown produced a s i g n i f i c a n t l y p o o r e r f i t t o t h e observed  spectrum.  The c h l o r i n e h y p e r f i n e t e n s o r f o r C1SS can be seen t o be v e r y anisotropic.  T h i s a n i s o t r o p y can r e s u l t from t h e one c e n t e r and two  - 123 -  F i g . 9.2  Computer s i m u l a t e d EPR spectrum of the S CI r a d i c a l .  - 124 -  g. 9.3  R e l a t i o n of the s p i n H a m i l t o n i a n parameters t o the m o l e c u l a r axes i n the S C1 r a d i c a l . 9  - 125 -  TABLE 9-1 E x p e r i m e n t a l l y determined  p r i n c i p a l values o f the s p i n Hamiltonian  parameters o f the  § 1  g  S  2  A  3  S2CI  A  x  (cm 2.0019  2.0225  (-.0002)  (-.0002)  2.0384  radical.  -5.9  (-.0002) (-.2)  A  2  3  - 1 4 xlO )  QD  QE (cm  +1.3  +3.5  +5.65  (-.2)  (±.2)  (-.2)  - 1 4 xlO ) -.1 (-.2)  The p r i n c i p a l d i r e c t i o n s o f the t e n s o r components a r e shown i n F i g . 9.3.  TABLE 9.2 Comparison of e x p e r i m e n t a l and c a l c u l a t e d v a l u e s f o r the EPR spectrum o f t h e S C 1 i n argon. 2  Peak  A B C D E F G H I J K L M  Observed p o s i t i o n (gauss) 3314.2 3317.9 3321.4 3325.0 3343.8 3348.0 3363.6 3369.5 3374.3 3379.6 3386.2 3389.7 3396.5  Calculated position (gauss) 3314.2 3317.8 3321.3 3325.0 3343.5 3347.7 3363.6 3369.2 3374.6 3379.6 3385.9 3389.7 3396.7  - 126 -  center  contributions to the c h l o r i n e hyperfine  tensor  described  g e n e r a l l y i n Appendix B and Chapter S i x , or from s p i n p o l a r i z a t i o n of t h e C l - S sigma bond or a c o m b i n a t i o n o f b o t h .  The f o l l o w i n g  a n a l y s i s shows t h a t t h e c o n t r i b u t i o n from two c e n t e r  terms i s  l i k e l y t o be s m a l l . U s i n g t h e method o f Appendix B, the two c e n t e r  i n t e g r a l s were  o  c a l c u l a t e d f o r a C l - S bond l e n g t h o f 2.057 A and an e f f e c t i v e nuclear  charge o f 5.45 f o r s u l f u r .  The t o t a l c o n t r i b u t i o n s o f  S "CI S S "CI s i n t e g r a l s o f the type <x3p |0 |x3p > and < 3 p J o J x 3 > were x  -4 -1 found t o be (-.26, - . 1 6 , .42) x 10 cm and (-.48, - . 4 8 , .96) x z  -4 10  -1 cm  respectively.  Even i f t h e s p i n d e n s i t y on t h e c e n t r a l  s u l f u r were r e a s o n a b l y l a r g e , these i n t e g r a l s would n o t c o n t r i b u t e significantly.  I t i s reasonable to neglect  a l l two c e n t e r  terms  i n any f u r t h e r a n a l y s i s . The t o t a l t e n s o r and  can be decomposed a c c o r d i n g  t o Eqn. [6.11]  the two a x i a l t e n s o r s a r e +1.62  T XX  T yy T zz _ (Again,  =  +2.37  ±5.48  ±4.73  =  +3.87  "±..75 ' ±.75  +  +2.37 _  _  +1.50 _  t h i s a n a l y s i s assumes t h a t the 3p o r b i t a l on c h l o r i n e does  not s i g n i f i c a n t l y c o n t r i b u t e . )  This a n a l y s i s suggests that  there  i s a p o s i t i v e s p i n d e n s i t y i n t h e c h l o r i n e 3p^ o r b i t a l and n e g a t i v e s p i n d e n s i t y i n t h e 3p  (which would be r e q u i r e d by s p i n p o l a r i z a t i o n ) .  - 127 -  T h i s a n a l y s i s i s a l s o c o n s i s t e n t w i t h t h e assignment o f t h e s m a l l e s t p r i n c i p a l v a l u e of the h y p e r f i n e c o u p l i n g constant  (A^) t o t h e  d i r e c t i o n p e r p e n d i c u l a r t o t h e CIS bond and i n t h e m o l e c u l a r  plane.  The s p i n d e n s i t i e s c a l c u l a t e d from t h e above r e s o l u t i o n a r e CI CI p 3 p = .04 and p 3 p = -.01. y  z  The s p i n d e n s i t i e s p r e d i c t e d from t h e  CI CI INDO/2 c a l c u l a t i o n s a r e p3p = .002 and p3p = -.04. The n u m e r i c a l X  z  agreement i s r a t h e r poor and t h e INDO/2 r e s u l t s would r e q u i r e t h e l a r g e s t h y p e r f i n e c o u p l i n g component t o l i e a l o n g t h e CIS bond w h i c h i s c l e a r l y i n c o m p a t i b l e w i t h t h e observed  results.  The c a l c u l a t i o n s  ' t h e n , tend t o o v e r e s t i m a t e t h e c o r e p o l a r i z a t i o n w h i l e the 3 p - s p i n d e n s i t y on c h l o r i n e . S  de-emphasizing  The Fermi c o n t a c t term i s p r e d i c t e d  to be p o s i t i v e (p3 - = .0002) and s m a l l , s u g g e s t i n g t h a t t h e i n n e r s g  o r b i t a l s on c h l o r i n e a r e b e i n g p o l a r i z e d by t h e 3 s - e l e c t r o n d e n s i t y l e a d i n g t o an o v e r a l l p o s i t i v e c o r e p o l a r i z a t i o n . The quadrupole  c o u p l i n g c o n s t a n t f o r C1SS i s a l s o o f some  interest.  The observed  v a l u e s o f t h e quadrupole  correspond  t o a pure quadrupole  f a i r agreement w i t h t h e observed  coupling constant  resonance o f 33.9 MHz w h i c h i s i n quadrupole  resonance o f 35.6 and  35.99 MHz f o r c h l o r i n e i n t h e p a r e n t $ 2 ^ 2 • quadrupole c o u p l i n g c o n s t a n t can be e s t i m a t e d from t o t a l e l e c t r o n d i s t r i b u t i o n C  around t h e c h l o r i n e n u c l e u s a p p r o x i m a t i o n s .  T  n  e  The f i e l d g r a d i e n t i n  the z d i r e c t i o n can be w r i t t e n as i n s i m p l e one c e n t e r  approximation  (127,146) as  V  zz  =  occ £ P..q ! ^—' 11 11 L  e  1  [8.1]  - 128 -  where P i s t h e bond o r d e r m a t r i x o r t o t a l d e n s i t y m a t r i x and  «ii  =  < +  l  -  IV  ^T 1  [8  2]  where 0 and r a r e the a n g l e and d i s t a n c e between t h e e l e c t r o n and the n u c l e u s .  e Qq  The quadrupole  2  = °f] P . . e Q q ? : v i i at 2  z  c o u p l i n g c o n s t a n t can be w r i t t e n as  C1  [8-3]  C  I  2 CI CI where e Q q i s the atomic quadrupole  coupling f o r a valence -4 -1  s h e l l p - e l e c t r o n and has t h e v a l u e 109.75 MHz  (36.6 x 10  cm  ).  U s i n g t h e r e l a t i o n s h i p [2.20] t h i s can be e x p r e s s e d i n terms o f the quadrupole  c o u p l i n g c o n s t a n t s QD and QE.  Using these a p p r o x i -  m a t i o n s , the e s t i m a t e d quadruple c o u p l i n g c o n s t a n t s a r e t a b u l a t e d i n T a b l e 9.3.  The r e s u l t s w h i l e o n l y f a i r i n agreement w i t h the  observed v a l u e tend t o c o n f i r m t h e s i g n c h o i c e of QD as b e i n g n e g a t i v e a l o n g the C l - S bond d i r e c t i o n .  - 129 -  TABLE 9.3 35 INDO/2 , CNDO/2 c a l c u l a t i o n o f t h e coupling constant i n C1S  Total electron density i n CI 3p o r b i t a l s . Z  C I quadrupole 9  QD  QE _, , (cm x l O )  1.9958  1.9984  1.1756  -7.52  .01  INDO(a)  1.9943  1.9967  1.2269  -7.04  .01  INDO(b)  1.9968  1.9969  1.5558  -7.71  .01  CNDO(a)  1.9954  1.9976  1.2077  -7.22  .01  CNDO(b)  (a)  U s i n g Benson and Hudson p a r a m e t e r i z a t i o n .  (b)  Using Santry p a r a m e t e r i z a t i o n .  CHAPTER TEN  R a d i c a l R e a c t i o n s w i t h SO^ 10.1  Introduction The  r e a c t i o n o f SC^ w i t h v a r i o u s m o l e c u l a r and atomic  species  has been t h e s u b j e c t o f many k i n e t i c s t u d i e s i n t h e l a s t decade m a i n l y because o f i t s i n v o l v e m e n t i n many o f t h e c h e m i c a l r e a c t i o n s o c c u r r i n g i n t h e upper atmosphere and a l s o because o f i t s i n d u s t r i a l significance.  The r e a c t i o n can be e a s i l y i n i t i a t e d by c h e m i c a l o r  p h o t o c h e m i c a l p r o c e s s e s and t h e r e a c t i o n mechanisms w h i c h a r e proposed a r e g e n e r a l l y complex and remain somewhat u n c e r t a i n . Generally, the intermediates  i n v o l v e d cannot be i d e n t i f i e d , and  t h e i r e x i s t e n c e can o n l y be i n f e r r e d from an a n a l y s i s o f t h e p r o d u c t s . The  k i n e t i c s o f t h e r e a c t i o n between hydrogen atoms and SC^  have been determined u s i n g v a r i o u s t e c h n i q u e s ' * ^  150)  r e a c t i o n between m e t h y l and e t h y l r a d i c a l s w i t h SG^ has been f o l l o w e d a t v a r i o u s temperatures i n t h e gas p h a s e - ^  3  )  >  r e s u l t s o f these f i n d i n g s i n d i c a t e t h a t complex r e a c t i o n paths a r e f o l l o w e d and i t has been suggested t h a t t h e f i r s t s t e p i n t h e reaction i s  R- + S 0  2  (+M)  >  RSCy  (+M)  - 131 -  E l e c t r o n paramagnetic resonance (EPR) s t u d i e s have been c a r r i e d out on t h e r e a c t i o n between trapped h y d r o c a r b o n polymers and S C ^ ^ " ^ , the r e s u l t s i n d i c a t i n g h y d r o c a r b o n - s u l p h o n y l recently, Adrian et a l . ^ ^ ^ ^  have o b t a i n e d  r a d i c a l formation. t h e NaSO^ r a d i c a l  More  species  by c o - d e p o s i t i o n o f a beam of sodium atoms w i t h a beam o f 1% SC^ i n argon and have determined t h e a n i s o t r o p i c components o f t h e g and A tensors.  M o r t o n and P r e s t o n ^ ' ^ ^ have a l s o r e c e n t l y c a r r i e d o u t  an EPR study o f t h e p h o t o c h e m i c a l r e a c t i o n o f h y p o f l u o r i t e s w i t h compounds o f t e t r a v a l e n t s u l p h u r . was p h o t o l y s e d  I n p a r t i c u l a r , when a h y p o f l u o r i t e  i n the presence o f SC^, a d d i t i o n o f b o t h t h e R0-  and F* fragments t o SC^ was observed t o g i v e t h e ROSC^ and FSC^ radical species.  I n a l l cases o n l y t h e i s o t r o p i c g and A t e n s o r  v a l u e s were r e p o r t e d . The  EPR s p e c t r a d e s c r i b e d h e r e were o b t a i n e d when hydrogen atoms,  f l u o r i n e atoms and m e t h y l r a d i c a l s were p h o t o l y t i c a l l y generated i n a k r y p t o n o r argon m a t r i x a t 4 K c o n t a i n i n g ^ 1% SC^.  The a n i s o t r o p i c  Zeeman and h y p e r f i n e t e n s o r s from t h e w e l l r e s o l v e d s p e c t r a w i l l be analysed  i n terms o f non c o i n c i d e n t g and A t e n s o r s .  Reactions of  the type suggested above occur i n t h e case o f hydrogen and f l u o r i n e atoms.  M e t h y l r a d i c a l s a l s o r e a c t b u t t h e t r u e n a t u r e o f the adduct  is uncertain. W h i l e these r e s u l t s may n o t be d i r e c t l y a p p l i c a b l e t o t h e k i n e t i c s i n t h e gas phase, they do demonstrate t h a t r a d i c a l of the type RSC^ a r e v i a b l e i n t e r m e d i a t e s .  species  - 132 -  10.2 R e s u l t s and D i s c u s s i o n 10.2.1  R e a c t i o n s of H Atoms w i t h  An HI/S02/Kr m i x t u r e was  S2 n  p h o t o l y z e d f o r a p p r o x i m a t e l y 15  minutes.  D u r i n g t h i s p e r i o d a broad s i g n a l w i t h u n r e s o l v e d  structure  appeared  c e n t e r e d on g = 2 as w e l l as the expected  atom s i g n a l s s e p a r a t e d by about 506 gauss. resulted  Continued i r r a d i a t i o n  i n an i n c r e a s e i n i n t e n s i t y of these two s i g n a l s .  m a t r i x was  then a l l o w e d to warm t o about 30 K.  up a weak p a i r of t r i p l e t s appeared,  The  D u r i n g the warm-  s e p a r a t e d by about 110 gauss  and g r a d u a l l y i n c r e a s e d i n i n t e n s i t y as the sample increased.  H  temperature  A t about 30 K, the k r y p t o n m a t r i x began d i f f u s i n g  from the d e p o s i t i o n s u r f a c e and each t r i p l e t had merged i n t o a s i n g l e l i n e i n d i c a t i n g t h a t i s o t r o p i c motion of t h e s p e c i e s had begun.  The sample was  then r e c o o l e d to 4.2  K.  The  isotropic  d o u b l e t a g a i n s p l i t i n t o a w e l l r e s o l v e d p a i r of t r i p l e t s ( F i g . 10.1)  i n d i c a t i n g t h a t a s i n g l e s p e c i e s w i t h orthorhombic  had formed.  The sample was  a g a i n a l l o w e d to warm and the i n t e n s i t y  of t h e s e l i n e s were observed t o i n c r e a s e i n d i c a t i n g a r e a c t i o n was o c c u r r i n g . species  symmetry  I t now  remains  further  t o i d e n t i f y the r a d i c a l  formed.  The p h o t o c h e m i s t r y o f SO2 has been w e l l s t u d i e d and  dissociation  of SO2 i n t o SO and oxygen atoms i s known not to o c c u r u n t i l 2180A  ( 7 7 )  which i s w e l l above the energy s u p p l i e d by the h i g h  p r e s s u r e mercury lamp.  The most l i k e l y r e a c t i o n which can o c c u r  then i s the a t t a c k o f H atoms on the SO2 m o l e c u l e . reaction  i s n o t observed  to occur a t 4.2  S i n c e the  K but o n l y on warming,  -  133  -  4J 25 G  a'bl  Observed EPR spectrum of the HSO^ k r y p t o n m a t r i x a t 4.2 K.  radical in a  - 134  -  the H atoms a r e supposed to d i f f u s e through t h e m a t r i x and r e a c t on e n c o u n t e r i n g an SC^ m o l e c u l e . for  There are two p o s s i b l e p o s i t i o n s  a t t a c k , e i t h e r a t the s u l p h u r or oxygen atoms, r e s u l t i n g i n  the symmetric s t r u c t u r e HSC^  or the asymmetric OSOH.  The l a r g e  i s o t r o p i c s p l i t t i n g of 1 1 2 gauss, i n d i c a t e s t h a t t h e r e i s a subs t a n t i a l s p i n d e n s i t y i n the hydrogen I s o r b i t a l and t h i s would be c o n s i s t e n t w i t h the symmetric s t r u c t u r e where the hydrogen i s a t t a c h e d t o the c e n t e r c o n t a i n i n g the u n p a i r e d e l e c t r o n .  The  asymmetric form would p l a c e the hydrogen too f a r from the u n p a i r e d e l e c t r o n t o g i v e an i s o t r o p i c c o u p l i n g of the s i z e observed. c a l c u l a t i o n s have been performed  INDO  f o r these two i s o m e r i c s t r u c t u r e s ,  u s i n g the known s t r u c t u r a l parameters l e n g t h s f o r HS and OH of 1 . 3 3 A and  for . 9 9 A.  S02^~^  and assumed bond  They show t h a t the  u n p a i r e d e l e c t r o n i s c o n c e n t r a t e d on the s u l f u r and t h a t the s p i n d e n s i t y on hydrogen i s about a f a c t o r of t e n l a r g e r i n the symmetric form.  The r a d i c a l s t r u c t u r e i s t e n t a t i v e l y a s s i g n e d then as the  s y m m e t r i c a l form  HSO2.  The geometry of t h i s form was  estimated  from the INDO c a l c u l a t i o n s , a minimum energy b e i n g a c h i e v e d when t h e HS bond was.45° below the very l i k e l y  S0  2  plane ( F i g .  10.2).  I t i s thus  t h a t the g and A t e n s o r s i n t h i s r a d i c a l w i l l be  c o i n c i d e n t and any f u r t h e r a n a l y s i s must take t h i s i n t o  non-  account.  S i n c e t h e r e a r e o n l y s i x l i n e p o s i t i o n s o b s e r v a b l e i n the powder spectrum  (any f o r b i d d e n t r a n s i t i o n s w i l l be h i d d e n i n the  broad c e n t r a l e n v e l o p e ) , t h e r e i s i n s u f f i c i e n t d a t a a v a i l a b l e to determine  the a n g l e between the t e n s o r s .  There i s a l s o the a d d i t i o n a l  - 135 -  Fig.  10.2  R e l a t i o n of the s p i n H a m i l t o n i a n parameters t o the m o l e c u l a r axes i n the HS0 r a d i c a l . o  - 136 -  problem, i n h e r e n t i n a n a l y s i n g any p o l y c r y s t a l l i n e spectrum, o f determining  t h e p a i r i n g o f l i n e s and a s s i g n i n g t h e c o r r e s p o n d i n g  p r i n c i p a l d i r e c t i o n s of the tensors.  Fortunately i n s e v e r a l of  the t r a i l s , p a r t i a l o r i e n t a t i o n was observed ( F i g . 10.3). was a c h i e v e d  This  by n o t a l l o w i n g the sample t o warm t o t h e p o i n t where  i s o t r o p i c m o t i o n began, b u t s i m p l y warming enough t o a l l o w some d i f f u s i o n o f t h e H atoms. molecules are deposited  I t i s q u i t e p r o b a b l e t h a t the SG^  i n some p a r t i a l l y o r i e n t e d manner as i s  (34) (34) observed w i t h s i m i l a r t r i a t o m i c m o l e c u l e s ( N C ^ , C l O ^ , NF 2  If the SC^ molecules are o r i e n t e d p r e f e r e n t i a l l y w i t h t h e i r planes p a r a l l e l t o t h e f l a t d e p o s i t i o n s u r f a c e , subsequent a t t a c k by t h e d i f f u s i n g hydrogen atoms may n o t d e s t r o y  this partial orientation.  I t would be expected t h a t i n t h e p y r a m i d a l the o r b i t a l c o n t a i n i n g the u n p a i r e d d i r e c t e d along the pyramidal  type s t r u c t u r e o f H S G ^ ,  e l e c t r o n on s u l f u r would be  a x i s and thus c o n s t i t u t e a " u n i q u e "  d i r e c t i o n i n the r a d i c a l .  I f t h i s o r b i t a l were a l s o d i r e c t e d  close to the perpendicular  from t h e r o d f a c e , then a marked change  i n t h e i n t e n s i t y o f t h e l i n e components a r i s i n g from t h i s d i r e c t i o n s h o u l d be o b s e r v a b l e  on r o t a t i o n o f t h e r o d f a c e by 90° such t h a t  the o r b i t a l would be d i r e c t e d p a r a l l e l t o t h e magnetic Such a change i n i n t e n s i t y does indeed  field.  occur, with the c c ' l i n e  component ( F i g . 10.1) i n c r e a s i n g i n i n t e n s i t y w h i l e t h e i n t e n s i t i e s of t h e o t h e r two components d e c r e a s e . observation  On t h e b a s i s o f t h i s  t h e l i n e p a i r c c ' i s e s t a b l i s h e d and we a s s i g n t o i t  the d i r e c t i o n o f t h e p y r a m i d a l  axis.  T h i s assignment w i l l s h o r t l y  ).  Fig.  10.3  E f f e c t of r o t a t i n g the sample d e p o s i t i o n s u r f a c e by  90°.  - 138 -  be f u r t h e r c o r r o b o r a t e d by an a n a l y s i s o f t h e g t e n s o r .  A problem  now a r i s e s o f d e t e r m i n i n g t h e p r i n c i p a l g and A t e n s o r v a l u e s f o r t h i s d i r e c t i o n s i n c e t h e g and A t e n s o r s w i l l undoubtedly  be non-  c o i n c i d e n t and i t i s n o t e v i d e n t w h i c h t e n s o r w i l l dominate t h e EPR spectrum. S i n c e HSG^ has  symmetry, the a x i s p e r p e n d i c u l a r t o t h e  symmetry p l a n e must be a common a x i s f o r b o t h t h e g and A t e n s o r s , w h i l e t h e r e m a i n i n g two p r i n c i p a l axes o f these t e n s o r s do'not n e c e s s a r i l y have t o be c o i n c i d e n t .  I t was shown i n Chapter  Four,  t h a t when t h e d i f f e r e n c e ( i n gauss) between t h e two components o f the A t e n s o r , which a r e i n the m o l e c u l a r symmetry p l a n e , i s o f t h e same o r d e r of magnitude as t h e d i f f e r e n c e ( i n gauss) between t h e c o r r e s p o n d i n g g t e n s o r components, then t h e l i n e p o s i t i o n s observed i n t h e powder spectrum do n o t n e c e s s a r i l y c o r r e s p o n d  t o t h e case  where t h e f i e l d  i s o r i e n t e d p a r a l l e l to e i t h e r the p r i n c i p a l g or  A t e n s o r axes.  U s i n g an assumed a n g l e o f 20° ( F i g . 10.2) f o r  r o t a t i n g t h e A-frame out o f t h e g-frame ( t h e r e a s o n f o r t h i s c h o i c e of a n g l e w i l l be e x p l a i n e d s h o r t l y ) , i t was p o s s i b l e t o d e t e r m i n e the f i e l d o r i e n t a t i o n w h i c h would produce l i n e p o s i t i o n s w h i c h correspond  t o t h e observed  of t h e observed at  line positions.  A l e a s t squares a n a l y s i s  powder l i n e p o s i t i o n s was then performed t o a r r i v e  t h e p r i n c i p a l components o f the g and A t e n s o r s .  T h i s was  c a r r i e d o u t f o r t h e two p o s s i b l e c h o i c e s f o r t h e l i n e p a i r i n g o f the r e m a i n i n g  f o u r powder t r a n s i t i o n s and a l s o f o r t h e two p o s s i b l e  c h o i c e s o f a x i s assignment s i n c e one s e t o f axes w i l l l i e i n t h e  - 139 -  r o t a t e d frame w h i l e t h e o t h e r s e t (g and A i n F i g . 10.2) a r e y y n e c e s s a r i l y c o i n c i d e n t by symmetry.  The t e n s o r s were a l s o c a l c u l a t e d  assuming c o - l i n e a r g and A t e n s o r s w i t h t h e r e s u l t t h a t o f f d i a g o n a l components o f t h e g t e n s o r c o u l d be c o n s i d e r e d n e g l i g i b l e and t h e g v a l u e s measured would be w i t h i n e x p e r i m e n t a l values.  e r r o r the p r i n c i p a l  The o f f d i a g o n a l components o f t h e A t e n s o r a r e s i g n i f i c a n t  and a r e dependent on t h e s i z e o f t h e a n g l e chosen between t h e g and A t e n s o r s .  I n t h e event t h a t t h e chosen a n g l e i s out by ± 10° -4 -1  the e r r o r i n t h e p r i n c i p a l v a l u e s would be no more than .5 x 10 The  cm  r e s u l t s o f t h i s a n a l y s i s a r e summarized i n T a b l e 10.1. The  h y p e r f i n e t e n s o r s have been s e p a r a t e d the a n i s o t r o p i c components.  i n t o i s o t r o p i c c o u p l i n g and  The p o l y c r y s t a l l i n e s p e c t r a w h i c h a r e  s i m u l a t e d u s i n g these parameters ( F i g . 10.4) assuming a 20° a n g l e between t h e g and A t e n s o r s i n t h e x,z p l a n e , w i l l o b v i o u s l y appear identical and  ( n e g l e c t i n g o f course  t h e unobserved f o r b i d d e n t r a n s i t i o n s )  t h e agreement between t h e s i m u l a t i o n and t h e observed spectrum  is excellent.  To d e t e r m i n e i f any o f these f o u r p o s s i b l e c h o i c e s  i s p r e f e r r e d , a comparison w i t h a s i m i l a r s p e c i e s might be enlightening. R a d i c a l s o f t h i s type t h a t have been p r e v i o u s l y observed a r e H C 0 ^  7  \  and FCO^O)  a  n  (  j they e x h i b i t t h e l a r g e i s o t r o p i c  w h i c h i s c h a r a c t e r i s t i c o f a h i g h l y bent a r a d i c a l . r a d i c a l which i s v a l e n c e  The H I S K ^ ^ " ^  i s o e l e c t r o n i c w i t h HSO^ has been found t o  be o n l y s l i g h t l y bent and t h e r e f o r e has a s m a l l i s o t r o p i c coupling.  coupling  hyperfine  M o r t o n ^ " ' ^ has s t u d i e d t h e r a d i c a l s formed i n i r r a d i a t e d  ammonium h y p o p h o s p h i t e and has i d e n t i f i e d one s p e c i e s as  HPO2  which  - 140 -  Hi  10.4  2 5 6  >i  Computer s i m u l a t e d EPR spectrum of the HSO^ r a d i c a assuming the n o n - c o i n c i d e n t a x i s system of F i g . 10  TABLE 10.1 Principal  V a l u e s f o r t h e S p i n H a m i l t o n i a n :Parameters f o r the HS0  H y p e r f i n e components 8  A  y  A X  y  A z  T. ISO  -1  f  (cm  T X  2  Radical.  4 x 10 ) T y  line pair T  t  x; z  z  2 .0028  2.0071  2.0082  ±103.6  ±101.0  ±109.8  ±104.8  +1.2  +3.8  ±5.0  ba ;ab *  2 .0028  2.0065  2.0090  ±104.1  ±103.1  ±107.3  ±104.8  + .7  +1.7  ±2.4  bb ;aa  2 .0028  2.0090  2.0065  ±104.8  ±106.8  ±102.7  ±104.8  0.  ±2.0  +2.0  aa';bb  2 .0028  2.0083  2.0070  ±105.3  ±108.9  ±100.2  ±104.8  ± .5  ±4.1  +4.6  ab' ;ba  2 .0019  2.0037  2.0035  ± 75.7  ± 74.7  ± 79.4  ±76.6  + .9  +1.9  ±2.8  * R e f . 18 (HP0 ) 2  t L i n e p a i r s r e f e r t o F i g . 10.1  1  1  - 142 -  i s i s o e l e c t r o n i c w i t h HSG^ and might be expected t o e x h i b i t characteristics.  similar  I n HPO^ t h e u n p a i r e d e l e c t r o n has been shown t o  occupy a a type o r b i t a l on phosphorous d i r e c t e d a l o n g t h e p y r a m i d a l axis.  From t h e s i n g l e c r y s t a l a n a l y s i s , the non c o l i n e a r i t y o f t h e  Zeeman and hydrogen h y p e r f i n e t e n s o r was e s t a b l i s h e d t o be 27° and the d e v i a t i o n from p l a n a r i t y o f the m o l e c u l e t o be about 60° - i e . the a n g l e between t h e H-P bond and t h e PG^ p l a n e .  I t was on t h i s  b a s i s t h a t t h e a n g l e between t h e g and A t e n s o r s i n HSC>2 was chosen as 20° ( s l i g h t l y l e s s than one h a l f t h e a n g l e between t h e HS bond and t h e SC^ p l a n e as determined from t h e INDO c a l c u l a t i o n s ) . i s noted t h a t i n  HPO2  the d i r e c t i o n of the pyramidal axis  to the minimum g - s h i f t from g about t h i s d i r e c t i o n .  g  corresponds  and t h a t t h e g t e n s o r i s n e a r l y  axial  The H-P bond d i r e c t i o n c o r r e s p o n d s t o t h e  l a r g e s t h y p e r f i n e c o u p l i n g and e x h i b i t s near a x i a l i t y about axis.  It  this  The a s s i g n e d p r i n c i p a l t e n s o r s i n t h e a x i s system s i m i l a r t o  F i g . 10.2 a r e g i v e n i n T a b l e 10.1 f o r comparison. By s t r i c t analogy w i t h  HPO2  i s t i c s and a p p l i e d them t o the  we have taken the b a s i c c h a r a c t e r -  HSO2  radical.  In a d d i t i o n to the  e v i d e n c e from p a r t i a l o r i e n t a t i o n , t h e assignment o f t h e c c ' l i n e p a i r as b e i n g a s s o c i a t e d w i t h t h e p y r a m i d a l a x i s d i r e c t i o n i s based on t h e o b s e r v a t i o n t h a t t h i s i s a l s o t h e p a i r which e x h i b i t s t h e minimum g - s h i f t .  Attempts t o f i t t h e spectrum w i t h l i n e p a i r s o t h e r  than c c ' r e s u l t e d i n g - v a l u e s which were much h i g h e r than g » I f e  the near a x i a l i t y o f t h e g and A t e n s o r s i n  HPO2  can be used as a  c r i t e r i o n f o r comparison, case (a) and (d) (Table 10.1) a r e t o be  - 143 -  s l i g h t l y p r e f e r r e d s i n c e they a r e c l o s e r t o b e i n g a x i a l than cases (b) and ( c ) , and case (a) would be p r e f e r r e d over (d) s i n c e t h e d i r e c t i o n o f maximum A i s a l o n g t h e H-S bond i n t h e former as i s the case w i t h HPG^.  T h i s analogy cannot be c a r r i e d t o o f a r however,  because o f t h e d i f f e r e n t c r y s t a l environments e x p e r i e n c e d  i n the  two c a s e s , t h e s i n g l e c r y s t a l environment p r o v i d i n g a l a r g e r p e r t u r b a t i o n than the r a r e gas m a t r i x . discrepancy  I n an attempt t o r e s o l v e t h e  a r i s i n g from t h e l i n e p a i r i n g , an experiment was performed  u s i n g HI e n r i c h e d t o about 10% i n D I . U n f o r t u n a t e l y t h e decreased c o u p l i n g s o f t h e d e u t e r i u m s p e c i e s caused t h e l i n e s t o l i e c o m p l e t e l y w i t h i n t h e broad c e n t r a l a b s o r p t i o n . h i g h e r microwave frequency  Experiments performed a t a  would a i d t h e d e t e r m i n a t i o n o f t h e l i n e  p a i r i n g due t o t h e i n c r e a s e d s i g n i f i c a n c e o f t h e g t e n s o r  anisotropy.  To c o n f i r m t h e assignment o f t h e t e n s o r o r i e n t a t i o n and t h e l i n e p a i r i n g a t h e o r e t i c a l e s t i m a t e o f t h e EPR parameters i s n e c e s s a r y . The a n i s o t r o p y o f t h e g t e n s o r i s v e r y s m a l l and t h e o r e t i c a l e s t i m a t i o n of t h e g - s h i f t s from t h e r e l a t i v e l y poor INDO w a v e f u n c t i o n s would n o t be r e l i a b l e .  S i n c e t h e MO c a l c u l a t i o n s show t h a t  HSO2  i s a a radical,  the l a r g e i s o t r o p i c h y p e r f i n e i n t e r a c t i o n i s due t o p o s i t i v e s p i n density at the proton.  This i s c o n s i s t e n t w i t h the c a l c u l a t e d s p i n  d e n s i t y i n t h e hydrogen i s o r b i t a l o f .3 w h i c h r e p r e s e n t s an a p p r o x i -4 mate i s o t r o p i c h y p e r f i n e c o u p l i n g o f ^ 139 x 10 ment w i t h t h e observed v a l u e s .  -1 cm  i n f a i r agree-  The l a r g e i s o t r o p i c c o u p l i n g i n d i c a t e s  2 t h a t t h e ground s t a t e i s A' as t h i s would p r o v i d e t h e n e c e s s a r y m i x i n g between t h e A' o r b i t a l s on s u l f u r and t h a t on hydrogen.  It is  -  -  144  r e a s o n a b l e t h e r e f o r e to assume t h a t  the major c o n t r i b u t i o n  to  the  a n i s o t r o p y i n the hydrogen h y p e r f i n e t e n s o r w i l l a r i s e from d i r e c t contributions  of the u n p a i r e d e l e c t r o n  d e n s i t y i n the  o r b i t a l s to the hydrogen o r b i t a l , i e . the d i p o l a r m o l e c u l a r o r b i t a l s i n HSC^ of A'  can  be  interaction.  symmetry o r b i t a l s , composed of s-,  z axis refers  to the H-S  p e r p e n d i c u l a r to t h i s and o r b i t a l s on s u l f u r are  p ,  and  -  p- o r b i t a l s where  w i t h the A'  o r b i t a l s and  w i l l be n e g l e c t e d .  tion.  The  the x a x i s i s  i n the symmetry p l a n e .  S i n c e the  symmetry, they cannot mix  their contribution  The  the o v e r a l l t e n s o r but  z  bond d i r e c t i o n and  of A"  to the  p-  efficiently  total  tensor  spin p o l a r i z a t i o n w i l l also contribute i t s e f f e c t w i l l be n e g l e c t e d i n the  small contribution  The  r e p r e s e n t e d as a l i n e a r c o m b i n a t i o n  X  the  sulfur  to  calcula-  from the oxygen o r b i t a l s w i l l a l s o  be  neglected. The  dipolar  i n t e r a c t i o n i s r e p r e s e n t e d by  i n t e g r a l s <x3p |0 S  X  |x3p > and  H  S  01 Oi  <x3p |o S  X  Z  H  the  |x3p >. S  QLQL  two  center  These were  calculated  Z  u s i n g a S l a t e r 3p-atomic o r b i t a l i n a manner d e s c r i b e d i n Appendix An  e f f e c t i v e n u c l e a r charge of 5.45  average H-S  bond l e n g t h was  was  chosen f o r s u l f u r and  chosen from a f a m i l y  o  compounds to be  1.33  A.  B.  an  of HS-type —  For  calculations  on HPG^  a P-H  bond l e n g t h  o  of 1.54  A and  an e f f e c t i v e n u c l e a r charge of 4.8  were chosen.  The  show t h a t  form of the d i p o l a r  the  i n the x and direction.  i n t e g r a l s f o r HSO^  y directions  and  are g i v e n i n T a b l e 10.2  t e n s o r w i l l be  l a r g e r and  Similar calculations  f o r phosphorous  s m a l l and  p o s i t i v e i n the  on HP0„ i n d i c a t e  z  and negative (bond)  the same shape f o r  - 145 -  TABLE 10.2 P r e d i c t e d A n i s o t r o p i c H y p e r f i n e Tensor Components f o r HS0  <3p |0 |3p > x  H  x  <3p |0 |3p > z  H  z  Total  -.03  -10.8  -1.32  -7.32  -10.8  -2.45  9  +7.35  +21.6  +3.77  p3  ? x  = .154  p3p^ = .122 z  - 146 -  the t e n s o r .  S i n c e HPC^ and HSO^ a r e i s o e l e c t r o n i c , t h e s p i n d e n s i t y  d i s t r i b u t i o n s s h o u l d be s i m i l a r .  The INDO c a l c u l a t i o n s f o r  HSO2  and  HPO„ show t h a t the s p i n d e n s i t i e s i n t h e p - and p - o r b i t a l s on s u l f u r 2  X  Z.  and phosphorous were lower by ^ 10% i n HSC^ w h i l e the hydrogen sdensity i s higher i n the observed  HSO2  couplings.  by ^ 25% w h i c h i s a g a i n c o n s i s t e n t w i t h U s i n g the known d i p o l a r t e n s o r f o r  HPO2  the s p i n d e n s i t i e s i n t h e 3p - and 3p - o r b i t a l s were c a l c u l a t e d X  2  from t h e v a l u e s g i v e n by t h e d i p o l a r i n t e g r a l s .  These s p i n d e n s i t i e s  were then reduced by ^ 10% and t h e d i p o l a r t e n s o r f o r calculated.  The c a l c u l a t e d t e n s o r f o r  HSO2  HSO2  was  i s seen t o f i t c l o s e l y  to c h o i c e s (a) and ( b ) , w h i l e n o t a g r e e i n g w i t h t h e near a x i a l tensors f o r choices  (c) and ( d ) .  The above c a l c u l a t i o n s a r e o f  c o u r s e dependent on the bond l e n g t h s chosen f o r each s p e c i e s and a l s o on the v a l u e s o f t h e o r b i t a l exponents.  I t i s possible that  b e t t e r o r b i t a l exponents may be chosen and t h a t t h e average bond l e n g t h s chosen a r e n o t a c c u r a t e , b u t t h e g e n e r a l shape o f t h e t e n s o r w i l l n o t be a l t e r e d s i g n i f i c a n t l y by even r e l a t i v e l y l a r g e v a r i a t i o n s i n these parameters.  I t i s f e l t that the r e s u l t s a r e s i g n i f i c a n t  enough t o a l l o w t h e d i p o l a r t e n s o r s (a) and (b) t o be chosen over (c) and ( d ) . due  A c h o i c e between (a) and (b) may n o t be s i g n i f i c a n t  t o t h e s m a l l d i f f e r e n c e s between t h e t e n s o r s .  10.2.2  R e a c t i o n o f F l u o r i n e Atoms w i t h SO?  M i x t u r e s o f CF^OF and SO2 i n argon were s u b j e c t e d t o i r r a d i a t i o n w i t h a h i g h p r e s s u r e mercury lamp.  ( I n i t i a l l y a low  - 147 -  p r e s s u r e mercury lamp was thought n e c e s s a r y  b u t produced no s i g n a l . )  A r e l a t i v e l y complex and i n t e n s e a b s o r p t i o n was observed about g = 2.  centered  T h i s i n i t i a l spectrum has n o t been a n a l y z e d b u t i s  presumably due t o CF^O r a d i c a l .  Continued  i r r a d i a t i o n produced  weak a b s o r p t i o n s i n t h e o u t e r wings composed o f a p a i r o f t r i p l e t s c e n t e r e d about g = 2 ( F i g . 10.5).  The most n o t a b l e f e a t u r e i s t h e  v e r y l a r g e c o u p l i n g e x h i b i t e d by t h e o u t e r p a i r o f l i n e s o f about 267 gauss.  The g e n e r a l shape o f t h e spectrum i n d i c a t e s t h a t t h e  s p e c i e s formed c o n t a i n s f l u o r i n e i n a p o s i t i o n i n w h i c h i t possesses considerable spin density. formed i s The  FSO2  I t i s very l i k e l y that the species  i n a r e a c t i o n s i m i l a r t o t h a t which produced  HSO2  lower s o f t e n i n g p o i n t o f argon has presumably a l l o w e d t h e  r e a c t i o n t o proceed w i t h o u t t h e warming w h i c h was n e c e s s a r y k r y p t o n m a t r i x used f o r  HSO2,  with  t h e s o f t e n i n g e f f e c t b e i n g produced  by t h e r e l a t i v e l y h i g h IR output o f t h e h i g h p r e s s u r e lamp. To c o n f i r m t h e assignment o f t h e r a d i c a l s p e c i e s as sulfuryl fluoride  (SO2F2)  FSO2,  was i r r a d i a t e d i n an argon m a t r i x w i t h a  hydrogen resonance lamp and y i e l d e d a v e r y complex spectrum w i t h s e v e r a l species present  ( F i g . 10.6).  One s p e c i e s w h i c h seems t o  be i n v a r i a b l y i n c l u d e d i n a l l e x p e r i m e n t s u s i n g a hydrogen resonance lamp i s t h e CH~. r a d i c a l .  The complete removal o f a l l o r g a n i c t r a c e s  from t h e sample gases and contaminants i n t r o d u c e d from s m a l l undetected  leaks i s extremely  difficult.  p r e s e n t i s due t o c o n t a m i n a t i o n fluoride.  The o t h e r r a d i c a l s p e c i e s  o f t h e s u l f u r y l f l u o r i d e by t h i o n y l  The s i m i l a r i t y between t h e i r b o i l i n g and m e l t i n g p o i n t s  - 148 -  - 149 -  Fig.  10.6  Observed EPR spectrum o f the F S O 2 r a d i c a l i n an argon m a t r i x a t 4.2 K (formed by the UV p h o t o l y s i s of  F S0 ). 2  2  - 150  -  makes f r a c t i o n a l d i s t i l l a t i o n as a p u r i f i c a t i o n t e c h n i q u e impossible.  The  i n pure  and has been a s s i g n e d  F2SO  i s considered  in  r a d i c a l s p e c i e s formed c o r r e s p o n d s e x a c t l y t o t h a t  F2SO2  mixture  mixtures.  CF2OF/SO2  The  g e t i c a l l y more f a v o u r a b l e  i n t e r a c t i o n of two  The  as  sample was  radical  c o r r e s p o n d s e x a c t l y t o t h a t observed l o s s of f l u o r i n e from  F2SO2  i s ener-  powder p a t t e r n than observed due  equivalent fluorines.  species i s assigned  remaining  On  to rewarm i n o r d e r to o b t a i n the  e v e n t u a l l y l o s t due  to v a p o u r i z a t i o n .  change i n the r e l a t i v e i n t e n s i t i e s of the components was  p a i r i n g and be made.  The detectable  observed.  t h e r e i s the ambiguous c h o i c e of  HSO2,  isotropic  observed  a l s o checked f o r p a r t i a l o r i e n t a t i o n , however no  A g a i n as w i t h  the  this basis, radical  c o u p l i n g but o n l y a g r a d u a l d e c r e a s e i n the i n t e n s i t y was  sample was  to  FSO2.  allowed  u n t i l the sample was  which  than l o s s of an oxygen w h i c h would a l s o  produce a more c o m p l i c a t e d  The  to the r a d i c a l s p e c i e s FSO  a d e t a i l i n Chapter E i g h t .  s p e c i e s i n the  virtually  line  t e n s o r o r i e n t a t i o n and s e v e r a l i n i t i a l assumptions must  I t i s reasonable  of the spectrum, (a) and  to assume t h a t the two  o u t e r components  (c') a r e a s s o c i a t e d w i t h the same d i r e c t i o n  i n the m o l e c u l e as o t h e r w i s e  u n r e a s o n a b l e g - v a l u e s a r i s e f o r the  components i n t h i s type of r a d i c a l .  Also since  FSO2  would  expected t o be a a type r a d i c a l , the l a r g e s t h y p e r f i n e s h o u l d be i n the m o l e c u l a r  plane.  INDO c a l c u l a t i o n s do  be  coupling indeed  2  i n d i c a t e that t h a t Walsh ^-'^  FSO2  has  a  A' ground s t a t e .  predicts that  FP0„,  I t might a l s o be n o t e d  which i s i s o e l e c t r o n i c w i t h  FS0„  - 151 -  s h o u l d be non p l a n a r .  Refinements on t h e m o l e c u l a r geometry u s i n g  t h e s t r u c t u r a l parameters o f F2S0-2''^^ i n d i c a t e s t h a t t h e F-S bond i s about 25° from the SG^ p l a n e .  The g and A t e n s o r s w i l l most  l i k e l y be n o n - c o i n c i d e n t i n t h i s case as w e l l  ( F i g . 10.7).  Using  t h e same arguments as were used f o r HS02» t h e a n g l e between g and A t e n s o r s has been assumed t o be 10°.  Since the anisotropy of the  A t e n s o r i s v e r y much l a r g e r than the g - a n i s o t r o p y , t h e powder l i n e s observed  a r e due t o t h e f i e l d b e i n g o r i e n t e d a l o n g t h e  A t e n s o r axes and o n l y the " e f f e c t i v e " g-values  principal  can be measured.  The o f f d i a g o n a l components o f t h e g t e n s o r w i l l be s m a l l however, and the non c o l i n e a r i t y o f t h e t e n s o r s may be n e g l e c t e d w i t h o u t s e v e r e e r r o r , b u t f o r completeness, non c o i n c i d e n t .  Least-squares  t h e t e n s o r s w i l l be assumed  f i t t i n g o f t h e powder l i n e p o s i t i o n s  r e s u l t e d i n t h e v a l u e s i n T a b l e 10.3 w h i c h a r e a g a i n r e p r e s e n t e d as a s e p a r a t i o n o f t h e i s o t r o p i c and a n i s o t r o p i c components.  The  l i n e s h a p e i n F i g . 10.8 was s i m u l a t e d u s i n g t h e parameters f o r t e n s o r (a) s i n c e t h e r e a r e a g a i n f o u r p o s s i b l e t e n s o r c h o i c e s each o f w h i c h w i l l e x a c t l y s i m u l a t e t h e spectrum. In  t h i s a n a l y s i s , the s p i n d e n s i t y i n the f l u o r i n e s - o r b i t a l  has been assumed t o be p o s i t i v e r e s u l t i n g i n a l a r g e p o s i t i v e -4 -1 i s o t r o p i c c o u p l i n g o f 132 x 10 cm and an i s o t r o p i c g-value o f 2.0026.  T h i s i s i n e x c e l l e n t agreement w i t h t h e i s o t r o p i c v a l u e s  r e p o r t e d f o r t h i s s p e c i e s by M o r t o n and P r e s t o n ' " ^ o f 130 t o 134 x -4 -1 10 . cm f o r t h e h y p e r f i n e t e n s o r and an i s o t r o p i c g v a l u e o f 2.0026.  - 152  A g z  Fig.  10.7  -  z  R e l a t i o n of the s p i n H a m i l t o n i a n parameters to the m o l e c u l a r axes i n . the FS0„ r a d i c a l .  - 153 -  TABLE 10.3 P r i n c i p a l Components o f t h e S p i n H a m i l t o n i a n Parameters f o r the FS0„ R a d i c a l .  H y p e r f i n e components (cm x l O )  g  x  g  y  g  z  A  A  A  X  y  T. z  T  T  ISO  X  y  line pair T  x; z z  2 .0014  2 .0016  2 .0049  ±79. 6  ±66..2  ±250. 3  ±132.  +52.4  +65. 8  ±118. 3  bb' ;ca  2 .0016  2 .0014  2 .0049  ±66. 2  ±79.,6  ±250. 3  ±132.  +65.8  +52. 4  ±118. 3  ca';bb  2 .0037  1 .9994  2 .0049  ±72. 7  ±73..0  ±250. 3  ±132.  +59.3  +59. 0  ±118. 3  ba';cb  1 .9994  2 .0037  2 .0049  ±73. 0  ±72..7  ±250. 3  ±132.  +59.0  +59. 3  ±118. 3  cb';bc  ±.0002  f L i n e p a i r s r e f e r t o F i g . 3.  ±.2  - 155 -  T h i s a l s o agrees remarkably  w e l l w i t h t h e p r e d i c t e d INDO s p i n  d e n s i t y i n the F 2 s o r b i t a l o f .005 w h i c h g i v e s an i s o t r o p i c h y p e r -4 f i n e c o u p l i n g o f 130 x 10  -1 cm  The a n i s o t r o p y o f t h e f l u o r i n e h y p e r f i n e t e n s o r w i l l  undoubtedly  be dominated by i t s own m o l e c u l a r o r b i t a l s and a f f e c t e d t o a s m a l l e r e x t e n t by the a n i s o t r o p y i n t r o d u c e d by t h e c o n t r i b u t i o n from t h e neighbouring  sulfur orbitals.  The e f f e c t o f s p i n p o l a r i z a t i o n  will  not be c o n s i d e r e d n o r w i l l t h e c o n t r i b u t i o n from t h e oxygen porbitals.  The a n i s o t r o p i c t e n s o r can be r e p r e s e n t e d by a form  s i m i l a r t o those o f Eqn. [ 6 . 7 ] .  The f i r s t t h r e e terms i n t h e  e x p r e s s i o n a r e t h e one c e n t e r c o n t r i b u t i o n u s i n g t h e INDO s p i n densities.  The c o n t r i b u t i o n o f t h e one c e n t e r term g i v e s t h e  a n i s o t r o p i c t e n s o r shown i n T a b l e 10.4. The c o m b i n a t i o n  o f t h e two  c e n t e r terms has been e v a l u a t e d s e p a r a t e l y t o i l l u s t r a t e t h a t  these  c o n t r i b u t i o n s a r e much l e s s than t h e one c e n t e r terms, and t h a t a one c e n t e r c a l c u l a t i o n g i v e s an adequate r e p r e s e n t a t i o n .  The a n i s o -  t r o p i c h y p e r f i n e t e n s o r i s then p r e d i c t e d t o have t h e major component p a r a l l e l t o t h e F-S bond and t h e i n t e r m e d i a t e component p e r p e n d i c u l a r to  t h e m o l e c u l a r p l a n e o f symmetry.  T h i s then a l l o w s a c h o i c e t o  be made between t h e f o u r axes and l i n e p a i r i n g c h o i c e s i n T a b l e 10.3. Only t h e case (a) f i t s t h e observed spin densities for  FSO2  tensor adequately.  Had t h e  n o t been a v a i l a b l e , t h e treatment  using  2  Eqn.  [6.9] would have p r e d i c t e d t h e same r e s u l t s (c = .01, c  2  = .1)  ( t a k i n g i n t o account t h a t t h e two c e n t e r terms a r e n e g l e c t e d ) b u t no c h o i c e c o u l d have been made between cases  (a) and ( d ) .  - 156 -  TABLE 10.4 P r e d i c t e d A n i s o t r o p i c H y p e r f i n e Components f o r the F S 0  2  radical. y  F i "F 2 > 0 x a  2px r  F  F  "F  2p r  P  1  -58.70  0  z  5.87  -2.94 -58.7  -2.94 117.4  F  = .005  P2p, P2p.  = .1  P3p  = .09  a  3 | 0 3P > *x a S  F  S  P  -.11  -.47  .58  .18  ,18  -.37  -1.28  .65  .63  X  3z V ' a P  r  3  3  P  S  |0  *x P r  S  z  1  F  a  |0 a  F  1  2p > x F  r  -.02  P3p„ „S  F  P3p 2p x  3.61  3.61  -7.23  = -.02 x  p3p 2p c  z  S S  c  = .05  z  = .111 XX  = -.244 zz  Total  -50.4  -57.6  108.7  i n cm - x l O" 1  4  - 157  10.2.3  -  R e a c t i o n of m e t h y l r a d i c a l s w i t h  A m i x t u r e of CH.JI/SO2/A  . 1mm:.. 1mm: 10mm)  w i t h a h i g h p r e s s u r e mercury lamp. w h i c h was  due  observed  spectrum.  The  photolyzed  and no o t h e r  secondary  On a l l o w i n g the m a t r i x t o warm to about  30 K and then r a p i d l y r e c o o l i n g to 4.2 r a d i c a l s p e c i e s was  a t 4.2K  I n i t i a l l y , an i n t e n s e spectrum  to m e t h y l r a d i c a l s was  s p e c i e s c o u l d be d e t e c t e d .  SO^  K, a weak, broad.secondary  d e t e c t e d which o v e r l a p p e d  the m e t h y l  radical  i r r a d i a t i o n of CH^I/A or SO2/A m i x t u r e s d i d not  produce t h i s s p e c i e s .  The new  r a d i c a l d i d not appear to e x h i b i t  any h y p e r f i n e s p l i t t i n g and showed o n l y the c h a r a c t e r i s t i c s of a r a d i c a l species possessing a n o n - a x i a l g-tensor.  The  three  observable  l i n e s are marked w i t h arrows i n F i g . 11.10, and have g-values 2.042, 2.010  and 2.002.  The l i n e a t g = 2.010  overlapped s t r o n g l y  w i t h a m e t h y l r a d i c a l h y p e r f i n e component and t h i s g-value what more u n c e r t a i n than the o t h e r two components. s e v e r a l p r o d u c t s w h i c h might be formed  of  i s some-  There a r e  i n t h i s mixture.  The a d d i t i o n  of i o d i n e atoms to SO2 i s u n l i k e l y because of i t s l a r g e s i z e and i t s l a c k of m o b i l i t y i n the r a r e gas l a t t i c e .  An i o d i n e atom has  n u c l e a r s p i n I = 5/2  t o produce a h y p e r f i n e  and would be expected  p a t t e r n i f a d d i t i o n t o SO2 o c c u r r e d . g = 2.042 was  not observed  a  The o u t e r l i n e component a t  i n the p h o t o l y s i s of H I / S O 2 m i x t u r e s  and i t i s thus u n l i k e l y t h a t t h i s s p e c i e s i s due  t o i o d i n e atom  addition. I t i s p o s s i b l e f o r CH^  r a d i c a l s to m i g r a t e through  l a t t i c e a t h i g h e r temperatures  and  to r e a c t w i t h the S 0  the r a r e gas o  molecules  - 158 -  Fig.  10.9  Observed EPR spectrum of the r a d i c a l s p e c i e s formed on UV p h o t o l y s i s of a CH I/SO /A m i x t u r e a t 4.2 K.  - 159 -  i n a manner s i m i l a r to hydrogen and f l u o r i n e atoms w i t h the a d d i t i o n o c c u r r i n g a t the s u l f u r o r oxygen atoms.  I f the a d d i t i o n were to  o c c u r a t the s u l f u r atom, a g t e n s o r s i m i l a r to t h a t observed f o r HSC>2 and FSO^  would be e x p e c t e d .  The s p i n d e n s i t y i n t h i s s y m m e t r i c a l  a d d i t i o n r a d i c a l would be l a r g e l y c o n c e n t r a t e d on the s u l f u r atom. The hydrogen atoms would then be i n a g p o s i t i o n r e l a t i v e to the s u l f u r atoms and would be expected to e x h i b i t the l a r g e h y p e r f i n e (68)  c o u p l i n g s which a r e observed i n s i m i l a r a l k y l r a d i c a l analogs  ,  and s i n c e t h i s i s not observed h e r e , the s y m m e t r i c a l a d d i t i o n r a d i c a l i s not a l i k e l y s t r u c t u r e .  I f the a d d i t i o n of a m e t h y l r a d i c a l were  t o occur a t the oxygen of SC^ to form the a s y m m e t r i c a l r a d i c a l CH^OSO.  In t h i s c a s e , the u n p a i r e d e l e c t r o n may  have an a p p r e c i a b l e  s p i n d e n s i t y on the t e r m i n a l oxygen atom w h i c h c o u l d produce a s t r o n g s h i f t i n the g f a c t o r s .  The h y p e r f i n e i n t e r a c t i o n of the p r o t o n s  would a l s o be expected to be v e r y s m a l l i n t h i s c a s e . The p r e s e n t e x p e r i m e n t a l e v i d e n c e i s n o t s t r o n g enough t o u n e q u i v o c a l l y e s t a b l i s h the s t r u c t u r e of t h i s r a d i c a l s p e c i e s and f u r t h e r experiments must be performed.  The p h o t o l y s i s of CD^I/SC^  m i x t u r e s would e s t a b l i s h whether the observed l i n e s a r e due t o a g f a c t o r a n i s o t r o p y and would c o n f i r m the l a c k of h y p e r f i n e c o u p l i n g .  CHAPTER ELEVEN  Chlorine Dioxide, ClO^ 11.1  Introduction C h l o r i n e d i o x i d e (CIC^) i s one o f t h e few s t a b l e f r e e r a d i c a l s  and  i n t h i s r e s p e c t i t becomes a r e l a t i v e l y easy compound t o study  by EPR s i n c e i t s f o r m a t i o n i s unnecessary.  through c h e m i c a l  reaction or photolysis  There have been many e x t e n s i v e EPR s t u d i e s on C I C ^  . . (161-167) , . . ..,(126,168-170) , . in solution and i n t h e s o l i d s t a t e and a l s o . . . * (171,172) i n t h e p o l y c r y s t a l l i n e s t a t e adsorbed on s u r f a c e s or (123) dissolved i n a frozen solvent considered  . Only one o f these s t u d i e s has  t h e l a r g e quadrupole c o u p l i n g o f t h e c h l o r i n e n u c l e u s  v * .(173,174) and E x t e n s i v e microwave s t u dj .i e s u have a l-s o . been performed the a n i s o t r o p i c h y p e r f i n e , Zeeman and quadrupole t e n s o r s a r e thus known f o r t h e gas phase and from EPR f o r t h e s o l i d s o r g l a s s e s . A study o f t h i s s p e c i e s i n a n o n - p o l a r m a t r i x would thus an e x c e l l e n t study  f o r comparison w i t h  CIO2  The paramagnetic p r o p e r t y o f C l O ^ p e r m i t s concentrations  of  CIO2  i n t h e " f r e e " gas s t a t e .  t h e use o f e x t r e m e l y low  i n t h e t r a p p i n g m a t r i x thus a l l o w i n g t h e wide  separation of neighbouring decreasing  provide  paramagnetic c e n t e r s , and thereby  any i n t e r a c t i o n s w i t h nearby  CIO2  molecules.  I t has been  - 161 -  shown i n s t u d i e s i n v o l v i n g t h e t r a p p i n g o f atoms i n i n e r t  matrices,  t h a t they can i n t e r a c t s u b s t a n t i a l l y w i t h t h e r a r e gas m a t r i x t o produce a c h a r a c t e r i s t i c s h i f t i n t h e Zeeman and h y p e r f i n e (8,9,13,14,66)  _ The  , . . t h e o r y developed t o e x p l a i n these  tensors  . ._ (66) shifts  has n o t been extended t o trapped paramagnetic m o l e c u l e s and s e m i q u a l i t a t i v e arguments based on t h e g e n e r a l t h e o r y o u t l i n e d i n Chapter F i v e w i l l be used.  11.2  I n t e r p r e t a t i o n of the Spectra CIG^ was d i l u t e d i n a neon, argon o r k r y p t o n m a t r i x t o a  c o n c e n t r a t i o n o f R;M ^ .1mm:300mm.  T h i s d i l u t i o n was found t o  g i v e e x c e p t i o n a l l y w e l l r e s o l v e d s p e c t r a w i t h no a p p r e c i a b l e b r o a d e n i n g due t o s p i n - s p i n c o u p l i n g o f nearby CIC^ n e i g h b o u r s . The powder spectrum observed i n argon i s shown i n F i g . 11.1 w i t h the magnetic f i e l d o r i e n t e d p a r a l l e l t o t h e f l a t f a c e o f t h e r o d on w h i c h t h e sample i s d e p o s i t e d .  F i g . 11.2 shows t h e e f f e c t o f  r o t a t i n g t h e d e p o s i t i o n s u r f a c e by 90°. Large changes i n t h e i n t e n s i t i e s o f t h e v a r i o u s l i n e components a r e i n d i c a t i v e o f t h e phenomenon o f p a r t i a l o r i e n t a t i o n , which h a s been w i d e l y observed . , _ . . . (14,19,34,76) i n many cases where r a d i c a l s a r e trapped i n t h e r a r e gases The  e f f e c t o f p a r t i a l o r i e n t a t i o n w i l l be d i s c u s s e d i n more d e t a i l  later. From t h e e l e c t r o n i c spectrum o f C I C ^ ' " ^ , t h e ground s t a t e has 7  2 been e s t a b l i s h e d t o be  B^ i n which t h e u n p a i r e d  e l e c t r o n occupies  2 the  B^ o r b i t a l on c h l o r i n e .  This o r b i t a l i s anti-symmetric  respect t o r e f l e c t i o n i n the molecular  plane.  with  C1C>2 i s thus a " T f - t y p e "  - 162 -  Fig.  11.1  E x p e r i m e n t a l EPR spectrums of CIC^ i n an argon m a t r i x at 4.2 K. H i s p a r a l l e l to the r o d f a c e .  - 163 -  F i g . 11.2  E x p e r i m e n t a l EPR spectrum of ClO^ i n an argon m a t r i x . H i s p e r p e n d i c u l a r t o the r o d f a c e . q  - 164  r a d i c a l and  -  s h o u l d be i n t e r p r e t e d a c c o r d i n g l y .  The Walsh c o r r e l a t i o n  (128) diagram  f o r an AJS^ s p e c i e s w i t h 19 e l e c t r o n s i n the v a l e n c e  s h e l l a l s o p r e d i c t s the odd  e l e c t r o n t o occupy a b^ o r b i t a l and  also  s u g g e s t s t h a t the m o l e c u l e i s s t r o n g l y bent and t h i s i s c o n f i r m e d by e l e c t r o n d i f f r a c t i o n s t u d i e s ^ ^ 6 ) ^ ^ t h e o r y of u r a d i c a l s e  would then r e q u i r e t h a t the s m a l l e s t s h i f t i n the g f a c t o r s h o u l d f o r the d i r e c t i o n p a r a l l e l to the TT o r b i t a l i n w h i c h the r e s i d e s and hyperfine  be  electron  t h a t t h i s d i r e c t i o n s h o u l d a l s o e x h i b i t the maximum coupling.  Comparison of the r e l a t i v e changes i n i n t e n s i t i e s made i t apparent t h a t the outermost l i n e s can be a s s o c i a t e d w i t h a unique d i r e c t i o n i n the m o l e c u l e .  Measurement of the h y p e r f i n e  coupling -4  and  g v a l u e f o r t h i s d i r e c t i o n l e a d s t o v a l u e s of 64.52 x 10  and  53.7  and  a g v a l u e of 2.0025.  x 10 ^cm  ^ f o r the h y p e r f i n e  the expected r a t i o of 1:83 magnetic moments and  The  of " ^ C l and  hyperfine  -1 cm  "^Cl respectively  components are c l o s e  to  w h i c h i s e x p e c t e d from the r a t i o of  the i n t e n s i t y r a t i o s of the two 35 37  c l o s e t o the expected r a t i o of .76:.24 ( t h e o r e t i c a l p r e d i c t i o n s t h i s leads ponent of the G and A t e n s o r s  CI:  CI).  isotopes  the are  From the above  to the assignment of t h i s com-  t o the d i r e c t i o n p e r p e n d i c u l a r  to  the m o l e c u l a r p l a n e which i s i n agreement w i t h p r e v i o u s i n t e r p r e t a tions. follows:  I n t h i s i n t e r p r e t a t i o n , the a x i s system i s d e f i n e d the x a x i s i s p e r p e n d i c u l a r  as  t o the m o l e c u l a r p l a n e ;  y a x i s i s p a r a l l e l to the 0-0  bond d i r e c t i o n and  a l o n g the b i s e c t o r of the  symmetry a x i s  the z a x i s i s  ( F i g . 11.3).  For  the  - 165  Fig.  11.3  -  M o l e c u l a r a x i s system f o r C I O 2 (x a x i s i s p e r p e n d i c u l a r to the m o l e c u l a r p l a n e and H i s the f i e l d d i r e c t i o n ) .  - 166 -  c o n v e n i e n c e a l l p o l a r a n g l e s w i l l be d e f i n e d w i t h t h e a n g l e 0 b e i n g measured from t h e x a x i s and t h e a n g l e cp b e i n g measured from t h e y axis. The t e n s o r components of t h e c e n t r a l r e g i o n o f t h e spectrum (Fig.  11.4) where t h e f i e l d  z a x i s must now be a s s i g n e d .  i s approximately  p a r a l l e l t o the y and  T h i s becomes a r a t h e r complex t a s k  because of t h e s t r o n g o v e r l a p o f t h e powder l i n e s i n t h i s r e g i o n . I t i s a l s o t o be expected t h a t " f o r b i d d e n " t r a n s i t i o n s ±1,  (Am^. =  ±2) w i l l c o n t r i b u t e s i g n i f i c a n t l y i n t h i s r e g i o n because of  the i n t e r a c t i o n o f t h e e l e c t r i c f i e l d g r a d i e n t w i t h t h e quadrupole moment o f c h l o r i n e and t h e n u c l e a r Zeeman i n t e r a c t i o n ^ " ^ ^ .  In  g e n e r a l , t h e most i n t e n s e l i n e s i n t h i s r e g i o n a r e a c t u a l l y t h e " f o r b i d d e n " t r a n s i t i o n s s i n c e t h e Am^ = ±1 l i n e s r e a c h t h e i r maximum i n t e n s i t y i n t h e r e g i o n 7O°<0$9O° and the Am^. = ±2 t r a n s i t i o n s (56) r e a c h t h e i r maximum i n t e n s i t y near 0 = 90°  .  Since the allowed  t r a n s i t i o n s show no f i r s t o r d e r e f f e c t o f t h e n u c l e a r Zeeman o r quadrupole c o u p l i n g  (see F i g . 2.1) a l l l e v e l s ; i n v o l v e d i n t h e  Am^. = 0 t r a n s i t i o n a r e s h i f t e d e q u a l l y .  Thus no r e l a t i v e s i g n  i n f o r m a t i o n o f t h e h y p e r f i n e components o r q u a d r u p o l e components can be o b t a i n e d .  However, s i n c e t h e m a j o r i t y o f l i n e s observed  i n t h e c e n t r a l r e g i o n o f t h e spectrum a r i s e from " f o r b i d d e n " t r a n s i t i o n s w h i c h w i l l show f i r s t o r d e r  shifts i n their relative  l i n e p o s i t i o n s w i t h a change i n r e l a t i v e s i g n , t h e assignment of the r e l a t i v e s i g n s o f t h e h y p e r f i n e and q u a d r u p o l e components can be e s t a b l i s h e d .  - 167 -  E x p e r i m e n t a l EPR spectrum of CIC^ (expanded c e n t r a l p o r t i o n of F i g . 11.2).  - 168  -  U s i n g the s i g n c o n v e n t i o n a s s i g n e d by Byberg mate H a m i l t o n i a n  parameters  the s i m u l a t e d spectrum was (Eqn. [ 2 . 2 3 ] ) .  and a p p r o x i -  measured from the observed s p e c t r a ,  computed u s i n g the complete  P l o t s of f i e l d v s . a n g l e ( F i g . 11.5)  Hamiltonian  f o r the  d i r e c t i o n of H v a r y i n g i n the t h r e e p r i n c i p a l p l a n e s , were drawn and compared w i t h the powder p a t t e r n which o b v i o u s , from the appearance of F i g . 11.5  they s i m u l a t e d .  It i s  t h a t a n a l y s i s of the  powder l i n e p o s i t i o n s w i l l be c o m p l i c a t e d by the o c c u r r a n c e of "angular a n o m a l i e s " ^ ^ 5 6  which occur o n l y near 0 = 90°.  (The  v a r i a t i o n of dH/dO near 0 = 0° i s much more r e g u l a r and a n o m a l i e s " a r e absent.)  "angular  The powder l i n e s were then a s s i g n e d a  t r a n s i t i o n type and a f i e l d o r i e n t a t i o n a n g l e (0,<f>) which to  corresponded  the minimum changes i n f i e l d w i t h r e s p e c t t o a n g l e ( e i t h e r  a n g u l a r anomaly or a p r i n c i p a l a x i s d i r e c t i o n ) . f i t t i n g procedure was  then performed  A least  on the H a m i l t o n i a n  A f t e r each r e f i n e m e n t , the f i e l d v s . a n g l e diagram was and t h i s procedure  cycled.  of  the random s i m u l a t i o n do not reproduce  of  the spectrum when H face.  of  partial  parameters. again p l o t t e d  o b t a i n e d assuming a random d i s t r i -  b u t i o n f o r the m o l e c u l a r o r i e n t a t i o n ( F i g . 11.6).  rod  squares  A f t e r successive c y c l i n g , a reasonable  f i t t o the observed spectrum was  q  an  The  intensities  the observed  intensities  i s e i t h e r p a r a l l e l or p e r p e n d i c u l a r t o the  T h i s i s because of the p r e v i o u s l y mentioned phenomenon orientation.  The d i r e c t i o n of p r e f e r e n t i a l o r i e n t a t i o n w i l l now be d i s c u s s e d . In  the p a r a l l e l o r i e n t a t i o n (H  p a r a l l e l to the rod f a c e ) the x  - 169 -  - 170 -  Fig.  11.6  Computer s i m u l a t e d EPR spectrum of C I O 2 u s i n g a c o m p l e t e l y random d i s t r i b u t i o n f u n c t i o n .  - 171  -  component l i n e s a r e seen t o be much weaker than i n the p e r p e n d i c u l a r orientation,  w h i l e t h e converse  i s t r u e f o r the y and z components.  S i n c e i t i s e s t a b l i s h e d t h a t the x component has t h e l a r g e s t  hyper-  f i n e c o u p l i n g , i t can then be supposed t h a t i n t h e p e r p e n d i c u l a r orientation,  t h e r e a r e more m o l e c u l e s  p a r a l l e l t o t h e magnetic f i e l d T h i s suggests  o r i e n t e d w i t h t h e i r x axes  than i n the p a r a l l e l  t h a t the CIG^ m o l e c u l e s  orientation.  are p r e f e r e n t i a l l y oriented  w i t h t h e i r molecular plane p a r a l l e l to the rod s u r f a c e . x components do n o t c o m p l e t e l y d i s a p p e a r i n the p a r a l l e l any f u n c t i o n d e s c r i b i n g t h e o r i e n t a t i o n  S i n c e the orientation,  d i s t r i b u t i o n of the m o l e c u l e s  w i t h r e s p e c t t o the r o d f a c e cannot go t o zero i n the p a r a l l e l orientation. A c y l i n d r i c a l l y symmetric d i s t r i b u t i o n f u n c t i o n can now be (19) a p p l i e d i n a manner analogous t o t h a t used by K a s a i e_t_ a l _ . account f o r p a r t i a l o r i e n t a t i o n orientation positions,  affects  of trapped r a d i c a l s .  to  Since p a r t i a l  o n l y the l i n e i n t e n s i t i e s and n o t the l i n e  a new s e t o f i n t e n s i t i e s T' can be d e f i n e d by T'(0,<j>) =  T(0,cp)P(a)  where T(0,cj)) a r e the p o l y c r y s t a l l i n e between l e v e l s  |mm>  transition  probabilities  and |m'm|> and P(a) i s a d i s t r i b u t i o n  f u n c t i o n where a i s t h e a n g l e between t h e r o d s u r f a c e and t h e r a d i c a l plane.  When the magnetic f i e l d  i s perpendicular to the rod  f a c e , t h e a n g l e s 0 and a become e q u i v a l e n t .  However, when t h e r o d  - 172  i s r o t a t e d by  90°  -  so t h a t the rod f a c e i s p a r a l l e l t o the m a g n e t i c  f i e l d , the d i s t r i b u t i o n f u n c t i o n becomes  ' ^ 3  ,0  o  where N i s a n o r m a l i z i n g i n t e g r a l was  c o n s t a n t , x = cosa and  evaluated numerically  From t r i a l and  the system ( F i g s . 11.7  the p e r p e n d i c u l a r  t i o n f u n c t i o n chosen. observed s p e c t r a f u n c t i o n was  ( 0 ^ 6 < T T / 2 rad.) - 11.9).  o r i e n t a t i o n s was The  = P(a).  f o r a g i v e n f u n c t i o n of  e r r o r s i m u l a t i o n , f o r the two  d i s t r i b u t i o n f u n c t i o n 1 - .38 describe  Q(x)  was  I t was  P(a).  orientations,  found t h a t  only distribu-  agreement between the s i m u l a t e d  and  a r e f i n e m e n t of the d i s t r i b u t i o n  not attempted s i n c e i t i s not known whether a  c y l i n d r i c a l l y symmetric f u n c t i o n i s adequate i n d e s c r i b i n g system and  the  found t o b e s t  h i g h l y s e n s i t i v e t o the  i s s a t i s f a c t o r y but  This  the  a more complex f u n c t i o n i n v o l v i n g the d i s t r i b u t i o n of  m o l e c u l e s about an a x i s p e r p e n d i c u l a r  to the m o l e c u l a r p l a n e may  be  necessary. S i m i l a r a n a l y s i s p r o c e d u r e s were c a r r i e d out w i t h the t r a p p e d i n neon and  krypton matrices.  The  CIC^  appearance of the  a r e e s s e n t i a l l y s i m i l a r e x c e p t f o r s l i g h t changes i n t h e l i n e of several components and  c o r r e s p o n d i n g s h i f t s i n the g v a l u e s .  r e s u l t s are p r e s e n t e d i n T a b l e The  spectra  f o r CIC^  spectra positions The  11.1.  t r a p p e d i n neon and  d i f f e r e n t from t h a t of s i t e I and  krypton are  s i t e I I i n argon.  slightly  To o b t a i n  an  - 173 -  Fig.  11.7  Computer s i m u l a t e d EPR spectrum o f C I O 2 u s i n g a d i s t r i b u t i o n f u n c t i o n o f 1-0.3 cosO. H i s p a r a l l e l t o the r o d f a c e .  - 174 -  F i g . 11.8  Computer s i m u l a t e d EPR spectrum of CIC^ p l o t of c e n t r a l p o r t i o n of F i g . 11.7).  (expanded  - 175 -  11.9  Computer s i m u l a t e d EPR spectrum of C I O 2 u s i n g a d i s t r i b u t i o n f u n c t i o n of 1-0.3 cos0. H i s p e r p e n d i c u l a r to the rod f a c e . Q  TABLE  11.1  EPR p a r a m e t e r s f o r c h l o r i n e  g. i s o  X  2.0036  2.0183  2.0088  2.0102  A x  4 -1 .(xlO cm )  +68.3  2.01667  to  +14.6  +10.8  to  ±69.84  2.01214 to  2.0101  (cm" ) 1  168  14.45  123 +10.21  +10.8  to  to  to  ±64.28  +8.34  +6.24  ±69.13  +12.38  +10.62  2.01154  2.002  2.015  2.013  2.0022  2.0159  2.0125  ±66.76  +10.91  2.0022  2.0157  2.0125  ±65.86  2.0023  2.0159  2.0125  2.0026  2.0164  2.0131  ±0.0002  ±0.0002  ±0.0002  work.  2.010  Ref.  QE 4  2.01614  This  QD (xlO )  2.00245  *  xso  y  ±65.9  2.0015 2.0016  A  dioxide.  15.21  ±0.3  ±2.95  169 173  ±0.2  ±3.02  Argon I I *  +9.33  ±0.5  ±2.63  Neon*  +10.88  +9.55  ±0.4  ±2.66  Argon I *  ±64.52  +10.91  +9.33  ±0.5  ±2.63  Krypton*  ±64.23  +9.69  +8.15  ±0.3  ±2.83  ±0.3  ±0.3  ±0.2  ±0.2  ±0.3  15.48  - 177 -  a c c u r a t e measurement o f t h e l i n e p o s i t i o n s i n Ne, Kr and A r , t h e usual p r a c t i c e of c a l i b r a t i n g a l l the l i n e p o s i t i o n s w i t h the proton magnetometer was abandoned s i n c e s h i f t s o f l e s s than one gauss a r e concerned  and t h e resonance p o s i t i o n o f p r o t o n l i n e from t h e magneto-  meter i s s t r o n g l y dependent on i t s p o s i t i o n i n t h e magnetic  field.  I n s t e a d , a s m a l l c r y s t a l o f DPPH was d i s s o l v e d i n benzene and t h e copper r o d l i g h t l y coated and a l l o w e d t o d r y .  The experiments i n  a l l t h r e e m a t r i c e s were then r e p e a t e d w i t h the DPPH s i g n a l (g = 2.0036) a c t i n g as an i n t e r n a l s t a n d a r d . An attempt was made t o o b t a i n a c o m p l e t e l y random spectrum i n argon by a l l o w i n g t h e sample t o s l o w l y warm. of t h e l i n e s  was observed  No m o t i o n a l  narrowing  up t o about 30 K a t which p o i n t t h e  o v e r a l l i n t e n s i t y o f t h e spectrum began d e c r e a s i n g .  I n s e v e r a l such  attempts however, t h e sample was a l l o w e d t o warm t o about 25 K and then r a p i d l y c o o l e d a g a i n t o 4.2 K.  Upon a n n e a l i n g i n t h i s manner,  the p a r t i a l o r i e n t a t i o n was not c o m p l e t e l y l o s t and s l i g h t of t h e l i n e components was observed second t r a p p i n g s i t e  narrowing  a l o n g w i t h the appearance o f a  ( F i g . 11.10), w i t h a s l i g h t l y l a r g e r c o u p l i n g  c o n s t a n t than t h a t o r i g i n a l l y observed  (Table 11.1).  On r o t a t i n g  the r o d by 90° from t h a t shown i n F i g . 11.10, t h e x component f e a t u r e due t o s i t e I was reduced  i n i n t e n s i t y (while the c e n t r a l  p o r t i o n i n c r e a s e d i n i n t e n s i t y ) b u t t h e s i t e I I x-component i n t e n s i t i e s were u n a f f e c t e d by t h e r o t a t i o n . decrease  On rewarming, a g r a d u a l  i n t h e x component i n t e n s i t i e s was observed  along w i t h a  s l i g h t i n c r e a s e i n the i n t e n s i t y o f t h e type I I s i t e which i n d i c a t e s  - 178 -  Fig.  11.10  Observed EPR spectrum of C I O 2 i n an argon m a t r i x a f t e r annealing. I and I I denote the two observed s i t e s .  - 179 -  a f u r t h e r c o n v e r s i o n from type I t o type I I s i t e s b u t the type I s i t e c o u l d n o t be c o m p l e t e l y annealed  out and p e r s i s t e d u n t i l the sample  d e p o s i t was l o s t due t o t h e warmup.  The same warmup procedure  was  t r i e d w i t h Kr and Ne m a t r i c e s b u t no m u l t i p l e t r a p p i n g s i t e s were o b s e r v e d , however, p a r t i a l o r i e n t a t i o n was p r e s e n t t o about t h e same e x t e n t as i n argon.  11.3  The H a m i l t o n i a n Parameters S i n c e t h e h y p e r f i n e , quadrupole  and Zeeman t e n s o r s a r e l i k e l y  c o i n c i d e n t f o r CIO,-,, t h e r e i s o n l y t h e q u e s t i o n o f a s s i g n i n g t h e tensor values obtained t o the p r i n c i p a l d i r e c t i o n s i n t h e molecule. T h e o r e t i c a l p r e d i c t i o n s are necessary f i r s t the g tensor. that L shifts  x  to establish t h i s ,  The c h a r a c t e r t a b l e f o r  transforms l i k e the B  2  symmetry shows  representation.  (Eqn. [6.15]) w i l l then o n l y a l l o w L  x  The t h e o r y f o r g  t o c o u p l e the  ground s t a t e w i t h an e x c i t e d s t a t e o f A,, symmetry. o r b i t a l f o r an A  2  s t a t e i s composed o f a n t i - b o n d i n g  c e n t e r e d m a i n l y on t h e t e r m i n a l oxygens.  Consider  The m o l e c u l a r orbitals  The wave f u n c t i o n f o r t h i s  s t a t e can be w r i t t e n as  cp. A  °1 °2 = (C" - C ) X x x px X  2  Since L I x ^ O , L state;  l  cannot couple, t h e A„ s t a t e w i t h t h e B  1  ground  t h e g s h i f t f o r t h i s d i r e c t i o n s h o u l d be z e r o as was e a r l i e r  d e s c r i b e d and the x a x i s then corresponds w i t h t h e minimum g s h i f t  - 180  (Ag = +.0002).  -  A c c o r d i n g to Walsh's c o r r e l a t i o n diagram f o r 2  systems, the ground s t a t e can be w r i t t e n as The  2  2  AB^  1 2  (..3b2la2^a^2b^; B ^ ) .  o r d e r i n g of the f i r s t t h r e e e x c i t e d s t a t e s of  C I O 2  has  been  e s t a b l i s h e d by a c c u r a t e LCAO-MO-SCF c a l c u l a t i o n s t o be E ( A - B . ) 2 E(B„-B ) > E(A - B . ) . Now the g s h i f t s f o r g and 2 1 2 1 1 1 y 0  g  1  a r e observed to be l a r g e and  p o s i t i v e , i n d i c a t i n g t h a t the  z  excited  s t a t e s m i x i n g w i t h the B^ s t a t e are formed by the e x c i t a t i o n of  an  e l e c t r o n from a low l y i n g f i l l e d o r b i t a l to the u n p a i r e d e l e c t r o n 1 2 2 orbital. C o n s i d e r f i r s t the e x c i t a t i o n (...4a^2b^; A ^ ) . The character  t a b l e shows t h a t L y  and w i l l  thus mix  t r a n s f o r m s l i k e the B., 1 2  s t a t e s whose symmetry i s  A^.  representation 2  S i n c e the  A^  l i e s l o w e s t i n energy i t i s expected t h a t t h i s s t a t e w i l l g i v e  state rise  t r a n s f o r m s as A 2 and w i l l c o u p l e 1 2 2 2 2 2 o n l y s t a t e s of B 2 symmetry (. . . 3b2la24a^2b^; B 2 ) • S i n c e the B 2 2 to a strong p o s i t i v e g s h i f t .  s t a t e i s of s l i g h t l y g r e a t e r s h i f t i s expected. +.0137) and  The  energy than the  A^ s t a t e a s m a l l e r  g  a x i s assignment i s then g^ = 2.0159 (Ag =  = 2.0125 (Ag = +.0102).  T h i s assignment i s i n agree-  ment w i t h the p r e v i o u s i n t e r p r e t a t i o n s . The now  r e l a t i v e s i g n s of the h y p e r f i n e  be e s t a b l i s h e d .  tropic hyperfine the f i e l d  From a s i m p l e one  coupling  tensor  and  quadrupole t e n s o r s  c e n t e r argument, the  remaining s i n g choice  aniso-  s h o u l d have a maximum v a l u e when  i s o r i e n t e d a l o n g the y (TT) a x i s and  t h i s o r b i t a l s h o u l d be p o s i t i v e .  can  the s p i n d e n s i t y  Having made t h i s c h o i c e , the  f o r A^ and A^  to b o t h be n e g a t i v e ,  since  i s the o n l y c o m b i n a t i o n w h i c h w i l l g i v e the observed i s o t r o p i c  in only this  - 181 -  (161—167) splitting  .  The temperature v a r i a t i o n o f t h e i s o t r o p i c  c o u p l i n g was found t o be v e r y s m a l l  a n  ambiguity i n the r e l a t i v e s i g n choice.  d thus t h e r e i s no  The s i g n o f t h e quadrupole  c o u p l i n g can now be determined e x p e r i m e n t a l l y . f o r a l l four p o s s i b l e s i g n choices and  the spectrum was s i m u l a t e d .  The l i n e p o s i t i o n s  f o r QD and QE were c a l c u l a t e d  Only one s i g n c h o i c e  f i t t e d the  observed spectrum w e l l and t h a t s i g n c h o i c e was w i t h QD and QE o f the same s i g n as A x  The  a n i s o t r o p i c part of the c h l o r i n e hyperfine  coupling  tensor  can be e s t i m a t e d u s i n g t h e method of Chapter S i x f o r I T r a d i c a l s (Eqn.  [6.10]).  lengths  The parameters used i n the c a l c u l a t i o n s were a bond  of 1.471 A and a bond a n g l e o f 117.6°  ' 178) ^  ^  be e x p e c t e d , t h e main c o n t r i b u t i o n t o t h e a n i s o t r o p i c t e n s o r from t h e one c e n t e r  term and i s a x i a l about t h e y a x i s .  c o n t r i b u t i o n s from t h e two c e n t e r make t h e a x i a l t e n s o r , n o n - a x i a l  and o v e r l a p (Table 11.2).  would comes  Smaller  i n t e g r a l tend t o The u n p a i r e d e l e c t r o n  i n t h e b^ o r b i t a l can a l s o p o l a r i z e t h e e l e c t r o n s i n t h e i n n e r a^ o r b i t a l on c h l o r i n e comprised o f 3s- and 3 p ~ atomic o r b i t a l s . z  This  s p i n p o l a r i z a t i o n c a n be approximated by i n c l u d i n g a term CI CI C I p3p < x3p 0 v3p >. *o a ' aa 'a r  be s m a l l  1  (Table 11.2).  The e f f e c t o f t h i s i n c l u s i o n i s seen t o The t o t a l a n i s o t r o p i c t e n s o r  agrees w e l l  w i t h t h e e x p e r i m e n t a l v a l u e s (+49.75, -25.65, -24.10) b u t p r e d i c t s that The  |A |<|A^| a f a c t w h i c h i s n o t i n agreement w i t h t h e d i f f e r e n c e i s s m a l l however and c o u l d be c o r r e c t e d  more s p i n p o l a r i z a t i o n were i n t r o d u c e d .  A recent  experimental.  i f slightly  "ab i n i t i o " SCF  - 182 -  TABLE 11.2 Calculated hyperfine i n t e r a c t i o n data f o r c h l o r i n e d i o x i d e u s i n g INDO/2 method.  Spin densities  A  A xx  yy  A zz  CI p3prr  0.39  48.49  -24.24  -24.24  0 p2p-rr  0.31  0.19  0.25  -0.44  Cl-0 p2 7r3p7r  -0.34  P  p3pa  0.0033  -3.05  +1.5  -0.2  -0.2  1.56  0.4  Total (gauss) (cm xl0 ) - 1  4  42.55  -20.94  -21.61  39.77  -19.70  -20.30  - 183 -  c a l c u l a t i o n has been performed on C l O ^  where t h e h y p e r f i n e  a n i s o t r o p y was c a l c u l a t e d t o be 31G, (.0029cm "*") f o r the p direction.  The 2p- and 3p- o r b i t a l s on c h l o r i n e , as w e l l as the  2p3p- o v e r l a p was c o n s i d e r e d , b u t c o n t r i b u t i o n s from t h e two c e n t e r terms and s p i n p o l a r i z a t i o n were n e g l e c t e d .  11.4  Matrix Effects When atoms o r s m a l l m o l e c u l e s  i t i s not unusual f i r s t observed  a r e trapped i n an i n e r t m a t r i x ,  t o observe m u l t i p l e t r a p p i n g s i t e s .  These were  f o r the hydrogen atoms trapped i n a r g o n , neon and (8)  krypton matrices  .  Each atom would be expected  t o r e f l e c t the  c h a r a c t e r of i t s p a r t i c u l a r environment and indeed i n  argon and  k r y p t o n , t h r e e d i s t i n c t p a i r s o f h y p e r f i n e l i n e s were o b s e r v e d , opposed t o the expected  one p a i r , and each possessed  d i f f e r e n t h y p e r f i n e and g t e n s o r v a l u e s .  as  slightly  These c o u p l i n g s were  s u c c e s s f u l l y i n t e r p r e t e d as b e i n g due t o hydrogen atoms trapped i n t e t r a h e d r a l , o c t a h e d r a l o r s u b s t i t u t i o n a l environments. M u l t i p l e (9 13) t r a p p i n g s i t e s have a l s o been observed a l s o f o r molecules  i n various matrices.  been a t t r i b u t e d t o e i t h e r i n t e r s t i t i a l w i t h the l a r g e r atoms o c c u p y i n g  f o r o t h e r atoms  '  and  The t r a p p i n g s i t e s have or s u b s t i t u t i o n a l  sites,  the s u b s t i t u t i o n a l s i t e s i n argon.  I t i s thought t h a t t h i s might a l s o be the case f o r  CIO2  i n argon.  o  The e f f e c t i v e r a d i u s o f a CIO2 m o l e c u l e i s about 2.5 A (as c a l c u l a t e d from the van der Waals r a d i i o f the atoms). The i n t e r s t i t i a l s i t e s o (9) i n argon has a f r e e r a d i u s o f about .78 A f o r the o c t a h e d r a l s i t e s  - 184 -  The  s u b s t i t u t i o n a l s i t e has a f r e e r a d i u s o f about 1.88 A and c o u l d  c o n c e i v a b l y accommodate t h e CIC^ m o l e c u l e w i t h o n l y a moderate lattice distortion.  When t h e CIC^ m i x t u r e  i sinitially  condensed,  t h e r e w i l l v e r y l i k e l y be c o n s i d e r a b l e s t r a i n s i n t h e l a t t i c e s t r u c t u r e and l a t t i c e d e f e c t s a r e e s p e c i a l l y p r e v a l e n t t o form s i n c e (89' the m a t r i x i s b e i n g condensed w e l l below o n e - h a l f i t s m e l t i n g p o i n t I n these d e f e c t s i t e s , t h e l a t t i c e o r d e r i s e s s e n t i a l l y i n t a c t , b u t l o c a l d i s t o r t i o n s o f t h e o v e r a l l c e l l geometry e x i s t .  These s i t e s  a l s o appear t o " a t t r a c t " an i m p u r i t y atom d u r i n g c r y s t a l  g r o w t h .  I t i s f e l t t h a t s i n c e t h e r e i s o n l y one s i t e observed when t h e m a t r i x i s condensed ( s i t e I ) , t h a t these l a t t i c e d e f e c t s form t h e major t r a p p i n g s i t e .  I f t h e CIG^ m o l e c u l e s a r e trapped  i n a sub-  s t i t u t i o n a l s i t e during d e p o s i t i o n , p e r f e c t ordering of the c r y s t a l s t r u c t u r e would be r e q u i r e d on c o n d e n s a t i o n rather unlikely.  and t h i s p r o s p e c t  seems  When t h e m a t r i x i s a l l o w e d t o warm g r a d u a l l y t h e  m a t r i x w i l l b e g i n t o s o f t e n and rearrangement o f t h e c r y s t a l s t r u c t u r e w i l l t a k e p l a c e , r e l i e v i n g any s t r a i n s imparted  on c o n d e n s a t i o n .  On  r e c o o l i n g t h e m a t r i x t o 4.2 K, t h e second t r a p p i n g s i t e appears i n d i c a t i n g t h a t p a r t i a l r e o r d e r i n g o f t h e c r y s t a l s t r u c t u r e has indeed  taken p l a c e and t o a c o n s i d e r a b l e e x t e n t s i n c e t h e " s i t e I I "  s i g n a l i s more i n t e n s e than t h e c o r r e s p o n d i n g The  " s i t e I " signals.  r e d u c t i o n i n i n t e n s i t y o f t h e x component l i n e s f o r s i t e I when  the d e p o s i t i o n s u r f a c e i s r o t a t e d by 90° and t h e c o r r e s p o n d i n g i n c r e a s e i n t h e y and z components, i n d i c a t e s t h a t t h e p a r t i a l  - 185 -  o r i e n t a t i o n of s i t e I i s n o t l o s t on a n n e a l i n g .  The i n t e n s i t y o f  the s i t e two x components i s u n a l t e r e d by t h e r o t a t i o n and i t can thus be i n f e r r e d t h a t the m o l e c u l e s i n t h i s s i t e a r e e s s e n t i a l l y randomly o r i e n t e d and a r e surrounded i s o t r o p i c a l l y by m a t r i x atoms. T h i s would be t h e case i f t h e m o l e c u l e s were t o occupy a s u b s t i t u t i o n a l s i t e i n t h e m a t r i x s i n c e t h e r e i s no " p r e f e r r e d " o r i e n t a t i o n i n t h e completely  symmetric environment o f t h e s u b s t i t u t i o n a l s i t e .  The  l a r g e r h y p e r f i n e c o u p l i n g t h a t i s observed f o r t h e s u b s t i t u t i o n a l s i t e i s a l s o c o n s i s t e n t w i t h t h e t h e o r y o u t l i n e d i n Chapter F i v e . The  l a t t i c e d e f e c t s would be expected t o have a l e s s  environment and c o n s e q u e n t l y atoms.  symmetrical  have a l a r g e r space between the m a t r i x  T h i s would have t h e e f f e c t of p e r t u r b i n g t h e m o l e c u l a r  o r b i t a l s on CIC^ t o a l e s s e r e x t e n t than t h e s u b s t i t u t i o n a l  site.  The wave f u n c t i o n f o r the odd e l e c t r o n o r b i t a l on c h l o r i n e would thus c o n t r a c t f o r the s u b s t i t u t i o n a l s i t e , g i v i n g r i s e t o an i n c r e a s e i n the h y p e r f i n e coupling  constant.  There were no m u l t i p l e t r a p p i n g s i t e s observed when C l O ^ was trapped  i n neon o r k r y p t o n m a t r i c e s .  Annealing  of neon i s v i r t u a l l y  i m p o s s i b l e due t o i t s low m e l t i n g p o i n t and a n n e a l i n g i n k r y p t o n produced no second s i t e s . d i f f e r e n t f o r each m a t r i x .  The powder l i n e p o s i t i o n s were, however, As can be seen from T a b l e 11.1, t h e  h y p e r f i n e v a l u e s d e c r e a s e w i t h an i n c r e a s e i n m a t r i x s i z e .  T h i s can  be q u a l i t a t i v e l y accounted f o r by t h e t h e o r y i n Chapter F i v e .  As  the m a t r i x s i z e i n c r e a s e s , t h e average d i s t a n c e between t h e e l e c t r o n i n the p - o r b i t a l on c h l o r i n e and t h e o r b i t a l s on t h e m a t r i x atom  - 186  will  increase.  -  T h i s w i l l l e a d to a r e d u c t i o n i n the P a u l i f o r c e s  a c t i n g on the c h l o r i n e pTT o r b i t a l and a r e s u l t i n g i n c r e a s e i n the van der Waals i n t e r a c t i o n . S i n c e the P a u l i f o r c e s are r e p u l s i v e and  the van der Waals f o r c e s a t t r a c t i c e , the o v e r - a l l e f f e c t w i l l  be a l l o w i n g the c h l o r i n e p - o r b i t a l to "expand" which w i l l r e s u l t i n a s l i g h t d e c r e a s e i n the s p i n d e n s i t y w h i c h i n t u r n w i l l the net h y p e r f i n e i n t e r a c t i o n . The x component of the  decrease  hyperfine  c o u p l i n g f o r the s u b s t i t u t i o n a l s i t e i n argon i s a l s o g r e a t e r t h a t i n neon.  S i n c e the CIC^  i s l i k e l y trapped  in a lattice  i n neon (which s h o u l d have l e s s f r e e space than one  than defect  i n argon) any  h y p e r f i n e c o u p l i n g g r e a t e r than t h a t i n neon would r e q u i r e an even t i g h t e r environment.  I t i s this large hyperfine s h i f t for s i t e I I  i n a r g o n t h a t l e a d s us t o p o s t u l a t e t h e s u b s t i t u t i o n a l t r a p p i n g The  site.  i n t e r p r e t a t i o n of the m a t r i x e f f e c t s on the g s h i f t s i s  more d i f f i c u l t  to e x p l a i n by s i m p l y c o n s i d e r i n g the P a u l i and  der Waals f o r c e s .  The  g - s h i f t s are a l l p o s i t i v e and  w i t h an i n c r e a s e i n m a t r i x s i z e .  tend to  van increase  S i n c e the p - e l e c t r o n i n c h l o r i n e  w i l l i n d u c e a s m a l l s p i n d e n s i t y i n the p - o r b i t a l s of the  matrix  atom, t h e r e w i l l be a s m a l l s p i n - o r b i t c o u p l i n g from the m a t r i x atom. I t may  be t h a t t h i s a d d i t i o n a l s p i n o r b i t c o u p l i n g w i l l  contribute  to g i v e an o v e r a l l p o s i t i v e g s h i f t or t h a t the e n e r g i e s of  the  e x c i t e d s t a t e s are d e c r e a s e d s l i g h t l y which would g i v e r i s e to an overall positive g shift. Comparison of the r e s u l t s i n T a b l e 11.1 d i f f e r e n c e between the H a m i l t o n i a n  show a s i g n i f i c a n t  parameters of C10  9  i n the  rare  - 187 -  gases and those i n t h e s i n g l e c r y s t a l environment.  This i s not  unexpected s i n c e t h e e l e c t r o s t a t i c f i e l d s produced i n a c r y s t a l l i n e environment would be expected t o be s u b s t a n t i a l , such f i e l d s o f c o u r s e b e i n g much s m a l l e r f o r the i n e r t m a t r i c e s . i n the i n e r t matrices and  Lattice vibrations  a t 4.2 K would a l s o be expected t o be m i n i m a l  t h i s w i l l v i r t u a l l y e l i m i n a t e any v a r i a t i o n s i n the Zeeman and  hyperfine  components t h a t a r e observed a t h i g h e r  temperatures i n  the s i n g l e c r y s t a l s . The mechanism f o r o b t a i n i n g p a r t i a l o r i e n t a t i o n i n a p o l y c r y s t a l l i n e matrix  i s n o t f u l l y understood b u t i t appears t o depend  on s e v e r a l f a c t o r s ^ '  1  8  ^ .  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C u r l , J r . , J . Chem. Phys., 37_, 779 (1962).  174.  R.F. C u r l , J r . , M o l . Phys., 9_, 585 (1965).  175.  G. Herzberg i n " E l e c t r o n i c S p e c t r a o f P o l y a t o m i c M o l e c u l e s " (D. v a n Nostrand Co. I n c . , P r i n c e t o n , New J e r s e y ) .  176.  A.H. C l a r k and B. B e a g l e y , J . Chem. S o c , ( A ) , 46 (1970).  177.  R.F. C u r l , J . L . K i n s e y , J . C Baker, D.H. B a i r d , G.R. B i r d , R.F.  H e i d e l b e r g , T.M. Sudgen, D.R. J e n k i n s and C N . Kenney,  Phys. Rev., 121, 1119 (1961).  - 199 -  178.  R.F. C u r l , R.F. H e i d e l b e r g and J . L . K i n s e y , Phys. Rev., 125, 1993  (1962).  179.  D.C. McCain and W.E. P a l k e , J . Chem. Phys., 56_, 4957 (1972).  180.  D.W.  181.  W. W e l t n e r , J r . , Adv. i n High Temp. Chem., 2, 85 (1969).  182.  P. K o t t i s and R. L e f e b v r e , J . Chem. Phys., 39, 393 (1963).  P a s h e l y , Adv. Phys., 14, 327 (1965).  - 200 -  APPENDIX A  The theory of t r a n s i t i o n p r o b a b i l i t i e s o u t l i n e d here i s based (182) on the theory o f L e f e b v r e  and has been extended to i n c l u d e the  n u c l e a r Zeeman i n t e r a c t i o n Expanding Eqn. [2.48] i n terms o f the d i r e c t i o n c o s i n e s o f Eqn.  [2.43] we have n  c .  =  ab  1  \<i>\ha (g a x x  (s  where  =  1  ' £G-1(IT +  + s ) -  > z  s  z  -  T  f—i. N  1  J=l  " i/2<yg y (S +  .  J  +  E  - S") -  x ^ ' v i  G  N  ( I  T  i .) } )  i  i  J  J  1-  2  [A  -  1]  g^/B^  T h i s can be f u r t h e r expanded  by s u b s t i t u t i n g the form of the  s t a t e v e c t o r s i|> , ty, i n t o t h e above e q u a t i o n as f o l l o w s : a b -S+l <\\**]\>-L  -I.  -I  £ - £ m' = 1 , m' I - i l I I n 1  m'=S s  n  =1  n  x <p(m ,m' • •-m')<j> (m ,m , • • *m S X X S X X n "n  -S  -I,  £ m =S-1 s  Z iru = 1 , I-, 1 I  )G(m ,m S J- —  x 6m' ni •••m: ,m {S(S+1) - m (m + 1 ) } I II I s s 1 n n  I  • • 'm X n  -I  . G* m;,  n  m  T  =1  I n  (  mi  •  n  ) 6m'. ,m S S  1  + 1  h  T  L,  JZ m =S-1 m,. s 1^  1  x  {S(S+1)  - m  G  m_ I n (m  (  m  +1 s  > - [ - ' • •m I n m  I  ,a)G(m .m^. • •-m ,b) x I n  [A. 2 ]  - 201 -  and s i m i l a r l y -S * |S"|*.> = £ m'=S-l  -I. E m„ =1, I, 1  a  --II  * G  m  (  m  s  '  m  T  =1 I n  * " '  m  I  T  T  •'.a)G(m'+l m  x (S(S+1) - (m'+Dm'}^ s s -S !  *a' z'V S  -I,  ^ m =S s  =  ^ m  * • •m. ,b) x I n  >  ]  n  [A.3]  -I  £ s m =1 I n n m  U  =1, I, • 1 1  T  G  ( m  s' l  " * I  m  T  m  l  » > ( a  n  G  m s  »°  I  • " I  m  i ' n  [A.4]  The nuclear Zeeman operators are equivalently -S V  -I,  -I  " l ^ l I -V 1 r n  S  defined  =1 1  m  i  -I " r+1  ^  l  m  l  =  I  n  n  *  G (m ,m •••m_ ,m +l,m_ •••m ,a) x s l . l . l •«• . i 1 r-1 r r+1 n T  T  1  x G(m ,m_ :",m_ ,*"m ,b){I (I +1) - m_ (m +1)} 2 s l . I i r r i i 1 r n r r T  "I  S  m •i  m =S  G  ^ s m  , m  i  L  '°' i " " r m  1  =1  -L  m  m  » ) a  I  n  =l - i I r  I m  -I I  =i  r+1 m  =  I  T  ~  [A.5]  b )  - 202 -  1  ••"V  . " j +l,m  -•••m ,b){I (I +l)-m_ (m +1)} n \  r-1 r  T  r+1  r  r  T  I  r  [A.6]  -s  - i  -I  x  I  <* |i> > a  E m =S s  b  n  E m_ = I "l, I I  m T m  l  =  I  n  r  * G (m ,m -  •••m_ ,a)G(m ,m • •-m T  1  'n  8  X  n  n [A.7]  The i n t e g r a l s can be evaluated f o r the a,b t r a n s i t i o n s  involved  since the G's are simply the c o e f f i c i e n t s of the eigenfunctions which are determined by diagonalizing  the spin Hamiltonian at the  resonance f i e l d .  Defining  j=l P  J  J  = -i/2[g {<4< |S -S-|V >} - £ Gj{<¥ |I+-IT-|? >}] j=l +  y  B  a  J  P  Z-^<* l JV " E^a'^IV s  }  a  wehaveT where  P X  »  P  Y  a b  = a  n  |rP d P  z  w  x  i  l P  +  l  y  1  b  e  Y +  l P | z  z  2  1  J  [A  '  8]  [A. 9]  complex functions of the c o e f f i c i e n t s G .  -  203 -  Expanding [A.9] we have  T  ab  =  ^  ^  V  2  + < C  <  P  ) 2 )  +  2 1  X  x ;^ i  P  ) X  ^  ( P  Y  )  + < t  (  p x  + 2I;I (IR(P )(R(P ) + € ( P ) C ( P ) ) + i y ( f K ( p ) 2  Z  x  Z  2ri («\(P )iR(p )  y  Z  +C(P xr;(p )) + i ( i ^ p )  z  Y  Z  X  Y  z  z  z  2  )^(  2  p Y  )  +C(P ) ) 2  Y  +C(P ) ) 2  Z  [A.io]  where |r\ and <D are the r e a l and complex parts of P. Substituting  for the d i r e c t i o n cosines from Eqn. [2.43] and  averaging over a l l n as i n Eqn. [2.45] the following expression i s obtained  2 ' 2 2 2 ' (sin 9 cos <p + s i n cf>) + C (cos 6 sin2<p) + C (sin20 coscb) xy xz 1  T . = C aD  xx  ' 2 2 ' ?' + C (sin20 s i n < ) > + cos cf>) + C (sin20 sincb) + C (cos 0 ) yy yz zz [A.11]  where 0  = 0 + 90° always.  (0 and 0  are as defined i n F i g . 2.3)  The c o e f f i c i e n t s A^ to A^ of Eqn. [2.49] are defined by A_  1  C  • A_  xx  where C  X X  =  2  C  jAy-  =  xy 2 = ( (P ) + A  Y  6  C  zz 2 (P ) ) etc. Y  A  When 0 = 0°; 0' = 9 0 °  (H//z- axis), [A. 11] becomes indeterminant.  Choosing <p = 0°, this function can be evaluated and gives the expression  - 204 -  T ^ (Z) = C + C ab xx yy  For the case where there i s no nuclear Zeeman interaction, [A.11] i s equivalent to the expression given i n Eqn.  [2.45].  - 205 -  APPENDIX B  The t h e o r y f o r the magnetic d i p o l e i n t e r a c t i o n between a p r o t o n and an u n p a i r e d e l e c t r o n i n a 2p atomic o r b i t a l on a carbon atom, has been d e r i v e d by M c C o n n e l l and S t r a t h d e e ( M  & S).  This  d i p o l a r i n t e r a c t i o n w i l l c o n t r i b u t e t o the a n i s o t r o p i c h y p e r f i n e i n t e r a c t i o n a t the p r o t o n .  As was p o i n t e d out by M and S, t h e t h e o r y  w h i c h was used t o approximate t h e a n i s o t r o p i c h y p e r f i n e c o u p l i n g was d e r i v e d f o r a C-H fragment b u t t h i s c o u l d be g e n e r a l i z e d t o an A-X fragment i f the a p p r o p r i a t e atomic o r b i t a l s on c e n t e r A a r e c o n s i d e r e d . The d e r i v a t i o n of M & S was c o r r e c t e d by P i t z e r e_t al_. ^"^^ f o r terms w h i c h were n e g l e c t e d .  There were a l s o s e v e r a l t y p o g r a p h i c a l  e r r o r s i n the M & S treatment w h i c h were c o r r e c t e d by B a r f i e l d ' ^ ^ . 2  A complete l i s t of t h e i n t e g r a l s f o r a 2p atomic o r b i t a l on c e n t e r A can be found i n B a r f i e l d ' s paper.  Because t h e b a s i c method f o r  the e v a l u a t i o n of t h e i n t e g r a l s , g i v e n by M & S i s c o r r e c t , no d e t a i l s of the d e r i v a t i o n w i l l be g i v e n h e r e and t h e e q u a t i o n s by M & S w i l l be r e f e r e n c e d  used  directly.  The d i p o l a r i n t e r a c t i o n o f i n t e r e s t h e r e i s between a n u c l e u s X and an u n p a i r e d e l e c t r o n i n a 3p atomic o r b i t a l on c e n t e r A.  The  I0^ Ix3p > i s the e a s i e s t t o e v a l u a t e and y aa y ~X w i l l be c o n s i d e r e d f i r s t . 0 i s the d i p o l a r o p e r a t o r d e f i n e d i n aa two c e n t e r i n t e g r a l  <x3p  1  Eqn. Six. to  1  r  [6.3] and the a x i s system i s the same as t h a t chosen i n Chapter (The odd e l e c t r o n i n c e n t e r A i s i n a 3 p  y  o r b i t a l perpendicular  t h e A-X bond; the A-X d i r e c t i o n d e f i n e s t h e z a x i s and the x a x i s  - 206 -  i s m u t u a l l y o r t h o g o n a l t o these two d i r e c t i o n s . ) The S l a t e r 3p o r b i t a l i s d e f i n e d y l^i—y Jp y = \ 3 .85 T T I  where K = Z/a  o  2  - p  p e  /  3  o  .i  [B.l]  sxn0 sinep  where Z i s t h e e f f e c t i v e n u c l e a r charge o f c e n t e r A  and p = Kr where r i s the v e c t o r  from.the c e n t e r A t o t h e e l e c t r o n .  S i n c e t h e a n g u l a r p a r t of t h e 3p^ atomic o r b i t a l i s t h e same as the 2py atomic  o r b i t a l , t h e i n t e g r a t i o n over the a n g u l a r p a r t w i l l  be t h e same as i n M & S .  The d i p o l a r s p i n H a m i l t o n i a n can be -  w r i t t e n f o r t h e c e n t e r X as  [B.2]  where  i s t h e s p i n d e n s i t y i n t h e u o r b i t a l on c e n t e r A.  The  i n t e g r a l can be w r i t t e n as  [B.3]  as d e f i n e d i n M & S (Eqn. 1 2 ) . E v a l u a t i n g t h e a n g u l a r p a r t o f t h e i n t e g r a l , t h e f o l l o w i n g e q u a t i o n s i m i l a r t o M & S Eqn. 20 w i l l 2a  6 -2p/3 p e i  2a  result.  8 -2p/3 dp P e  - 207 -  -16a 3 -2p/3 j , 2 p e dp t + P cos0 cos2tp 15 - I ^2a J  r  i  3  J  6 0 a ^  2 a  P  n  6 -2p/3, 6  d  p  1  +  3 r°° a r ° 3 -2p/3, j J ^ P d dpj  8  J  n  [B.4]  KR where a = 2— and R i s t h e A-X i n t e r n u c l e a r d i s t a n c e . The P™ (cos 6 ) a r e t h e Legendre p o l y n o m i a l s d e f i n e d by M.& S. I f t h i s i n t e g r a l on p i s e v a l u a t e d , t h e r e s u l t i s 189 . \ 64  n 1  1/R"  j  +  <  5a  , 189  77  +  + 1/R"  +  r  -4a/3  64  10a'  3645  +  . 376 a + 405  4  ( 405  189  84  a  126  +  189  5a  3  +  a  184 a 45  a  5  , +  32  a  , 88  4  + — —  1215  135  =|  10a  2K~  OtOu  3  ,. 112 a  +  45  2  112 a 45  [B.5]  |x3p > i s done i n an analogous z  orbital  2 -2p/3 , p e cosf  3?5TT  a  2(1 - c o s 0) cos2tj)  -4a/3  Substituting the Slater  z  252 h 5a  2  Z  X3p  , 68 a , 163 H + 5 5  (l-3cos 8)  The e v a l u a t i o n o f t h e i n t e g r a l <x3p |0 manner.  2  [B.6]  i n t o Eqn. 12 o f M & S, an e q u a t i o n i d e n t i c a l t o M & S Eqn. 17 i s obtained.  I f t h e i n t e g r a t i o n o f these e q u a t i o n s i s c a r r i e d o u t over  cp w i t h t h e 3 p o r b i t a l s , and then t h e i n t e g r a t i o n over 0 i s performed, z  the i n t e g r a l w i l l have t h e form.  - 208 -  <x3p  x3p  0  > =  -2K' 3§5  3 -2p/3  - 16  a  15  p  e  d p  Performing the i n t e g r a t i o n  , . 378  1/R-  , 488 a  T  45  (l/3a  +  2,_ 5, 6 -2p/3, p  /5a  )p  J  [B.7]  on p , the f o l l o w i n g  98415  dp  e  |  ( 1024 a  5a  2a  p^Ccose)  7  .  256 10935  a  6  ^  formula i s obtained.  512 a  5 J  32 a  1232 a  4 x  45  3645  . 468 a . 341 . 504 378 / -4a/3 -t-t+ + — — > e 15 5a 5a  3  405  (1-3  cos 0) 2  [B.8]  The term  1024 98415  a  i s t h e c o r r e c t i o n term added t o t h i s  f o r the case where r -> R.  This c o r r e c t i o n t e r m '  0 5  ^  integral  i s ^r~ z  where f ( R ) i s t h e square o f t h e r a d i a l p a r t o f t h e S l a t e r  f  ^  orbital,  e v a l u a t e d a t r = R (p = KR). These i n t e g r a l s , Barfield'^ ^ 2  a l o n g w i t h t h e 2p i n t e g r a l s  t a b u l a t e d by  were programmed f o r an IBM 360 computer.  1  

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