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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 JOHN CHARLES TAIT B.Sc, University of British 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 this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA March, 1974 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my D e p a r t m e n t o r by h i s r e p r e s e n t a t i v e s . It i s u n d e r s t o o d that c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l owed w i thout my w r i t t e n p e r m i s s i o n . Department o f The U n i v e r s i t y o f B r i t i s h Co lumbia Vancouver 8, Canada Date - i -Supervisor: C. A. McDowell ABSTRACT The technique of electron paramagnetic resonance (EPR) has been used to investigate the electronic structure and geometry of several small triatomic or tetraatomic radicals which have been trapped at 4.2 K in the inert matrices of neon, argon or krypton. The EPR spectra were analyzed by using an extensive computer simulation program based on a detailed general spin Hamiltonian which includes the Zeeman, nuclear Zeeman, hyperfine and quadrupole interaction terms. A general method for analyzing the EPR spectrum of a poly-crystalline sample has been discussed with particular emphasis being placed on systems for which the principal axes of the electronic g-tensor and hyperfine tensors are not coincident. The chloroperoxyl radical (C100) was previously studied in several polar environments and i n an argon matrix, but the EPR parameters were somewhat in disagreement. A study of this radical, formed by the UV irradiation of chlorine dioxide (CIG^) trapped in an inert matrix was undertaken with a view to improving the accuracy of the EPR parameters. The electronic g-tensor and hyperfine tensor were found to be non-coincident. The radical species FSO has been produced by the far UV photolysis of thionyl fluoride (F2SO) in an argon matrix. The spin Hamiltonian parameters were obtained for this radical and found to be remarkably similar to the well known species F00. The hyperfine components were interpreted in a manner similar to F00. - i i -The chlorodisulfonyl radical (C1SS) was produced by the near UV photolysis of the dichlorodisufane molecule C^C^) i n an argon matrix. The electronic 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 principal axes of the hyperfine and quadrupole tensors had to be rotated by ^ 10° from those of the electronic g-tensor. The radical species HSO2 and FSO^ were produced by the UV photolysis of HI/S0 2 or trifluoromethylhypofluorite (CF 3OF)/S0 2 mixtures in the rare gas matrices. The FSO2 radical was also produced by the far UV photolysis of sulfuryl fluoride (^SC^). The EPR parameters were determined assuming non-coincident axes for the hyperfine and electronic g-tensors. Another species was produced i n the reaction of methyl radicals with SC>2 but the nature of the adduct i s uncertain. Chlorine dioxide (ClO^) was studied i n several inert matrices and the spin Hamiltonian parameters were determined for each matrix. Par t i a l orientation has been observed in a l l the matrices. The preferred orientation i s with the plane of the radical parallel to the deposition surface. The spectrum has been simulated using an approximate distribution function for the molecular orientations. A second trapping site has been observed on annealing the argon matrix. This site exhibits s l i g h t l y different hyperfine and Zeeman interactions and i s thought to mean that the site i s a substitutional one. The matrix shifts of the electronic g-tensor and hyperfine tensor are discussed in terras of the van der Waals and Pauli interaction forces. - i i i -TABLE OF CONTENTS Page ABSTRACT i LIST OF TABLES v i LIST OF FIGURES v i i ACKNOWLEDGEMENTS x CHAPTER ONE: INTRODUCTION 1 CHAPTER TWO: ELECTRON PARAMAGNETIC RESONANCE 6 2.1 The Spin Hamiltonian 6 2.1.1 The E l e c t r o n i c Zeeman 6 2.1.2 The Nuclear Zeeman I n t e r a c t i o n 8 2.1.3 The Hyperfine I n t e r a c t i o n 9 2.1.4 The Quadrupole I n t e r a c t i o n 10 2.2 Thermal E q u i l i b r i u m 14 2.3 Lineshape 17 2.4 So l v i n g f o r the Resonance F i e l d s 19 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 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 Pre p a r a t i o n 34 - i v -Page 3.5 Sample Gases 3 6 3.5.1 C h l o r i n e Dioxide (C10 2 ) 3 6 3.5.2 D i c h l o r o d i s u l f a n e ( S 2 C 1 2 ) 3 6 3.5.3 T h i o n y l F l u o r i d e (SOF 2) 37 3.5.4 S u l f u r y l F l u o r i d e ( S 0 2 F 2 ) 37 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 (CF3OF) 3 8 3 . 5 . 6 S u l f u r d i o x i d e ( S 0 2 ) 3 8 3.5.7 Hydrogen Iodide (HI) 3 8 3 . 5 . 8 Neon, Argon, Krypton 39 3 . 6 Molecular O r b i t a l C a l c u l a t i o n s 39 CHAPTER FOUR: EPR POWDER SPECTRA 4 0 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 4 0 4.2 Non Coincident g and A tensors i n P o l y c r y s t a l l i n e Spectra 4 6 4.3 Computer Simulation of P o l y c r y s t a l l i n e Spectra 55 CHAPTER FIVE: MATRIX ISOLATION TECHNIQUES 59 5.1 M a t r i x I s o l a t i o n 49 5.2 Generation of Free R a d i c a l s 6 4 5.3 M a t r i x E f f e c t s 6 8 CHAPTER SIX: INTERPRETATION OF THE HAMILTONIAN PARAMETERS 73 CHAPTER SEVEN: CHLOROPEROXYL RADICAL, C100 8 5 7.1 I n t r o d u c t i o n 8 5 7.2 R e s u l t s and D i s c u s s i o n 8 7 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: FLUOROSULFINYL RADICAL, FSO 103 8.1 Re s u l t s and D i s c u s s i o n 103 CHAPTER NINE: CHLORODISULFONYL RADICAL, C1SS 9.1 P h o t o l y s i s of S u l f u r Monochloride (S 2C1 2) 115 9.2 R e s u l t s and D i s c u s s i o n 116 CHAPTER TEN: RADICAL REACTIONS WITH S0 2 130 10.1 I n t r o d u c t i o n 130 10.2 Results and D i s c u s s i o n 132 10.2.1 Reaction of H atoms w i t h S0 2 132 10.2.2 Reaction of F atoms w i t h S0 2 146 10.2.3 Reaction of methyl r a d i c a l s w i t h S0 2 157 CHAPTER ELEVEN: CHLORINE DIOXIDE, C10 2 160 11.1 I n t r o d u c t i o n 160 11.2 I n t e r p r e t a t i o n of the Spectra 161 11.3 The Hamiltonian Parameters 179 11.4 M a t r i x E f f e c t s 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 of the s p i n Hamiltonian parameters f o r the C100 r a d i c a l 94 8.1 P r i n c i p a l components of the s p i n Hamiltonian parameters f o r the FSO r a d i c a l 109 8.2 C a l c u l a t e d ( IND0/2) and pr e d i c t e d s p i n d e n s i t i e s f o r the FSO r a d i c a l 109 9.1 Experimentally determined p r i n c i p a l values of the spi n Hamiltonian parameters of the S2CI r a d i c a l 125 9.2 Comparison of experimental and c a l c u l a t e d values f o r the EPR spectrum of the S2CI r a d i c a l i n argon 125 9.3 IND0/2, CND0/2 c a l c u l a t i o n of the 3 5 C 1 quadrupole coupling constant i n CIS2 129 10.1 P r i n c i p a l values f o r the s p i n Hamiltonian parameters f o r the HS0 2 r a d i c a l 141 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 2 145 10.3 P r i n c i p a l components of the s p i n Hamiltonian parameters f o r the FSO2 r a d i c a l 154 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 r a d i c a l 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 C a l c u l a t e d h y p e r f i n e 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 using IND0/2 method 182 - v i i -LIST OF FIGURES Figure Page 2.1 Hyperfine 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 commonly observed i n EPR s p e c t r a 18 2.3 S p h e r i c a l p o l a r 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 23 3.1 L i q u i d helium c r y o s t a t 31 4.1 Angular v a r i a t i o n of the h y p e r f i n e resonances i n the three p r i n c i p a l planes f o r a h y p o t h e t i c a l S = 1/2, I = 1/2 system 42 4.2 T h e o r e t i c a l and broadened EPR lineshapes f o r a p o l y c r y s t a l l i n e sample. a) absorption lineshape b) f i r s t d e r i v a t i v e of the absorption 44 4.3 R e l a t i o n of the g and A tensors i n a h y p o t h e t i c a l case where the tensors are non-coincident 47 4.4 Angular 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 tensors are non-coincident ( F i g . 4.3). Only Am-j- = 0 t r a n s i t i o n s are considered 48 4.5 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 4.6 E f f e c t of changing (f>, the angle between A and g x i n F i g . 4.3 X 54 7.1 Observed EPR spectrum of the C100 r a d i c a l i n an argon matr i x at 4.2 K 88 7.2 A x i s system f o r the C100 r a d i c a l 90 7.3 Computer simulated EPR spectrum of the C100 r a d i c a l assuming c o i n c i d e n t axes ( 3 5C1 only) 92 - v i i i -Figure Page 7.4 Simulated EPR spectrum of the C100 r a d i c a l assuming the non-coincident a x i s system of F i g . 7.2 96 8.1 Observed EPR spectrum of the FSO r a d i c a l i n an argon matr i x at 4.2 K 105 8.2 Computer simulated EPR spectrum of the FSO r a d i c a l 108 8.3 Molecular a x i s system f o r the FSO r a d i c a l 113 9.1 Observed EPR spectrum of the S 2 C1 r a d i c a l i n an argon matr i x a t 4.2 K 118 9.2 Computer simulated EPR spectrum of the S2CI r a d i c a l 123 9.3 R e l a t i o n of the s p i n Hamiltonian parameters to the molecular axes i n the S 2 C1 r a d i c a l 124 10.1 Observed EPR spectrum of the HSO2 r a d i c a l i n a krypton m a t r i x at 4.2 K 133 10.2 R e l a t i o n of the s p i n Hamiltonian parameters to the molecular axes i n the HSO2 r a d i c a l 135 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 surface by 90° 137 10.4 Computer simulated EPR spectrum of the HSO2 r a d i c a l assuming the non-coincident a x i s system of F i g . 10.2 140 10.5 Observed EPR spectrum of the FSO2 r a d i c a l i n an argon matr i x at 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 10.6 Observed EPR spectrum of the F S 0 2 r a d i c a l i n an argon matrix at 4.2 K (formed by the UV p h o t o l y s i s of F 2 S 0 2 ) 149 10.7 R e l a t i o n of the s p i n Hamiltonian parameters to the molecular axes i n the FSO2 r a d i c a l 152 10.8 Computer simulated spectrum of the FSO2 r a d i c a l 153 - i x -Figure Page 10.9 Observed EPR spectrum of the r a d i c a l species formed on UV p h o t o l y s i s of a CH3I/SO2/A mixture at 4 , 2 K 1 5 8 11.1 Experimental EPR spectrum of CIO 2 i n an argon matrix at 4 . 2 K. H D i s p a r a l l e l to the rod face 1 6 2 11.2 Experimental EPR spectrum of CIO2 i n an argon matrix. H q i s perpendicular to the rod face 1 6 3 11.3 Molecular a x i s system f o r CIO2 (x a x i s i s perpendicular to the molecular plane and H Q i s the f i e l d d i r e c t i o n ) 1 6 5 11.4 Experimental EPR spectrum of CIO2 (expanded c e n t r a l p o r t i o n of F i g . 11.2) 167 11.5 P l o t of angle against f i e l d f o r t r a n s i t i o n s which have appreciable i n t e n s i t y . Upper p l o t i s i n x,z plane and lower i n x,y plane. The numbers above the l i n e s denote the Am^ . values 1 69 11.6 Computer simulated EPR spectrum of C 1 0 2 u s i n g a completely random d i s t r i b u t i o n f u n c t i o n 1 7 0 11.7 Computer simulated EPR spectrum of 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 of 1-0.3 cos0. H Q i s p a r a l l e l to the rod face 1 7 3 11.8 Computer simulated EPR spectrum of C 1 0 2 (expanded 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) 1 7 4 11.9 Computer simulated EPR spectrum of C 1 0 2 using 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 cos8. H Q i s perpendicular to the rod face 1 7 6 11.10 Observed EPR spectrum of CIO2 i n an argon matri x a f t e r annealing. I and I I denote the two observed s i t e s 1 7 8 - X -ACKNOWLEDGEMENTS I would l i k e to express my g r a t i t u d e to 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 support throughout a l l aspects of t h i s t h e s i s . I am a l s o g r a t e f u l to Dr. F. G. He r r i n g f o r many h e l p f u l d i s c u s s i o n s on the 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 aspects of t h i s t h e s i s . I wish a l s o to thank Dr. P. Raghunathan f o r h i s help and u s e f u l comments i n the pr e p a r a t i o n of s e v e r a l aspects of t h i s work. In a d d i t i o n I wish to extend my thanks to Dr. J . A. Hebden f o r p r o v i d i n g access to s e v e r a l of the computer programs he has developed and f o r p e r m i t t i n g the use of 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 to Mr. T. Markus and Mr. J . S a l l o s f o r t h e i r continued care of the EPR spectrometer; to other members of t h i s l a b o r a t o r y f o r many h e l p f u l d i s c u s s i o n s ; and an e s p e c i a l thanks to my w i f e f o r her patience and help i n the preparation.of 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 the r e c e i p t of a N a t i o n a l Research C o u n c i l of Canada bursary 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 the Department of Chemistry. CHAPTER ONE I n t r o d u c t i o n Although 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 the r e a c t i o n s s t u d i e d by e a r l y chemists, the existence of f r e e r a d i c a l s as a separate e n t i t y was widely r e f u t e d even as l a t e as the 1930's. One of the f i r s t f r e e r a d i c a l s proved capable of independent ex i s t e n c e was the tr i p h e n y l m e t h y l r a d i c a l discovered by G o m b e r g . L a t e r , (2) Paneth -et al_. succeeded i n i d e n t i f y i n g the methyl r a d i c a l formed by heating tetramethyl lead. These r a d i c a l s could not, however, be preserved i n the f r e e s t a t e f o r any length of time because of r a d i c a l recombinations. I t was not u n t i l the e a r l y 1940's that Lewis and (3) L i p k i n succeeded i n s t a b i l i z i n g a s e r i e s of organic f r e e r a d i c a l s i n a r i g i d medium at a low temperature. In t h e i r study, an organic molecule was d i s s o l v e d i n a mixture of organic s o l v e n t s which formed a c l e a r " g l a s s " when cooled w i t h l i q u i d a i r . The r e s u l t i n g frozen 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 (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 which was as c r i b e d to the formation of e i t h e r a f r e e r a d i c a l or the d i s s o c i a t i o n of the organic molecule i n t o p o s i t i v e and negative i o n s . An o p t i c a l study of these species could then be performed at t h e i r l e i s u r e s i n c e they were found to - 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 . This then was the 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 form. The technique of using 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 Zaviosky i n 1945 and l a t e r by Bleaney et_ al_. ^  . I n i t i a l l y , only the paramagnetic t r a n s i t i o n metal complexes were stud i e d because the s e n s i t i v i t y of the instrumentation was very low and high concentrations of r a d i c a l centers were necessary to be e a s i l y detected. The EPR study of f r e e r a d i c a l s trapped i n a glassy medium d i d not gain p o p u l a r i t y u n t i l the mid 1950's because of t h e i r r e l a t i v e l y low concentrations and the complexity of the EPR spectrum of a po l y -c r y s t a l l i n e sample. For these reasons, the EPR s t u d i e s were mainly 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 or of t r a n s i t i o n metal complexes s u b s t i t u t e d i n an appropriate c r y s t a l host. The study of a r a d i c a l center which i s trapped i n a s i n g l e c r y s t a l host, w i l l i n h e r e n t l y provide more in f o r m a t i o n about the trapped species than w i l l a s i m i l a r study on the same species generated i n a glassy 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 (with only one r a d i c a l s i t e ) , a l l of the r a d i c a l centers w i l l have the same o r i e n t a t i o n w i t h respect to 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 of these centers w i l l have the same o r i e n t a t i o n w i t h respect to the magnetic f i e l d and w i l l t h e r e f o r e produce the same - 3 -EPR spectrum. The r e s u l t s of t h i s EPR study combined w i t h an x-ray c r y s t a l l o g r a p h i c study 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 to 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 . This assignment to the molecular axes i s not e a s i l y accomplished 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 centers are g e n e r a l l y randomly o r i e n t e d . The s i n g l e 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. 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 and the range of r a d i c a l s which can be studied 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 frozen organic s o l v e n t s or some sub s t r a t e which 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 species i t s e l f when subjected to UV p h o t o l y s i s . These trapping matrices however, provided a h i g h l y p o l a r environment f o r the trapped r a d i c a l s , which consequently r e s u l t e d i n an increase i n the EPR s p e c t r a l l i n e w i d t h . The temperatures which were commonly a v a i l a b l e f o r studying the trapped species were g e n e r a l l y only as low as l i q u i d n i t r o g e n (77 K), and i n some cases, t h i s was i n s u f f i c i e n t to prevent random tumbling motions of the r a d i c a l species. This l e d to a decrease i n the s t r u c t u r a l information about the r a d i c a l center. When the technique of using l i q u i d helium as a coolant (4.2 K) became more f e a s i b l e , a wider range of trapping media were explored. The r a r e gases, neon, argon, krypton and xenon have now been e x t e n s i v e l y - 4 -used as a trapping matrix because of t h e i r non-polar c h a r a c t e 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 r a d i c a l s and t h e i r general ease of handling. The f i r s t r a d i c a l systems to be studied i n the r a r e gas matrices were the atomic s p e c i e s ^ followed by the more complex molecular species of which a great number are now r e p o r t e d 4 0 ) ^ (There have been s e v e r a l comprehensive reviews s p e c i f i c a l l y covering species (41-45) studi e d i n a p o l y c r y s t a l l i n e medium .) With l a r g e r systems being s t u d i e d , the complexity of the EPR spectra increased and t h i s prompted a great deal 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. Subsequently, a wide v a r i e t y of computer programs were developed to simulate 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 to the problem which was c u r r e n t l y being i n v e s t i g a t e d and consequently they could 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 ma t r i x i s o l a t i o n at low temperatures has now 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 geometrical c o n f i g u r a t i o n of those h i g h l y a c t i v e and t r a n s i e n t s p e c i e s . With the t e c h n o l o g i c a l advances i n the instrumentation during the l a s t two decades, the p r e c i s i o n of the s p i n Hamiltonian parameters obtained from a p o l y -c r y s t a l l i n e EPR study can i n c e r t a i n circumstances, now r i v a l that which can be achieved w i t h a s i n g l e c r y s t a l study. In the work presented here, EPR w i l l be used to study s e v e r a l new 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 matrices at 4.2 K. - 5 -A b r i e f i n t r o d u c t i o n to the theory of EPR w i l l be given, which w i l l among other things describe the o r i g i n of the parameters of the s p i n Hamiltonian. This i s followed by a d i s c u s s i o n of the techniques of a n a l y s i n g the spectrum of a p o l y c r y s t a l l i n e sample. Several 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 described w i t h p a r t i c u l a r emphasis on systems whose s p i n Hamiltonian parameters are not d i r e c t e d along a common molecular 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 to simulate a general powder spectrum f o r S = 1/2 systems, w i l l a l s o be presented. The r a d i c a l s which are trapped i n an i n e r t matrix w i l l be s l i g h t l y perturbed by the matrix 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. In g e n e r a l , these changes w i l l be c h a r a c t e r i s t i c of the matrix. A d i s c u s s i o n 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 given, based on the theory developed f o r atomic species . 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 production 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 eal w i t h the i n t e r p r e t a t i o n of the EPR s p e c t r a of s e v e r a l new r a d i c a l species w i t h the emphasis being placed on the determination of t h e i r s t r u c t u r e and e l e c t r o n i c c o n f i g u r a t i o n s . 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 presented w i t h s p e c i a l c o n s i d e r a t i o n being given to studying 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 TWO E l e c t r o n Paramagnetic Resonance 2.1 The Spin Hamiltonian 2.1.1 The E l e c t r o n i c Zeeman I n t e r a c t i o n I f a magnetic d i p o l e , u, i s placed i n a homogeneous magnetic f i e l d H, 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 given b y(67-70) -M-H [2.1] and f o r an e l e c t r o n H = "g e6S [2.2] where g - 2, 6 i s the Bohr magneton and S i s the s p i n angular momentum operator 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 " . The magnetic Hamiltonian d e s c r i b i n g 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 eSS-H [2.3] - 7 -I f the magnetic f i e l d d i r e c t i o n i s taken to de f i n e the z a x i s i n a la b o r a t o r y reference frame the p r o j e c t i o n of S on H w i l l be S_z and the energy of t h i s system i s then where M g i s the magnetic quantum number rep r e s e n t i n g the value 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 to the magnetic f i e l d g i v i n g r i s e to 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 of energy necessary to induce a t r a n s i t i o n of the type = ±1 i s given by the resonance c o n d i t i o n where v i s the frequency of an o s c i l l a t o r y r . f . f i e l d a p p l i e d perpen-d i c u l a r to the magnetic f i e l d H. I t i s found i n the s o l i d s t a t e , that the Zeeman i n t e r a c t i o n depends not only on the angle between the e f f e c t i v e s p i n vector S and the magnetic f i e l d but a l s o on the angle that H makes w i t h a molecule based set of axes. This w i l l give r i s e to anisotropy i n the g f a c t o r and equation [2.5] can be more g e n e r a l l y w r i t t e n as E = g 8HM s 6 e s [2.4] s E = hv = g $H [2.5] [2.6] - 8 -or more f u l l y = ^ x ^ y ' V / g x x g x y g x z £ £ g °yx °yy yz g g g ' V S ' [2.7] & z x 6 z y 6 z z * L J where g i s a symmetric tensor. A s u i t a b l e reference frame (the p r i n c i p a l frame) can always be chosen to d i a g o n a l i z e the g tensor which i s then represented by i t s p r i n c i p a l g values g x x» ^yy' 8 Z Z" 2.1.2 The Nuclear Zeeman I n t e r a c t i o n I f the nucleus a l s o possesses a s p i n , an analogous expression to [2.2] can be w r i t t e n as v = g 3 I [2.8] -N SN PN- L J where g^ i s the nuclear g f a c t o r , 3^ i s the nuclear magneton and I i s the nuclear s p i n angular momentum v e c t o r . The Hamiltonian which represents the e l e c t r o n i c and nuclear Zeeman c o n t r i b u t i o n i s then given by \'l ~ I [2-9] The anisotropy i n the nuclear g f a c t o r has been neglected here as i t i s very small and normally cannot be detected by EPR. - 9 -2.1.3 The Hyperfine I n t e r a c t i o n The e l e c t r o n a l s o induces an e l e c t r i c f i e l d at the nucleus and i n t e r a c t s w i t h the nuclear moment to produce a d i p o l a r i n t e r a c t i o n term i n the Hamiltonian. This operator can be w r i t t e n as k k ( | k l 3 ( I . r k ) ( S _ k - r k ) 3 5 r r [2.10] where 5 ( r ^ - r^) i s zero unless the e l e c t r o n i s at the nucleus, r i s the v e c t o r connecting the nuclear 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 vanishes f o r r > 0 and i s r e f e r r e d to as the i s o t r o p i c or Fermi contact term and has a c o n t r i -b u t i o n only i f the e l e c t r o n has s - o r b i t a l character s i n c e the p- or higher o r b i t a l s have nodes at the nucleus. The second term i s the a n i s o t r o p i c or d i p o l a r i n t e r a c t i o n and vanishes at r = 0. This term w i l l c o n t r i b u t e then only i f the e l e c t r o n has p- or higher o r b i t a l character and vanishes when the e l e c t r o n cloud i s s p h e r i c a l . The Hamiltonian f o r t h i s operator can be expressed as aS-I + S-T-I = §' A -i [2.11] where a i s the energy of the contact c o u p l i n g , T i s the magnetic d i p c l e tensor and A i s the t o t a l h y p e r f i n e tensor. In the EPR of s o l i d s , the d i p o l e tensor 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. anisotropy of' the h y p e r f i n e tensor. The e v a l u a t i o n of t h i s term i s - 10 -important i n determining the e l e c t r o n d i s t r i b u t i o n i n a molecule and w i l l be considered i n Chapter S i x . For a nucleus which has a s p i n I > 1/2, a term accounting f o r the i n t e r a c t i o n between the nuclear e l e c t r i c quadrupole moment and the gradient of the e l e c t r i c f i e l d at the nucleus 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 given by I f t h i s expression i s expanded i n a Taylor s e r i e s about the o r i g i n , only one term i n the expression, the quadrupole term, i s of i n t e r e s t , a l l lower order poles v a n i s h or do not c o n t r i b u t e and a l l higher 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 2.1.4 The Quadrupole I n t e r a c t i o n [2.12] [2.13] where a,3 = x v a3 3V 3a33 r = 0 [2.14] - 11 -which can be represented as a quantum mechanical expression by r e p l a c i n g Q^g by Q the quadrupole operator. U = ^ ( 3 a k 3 k " 6 a 3 r k ) [ 2 ' 1 5 ] where the summation runs over k nuclear p a r t i c l e s and ^ - 1/6 E V a g Q a g [2.16] ap E v a l u a t i n g the matrix elements of Q by employing the Wigner-Eckart theorem, Q „ becomes a 6 a P 1(21-1) e Q i\ ( I I . + I . I ) - 6 R I 2 | [2.17] I _ 1 s \ 2 a 3 3 a otg ) and ^ = 6lT2W a5 Va3{f ( I a h + h V " & a / } [ 2 ' 1 8 ] where e i s the proton charge and Q i s the quadrupole moment of the nucleus. A set of p r i n c i p a l axes can be chosen which w i l l d i a g o n a l i z e the Hamiltonian w i t h the V as the p r i n c i p a l v a l u e s . <^&T = O T < , ^ ( v I 2 + V I 2 + V I 2 > [2.19] Q 21(21-1) ( xx x yy y zz z ) L J Since the tensor V i s t r a c e l e s s and symmetric, the Hamiltonian can a l s o be described by two independent constants QD and QE defined by - 12 -and n D / eQ \ 3 . I eO, ) ^xx V r , Q D " \ 21(21-1) j' 2 zz * Q l 1 \2I(2I-1)| 2 [ Z ' Z U J = Q D ( I z 2 - ( 1 / 3 ) I 2 ) + Q E ( I x 2 - I y 2 ) [2.21] or e q u i v a l e n t l y the e f f e c t i v e s p i n Hamiltonian can be w r i t t e n i n tensor form < ^ = I-Q-I [2.22] Thus the t o t a l s p i n Hamiltonian f o r an S = 1/2 system i s described b y < 7 1 ) = eeH-g-S + S-A-I + I-g-I - g NB NH-I [2.23] The l a s t two terms are g e n e r a l l y small 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 the hy p e r f i n e tensor i s of the order of the nuclear Zeeman s p l i t t i n g or the quadrupole c o u p l i n g . A schematic 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 the c o n t r i b u t i o n s from each term i n the s p i n Hamiltonian (not n e c e s s a r i l y to scale) are represented at 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). The normally "allowed" EPR t r a n s i t i o n s are Amg = ±1, Am^ . = 0. However, higher order "forbidden" t r a n s i t i o n s (Am^ . = ±1, ±2) are 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 there i s a nuclear 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 to promote mixing between h y p e r f i n e l e v e l s or i f the hyper-f i n e anisotropy i s very l a r g e . - 13 -1 / 2 - 1 / 2 < % » > Ar t y 0 ± 1 ±2 It • + 3 / 2 - 1 / 2 - 1 / 2 - 3 / 2 - 3 / 2 - 1 / 2 - 1 / 2 - + 3 / 2 ^ = gpH-S + S-A-I • I-Q-I - 9NPNH-I F i g . 2.1 Hyperfine 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, 1 = 3 / 2 system. - 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 already mentioned, are induced by a r a d i o frequency f i e l d , ( u s u a l l y ^ 9GHz) a p p l i e d perpen-d i c u l a r l y to the magnetic f i e l d . In order f o r a t r a n s i t i o n to be observed, there must be a popul a t i o n d i f f e r e n c e between the upper and lower e l e c t r o n i c Zeeman l e v e l s . For a system which i s i n thermal e q u i l i b r i u m , the r a t i o of the number of spins i n the lower s t a t e , N , to those i n the upper s t a t e , N^, i s given by the Boltzmann law: N ^ = exp |g eBH/kT| [2.24] b where k i s the Boltzmann constant. For temperatures above 1 K i t can be assumed that g eSH«kT. Time-dependent p e r t u r b a t i o n theory shows that the p r o b a b i l i t y , P, that a time-dependent p e r t u r b a t i o n V ( t ) w i l l cause a t r a n s i t i o n between the l e v e l s whose energies are E and E , i s a b Pab = r T l < a M b > | 2 6 ( E a - E b - hv) [2.25] The pop u l a t i o n d i f f e r e n c e n, between the two l e v e l s i s n = N - N, = n(0) exp (-2Pt) [2.26] a b where P = P ^  = P^a a n d n(0) i s the popu l a t i o n d i f f e r e n c e at t = 0. (68) The r a t e of absor p t i o n of energy from the r . f . f i e l d i s given by - 15 -§ | = nP(E -E ) dt a b [2.27] However, these r e l a t i o n s imply that upon a p p l i c a t i o n of a p e r t u r b i n g f i e l d , the s p i n populations w i l l be i n i t i a l l y unbalanced but 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 populations become equal or become "sat u r a t e d " . This i m p l i e s that the r a t e of absorption w i l l a l s o decrease causing the resonance l i n e to e v e n t u a l l y disappear. In the absence of a magnetic f i e l d , the s p i n populations of the two l e v e l s are equal, 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 re t u r n s to thermal e q u i l i b r i u m and thus there must be a mechanism through which the spi n s are able to i n t e r a c t w i t h the surroundings causing the s p i n o r i e n t a t i o n to change. This process 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 the time r e q u i r e d to r e e s t a b l i s h e q u i l i b r i u m . Equation [2.27] can be r e w r i t t e n to account f o r t h i s mechanism, the r e s u l t being 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 to the square of the i n c i d e n t power and so to avoid s a t u r a t i o n e f f e c t s i t i s best to work at a lower i n c i d e n t power. The p r o b a b i l i t y equation [2.25] shows that absorption w i l l take place only when the 6-function c o n d i t i o n s are 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-function [2.28] - 16 -lineshape. However, t h i s lineshape i s not observed experimentally because of mechanisms which broaden the 6-function to a f i n i t e l i n e -w idth. Since the processes are r e s t o r i n g thermal e q u i l i b r i u m , the p o p u l a t i o n of the Zeeman l e v e l s w i l l have a f i n i t e l i f e t i m e which w i l l r e s u l t i n a l i n e broadening of the order of 1/T^. Other processes a l s o occur which 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 energies of the s p i n l e v e l s . This can be caused by the f l u c t u a t i o n of the f i e l d at the unpaired e l e c t r o n due to the presence of l o c a l magnetic n u c l e i or other unpaired e l e c t r o n s . This process i s termed the 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 are no longer sharp but d i f f u s e , a band of energies e x i s t s over which the t r a n s i t i o n s can occur 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 T^) 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 to the l i n e w i d t h . These two processes are by no means the only mechanisms which c o n t r i b u t e to l i n e broaden-(72) i n g . P o r t i s gives an account of s e v e r a l other l i n e broadening processes which are termed homogeneous broadening s i n c e the thermal e q u i l i b r i u m of the s p i n system i s preserved during a t r a n s i t i o n and the energy absorbed i s transmitted to a l l the spins i n the system. They in 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) motion 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 f l u c t u a t i o n s i n the l o c a l f i e l d . In homogeneous broadening (which does not maintain the s p i n system i n e q u i l i b r i u m ) i s represented by such processes as: hyper-f i n e i n t e r a c t i o n , a nisotropy broadening, and inhomogeneities i n the a p p l i e d magnetic f i e l d . - 17 -2.3 Llneshape A broadened lineshape can be expressed 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), which describes the v a r i a t i o n of energy abs o r p t i o n when the resonance c o n d i t i o n i s s a t i s f i e d . 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]) consequently becomes P a b ( H ) = ^ |<a|v|b>|2 g(H) [2.29] where g(H) s a t i s f i e s the n o r m a l i z a t i o n c o n d i t i o n | °° g(H)dH = 1 and V i s a p e r t u r b i n g p o t e n t i a l (the r . f . f i e l d i n t h i s case). I t i s experimentally observed that the lineshape f u n c t i o n s f a l l i n t o two main types. In l i q u i d s , the Lorentz lineshape i s most commonly observed T 2 1 g(H) = — ^ =• (absorption mode) [2.30] * 1 + T 0 Z(H-H r 2 o whereas i n s o l i d s , gaussian lineshapes predominate T2 ( 1 2 2 ) g(H) = e x P | ~ 2* T2 ^ H - H o ^ I (absorption mode) [2.31] where H i s the f i e l d of the centre of resonance and H i s the v a r i a b l e o magnetic f i e l d . Since 1^ i s i n v e r s e l y p r o p o r t i o n a l to the l i n e w i d t h , (AH ), and si n c e i n EPR the d e r i v a t i v e of the abso r p t i o n curve i s PP (73) most commonly seen, these lineshapes can be w r i t t e n as - 18 -LORENTZIAN absorption curve F i g . 2 . 2 Lineshapes commonly observed i n EPR s p e c t r a - 19 -L o r e n t z i a n : g'(H) = 2/3 AH (H-H ) PP 0 3AH 2 + (H-H ) 2 PP 0 and gaussian: g'(H) (H-H ) o /2TTAH exp PP -(H-H y o 2 H PP [2.32] [2.33] A comparison between these two lineshapes i n the absorption 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 the Resonance F i e l d s The resonant 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 are c a l c u l a t e d from an exact s o l u t i o n to the general s p i n Hamiltonian (eqn. [2.23]). The b a s i s of the m e t h o d i s to d i v i d e the s p i n Hamiltonian i n t o 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] nuc h.(B eg-S - B N £ g n k I k ) [2.36] and h i s the u n i t v e c t o r i n the d i r e c t i o n of the magnetic f i e l d . Then, f o r a given i n i t i a l guess (H ) at the true resonance f i e l d - 20 -(H ), the 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 the res res st preceding terms. The i n i t i a l guess H i s n o n - c r i t i c a l , but i s p r e f e r a b l y w i t h i n 30% of ( a poor guess w i l l o n l y i n c r e a s e the number of c y c l e s necessary to converge to H r e s ) • The matrices of ^ ^ ^ a n d ^ ^ ^ HQ and H^ r e s p e c t i v e l y , are constructed i n the m , m_,...,m_ > b a s i s and the combined terms H A - H H, are 1 s I ' I. =0 s t = l k d i a g o n a l i z e d e x a c t l y to provide a set of unperturbed, zeroth order energies and eigenvalues. A set of p e r t u r b a t i o n energies can now be w r i t t e n i n terms of the zeroth order wave fu n c t i o n s and energies w i t h ^ ^ ^ a c t i n g as the p e r t u r b i n g Hamiltonian i n a seventh order, complex degenerate p e r t u r b a t i o n procedure. I t might be noted that t h i s procedure i s independent of the p e r t u r b a t i o n c o e f f i c i e n t ( H r e s - H g t ) and t h a t < ; : ^ ^ i s i t s e l f independent of f i e l d . Having thus obtained a set of seventh order p e r t u r b a t i o n energies, a power s e r i e s i n H and these energies can be constructed from the resonance c o n d i t i o n as f o l l o w s : hv = £ H n ( E ( n ) - E ( n ! ,) [2.37] n^O m i m S m i m S where hv i s the microwave quantum and E^ n^ are the order m i m s p e r t u r b a t i o n energies of the mm 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 . This power s e r i e s can be solved f o r H by the Newton-Raphson method, a s t a r t i n g value of H f o r the i t e r a t i v e procedure being obtained by r e v e r s i o n of the s e r i e s . The s o l u t i o n to 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 ext r a c t e d to r v res s t res become the new s t a r t i n g guess H fc. The e n t i r e procedure i s cy c l e d u n t i l the s i x t h and seventh order terms i n the 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 to the energy l e v e l s i nvolved i n the -3 t r a n s i t i o n . At t h i s p o i n t the value H i s accurate to 10 gauss, res and convergence i s assumed. I t i s g e n e r a l l y found that w i t h a j u d i c i o u s choice of H g t, convergence i s obtained i n the f i r s t c y c l e . To o b t a i n the c o r r e c t wave f u n c t i o n s necessary f o r the 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 d i a g o n a l i z e d 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 the 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 . 12 i s necessary to evaluate the matrix expression ••|<a-|V|b>| of eqn. [2.25]. Consider the case of a system which e x h i b i t s no h y p e r f i n e , nuclear 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 Hamiltonian i s given 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 ) [2.38] (/Is & x x x °y y y °z z z where the p r i n c i p a l a x i s system has been chosen f o r the g tensor and 1 ,1 ,1 are the d i r e c t i o n cosines between the magnetic - f i e l d H and x y z 6 the p r i n c i p a l axes x,y,z. For any general o r i e n t a t i o n of H, the a x i s system can be transformed i n t o a r e p r e s e n t a t i o n which i s diag o n a l i n a new s p i n sens; 2 2, 2 ^ 2 2 2. 2 where g = g l + g 1 + g l 6 & x x y y z z [2.39] - 22 -A Hamiltonian r e p r e s e n t a t i o n f o r the p e r t u r b i n g , l i n e a r l y p o l a r i z e d microwave f i e l d can be w r i t t e n as ffi? = H.coscot (g 1 S + g l's + g l's ) [2.40] C l s l 1 °x x x °y y y °z z z L J and transforming i n t o the same a x i s system as the s p i n Hamiltonian: ^ = Hjcosut ( § 1 S ^ + g ^ + g^) [2.41] where g 2 = 1/g2 \ g V d ' l - 1 l') + g 2g 2 ( l ' l - 1 l') °1 & < e,x°y x y x y & z e x z x z x 2 9 ' ' , [ 2 - 4 2 ] + g g ( 1 1 - 1 1 ) } y z y z y z ' The 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 the 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 2 ' to <mg |^£jjmg±l>| and consequently S z w i l l be i n e f f e c t i v e i n coupling the m s t a t e s and only S and S w i l l be e f f e c t i v e i n inducing s x y t r a n s i t i o n s ( i e . the components of the r . f . f i e l d which are perpen-d i c u l a r to the magnetic f i e l d ) . This r e p r e s e n t a t i o n i s not convenient 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 obtained by transforming to s p h e r i c a l p o l a r coordinates ( f i g . 2.3). The d i r e c t i o n cosines of the magnetic f i e l d are expressed i n terms of the polar angles 0 and (j) and the d i r e c t i o n cosines of the r . f . f i e l d i n the z, P, Q frame T are expressed i n terms of the p o l a r angles n, 8 . A new set of i i i d i r e c t i o n cosines 1 , 1 , 1 can now be defined i f the 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 in the x,y,z molecular frame and b) the r . f . f i e l d H-, in a z,P,Q frame. - 24 -coordinates are transformed i n t o the x,y,z frame. I T 1 = s i n n s i n 9 cos <j> - cos r| s i n <b x i i 1 = s i n n s i n 0 s i n <J> + cos n cos c|> [2.43] i t 1 = s i n n cos e z S u b s t i t u t i n g i n t o eqn. [2.42], an expression i s obtained which 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 2 j 2 S l = 1 / g j S x 8 2 2 .2 cos n s i n y 2 2 2 1 2 2 + g {sin n s i n (9 -9) [g s i n <j> z y 2 2 2 2 2 2 2 2 + g cos $] + cos n cos 9 [g cos <(> + g s i n <j>] x y x + 2 s i n n cos n s i n 4> cos <t>" s i n (9* - 9) cos 0 ( g y 2 - g ^ ) } [2.44] 2 I t i s c l e a r from t h i s expression that g^ w i l l have a maximum value i f i s perpendicular to the magnetic f i e l d , that i s , when 0 -0 = 90°, which i s the normal case i n most EPR experiments. For s t u d i e s on s i n g l e c r y s t a l s , n i s a known value, and f o r a re 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 . For the case when H i s p a r a l l e l to the x molecular a x i s (0 = 90°, <j> = 0°) - 25 -2 the t r a n s i t i o n 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 . However when H i s p a r a l l e l to the y molecular a x i s (9 = 90°, <j> = 90°) the t r a n s i t i o n 2 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 g^ . Thus i n cases where a h i g h l y a n i s o t r o p i c g tensor i s present, the o r i e n t a t i o n of the r . f . v e c t o r must be known i n order to p r e d i c t the c o r r e c t i n t e n s i t y of a t r a n s i t i o n . In the case of a p o l y c r y s t a l l i n e sample, a l l values of n w i l l t be e q u a l l y probable. When 0 - 0 = 90°, there w i l l be an ensemble of molecules o r i e n t e d i n such a manner, that even though H may mag be along the same d i r e c t i o n i n each, there 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 of the plane perpendicular to t h i s d i r e c t i o n . For example i f H i s p a r a l l e l to the z a x i s , the r . f . v e c t o r can l i e anywhere i n the x, y plane g i v i n g r i s e to 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 to g s i n n + g cos n. x y Thus n can range from 0 -»• TT f o r any given 0 and <j> and the 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 "see" an e f f e c t i v e g valu 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 taken over a l l values of n by i n t e g r a t i n g g^ as y" 2 T rg^ 2 dn/2ir. This i n t e g r a l i s e a s i l y computed and has the value of 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 - 0 = 90° being 2 T 2 2 2 2 2 2 2 2 g l = g x g y S ^ n ® + g y g z ^s-""n ^ + c o s 9 c o s ^ 2 2 2 2 2 ~1 2 + g g {cos c|> + cos 9 s i n 2/g [2.45] Z X _J Thus the 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 only upon the p o l a r angles 9 and <f> of the magnetic f i e l d . - 26 -This of course i s a very simple case i n which there i s no hyperfi n e or nuclear i n t e r a c t i o n . In most cases however, these i n t e r a c t i o n s w i l l be present and the general form f o r c a l c u l a t i n g 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. For a given set of b a s i s v e c t o r s , {<j>(m . m T , . . . n i ) } , the s t a t e vector il> can be s i I p n (7174) expressed as a l i n e a r combination of these v e c t o r s . ' -S .1 ,n ^ p = ^ S G ^ m s ' m i '••• m I »k) ^ g ^ x '.•••mI ) [2.46] m =S mT =1, mT =1 I n I n s IT 1 I n 1 n where G i s a complex matrix of mixing c o e f f i c i e n t s obtained from the d i a g o n a l i z a t i o n of the s p i n Hamiltonian (eqn. [2.23]). at a p a r t i c u l a r resonant f i e l d . The most general t r a n s i t i o n p r o b a b i l i t y can be expressed as [2.47] where u i s a set of d i r e c t i o n cosines of the r . f . f i e l d i n the molecular a x i s system. To adapt t h i s equation to the c a l c u l a t i o n of 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 p r o b a b i l i t i e s , three assumptions w i l l be made. i 1. H^ i s always perpendicular t o H ( ( 6 - 0 ) = 90°). 2. The p r i n c i p a l a x i s system i s always the diagonal g-frame. 3. g^ i s i s o t r o p i c . Expanding [2.47] i n terms of the s p i n operations S +, S , S^, l + , I , I the t r a n s i t i o n p r o b a b i l i t y becomes - 27 -Tab • i K i W s + + s _ ) + V y ( s + - s _ ) + 2 ' A _ V ^ j l , ( I + + I . - ) + l ' ( I + - I . - ) + 2 l ' l ( | V | ' B J x i i y i 1 z z ( 1 Tb y i i=l e < [2.48] I f the operators are evaluated and the expressions f o r the d i r e c t i o n cosines (eqn. [2.43]) are s u b s t i t u t e d an expression equivalent to eqn. [2.44] can be obtained on averaging o v e r a l l values of n. 2 1 2 2 2 1 2 1 T , = A. ( s i n 6 c o s d> + s i n <J>) + A 0 ( c o s 8 sin2((>) + A _ ( s i n 8 c o s t ) ) ) ab 1 2. 5 2 i 2 2 ' 2 ' + A ^ ( s i n 9 s i n <j) + c o s (j>) + A^(sin28 sincj>) + A ^ ( c o s 8 ) [2.49] where the A^ are a set of complex c o e f f i c i e n t s which are dependent on the e l e c t r o n i c and nuclear g-values and the c o e f f i c i e n t s G i n eqn. [2.46]. I t may be noted that t h i s expression i s dependent i only on the p o l a r angles of the magnetic f i e l d (8 = 8 + 90°). A more f u l l y derived expression i s given i n Appendix A w i t h the values A 1 - A A more f u l l y expanded. CHAPTER THREE Experimental 3.1 The Spectrometer An X-band, super-heterodyne spectrometer was used f o r the d e t e c t i o n of the EPR. s i g n a l s . The spectrometer was constructed by the U.B.C. Chemistry Department E l e c t r o n i c s Shop, from commer-c i a l l y a v a i l a b l e components. I t was based on a design developed l a r g e l y by Profess o r J . B. Farmer of t h i s U n i v e r s i t y . The two microwave sources were V a r i a n type V153C k l y s t r o n s which were tuneable from about 8.5 GHz to 9.8 GHz. A Hewlett-Packard (HP) 716-E k l y s t r o n power supply was used. The microwaves were c a r r i e d to the EPR c a v i t y through standard waveguide components. Because of the low frequency s e n s i t i v i t y of the microwave system, a l l waveguide components were securely braced to a p l a t f o r m mounted on the magnet yoke. A fou r - p o r t c i r c u l a t o r was used to d i r e c t the microwaves r e f l e c t e d from the resonance c a v i t y to the d e t e c t o r . Microwave As s o c i a t e s 1N23G diodes were used f o r d e t e c t i o n and were mounted i n an LEL XBH-2 intermediate frequency ( i . f . ) mixer p r e a m p l i f i e r . A second k l y s t r o n , operating at frequency of 28 MHz - 29 -above or below the frequency of the f i r s t k l y s t r o n , t r a n s m i t t e d to the second port of the i . f . mixer 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 the 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 the 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 modified two stage i . f . a m p l i f i e r (LEL model IF 30B 50). The a m p l i f i e d s i g n a l was then passed to a phase s e n s i t i v e d e tector ( 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 recorder or a Moseley 680 s t r i p chart recorder. 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 automatic frequency 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 Varian V4500-10 AFC c i r c u i t . The frequency of the second k l y s t r o n was allowed to d r i f t s i n c e the band width of the i . f . p r e a m p l i f i e r (^  3 MHz at 28 MHz) was s u f f i c i e n t to al 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 frequencies of the two k l y s t r o n s . The magnetic f i e l d was sup 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 pole pieces of the magnet to 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 . The f i e l d modulation frequency was 108 Hz and was sup p l i e d by a HP model 200-J audio 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 modulation frequency i s necessary s i n c e the modulation must penetrate the t h i c k w a l l s of the metal c r y o s t a t . The highest frequency that could be used without a s i g n i f i c a n t l o s s of modulation amplitude was ^ 300 Hz. The audio o s c i l l a t o r a l s o supplied the reference 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 the f i r s t d e r i v a t i v e of the absorption mode. - 30 -A HP 431-C power meter was used to measure the i n c i d e n t micro-wave power of the primary k l y s t r o n . T y p i c a l power l e v e l s were about • 1 mW and were always below 2 mW. The microwave frequency was measured w i t h a HP 5245-L frequency counter equipped w i t h a HP 5255-A frequency converter to cover the range 8.5 GHz to 12.8 HGz. The magnetic f i e l d was measured by an e x c e p t i o n a l l y s t a b l e magnetometer constructed by the U.B.C. Chemistry 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 to the center of the magnet pole p i e c e s , a t h i n magnetometer probe was constructed which 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 averaging computer was used i n s e v e r a l e x p e r i -ments to 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 standard rectangular c a v i t y operating i n the TE^.^ m°de. Wide s l i t s were cut i n the end p l a t e of the c a v i t y to permit the i n s i t u UV i r r a d i a t i o n of the sample which was deposited on a c e n t r a l l y mounted, f l a t copper rod. 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 metal, r o t a t a b l e l i q u i d helium 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 design to the c r y o s t a t s of other workers (7,34,76)^ ^ o p r e v e n t t a e i o w frequency mechanical 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 inner l i q u i d helium dewar was f i t t e d w i t h a T e f l o n spacer which was braced against the r i g i d l i q u i d n i t r o g e n s h i e l d w i t h a minimum of contact p o i n t s . The heat conduction to the helium dewar through t h i s spacer r e s u l t e d i n a s l i g h t increase - 31 -Mixed Gas (Sample) F i g . 3.1 L i q u i d helium c r y o s t a t . - 32 -i n the b o i l - o f f r a t e of the l i q u i d helium but t h i s was more than compensated f o r by a s i g n i f i c a n t increase i n the s i g n a l to noise r a t i o of the 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 high speed Welch vacuum pump. T y p i c a l pressures i n the dewar system were ^ 5 x 10 7 mmHg-. . The EPR c a v i t y was i n d i r e c t contact w i t h the t a i l of the l i q u i d helium dewar. A t h i n w a l l e d , s t a i n l e s s s t e e l waveguide connected the c a v i t y to the e x t e r n a l waveguide system. The sample d e p o s i t i o n surface c o n s i s t e d of a t h i n , f l a t copper rod which was mounted i n the center of the c a v i t y and connected d i r e c t l y to the t a i l of the helium dewar. The t a i l of the dewar was constructed to a l l o w the rod to be ro t a t e d w h i l e the c a v i t y could remain f i x e d . The sample gas was sprayed onto the f l a t s u rface of the l i q u i d helium cooled copper rod by using a t h i n S u p r a s i l quartz nozzl e w i t h a f i n e o r i f i c e , which projected i n t o the bottom of the c a v i t y . The bottom of the nozzle was connected to an outer spray l i n e which was connected to the sample v e s s e l . The sample gas flow r a t e was c o n t r o l l e d by a Te f l o n needle v a l v e stopcock such that the t o t a l pressure i n the spray l i n e d i d not exceed .1 mmHg (as measured by a thermocouple gauge). At t h i s spray r a t e , the pressure i n the dewar d i d not r i s e above 2 x 10 ^  mmHg. The helium c r y o s t a t o u t l e t was connected by vacuum tubing to a heat exchanger c o n s i s t i n g of a c o i l e d copper tube immersed i n a water bath. The o u t l e t from the heat exchange was connected to a high speed Welch Duo-seal vacuum pump whose exhaust was connected - 33 -to a helium recovery l i n e . For most experiments, the temperature of l i q u i d helium at S.T.P. (4.2 K) was used. For s e v e r a l e x p e r i -ments, the vapour pressure above the l i q u i d helium was reduced by pumping to about 40 mmHg which corresponds to a temperature of the l i q u i d helium of 2.2 K. This technique was used i n an attempt to increase the s i g n a l to n oise r a t i o but no appreciable enhancement could be detected. 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 experiments, a high pressure mercury lamp (500W PEK) was used. This lamp has an almost continuous out-o put of l i g h t extending from about 3000 A i n t o the i n f r a - r e d . To decrease the warming of the deposited sample gas due 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 unsuccessful i n preventing the warming of the sample. Short i r r a d i a t i o n periods were thus r e q u i r e d to minimize t h i s warming. For samples r e q u i r i n g a higher energy to d i s s o c i a t e i n t o r a d i c a l fragments, a low pressure mercury lamp w i t h a maximum i n t e n s i t y at about 2537 1. and 1849 k was used. This lamp c o n s i s t e d of a sealed quartz 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 sealed i n t o the ends of the quartz tube and these were connected to a high voltage DC source. For higher energies, gas resonance lamps were used. These were two types; a sealed lamp or a flow discharge lamp. The sealed lamp co n s i s t e d of a s t r a i g h t quartz tube f i t t e d w i t h a s i d e arm that would - 34 -be immersed i n a CC^/acetone s l u s h bath which was necessary to remove any traces of moisture or i m p u r i t i e s . The lamp was f i l l e d to a pressure of about 1 mm w i t h e i t h e r argon or krypton whose resonance l i n e s are at (1067 A; 1048 A) and (1236 A; and 1165 X) r e s p e c t i v e l y . One end of the quartz tube w a s . f i t t e d w i t h a L i F window which was po l i s h e d f l a t . The lamp was then mounted d i r e c t l y on the dewar i n place of the quartz window. The gas was discharged 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 generator operating at 2.45 GHz. The flow discharge lamp was constructed i n a manner s i m i l a r to the above sealed lamp, except that i t was connected to a vacuum pump. Hydrogen gas was mixed with a stream of helium gas which served as a d i l u t e n t . The gas flow rates were adjusted u n t i l a f a i n t pink glow appeared when the system was discharged w i t h a microwave generator. Because of the high i n t e n s i t y of the hydrogen l i n e (1216 A) and the high energy i n v o l v e d , the i r r a d i a t i o n times to produce a reasonable EPR s i g n a l were very s h o r t . A f u r t h e r d e s c r i p -t i o n of l i g h t sources can be found i n C a l v e r t and P i t t s . 3.4 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 handled i n a pyrex g l a s s vacuum system constructed by the U.B.C. Chemistry Department Glass Blowing Shop. To reduce the l i k e l i h o o d of contamination from vacuum grease, high vacuum Te f l o n stopcocks 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 necessary, a f l u o r o -- 35 -carbon grease (Fluorolube) was used. This was necessary because s e v e r a l of the gases handled reacted v i o l e n t l y w i t h hydrocarbon greases. The vacuum manifold was degassed w i t h a heating tape which could be heated to 400 K i f necessary. The manifold was heated between sample preparations to prevent the adsorption of sample gases on the w a l l s of the vacuum l i n e which might contaminate subsequent samples. Pumping of the vacuum system was through a Veeco o i l d i f f u s i o n pump backed by a Welch Duo-seal vacuum pump. Pressures were measured by an NRC type 401 i o n gauge or an NRC type 531 thermocouple used i n conjunction w i t h an NRC type 531 dete c t o r . Gas pressures i n the vacuum system during sample pre-p a r a t i o n were 10 ^  - 10 ^  mmHg. Pressures above 1 mmHg were measured w i t h a gas s p i r a l gauge ra t h e r than a mercury manometer to prevent the i n t r o d u c t i o n of mercury vapour i n t o the sample. The e n t i r e vacuum system was mounted i n a fume cupboard because of the t o x i c i t y of the sample gases. The v e s s e l c o n t a i n i n g the sample was u s u a l l y a 500 ml or 1 l i t e r blackened bulb f i t t e d w i t h a Tef l o n stopcock. The volumes of the vacuum manifold and the sample bulbs were roughtly c a l i b r a t e d to a l l o w the r a t i o s of pressures of the d i l u t e n t gas and sample gas to be c a l c u l a t e d . The sample gases were prepared about one hour before the experiment to all o w complete mixing of the 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 Dioxide (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 of pre p a r a t i o n i s the 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 a c i d s o l u t i o n . The r e a c t i o n i s 2KC10,. + 2H„S0. + H„C o0.-2H o0 2C10 o + 2C0 o + 4H„0 + 2KHS0, •i 2 4 2 2 4 2 L 2 2 4 The ClO^ and CO^ evolved was passed over a ?2°5 dr y i n g tube and the CO2 can be f r a c t i o n a t e d from the CIC^ by trap to trap d i s t i l l a t i o n from a dry i c e cooled trap (195 K) to a l i q u i d n i t r o g e n cooled trap (77 K). Extreme care was exe r c i s e d i n handling t h i s compound as i t (78) has been found to e x p l de f o r no obvious reason . A l l j o i n t s on the vacuum apparatus were greased w i t h Fluorolube and room l i g h t s were turned o f f when the sample was prepared s i n c e CIC^ w i l l decompose on i l l u m i n a t i o n . The p u r i f i e d CIG^ was stored i n a gl a s s tube w i t h a T e f l o n stopcock. The sample tube was kept at 195 K i n a dry i c e / t r i c h l o r o e t h y l e n e bath and kept away from room l i g h t . The CIC^ was found to be i n d e f i n i t e l y s t a b l e at t h i s temperature but was p u r i f i e d to remove any p o s s i b l e decomposition products immediately p r i o r to use. 3.5.2 D i c h l o r o d i s u l f a n e (S2CI2) Commercially a v a i l a b l e S2CI2 was purchased from B r i t i s h Drug House. The sample was a reddish orange i n d i c a t i n g the presence - 37 -of S C I 2 i m p u r i t i e s . The S^C^ was d i s t i l l e d at atmospheric pressure and the 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 trap to trap vacuum d i s t i l l a t i o n . The S 2 C 1 2 w a s P l a c e d i n a c o l d trap at 209 K (Chloroform/ l i q u i d n i t r o g e n slush) and vacuum d i s t i l l e d to a trap cooled to 177 K (T o l u e n e / l i q u i d ^ s l u s h ) . The r e s u l t i n g s o l i d was pumped to remove a l l traces of higher b o i l i n g i m p u r i t i e s . This p u r i f i c a t i o n process was repeated s e v e r a l times w i t h the f i n a l product being a c l e a r y e l l o w s o l u t i o n . The p u r i f i e d sample was stored i n a dry 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 procedure was repeated p r i o r to each experiment. The vapour pressure of S 2 ^ 2 a t 209 K ( C h l o r o f o r m / l i q u i d ^ slush) was used i n preparing the sample. 3.5.3 T h i o n y l f l u o r i d e (SOF,,) The 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 was > 99% pure. The SOF2 was passed through a c o l d trap at 177 K ( t o l u e n e / l i q u i d n i t r o g e n slush) and condensed i n a c o l d trap at 144 K (n-pentane/liquid n i t r o g e n s l u s h ) . The s o l i d sample was pumped -4 to 10 mmHg at t h i s temperature. The vapour pressure of SOF2 at 177 K was used to prepare the sample. 3.5.4 S u l f u r y l f l u o r i d e ( S O ^ ) The s u l f u r y l f l u o r i d e was purchased from Matheson Chemicals. Although s t a t e d to be 99.5% pure, the S ° 2 F 2 c o n t a i n e d S 0 F 2 a s a n i m p u r i t y . This impurity could not be e a s i l y removed by trap to trap d i s t i l l a t i o n due to the small 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 mixture was passed through a c o l d trap at 177 K and trapped i n a c o l d trap at 144 K. The frozen gas was pumped u n t i l a pressure -4 of 10 mmHg was reached. The vapour pressure of the l i q u i d at 177 K was used to prepare the 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 CF^OF was purchased from PCR Chemicals and was 75% pure. The i m p u r i t i e s were CG^, CF^, S i F ^ and CG^. These could be removed by s u i t a b l e d i s t i l l a t i o n techniques. A l l the i m p u r i t i e s have a b o i l i n g point above l i q u i d n i t r o g e n (77 K). The gas was condensed i n a l i q u i d n i t r o g e n trap and l i g h t l y pumped. The vapour pressure of CFgOF at l i q u i d n i t r o g e n temperatures was used to prepare the sample. Sample pr e p a r a t i o n was done i n a darkened room to avoid decomposition of the CF^OF. 3.5.6 S u l f u r d i o x i d e ( S O j The SC>2 was obtained from Matheson Gas Products. The p u r i t y was 99.9%. The SG^ was condensed at 195 K and pumped to remove any traces of oxygen. The vapour of SO^ as i t melted was used i n the sample p r e p a r a t i o n . 3.5.7 Hydrogen Iodide (HI)) The HI was purchased from Matheson Gas Products. The decomposition products H 2 and were removed by successive d i s t i l l a t i o n u n t i l the condensed gas was c o l o r l e s s . The vapour pressure of HI at 227 K (chlorobenzene/liquid n i t r o g e n slush) was used i n the sample p r e p a r a t i o n . - 39 -3.5.8 Neon, Argon, Krypton The rare gases used were Matheson research grade and were used without f u r t h e r p u r i f i c a t i o n . 3.6 Molecular O r b i t a l C a l c u l a t i o n s In t h i s work the LCAO-MO-SCF c a l c u l a t i o n s were performed using two molecular 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 the 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. The b a s i s set was l i m i t e d to s-, p-, and d- S l a t e r type o r b i t a l s . This program, however, was not parameterized to perform IND0/2 c a l c u l a t i o n s on molecules c o n t a i n i n g second row elements. Instead, the I N D 0 / 2 ^ ^ c a l c u l a -t i o n s were performed using a program developed by Dr. F. G. Herring (81) of t h i s U n i v e r s i t y . The b a s i s set was l i m i t e d to s- and p-S l a t e r type o r b i t a l s . The IND0/2 parameterization used f o r the (82 ) second row elements i s that of Benson and Hudson w h i l e the (83) para m e t e r i z a t i o n of Santry was used f o r the CND0/2 c a l c u l a t i o n s . CHAPTER FOUR 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 Consider the 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 of a para-magnetic molecule which has orthorhombic symmetry and one nucleus wi a nuclear s p i n I = 1/2 and one unpaired 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 along a p a r t i c u l a r d i r e c t i o n 6, <t> w i t h respect to the molecular axes ( c f . f i g . 2.3a) an energy l e v e l system s i m i l a r to that i n f i g . 2.1 w i l l r e s u l t (the 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 case). When the magnetic f i e l d i s swept at a constant microwave frequency, two types of t r a n s i t i o n s may be observed corresponding to Am^ . = 0, ±1. The Am = ±1 t r a n s i t i o n s are "forbidden" and g e n e r a l l y are much l e s s intense than the Am^ . = 0 t r a n s i t i o n s . I f an angular dependence study of the 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 the sample about a molecular 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 vs H. The numbers above the curves i n d i c a t e the Am^ = 0, ±1 t r a n s i t i o n s . When the magnetic f i e l d i s p a r a l l e l to the molecular axes, a unique set of parameters can r e a d i l y be e s t a b l i s h e d f o r the g and A tensors. In most molecules, the g and A tensors w i l l be c o i n c i d e n t and the s p i n Hamiltonian - 41 -parameters w i l l be defined i n the di a g o n a l , molecular frame. I f the o r i e n t a t i o n of the molecule w i t h i n the c r y s t a l s t r u c t u r e i s known, the tensor can be assigned to s p e c i f i c d i r e c t i o n s i n the 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 center i s ground to a f i n e powder, or a s o l u t i o n of a paramagnetic center i s f r o z e n or formed i n a glassy or condensed m a t r i x , i t i s to be expected that a l l o r i e n t a t i o n s of the molecular axes of the center w i l l be e q u a l l y probable. Thus when the 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 set of " s i n g l e c r y s t a l " resonances. The absorption spectrum w i l l thus c o n s i s t of the sum of a l l such resonances and w i l l extend from some H . to some H as given i n f i g . 4.1. The d i f f e r e n t i a l min max p r o b a b i l i t y dP(H) that a resonance w i l l occur 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 the f i e l d s H and H + dH i s p r o p o r t i o n a l to the s o l i d angle of d5(9,(J>) f o r which the resonant f i e l d l i e s i n t h i s i n t e r v a l ( i e . the molecules are o r i e n t e d between 6 and 6 + d9, cj) and <J) + dd> w i t h respect to the magnetic f i e l d ) . The 2 area of a c i r c u l a r element of area about the z a x i s i s 2-nv • s i n 0d9d<j> and hence the s o l i d angle i t subtends i s the r a t i o of t h i s area to the surface area of the sphere. d£(9,<l>) = 1/2 s i n 6d9d<j) = -1/2 dcos0d<j> [4.1] sinc e 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 s o l i d angle, the shape of the powder spectrum can be described by F i g . 4.1 Angular v a r i a t i o n of the h y p e r f i n e resonances i n the three p r i n c i p a l planes f o r a h y p o t h e t i c a l S = 1/2, I = 1/2 system. - 43 -dPiy  a-- (dH/dcos9d(j)) 1 [4.2] dH T h i s e x p r e s s i o n can be e v a l u a t e d n u m e r i c a l l y and the computer program which was de v e l o p e d to p e r f o r m t h i s w i l l be d i s c u s s e d l a t e r . The powder l i n e s h a p e i s t h e r e f o r e dependent upon the r a t e o f change of f i e l d p o s i t i o n of a p a r t i c u l a r t r a n s i t i o n w i t h a change i n m o l e c u l a r o r i e n t a t i o n dH/dcos6d<)>. E x p e r i m e n t a l l y , the resonance peaks i n a powder spectrum o c c u r o n l y where (dH/dcos6dct>) -* 0 . L o o k i n g a t f i g . 4.1, i t can be seen t h a t t h i s r a t e of change i s l e a s t when the f i e l d i s o r i e n t e d near a m o l e c u l a r a x i s . A l t h o u g h t h e r e a r e many m o l e c u l e s w i t h s l i g h t l y d i f f e r e n t o r i e n t a t i o n s i n a r e g i o n where t h i s r a t e i s s m a l l , the re s o n a n t l i n e p o s i t i o n s w i l l change l e a s t f o r these m o l e c u l a r o r i e n t a t i o n s , and as a r e s u l t t h e s e m o l e c u l e s w i l l c o n t r i b u t e more s i g n i f i c a n t l y t o the a b s o r p t i o n i n t e n s i t y than those m o l e c u l e s whose o r i e n t a t i o n i s such, t h a t the r a t e o f change, dH/dcos9dcj), i s l a r g e . Thus f o r the s i m p l e case under c o n s i d e r a t i o n , i t i s expec t e d t h a t t h e r e w i l l be s i x c h a r a c t e r i s t i c Am^ = 0 t r a n s i t i o n s c o r r e s p o n d i n g t o H b e i n g a l o n g the t h r e e m o l e c u l a r axes. The d e l t a - f u n c t i o n and G a u s s i a n broadened powder l i n e s h a p e i i f o r t h i s case i s r e p r e s e n t e d i n f i g . 4.2a where A_„ and g ar e v a l u e s of the h y p e r f i n e and g t e n s o r a l o n g the m o l e c u l a r axes. F i g . 4.2b i s the d e r i v a t i v e r e p r e s e n t a t i o n . The p r i n c i p a l v a l u e s , which a r e g i v e n i n f i g . 4.2b, have been taken d i r e c t l y from the s i n g l e c r y s t a l assignment ( f i g . 4.1). In most c a s e s , however, F i g . 4.2 T h e o r e t i c a l sample, a) absorption. and broadened EPR lineshapes f o r a p o l y c r y s t a l l i n e absorption lineshape b) f i r s t d e r i v a t i v e of the - 45 -the s i n g l e c r y s t a l data are not a v a i l a b l e and the p r i n c i p a l values must be assigned from the p o l y c r y s t a l l i n e spectrum alone. This presents a much more d i f f i c u l t task 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 to 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 without 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' could 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 lineshape 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 , using these parameters would give r e s u l t s i d e n t i c a l to 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 choices f o r assignment of the p r i n c i p a l values. Most of these choices w i l l u s u a l l y lead to u n r e a l i s t i c tensor values f o r the species 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 estimates 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 so, may s t i l l leave the a x i s and tensor assignment u n c e r t a i n . There are c e r t a i n i n s t a n c e s , however, where an unambiguous assignment of tensor values and d i r e c t i o n s can be made. I f the nuclear 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 strong to allow mixing of the h y p e r f i n e l e v e l s , the "forbidden" 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 " the powder l i n e s . In other cases, i t may be p o s s i b l e to s u b s t i t u t e the magnetic nucleus w i t h an isotope of d i f f e r e n t nuclear 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 l i n e p o s i t i o n s . I f t h i s i s not f e a s i b l e , repeating the experiment at a higher microwave frequency may a i d the assignment, s i n c e the hyper-f i n e terms are 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 are f i e l d dependent. The components of the tensor can then be assigned from the g - s h i f t s between the two frequencies. In the case of a system which has i n t e g r a l nuclear s p i n , the p r i n c i p a l g values are immediately given by the f i e l d p o s i t i o n s of the Am^ = 0 t r a n s i t i o n s i n the 1 = 0 , manifold and the only remaining task i s to a s s i g n the p r i n c i p a l values to d i r e c t i o n s i n the molecule. O c c a s i o n a l l y , w i t h molecules trapped i n r a r e gas matrices at 4.2°K, (19 33 34 40) the phenomenon of p a r t i a l o r i e n t a t i o n i s observable. ' ' ' In t h i s i n s t a n c e , at l e a s t one p r i n c i p a l value can be assigned simply by observing 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 as the sample i s r o t a t e d through 90° i n the magnetic f i e l d - those l i n e s which change i n t e n s i t y i n the same manner are 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 molecular d i r e c t i o n . 4.2 Non-coincident 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 evident through the course of the work presented 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 present or when a molecule has a very low symmetry (eg. C ) and the g and A tensors 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) which has orthorhombic symmetry i n the g and A tensors. The g and A tensor d i r e c t i o n s have been chosen such that they have one tensor d i r e c t i o n i n common (z a x i s ) and the A tensor has been r o t a t e d about t h i s a x i s by 20° from the g tensor frame as shown i n f i g . 4.3. - 47 -A Z'9 Z F i g . 4.3 Relation of the p r i n c i p a l axes of the g and A tensors. In the analysis of t h i s system, only the Am^  = 0 t r a n s i t i o n s were considered. In the examples chosen, g , g , g , A and A have x y z x z been chosen to have constant values while A . was allowed to change y i t s value according to the following scheme. The diffe r e n c e between g and g was chosen to be Ag = .0024 (^ 4 gauss at 9 GH ; x y z Ag (gauss) = h v / 3 (g.,-g„)) A was then chosen such that AA = A -A = 0 0 °1 2 y x y mAg (Ag i s expressed i n gauss units) where m = .25, .5,. 1, 2, 4 and 8. The cases range then, from the case where the A tensor anisotropy (AA) i s the governing term to the case i n which the g tensor anisotropy (Ag) i s dominant. F i g . 4.4 represents the <t> vs. H p l o t for these cases and Table 4.1 l i s t s the values chosen. The g tensor frame was chosen as the reference frame so the f i e l d w i l l be p a r a l l e l to the p r i n c i p a l g axis at <J> = 0° and g axis at x y <j> = 90° while i t i s p a r a l l e l to the p r i n c i p a l A axis at cj> = 20° - 48 -3350 3360 3370 3380 3390 3350 3360 3370 3380 3390 H (gauss) H (gauss) F i g . 4.4 Angular 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 tensors are non-coincident ( F i g . 4.3). Only Am =0 t r a n s i t i o n s are considered. - 49 -and Ay a x i s at c|> = 110° (the angles at which the f i e l d i s p a r a l l e l to the A frame are 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 m(AA = m, 39.0 0.25 38.0 0.5 36.0 1.0 32.0 2.0 24.0 4.0 8.0 8.0 g = 2.0064, g = 2.0040, g = 2.0020, x y z A =40.0 gauss, A =80.0 gauss X z From the previous 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 of p o l y c r y s t a l l i n e s p e c t r a , i t i s expected that powder l i n e s w i l l appear at the po i n t s where the magnetic f i e l d i s d i r e c t e d along a molecular or tensor a x i s . In t h i s case, i t i s not c l e a r which tensor a x i s w i l l r e s u l t i n a minimum change i n dH/dcos8dcf) or i f the f i e l d i s n e c e s s a r i l y p a r a l l e l to 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 value w i t h respect to a change i n o r i e n t a t i o n . This - 5 0 -i s c e r t a i n l y the case here, as can be seen from f i g . 4.4 which shows the angles at which a minimum or maximum f i e l d p o s i t i o n i s reached for each m^. l i n e . These points correspond to a stationary value for the f i e l d and w i l l give r i s e to a powder peak at th i s p o s i t i o n . It i s observed that as the differ e n c e between the A values increases, the angles at which a powder peak appears w i l l approach the case where the f i e l d i s oriented p a r a l l e l to the A tensor axes (AA>8Ag). As the A tensor anisotropy i s decreased to the point where i t i s less than the g anisotropy, the stationary points approach the case corresponding to H being aligned p a r a l l e l to the g tensor axes. The implications of t h i s are that when the A tensor anisotropy i s much greater than the g tensor anisotropy (AA>8Ag), the separation between the powder peaks w i l l represent the true A values but w i l l give only the g values along the A tensor axes ( i e . the g values i n the A frame). The g values, diagonal i n t h e i r own frame are not inte r p r e t a b l e from the powder spectrum i n t h i s case. If the A tensor anisotropy i s much less than the g tensor anisotropy the powder peak separation i s representative of the hyperfine tensor value i n the g frame and w i l l give the true g value. The information present i n a powder spectrum of t h i s type does not contain s u f f i c i e n t information to determine the diagonal components of both tensors as well as the angle between the two tensors. I f , as i n the previously d i s -cussed example, some forbidden t r a n s i t i o n s are observable, they may provide s u f f i c i e n t information to determine the angle between - 51 -the tensor axes. A l s o , i f i s o t o p i c s u b s t i t u t i o n i s p o s s i b l e w i t h an isotope of i n t e g r a l s p i n , the 1 = 0 powder manifold w i l l give 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 to the g tensor a x e s ^ ^ and should then give the e x t r a i n f o r m a t i o n necessary to determine the angle between tensors, provided that the case does not f a l l i n t o the category where the powder p a t t e r n i s already governed by H being p a r a l l e l to the g tensor axes (AA<.5Ag). In the case where the A tensor anisotropy i s of the order of the g tensor anisotropy (l£m£2) s p e c i a l care must be taken i n attempting to e x t r a c t the tensor values s i n c e the l i n e s i n the powder spectrum cannot simply be " p a i r e d " . The s t a t i o n a r y p o i n t s occur at a d i f f e r e n t angular o r i e n t a t i o n . (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 are not observable or i s o t o p i c s u b s t i t u t i o n i s not f e a s i b l e , the spectrum can be analyzed by performing the INDO or CNDO c a l c u l a t i o n on the system f o r d i f f e r e n t assumed molecular geometries u n t i l a minimum t o t a l energy i s achieved. Having i n that way estimated the bond angle i t i s then p o s s i b l e to achieve a f i t to the powder spectrum. Geometries chos en by t h i s method cannot be expected to be more accurate than about ±5°. The general observations made i n t h i s s e c t i o n are expected to hold r e g a r d l e s s of the magnitudes of A and g or the angle of r o t a t i o n . As the angle of r o t a t i o n i s decreased, the magnitude of the e f f e c t s i s expected to decrease. The e f f e c t of 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 and A ) i s shown i n f i g . 4.5. The only change observed i s that X y ° J O the maxima and minima f o r each l i n e have s h i f t e d by 90° or the high f i e l d 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 ambiguity i n choosing the 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 f i g . 4.5. The choice of axes f o r cases 1 and 3 (or cases 2 and 4) would both 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 values o c c u r r i n g at the same angles i n both cases. The general observations made i n t h i s s e c t i o n are a l s o expected to h o l d , regardless of the angle of r o t a t i o n . I f the angle of r o t a t i o n i s increased, the l a r g e r w i l l have to be the d i f f e r e n c e between AA and Ag before the f i e l d i s a l i g n e d along the A or g axes ( i e . m must be >> 8 or << .25). The converse i s of course true when the angle between the tensors i s reduced. This i s i l l u s t r a t e d f o r the case of m = 4 and m = .5 f o r <{> = 40° and 10° i n f i g . 4.6. I t can be seen that f o r <j> = 40°, the maxima and minima do not correspond to H along a tensor a x i s , w h i l e f o r <j) = 10° the f i e l d i s o r i e n t e d along the g tensor axes f o r m = .5 and i s much c l o s e r to being o r i e n t e d along the A tensor axes w i t h m = 4 than i s the corresponding cf> = 40° case. Golding and T e n n a n t ^ ^ have r e c e n t l y made a study of t h i s e f f e c t on ESR s p e c t r a . In the t e s t case which they have chosen to i l l u s t r a t e the e f f e c t of n o n - c o l i n e a r i t y of Zeeman and hy p e r f i n e tensors on p o l y c r y s t a l l i n e s p e c t r a , the r e l a t i v e magnitudes of the a x i a l Zeeman and h y p e r f i n e tensors remained constant w h i l e the angles of r o t a t i o n were changed. (In t h e i r case, there was no r e s t r i c t i o n on having one common a x i s . ) They have not attempted, however, to i n t e r p r e t the r e s u l t s i n the l i g h t of the r o t a t i o n - 53 -F i g . 4.5 E f f e c t of changing the sign of AA and/or Ag i n the system shown i n F i g . 4 . 4 . - 55 -angles or tensor magnitudes and have not i l l u s t r a t e d how one can begin to i n t e r p r e t powder spec t r a which f a l l i n t o t h i s c l a s s but only warn that h y p e r f i n e estimates from these type of sp e c t r a could be erroneous. I t i s f e l t that the a n a l y s i s c a r r i e d out here should form a reasonable framework from which a system w i t h non-coincident Zeeman and hyper f i n e tensors can be analyzed. 4 . 3 Computer s i m u l a t i o n of p o l y c r y s t a l l i n e s p e c t r a There are a number of computer programs a v a i l a b l e which w i l l • i + i . I T ( 5 1 , 5 3 , 5 4 , 5 6 , 5 8 , 6 0 , 6 5 , 8 5 ) simulate p o l y c r y s t a l l i n e s p e c t r a . Many of these cont a i n such severe r e s t r i c t i o n s as to the type of system which may be s t u d i e d , ( a x i a l symmetry, second order 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 of quadrupole, p a r a l l e l tensor axes, etc.) that a program was developed which could be completely general and handle v i r t u a l l y any s p i n Hamiltonian (with the exception of sp i n m u l t i p l e t s t a t e s where S > 1 / 2 ) . I f the Hamiltonian can be w r i t t e n i n a closed 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 to second order i n h y p e r f i n e i n t e r a c t i o n ) the expression [ 4 . 2 ] can be evaluated d i r e c t l y simply by d i f f e r e n t i a t i n g the closed form f o r the 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 e v a l u a t i o n of t h i s expression from the exact resonance c o n d i t i o n of eqn. [ 2 . 2 3 ] i s not f e a s i b l e f o r orthorhombic symmetry s i n c e a closed form f o r the d i f f e r e n t i a l i s not p o s s i b l e . A computer program was thus - 56 -developed to n u m e r i c a l l y evaluate the lineshape f u n c t i o n f o r the case of orthorhombic symmetry. For cases of higher symmetry s e v e r a l options are a v a i l a b l e which can considerably reduce the computation time. The general s p i n Hamiltonian (eqn. [2.23]) i s solved e x a c t l y by the method p r e v i o u s l y described 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 at 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 respect to the p r i n c i p a l g tensor frame. The f i e l d o r i e n t a t i o n s are chosen f o r an equal i n t e r v a l spacing to form a g r i d covering a cos 6 - <j> space. For the case of a x i a l symmetry only the cos 0 space (0 < cos 6<1) need be spanned. For cases w i t h lower symmetry, the <j> space must a l s o be covered (0<CJXTT/2) , and i f only one p r i n c i p a l a x i s i s common to a l l tensors, i t i s chosen as the z a x i s and the <j> space must then cover the region (0<<f)<Tr) i n order to account f o r a l l p o s s i b l e resonances. The 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 t r a n s i t i o n p r o b a b i l i t i e s T(0,<j>) are then t r a n s f e r r e d to a lineshape s i m u l a t i o n program where they are subjected to a polynomial i n t e r p o l a t i o n r o u t i n e . This r o u t i n e assumes that the resonant f i e l d s vary smoothly w i t h any change i n the f i e l d o r i e n t a t i o n d0dc|> ( i e . dH/dcos0d<j> i s a w e l l behaved f u n c t i o n which e x h i b i t s no d i s -c o n t i n u i t i e s ) and a l s o that 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 which may c o n t a i n 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) using 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 polynomial w i t h a polynomial degree of not l e s s than seven. The f i n a l m a t r i x , which may be as l a r g e as 180 x.180 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 . This corresponds to an angular s e p a r a t i o n between po i n t s i n the <}> space of .5 degrees and from 6° near 0 = 0° to .3° near 0 = 90°. The 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 i n a s i m i l a r manner and the r e s u l t i n g matrices H and T are con-s t r u c t e d as an (n x 2) " p a i r e d " v e c t o r , the f i r s t part 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 part i t s i n t e n s i t y . This v e c t o r i s then n u m e r i c a l l y sorted " p a i r w i s e " i n t o ascending sequence over the f i e l d p o s i t i o n s , the r e s u l t being a histogram 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 > t r a n s i t i o n . A normalized d e r i v a t i v e gaussian or L o r e n t z i a n l i n e s h a p e o f appropriate l i n e w i d t h and i n t e n s i t y i s then constructed about each f i e l d p o s i t i o n and these lineshapes envelopes summed to give the powder lineshape envelope of one t r a n s i t i o n . This procedure i s then repeated 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 being c o r r e c t l y p o s i t i o n e d and summed w i t h the previous t r a n s i t i o n envelope. I f i s o t o p i c species are present or i f secondary species are to be overlapped, the e n t i r e procedure 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 overlapping species scaled to give the c o r r e c t o v e r a l l i n t e n s i t y r a t i o . 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 i n t e n s i t i e s as the t o t a l lineshape are then p l o t t e d f o r comparison w i t h e x p e r i -mental s p e c t r a . The program as w r i t t e n does have a minor l i m i t a t i o n . The method of using a cos 6 manifold i n s t e a d of equal d i v i s i o n s over 9 may not be g e n e r a l l y a p p l i c a b l e . The use of a cos 9 spacing 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 quadrapolar couplings - 5 8 -are present or strong angular anomalies are evident. In both cases, these are expected to have t h e i r l a r g e s t e f f e c t when 6 > 6 0 ° ^ ^ . Due to the cos 0 spacing, the region where 0 > 60° w i l l have a much higher d e n s i t y of c a l c u l a t e d p o ints than 0 < 60° and the f i e l d vs. angle curves i n t h i s r e g ion (0 > 60°) w i l l be b e t t e r described than they would, had an equal i n t e r v a l spacing over 0 been chosen. There may however be cases where the region near 8 = 0 ° should be described more a c c u r a t e l y before the i n t e r p o l a t i o n procedure. In t h i s case the lineshape f u n c t i o n w i l l have to be described by , s 1 T T s i n 8d8dcb ,„ , ., . ., . „ , -, , g(v)dH = — dH and an equal i n t e r v a l spacing over 8 should an be chosen and the lineshape m u l t i p l i e d by s i n 8. This was not considered necessary f o r any of the cases studied here. CHAPTER FIVE M a t r i x I s o l a t i o n Techniques 5.1 M a t r i x I s o l a t i o n 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 mul t i - p a t h r e a c t i o n scheme so that the intermediate species i n v o l v e d can sometimes only be i n f e r r e d from an a n a l y s i s of the f i n a l products. To study and i d e n t i f y short l i v e d r a d i c a l s p e c i e s , one must imploy a technique that i s capable of i m m o b i l i z i n g the t r a n s i e n t species and preventing 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 to r i s e to a l e v e l where i t can e a s i l y be detected. (87) (88) Pulse r a d i o l y s i s and f l a s h p h o t o l y s i s have been employed to increase the concentration of r a d i c a l species f o r a short time. R a d i c a l species can a l s o be formed by X-ray, gamma or u l t r a - v i o l e t i r r a d i a t i o n of s i n g l e c r y s t a l s or a s i n g l e c r y s t a l host, doped w i t h the precursor species of i n t e r e s t . R a d i c a l s s t u d i e d by t h i s method are commonly s t a b l e f o r only short periods of time (hours to weeks) at room temperature and must be kept at low temperatures i f decay i s to be i n h i b i t e d . X- or 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 to the h i g h energies i n v o l v e d and a v a r i e t y of r a d i c a l fragments i s l i k e l y to r e s u l t - 6 0 -on i r r a d i a t i o n and c r y s t a l s are u s u a l l y allowed to "anneal" at room temperature to 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 to recombine i n order that the more s t a b l e species may be s t u d i e d . The method commonly used and which w i l l be discussed i n some d e t a i l i s matrix i s o l a t i o n , where the r a d i c a l species i s trapped at a low temperature, as a d i l u t e component i n a non-reactive or " i n e r t " m a t r i x . There are a number of c r i t e r i a which should be considered when choosing the matrix m a t e r i a l . The f i r s t , and most important f a c t o r i s the " i n e r t n e s s " of the matrix. R a d i c a l intermediates are u s u a l l y h i g h l y r e a c t i v e and a host must be chosen which w i l l prevent r a d i c a l t e r m i n a t i o n . Substrates such as fluorocarbons, hydrocarbons and should be used w i t h some ca u t i o n , s i n c e when r a d i c a l s are formed i n s i t u , they possess a con s i d e r a b l e amount of energy which may be enough to r e a c t w i t h the matrix r e s u l t i n g i n atom a b s t r a c t i o n or a d d i t i o n to the matrix m a t e r i a l . 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 to use a matrix which i s s u i t a b l y transparent. Many f r e e r a d i c a l s are generated by i r r a d i a t i o n i n the near or f a r u l t r a - v i o l e t r e g i o n . The matrix should not absorb or be d i s -s o c i a t e d by the i r r a d i a t i o n source i n the wavelength region where p h o t o l y s i s of the r a d i c a l precursor occurs. I t i s , however, o c c a s i o n a l l y u s e f u l to use the i n e r t matrix as a p h o t o s e n s i t i z e r i n promoting the d i s s o c i a t i o n of a trapped parent molecule i n t o a r a d i c a l component. For example, when using a krypton matrix w i t h a krypton resonance lamp, the f o l l o w i n g r e a c t i o n path i s p o s s i b l e . - 61 -Kr +• Kr* + RY Kr + R- + Y-(Kr lamp) Mercury can a l s o be co-deposited w i t h the sample and a Hg resonance lamp used as the photochemical source f o r the ph 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 the r a d i c a l species has been trapped and condensed from the gas phase or formed i n s i t u , there i s the p o s s i b i l i t y of r a d i c a l recombination r e s u l t i n g from the r e a c t i o n between neighbouring r a d i c a l p a i r s or from d i f f u s i o n of the r a d i c a l fragment through the matri x u n t i l i t c o l l i d e s w i t h another fragment. The former can be prevented by i n s u r i n g that the r a d i c a l : m a t r i x r a t i o i s q u i t e s m a l l . 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 are u s u a l l y s u f f i c i e n t to prevent neighbouring p a i r s from recombining and a l s o i s o l a t e the r a d i c a l s from one another to a s u f f i c i e n t degree that i n t e r m o l e c u l a r s p i n -s p i n i n t e r a c t i o n s 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 choosing a matrix which has a r i g i d c r y s t a l s t r u c t u r e at the condensed temperature. This i s u s u a l l y the case i f the temperature of the matrix 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 true at 4.2°K. I t has been shown that d i f f u s i o n of molecular species w i t h l e s s than 10 atoms w i l l occur i n a matrix i f the temperature of the m a t r i x r i s e s to w i t h i n .4 to .6 of the melti n g p o i n t , T^, of the matrix. I f the matrix does not have an ordered c r y s t a l s t r u c t u r e but c o n s i s t s of l a t t i c e defects and m i c r o c r y s t a l l i t e s (which i s u s u a l l y the case i f the matrix i s condensed at 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 range over which d i f f u s i o n occurs may be lowered to .1 to .4 T,,. In c e r t a i n cases, however, con-t r o l l e d d i f f u s i o n may be v a l u a b l e . I f the m a t r i x i s allowed to warm s l i g h t l y and then recooled (annealing) then l a t t i c e imper-f e c t i o n s around the r a d i c a l trapping 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 a l s o 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 be present, consi d e r a b l y s i m p l i f y i n g the EPR s p e c t r a . Moreover, i f two r a d i c a l s have managed to occupy adjacent trapping s i t e s , they may be allowed to e i t h e r recombine or d i f f u s e apart, both 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 broadening due to s p i n - s p i n i n t e r a c t i o n s . The r a r e gases from argon to xenon are a l l e a s i l y annealed (argon i s r i g i d below 20°K but becomes s o f t and allows d i f f u s i o n at 30°K), but neon, due to i t s low m e l t i n g p o i n t , i s extremely d i f f i c u l t to anneal and i s u s u a l l y vapourized 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 should a l s o be compact enough to prevent any l a t e r a l motions w i t h i n the matrix. Since one i s u s u a l l y t r y i n g to o b t a i n i n f o r m a t i o n regarding the a n i s o t r o p i c tensor components of the s p i n Hamiltonian, the trapping s i t e s should a l s o be small enough to prevent tumbling motions of the r a d i c a l s p e c ies. 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 , are those of the r a r e gas elements, N 2 and CO,,. There are s e v e r a l other f a c t o r s which should a l s o be con-s i d e r e d . In most cases, the sample i s deposited from the gas phase onto a cooled surface (see experimental s e c t i o n ) . I t i s d e s i r a b l e then to choose a matrix which has a high vapour pressure - 63 -to enable the sample to be e a s i l y prepared and evenly mixed w i t h the r a d i c a l precursor. I t should a l s o have a f a i r l y low m e l t i n g point so that i t i s not condensed prematurely i n the spray n o z z l e . (The r a d i c a l precursor should a l s o have a high vapour pressure (54) f o r the same reasons, although t h i s i s not s t r i c t l y necessary) Once the mixture i s condensed, i t should have a very low vapour -4 pressure (10 Torr) so that the sample i s not pumped o f f a f t e r d e p o s i t i o n . The i n e r t gases Ar, Kr, and Xe have vapour pressures of 10 ^ Torr at 20°K w h i l e Ne reaches t h i s vapour pressure at 5°K making i t one of the more d i f f i c u l t matrices to use. The matrix should a l s o have a reasonable thermal c o n d u c t i v i t y to e f f e c t i v e l y t r a n s f e r heat from the condensing gas forming the new l a y e r to the surface of the supporting m a t e r i a l , thus m i n i -mizing the amount of " b o i l - o f f " due to the impinging 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 eating w i l l occur as the parent molecule fragments. The r a p i d t r a n s f e r of excess energy to the matrix w i l l thus a l s o be an important f a c t o r i n s t a b i l i z i n g the fragment as w i l l the r a t e at which the fragments can d i f f u s e away from each other before recombination occurs. The l o c a l h eating may help i n s o f t e n i n g the matrix enough to a l l o w l i m i t e d d i f f u s i o n to occur. I t i s a l s o d e s i r a b l e to choose a matrix which has no magnetic n u c l e i . A matri x such as xenon i s not o f t e n used because i t has 129 131 two abundant isotopes Xe a n d ^ e w i t h nuclear spins 1/2 and 3/2 r e s p e c t i v e l y . The c l o s e proximity of the r a d i c a l species and - 64 -matrix 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 superhyperfine i n t e r a c t i o n or l i n e broadening (8) of the r a d i c a l spectrum. The most advantageous reason f o r using an i n e r t s ubstrate i s to reduce matr i x p e r t u r b a t i o n s on the r a d i c a l . Since the r a r e gases are closed s h e l l atoms and have very low l a t t i c e energies, i n t e r a c t i o n s are expected to be minimal and data from a " g a s - l i k e " environment can be r e a d i l y obtained. M a t r i x e f f e c t s , although s m a l l , are present and u s u a l l y can be detected by small p e r t u r b a t i o n s on the s p i n Hamiltonian i n EPR. These e f f e c t s w i l l be discussed 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 production of f r e e r a d i c a l s p e c ies. Some species are n a t u r a l l y paramagnetic and (34) r e q u i r e only warming of t h e i r dimers (NO.-,, NF 2 ) or d i l u t i o n (C10 2) i n order 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 . In these cases, i t has been experimentally found that 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 are necessary to avoid s p i n - s p i n i n t e r a c t i o n and the r e s u l t i n g lineshape broadening. To produce t r a n s i e n t s p e c i e s , a method must be employed which w i l l cause a parent molecule to be fragmented or enable i t to be attacked by another atomic or molecular f r e e r a d i c a l . There are two general c a t e g o r i e s i n t o which the formation of r a d i c a l species can be d i v i d e d : a) those formed i n the gas phase and subsequently 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 generated i n s i t u . - 65 -In the f i r s t case, a technique commonly employed i s that of -, - i j . . I 7 , . (23,54,90,91) p y r o l y s i s or thermal decomposition, weltner e_t a l . have used t h i s technique to great advantage to study a v a r i e t y of t r a n s i t i o n and heavy metal complexes. The parent complex i s placed i n a furnace and heated to temperatures > 800°K i n vacuo at which time the r a d i c a l vapour i s d i f f u s e d along w i t h the matrix onto a c o l d surface. Gas phase r e a c t i o n s can a l s o be accomplished by t h i s method. A pure metal i s heated i n the same manner and allowed to react w i t h atomic or molecular species such as F, 0, H, OH generated i n a second furnace. The r e s u l t i n g MX r a d i c a l species (27) i s then trapped i n a c a r r i e r m a trix. Gordy e_t al_. have used the technique of gamma r a d i o l y s i s to produce r a d i c a l s from the Group IV and V hydrides. This technique 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 excessive fragmentation or i o n formation e x i s t s . The study of anions such as CO2 , , 2 6 ' - (95) CgHg have a l s o been stu d i e d by the technique of matrix i s o l a t i o n through d e p o s i t i o n of a small 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 of the mixture i n s i t u the i o n i c species are formed. The a l k a l i metal elements can a l s o be used to generate r a d i c a l s from an organic h a l i d e by the r e a c t i o n RX + Na- *-'NaX + R* - 66 -R a d i c a l species can a l s o be produced by passing a sample mixture through a microwave discharge immediately p r i o r to d e p o s i t i o n . This technique i s again 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 fragmen-t 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 molecules. The technique a l s o has the disadvantage that 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 organic 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 annoying background of methyl or hydrogen atom s p e c i e s . I t i s g e n e r a l l y found that no matter how 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 generation. Another f r u i t f u l method of r a d i c a l generation i s that 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 that the wavelength 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 other 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 and have a v i r t u a l continuum above 2500 A the most intense l i n e being at 3650 A but t h e i r main disadvantage being a high output of i n f r a -red i r r a d i a t i o n . Various 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 width. The usefulness of the high pressure lamp i s l i m i t e d below 2600 A. I f a low pressure mercury lamp i s employed, the region from 1800 A to 3000 A i s a c c e s s i b l e being l i m i t e d u s u a l l y by the type of window employed on the dewar. For the high or low pressure mercury lamp, a quartz window i s u s u a l l y used which 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 high outputs o i n the f a r u l t r a - v i o l e t below 2000 A. The gas resonance lamps of - 67 -hydrogen and xenon have intense bands at 1215 A and at 1295 A:1470 A r e s p e c t i v e l y . I f s t i l l g reater energies are required an argon resonance lamp can be used (1048 A:1066 A) or even a helium resonance lamp (548 I) although i n the l a t t e r case a s p e c i a l aluminum window must be employed. The disadvantages 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 long i r r a d i a t i o n times ranging from 1/4 - 2 hr. i n order to achieve a reasonable l e v e l of r a d i c a l concentra-t i o n . The reasons f o r t h i s are twofold. L i g h t s c a t t e r i n g by the mat r i x (and l i g h t absorption 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 . The "cage e f f e c t " w i l l a l s o reduce r a d i c a l pro-d u c t i o n . When a molecule i s d i s s o c i a t e d , the surrounding case of mat r i x w i l l tend to hold the fragments together f o r a long enough time to a l l o w t h e i r recombination. A l s o , i f the m a t r i x i s capable of removing the e x c i t a t i o n energy of a molecule r a p i d l y enough, fragmentation 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 recombination w i l l occur and the "cage e f f e c t " w i l l be unimportant. This method w i l l be used here to generate 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 to note that 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 concentration of r a d i c a l s that can be trapped i n an i n e r t m a trix. Golden has derived a s t a t i s t i c a l model of the s t a b i l i z a t i o n process and concludes that the r a d i c a l concentra-t i o n condensing from the gas phase i s about 10-14%. Jackson and (97) M o n t r o l l had a l s o a r r i v e d at t h i s f i g u r e as a l i m i t i n g value f o r the c o n c e n t r a t i o n . However f o r systems stu d i e d by t h i s method, the - 68 -maximum concentration thus f a r obtained i s l e s s than 2 % ^ ^ . _g However the lower l i m i t d e t e c t a b l e by EPR i s of the order of 10 molar so t h i s does not become a se r i o u s i n h i b i t i n g f a c t o r . There are two b a s i c techniques now commonly used f o r d e p o s i t -i n g the mixture on the c o l d s u r f a c e . The most o f t e n used i s that of slow spray on (SSO) i n which the gas i s deposited i n a continuous stream over periods of an hour or longer. This method i s g e n e r a l l y b e l i e v e d to i s o l a t e the species very e f f e c t i v e l y . Recently IR s p e c t r o s c o p i s t s > 1 0 0 ) ^ave s h o w n that pulsed m a t r i x i s o l a t i o n (PMI) where the gas deposited i n s h o r t , high pressure pulses can be e q u a l l y e f f e c t i v e i f not more so i n i s o l a t i n g trapped species. The deposited m a t r i x was observed to be more transparent when the pulsed matrix technique was employed r a t h e r than the slow spray method. A second advantage of PMI i s that small amounts of i m p u r i t i e s r e s u l t i n g from apparatus leaks w i l l be much l e s s important w i t h PMI s i n c e the time of d e p o s i t i o n i s reduced. 5.3 M a t r i x E f f e c t s Although the r a r e gas matrices provide 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 to perturb the trapped . (8-10,13,14,66) ™ . _ . , „. species . The theory of matrix p e r t u r b a t i o n s i n ( 66" ) EPR has been developed by Adrian f o r hydrogen atoms s t a b i l i z e d i n the r a r e gas matrices and has been extended to semi-quantita-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 ' , a l k a l i atoms (13) and s e v e r a l group VA atoms . A s e m i - q u a l i t a t i v e explanation of ma t r i x s h i f t s has been given f o r copper, s i l v e r and gold atoms - 69 -j , _ . (14) trapped xn the r a r e gas matrices The e s t i m a t i o n of 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 the EPR spectrum of these atoms has been shown i n most cases to agree q u i t e c l o s e l y w i t h the experimentally observed s h i f t s . There are, however, s e v e r a l d i s c r e p a n c i e s which the theory can not 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 of the a l k a l i atoms . This i s probably due to the approximations used and the r e l a t i v e d i f f i c u l t y i n e s t i m a t i n g the e f f e c t s of the van der Waals and P a u l i f o r c e s . As the theory has not been extended to cover molecular 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 of the theory of matri x s h i f t s w i l l be presented here which can then be a p p l i e d to e x p l a i n trends i n matrix s h i f t s on paramagnetic molecular species. An understanding of these e f f e c t s becomes important i n the i n t e r p r e -t a t i o n of the complicated powder spe c t r a that may a r i s e due to these e f f e c t s . The matrix atoms can cause p e r t u r b a t i o n s i n the trapped species i n s e v e r a l ways. The matrix f i e l d w i l l tend to a l t e r the s p i n d e n s i t y at the magnetic nucleus, r e s u l t i n g i n a change i n the hyper-f i n e s t r u c t u r e s p l i t t i n g constants from the " f r e e gas" value. This f i e l d w i l l a l s o a l t e r the Zeeman coupling due to s p i n - o r b i t i n t e r -a c t i o n s of the unpaired e l e c t r o n w i t h the matrix atoms. 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 the matrix atoms are packed around the trapped species and a l s o on the type of matri x atom. The r a r e gases have a l l been shown to c r y s t a l l i z e i n a face-centered cubic s t r u c t u r e ^ " ^ " ^ and i f one assumes p e r f e c t order 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 three s i t e s i n the l a t t i c e ; the i n t e r s t i t i a l 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 octahedral 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 species and the nearest neighbouring matrix 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 highest overlap between the charge clouds on the m a t r i x and trapped 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 consequently l e s s overlap. I t can thus be concluded at t h i s p o i n t that species which are trapped i n t e t r a -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 matrix s h i f t from the free gas value and these s h i f t s would be expected to decrease i n the octahedral and s u b s t i t u t i o n a l s i t e s . With the atomic s p e c i e s , these expectations have been confirmed w i t h the ( 8 ) observation of a l l three trapping s i t e s . The cramped s i t e s are the most s e n s i t i v e to any changes i n the l o c a l environment where any change i n the nearest neighbour 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 . A l s o , any l a r g e d i s o r d e r i n the environment w i l l l i k e l y r e s u l t i n severe l i n e broadening. I t remains now to e x p l a i n the cause of these s h i f t s . The i n t e r a c t i o n s which are necessary to consider are the Van der Waals forces and P a u l i e x c l u s i o n forces which are long range, a t t r a c t i v e forces and short range, r e p u l s i v e forces 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 -to compete, the former predominating i n the 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 the l a t t e r w i l l predominate i n the cramped octahedral or t e t r a h e d r a l s i t e s . The van der 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 instantaneous e l e c t r o n d i p o l e moments, one of the trapped r a d i c a l and the other on the matrix p a r t i c l e , so that as the p a r t i c l e s are brought together a net 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 ^ ^ that f o r atoms, the r e s u l t of t h i s i n t e r -a c t i o n i s to cause a s l i g h t e l e c t r o n i c cloud expansion i n the two p a r t i c l e s , which has the e f f e c t of reducing the i n t e r a c t i o n between the e l e c t r o n and the nucleus, which i n turn r e s u l t s i n an o v e r a l l decrease i n the hy p e r f i n e 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 separation becomes s u f f i c i e n t l y s m a l l , the e l e c t r o n charge clouds of the trapped species and the matrix atoms w i l l overlap s u b s t a n t i a l l y . The exchange or P a u l i e x c l u s i o n forces w i l l not permit two e l e c t r o n s of the same s p i n to occupy the same region of space. The matrix o r b i t a l whose s p i n i s the same as the unpaired e l e c t r o n on the trapped species w i l l c o n t r a c t s l i g h t l y as w i l l that of the unpaired e l e c t r o n i n order to reduce the overlap. This c o n t r a c t i o n r e s u l t s i n an increase i n the charge d e n s i t y at the nucleus of the trapped species and w i l l tend to increase the hyp e r f i n e i n t e r a c t i o n . The c o n t r a c t i o n of the matrix o r b i t a l w i l l r e s u l t i n a net s p i n unbalance as only that o r b i t a l of the same s p i n as the unpaired e l e c t r o n c o n t r a c t s . Since the ra r e gas matrices used f o r trapping have a complete outer 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 n u c l e i . This w i l l u s u a l l y have the e f f e c t of l i n e broaden-in g of the EPR powder spectrum. Since the unpaired 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, there 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 lead to 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 the trapped species has i t s unpaired e l e c t r o n i n an outer p-s h e l l , i t w i l l a l s o experience a g - s h i f t from the "free-gas" value due to the 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 competition between these two s h i f t s w i l l be the 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 of the two opposing van der Waals and P a u l i forces w h i l e the g - s h i f t s are due predominantly to the s h o r t range P a u l i f o r c e s . ) In the case of the atomic s p e c i e s , the wavefunctions and the average e x c i t a t i o n energies of the atoms were obtainable and expressions f o r the hype r f i n e and g - s h i f t s could be derived from a p e r t u r b a t i o n treatment and the expected s h i f t s roughly estimated. In the case of a molecular species however, the q u a n t i -t a t i v e aspects of t h i s treatment 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 aspects can be used to 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 the Hamiltonian Parameters The i n t e r p r e t a t i o n of the Hamiltonian parameters of the r a d i c a l s of the type ABC or ABG^ can g e n e r a l l y be based on a very simple model and the r e s u l t s achieved 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 which w i l l be followed here, centre A w i l l have a nuclear s p i n I > 0 w h i l e the remaining centers w i l l have 1 = 0 . Since many of the arguments used are common to these s p e c i e s , a b r i e f t r e a t -ment of the 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 given. Since only non planar ABO^ systems w i l l be considered, these species belong to the C g symmetry c l a s s possessing only a plane of symmetry. Due to t h i s l i m i t e d symmetry, the ground s t a t e s of these r a d i c a l s can be 2 expressed as e i t h e r A", where the unpaired 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 perpendicular to the symmetry plane and i s 2 . antisymmetric w i t h respect to r e f l e c t i o n i n the symmetry plane, or A where the e l e c t r o n i s confined to molecular o r b i t a l s which are symmetric w i t h respect to r e f l e c t i o n i n the molecular symmetry plane. 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 * = I W 2 •••• W n l - 74 -where <|> i s the odd e l e c t r o n o r b i t a l and the symmetry of the wave f u n c t i o n should 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 expressed as a l i n e a r combination of atomic o r b i t a l s on each 2 nucleus. For a A' s t a t e these w i l l be <j> = C A X + c Ax + c A x + C B X + [6.1] n x s x px z pz s s 2 and f o r a A" s t a t e |> = C A X + C E X + . . . [6.2] n y Apy y Apy where the C's are the c o e f f i c i e n t s of the atomic o r b i t a l s x on each center. The a x i s system i s defined as f o l l o w s : the x a x i s i s perpendicular to the A-B bond and i n the molecular symmetry plane y i s perpendicular to the molecular symmetry plane and z i s p a r a l l e l to the A-B bond. The d i p o l a r operator i n equation [2.10] (102) can be w r i t t e n i n the form 6 = (3r. r 1 Q - r 2 6 J r 5 [6.3] a p l a 13 1 aB 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 coupling constant T can then be (103) w r i t t e n as T a 3 = g e W N S " 7 6 a 3 Q S ( r l ) d T - 75 -where Q g(r 1)/S is a normalized spin density function which can be expressed in terms of the expansion coefficients of the atomic orbitals, Q (r )/S = EE C c \ ( r ) / ( r ) b i p q p q p q In this expression, a restricted wave function has been used where the spins of the doubly occupied molecular orbitals exactly cancel and the only term contributing to the spin density matrix i s then the spin in the odd electron m.o. orbitals. Thus T „ can ag be expressed as Ta3 = ge%Wp Eq Cp Cq < XP ^ 1 °a B • *p ( r ) > Consider now the contributions to the anisotropic hyperfine 2 tensor or a "a-radical" ( A' ground state). Expanding [6.6] using the ground state wave function [6.1] „ A 2 A |2A ,A J . 2 A ."A ,A , .k k A ,:A ,A T a g = V X P x l 0 a g | X P X > + C z < X p J . O o B | X P Z > + 2 C x xpjoj X P Z > + B c 2 < B X P |0AJBxp > + V<Bxp |0 AJ B Xp > + ... x rx' ag 1 x z *z 1 ag • z + ^ A^xi^i V + ^ V»,i^iV +- • • [6-7! The f i r s t three terms are the one center integral contributions and for most molecules this is the dominant term since the dipole - 76 -3 operator has a 1/r dependence and the 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 are the two center i n t e g r a l c o n t r i b u t i o n s from the neighbouring nucleus to the anisotropy i at center A. These i n t e g r a l s can be evaluated by the method of McConnel and S t r a t h d e e ^ ' ^ as cor r e c t e d by P i t z e r et a l . ^ ^^^. These f u n c t i o n s ( i n c l u d i n g the c o n t r i b u t i o n s from i n t e g r a l s of the Ai~A i B type <xs 0 0[xp > which have been neglected here) are tabulated f o r ot p a S l a t e r 2p o r b i t a l on center 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 derived and are given i n Appendix B. The l a s t two terms represent the overlap i n t e g r a l c o n t r i b u t i o n and can be approximated using the method of M u l l i k e n ^ ^ ^ where < V c K e l *V ~~ h s ™ ( < *?xl V *V + < XPXBI *PX» [ 6 - 8 ] where S i s the value of the overlap i n t e g r a l and can be evaluated XX by M u l l i k e n ' s method^^^^. For the case where A i s a hydrogen, the one center i n t e g r a l s w i l l not c o n t r i b u t e to the anisotropy and the main c o n t r i b u t i o n s w i l l come from the two center i n t e g r a l s and w i l l g e n e r a l l y have the form (-a, -g, 6) where |a|<JB|<|6| f o r the p - o r b i t a l on B perpendicular to the 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 the case where A i s not hydrogen, and the 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 the 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 center A. This i s the one center c o n t r i b u t i o n described above. ( I t should be noted here that 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 to the anisotropy and w i l l be neglected. A l s o i n the argument f o r a " o - r a d i c a l " the 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 neglected.) The t o t a l c o n t r i b u t i o n from the one center terms on A to the a n i s o t r o p i c tensor can be w r i t t e n as T X % 2 2 2c - c x z 0 3/2c c X z T y = 0 2 2 - c - c X z 0 B [6.9] o T z 3/2c c X z 0 2 4. 9 2 - c + 2c x z where i s the a n i s o t r o p i c h y p e r f i n e of an e l e c t r o n i n a p - o r b i t a l on center A and T i s the observed a n i s o t r o p i c h y p e r f i n e tensor. The 2 2 c e n t r a l term (-c - c )B can then be equated to 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 of one component of the a n i s o t r o p i c tensor can be e s t a b l i s h e d , only one choice f o r the o r i e n t a t i o n of the other two components w i l l be 2 2 compatible s i n c e c x and c^ are p o s i t i v e . The 2x2 s e c u l a r determinant 2 2 can then be solved f o r c and c which w i l l be r e p r e s e n t a t i v e of the x z 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 . This a n a l y s i s always r e q u i r e s that the h y p e r f i n e component whose absolute value i s intermediate between the other components, w i l l l i e perpendicular to the symmetry plane. Of course i f t h i s approach proves to be inadequate, the con-- 78 -t r i b u t i o n s from the two center i n t e g r a l s of the type <p B|o A |pB> Bi"A i A and overlap i n t e g r a l s of the type <p 0 „ p > must be considered. r p ' aB v The one center 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 tr e a t e d i n a s i m i l a r manner except that the ground s t a t e i s now considered as 2 a A" s t a t e and the expansion of T [6.6] becomes A 2 A i n A iA , B Z B l ^ A i B T = c < X p 0 o x p > + c < x p 0 . h p > + ... ag y A r y ' ag 1 A t y y A t y ' ag 1 y + 2 Ac B c < A X P |0 A | B X P > + ... [6.10] y y ^ r y l ag' r y where the f i r s t i n t e g r a l i s the one center c o n t r i b u t i o n , the second i n t e g r a l i s the two center i n t e g r a l and the t h i r d i s the overlap i n t e g r a l . For the case where A i s hydrogen, the only c o n t r i b u t i o n to the anisotropy a r i s e s from the two center terms. This c o n t r i b u -t i o n w i l l be of the form .(-g,-a,-<5) where |a|<|g|<|6|. The one center treatment f o r a non-hydrogen c o n t a i n i n g M T r - t y p e " 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 to that of 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 of the 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 considered. In t h i s case, the an i s o -t r o p i c h y p e r f i n e tensor can be represented as the sum of two a x i a l t ensors, one o r i e n t e d along the ir o r b i t a l (y) and one o r i e n t e d along 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 the p o r b i t a l on A should 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 the P z(o0 o r b i t a l should be negative 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 the B o r b i t a l w i l l induce 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 forming the AB bond. This should tend to induce a s l i g h t negative s p i n d e n s i t y - 79 -i n the bond p o r b i t a l on A. The one center c o n t r i b u t i o n s can then z be w r i t t e n as 2 j . 2 -c + c y z 0 2c + c y z -c - 2c y z [6.11] 2 2 where c y and c^ are r e p r e s e n t a t i v e of the s p i n d e n s i t i e s i n the r e s p e c t i v e p o r b i t a l s . Here again a choice must be made as to the o r i e n t a t i o n of one component of the h y p e r f i n e tensor (perhaps based on the r e l a t i v e magnitudes of the g values) and then two simultaneous 2 2 equations may be solved f o r c y and c^. As before, a more accurate 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 terms. In any attempt to e x p l a i n the g values of a "TT" or "a type" r a d i c a l , a one center 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 estimate 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 w i l l r e q u i r e accurate wavefunctions f o r the ground and e x c i t e d s t a t e s and a good estimate of the energy d i f f e r e n c e between these s t a t e s . These q u a n t i t i e s are r a r e l y both a v a i l a b l e f o r most systems and only a q u a l i t a t i v e estimate can be made. The s h i f t i n the g f a c t o r (Ag^g where a,3 = 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 s p i n o r b i t c o u p l i n g . To f i r s t order i n energy, the s h i f t i n the g value - 80 -i s zero, i e . g = g g . By u t i l i z i n g f i r s t order p e r t u r b a t i o n theory, a modified wave f u n c t i o n which inc l u d e s the admixture or e x c i t e d s t a t e s can be w r i t t e n as ±> + <n £L-S Y ±> m |<P±> = | V > ^ - g — : g |n> [6.12] n m where m i s the ground s t a t e , n i s the t o t a l wavefunction of the ex c i t e d s t a t e , L i s the angular momentum operator and £ i s the s p i n o r b i t c o u p l i n g constant. The true magnetic Hamiltonian f o r the magnetic i n t e r a c t i o n can be w r i t t e n as = 3H-L + g BH-S [6.13] mag e and the t o t a l g tensor i s then described by g = < f ± l ^ l g l y ± > t 6 - 1 * ] I f t h i s i s s o l v e d ^ ^ 7 ) ^ the expression f o r the g f a c t o r can be (108,109) w r i t t e n as 8aB = 8 e ( 1 + A » a B ) m-1 <m|^|n><n| ZLg'?t|m> n <m | E L * | n><n | |m> where Ag „ = / J - V* &aB /-i E. - E E. - E i = l l m J=m+1 2  m [6.15] - 81 -The sum over t runs over a l l atoms i n the molecule and to a f i r s t approximation ^ operate only on those o r b i t a l s centered on t . I t should be noted here that a l l e x c i t e d s t a t e s w i l l have an energy greater than the ground s t a t e and thus the energy d i f f e r e n c e s w i l l always be p o s i t i v e . The f i r s t term corresponds to an e x c i t a t i o n from a doubly occupied o r b i t a l to the s i n g l y occupied o r b i t a l and the second term corresponds to an e x c i t a t i o n from the s i n g l y occupied o r b i t a l to a v i r t u a l s t a t e . This represents a p o s i t i v e c o n t r i b u t i o n to the g s h i f t from the f i r s t term and a negative c o n t r i b u t i o n from the second term. Expressions can now be w r i t t e n f o r the g s h i f t i n the three 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 to s i m p l i f y the expression f o r the g s h i f t . In order f o r Ag to be non zero, the 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 s t a t e T and the ground s t a t e Y must be contained i n TL^, the i r r e d u c i b l e n m a re p r e s e n t a t i o n of the o r b i t a l angular momentum operator. The o r b i t a l angular momentum operator has the e f f e c t of 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 equivalent to the symmetry operator R^. From the symmetry t a b l e f o r C , L and L transform as A" and w i l l thus S X z connect only those e x c i t e d and ground s t a t e s whose symmetries are d i f f e r e n t . For a "TT" or "a" r a d i c a l , <A"|L IA'> ^ 0 and a s h i f t 1 x, z 1 from g £ i s expected. For a "a r a d i c a l " the ground s t a t e i s A' and <A'|L |A'> must be evaluated. Since the A' s t a t e can be w r i t t e n i y' as a l i n e a r combination of p and p atomic o r b i t a l s and L p > = *x *z y'*x - | i p >; L |p > = |ip >, the i n t e g r a l w i l l have a non zero value, 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 molecular o r b i t a l s are composed of l i n e a r combinations of p y o r b i t a l s , but L |p > = 0 so there 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 y d i r e c t i o n from the one center 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 hyper-f i n e c o u p l i n g , two center terms may a l s o be included i n the g s h i f t . These terms w i l l have the same form as equation [6.15] except that L*" now operates on the center adjacent to the t as w e l l . I t should be pointed out that these arguments are 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 f o r the observed h y p e r f i n e tensor or g tensor s h i f t . To i l l u s t r a t e , two w e l l known examples can be analysed by t h i s method. The H00 r a d i c a l » H - 2 ) which has been e s t a b l i s h e d as a IT r a d i c a l from accurate LCAO - MO - SCF c a l c u l a t i o n s 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) ^ h a s a h y p e r f i n e tensor that cannot be reasonably accounted f o r by the two center c o n t r i b u t i o n s from the c e n t r a l oxygen alone. The form of the two center 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 value to l i e p a r a l l e l to the T 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 f a c t intermediate ( i n absolute value) between the x and z components. There are thus other terms which must c o n t r i b u t e to give the tensor i t s o v e r a l l shape. The g tensor, i s a l s o not s t r a i g h t f o r w a r d . The g tensor theory j u s t discussed, p r e d i c t s a s h i f t of zero f o r the ir, (y) d i r e c t i o n . The a c t u a l g tensor 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 represents a f a i r l y strong p o s i t i v e g s h i f t - 83 -of +.0019. The one center approximation i s inadequate and c o n t r i b u -t i o n s from the two center terms i n the g s h i f t must be considered. (26) A more ambiguous case i s the F00 r a d i c a l which has been widely i n t e r p r e t e d as a i r a d i c a l . A recent non-empirical LCAO -MO - SCF c a l c u l a t i o n ^ " * " 1 ^ has reported that the ground s t a t e i s 2 A' ( i e . the unpaired e l e c t r o n r e s i d e s i n a symmetric "a o r b i t a l " ) . 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 tensor as a a r a d i c a l can be c a r r i e d out using equation [6.9]. The h y p e r f i n e tensor can be l a r g e l y accounted f o r by the one center approximation (the two center 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 are r e l a t i v e l y small) and give 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 x | = .18 and | c z | = .29 and the square of these c o e f f i c i e n t s i s approximately equivalent to the s p i n d e n s i t y i n these p o r b i t a l s . This a n a l y s i s w i l l not change the reported o r i e n t a t i o n of the h y p e r f i n e tensor and i s c o n s i s t e n t i n that i n most a r a d i c a l s of t h i s type, the c l o s e s t value Is to f r e e s p i n g i s l o c a t e d i n the molecular symmetry plane ( i n t h i s case Ag^ = -.0001). The s m a l l i s o t r o p i c h y p e r f i n e coupling must now be explained by e i t h e r a very 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 bulk 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 Fermi contact term by the induced s p i n p o l a r i z a t i o n of the inner Is o r b i t a l on f l u o r i n e by the outer 2s o r b i t a l . The 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 unusually high s p i n p o l a r i z a t i o n of the halogen 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 coupling i n t h i s - 84 -d i r e c t i o n . This a n a l y s i s w i l l a l s o r e q u i r e that the g f a c t o r perpendicular to the molecular plane i s not the g f a c t o r w i t h the s m a l l e s t s h i f t g = (2.0022, 2.0008, 2.0080). The s m a l l h y p e r f i n e 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 T r a d i c a l i n t e r p r e t a t i o n . This would seem to i n d i c a t e that i n c e r t a i n cases, the r e s u l t s of EPR alone 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 IT and a type r a d i c a l and that a d d i t i o n a l i n f o r m a t i o n such as non e m p i r i c a l MO 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 necessary to determine the ground s t a t e . CHAPTER SEVEN Chloroperoxyl R a d i c a l , C100 7.1 I n t r o d u c t i o n 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 as an intermediate i n the gas-phase p h o t o l y s i s of C l 2 and 0^^^ The existence of C100 was again supported i n an i n v e s t i g a t i o n of the mechanism of the halogen monoxide f o r m a t i o n . Rochkind and Pimentel i n an IR s t u d y ( H ^ ) ^ n a v e suggested that the species formed i n the UV i r r a d i a t i o n of trapped ClO^, was C100. A r k e l l and S c h w a g e r h a v e reported the IR study of the p h o t o l y s i s of C l 2 i n an 0 2 m a t r i x and a l s o on C10 2 photolyzed i n an argon m a t r i x at 4 K. They presented the f i r s t c o n c l u s i v e evidence that the C100 r a d i c a l was formed as an intermediate i n these two processes. Subsequent c a l c u l a t i o n s of the f o r c e constants and i s o t o p i c frequen-c i e s using assumed molecular s t r u c t u r a l parameters l e d to e x c e l l e n t agreement w i t h the experimentally measured v a l u e s , confirming that the r a d i c a l species was C100. Further evidence was presented when the UV spectrum was o b s e r v e d a n d molecular modulation k i n e t i c (122) s t u d i e s i n the 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 of t h i s (123,124) species went misassigned f o r s e v e r a l years as the CIO species - 86 -(123 126) Eachus e_t al. ' reassigned the r a d i c a l as C100 from observa-t i o n s of the decay and regrowth of paramagnetic species i n the 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 of 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 of 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 tensors i n t h i s species and that (26) i n F00 and other 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) evidence 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 of a C l 2 / n 2 mixture i n argon at 4 K. They were able to o b t a i n from the powder spectrum not only the Zeeman and hy p e r f i n e tensors but a l s o the nuclear quadrupole tensor as had Byberg i n h i s s t u d i e s on y A- * A „ n m - i ( 1 2 4 > T? i * i (123,125,126) . , i r r a d i a t e d KCIO^ c r y s t a l s . E a r l i e r workers had neglected the i n c l u s i o n of the nuclear quadrupole term, which has now been shown to 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 accuracy of Adrian'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 of a set of s t r o n g l y overlapping l i n e s near g = 2. The l a r g e nuclear 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 to overlap i n a 1:2:1 t r i p l e t whose outer components could not 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 of the parameters f o r the tensor i n t h i s d i r e c t i o n . In the present study, the 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 matrices at 4 K w i l l be reevaluated i n order to improve the accuracy of the s p i n Hamiltonian parameters. The EPR parameters were determined from a combination of l e a s t squares f i t t i n g of l i n e p o s i t i o n s and lineshape 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 mixture of CIC^ i n an argon or krypton matrix (R:M^1:3000) was i r r a d i a t e d w i t h a high pressure mercury lamp. A gradual decrease i n the CIC^ EPR absorption l i n e s was observed along w i t h the eventual buildup of a secondary species ( F i g . 7.1). The strong l i n e from CIO2 at ^ 3335 G, could never be completely bleached out.by i r r a d i a t i o n but could be reduced i n i n t e n s i t y u n t i l i t c o n t r i b u t e d only i n s i g n i f i c a n t l y to the spectrum of the secondary species. A l e s s intense mercury i r r a d i a t i o n source using a monochrometer to 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 species s t a r t i n g at ^  4350 A where ClO^ begins to absorb. Although the CIO2 was p a r t i a l l y o r i e n t e d before i r r a d i a t i o n the secondary species was not p a r t i a l l y o r i e n t e d . A l l o w i n g the sample to warm to the s u b l i m a t i o n p o i n t d i d not permit i s o t r o p i c motion of the new species and thus the i s o t r o p i c value of the coupling constant and the g-value were not obtained. On comparison of the observed spectrum w i t h that of e a r l i e r workers, the species 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 r a d i c a l (C100) and measurements of the l a r g e s t component of the h y p e r f i n e tensor c o u p l i n g constant and g-value, agree favourably w i t h e a r l i e r fc (35,123-126) „ , . . ,. . , „. , assignments . However, the high f i e l d p o r t i o n of the spectrum i s complicated by a l a r g e nuclear quadrupole i n t e r -C35 X2A) a c t i o n ' . The assignment of the hyperfine, Zeeman and quadrupole tensor values f o r t h i s r e gion was accomplished by B y b e r g f r o m the s i n g l e c r y s t a l r e s u l t s and an assignment of the r e l a t i v e signs of the hyperfine and quadrupole tensors was made f o r a l l tensor - 88 -F i g . 7.1 Observed EPR spectrum of the C100 r a d i c a l i n an argon matrix at 4.2 K. - 89 -components except the l a r g e s t h y p e r f i n e constant (A^ i n our a x i s system) and the s i g n of t h i s component was assigned by Byberg to (35) be t e n t a t i v e l y p o s i t i v e . A d rian e_t al_. assigned the components from the C100 species i s o l a t e d i n argon at 4.2 K, however they d i d not determine the s i g n of the h y p e r f i n e coupling constants. The a n a l y s i s of the powder spectrum i s very d i f f i c u l t because of the 37 strong overlap of l i n e s and the presence of the CI isotope which has a s l i g h t l y smaller h y p e r f i n e and quadrupole c o u p l i n g . Adrian et a l . analysed the powder spectrum on the b a s i s that "each component of 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 three ' l i n e s ' i n a powder ESR spectrum... The low f i e l d l i n e resembles an absorption l i n e ; the middle l i n e resembles the f i r s t d e r i v a t i v e of an absorption l i n e ; and the hig h f i e l d l i n e resembles an absorption l i n e whose s i g n i s opposite to that of the 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 acceptable f o r w e l l resol v e d h y p e r f i n e components or p r e l i m i n a r y assignments of l i n e components, can lead to erroneous assignments of l i n e p o s i t i o n s when l i n e s of the above three types overlap s t r o n g l y or where "anomalous" t r a n s i t i o n s c o n t r i b u t e to the spectrum and i n p a r t i c u l a r can be misl e a d i n g i n cases where the l i n e p o s i t i o n s are i n f l u e n c e d by a l a r g e quadrupole coupling constant. The assignment of the magnitude of the Zeeman, h y p e r f i n e and quadrupole tensors i n t h i s work i s based on the agreement between the simulated and observed spectrum. I f , as i n previous 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 three tensors are assumed c o i n c i d e n t , - 90 -the question of molecular a x i s assignment does not a r i s e when the parameters are chosen to simulate the spectrum. The C l - 0 bond a x i s ( F i g . 7.2) i s chosen as the z p r i n c i p a l d i r e c t i o n f o r con-venience i n the s i m u l a t i o n method. This d i r e c t i o n should d e f i n e the p r i n c i p a l d i r e c t i o n of the quadrupole tensor*" 1 2^QD, which should e x h i b i t near a x i a l or a x i a l symmetry about t h i s d i r e c t i o n . The l a r g e s t component of the hy p e r f i n e tensor should a l s o l i e along t h i s a x i s s i n c e the separations between the m^. components e x h i b i t no s i g n i f i c a n t quadrupolar s h i f t . This i s expected f o r the case where a h y p e r f i n e component i s p a r a l l e l to the p r i n c i p a l quadrupole d i r e c t i o n (cf S 2 C I ) . ( I t may al s o i n d i c a t e a very s m a l l quadrupole i n t e r a c t i o n but as w i l l be seen t h i s i s c l e a r l y not the case.) With these assumptions, the i n i t i a l values f o r the p r i n c i p a l com-ponents of the tensors were chosen using Byberg's s i g n convention, and the powder spectrum was simulated. F i g . 7.2 Axis system f o r the 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 simulated powder spectrum were measured and compared w i t h the c a l c u l a t e d f i e l d vs. angle p l o t s of l i n e p o s i t i o n s to determine the t r a n s i t i o n s which produce the powder l i n e s . This assignment was then used as the b a s i s f o r a l e a s t squares f i t t i n g procedure which determined the best set of tensor values which f i t the a c t u a l spectrum. 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 reasonable s i m u l a t i o n was obtained, but the i n t e n s i t i e s of s e v e r a l t r a n s i t i o n s were anomalously high. Exact agreement between the experimental and simulated i n t e n s i t i e s i s not expected due to the r e l a t i v e l y l a r g e dependence of the s p e c t r a l i n t e n s i t i e s on temperature, a change of 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 at 3390 G as w e l l as a l t e r i n g other l i n e i n t e n s i t i e s . D i f f e r e n t experimental 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 the CIG^ parent molecule, spray r a t e and degree of r e s o l u t i o n i n the CIG^ precursor a l s o appear to a l t e r the observed i n t e n s i t i e s . The s i m u l a t i o n was f i t then, to the observed s p e c t r a which most con-s i s t e n t l y showed the i n t e n s i t i e s represented i n F i g . 7.1 over s e v e r a l sets of experiments. The strong overlapping of 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 , precluded any determination of the magnitude of the a x i a l component of the quadrupole tensor (QE) as the observable l i n e s i n t h i s r e g ion were r e l a t i v e l y i n s e n s i t i v e to t h i s value. A value of QE = 0 was chosen because i t has been shown to be l e s s than .2 G ^ 1 2 4 \ which i s about the l i m i t of the accuracy of the experimental data. The s i m u l a t i o n using the parameters f o r the p a r a l l e l a x i s system i n Table 7.1 i s shown i n F i g . 7.3. F i g . 7.3 Computer simulated EPR spectrum of the C100 r a d i c a l assuming c o i n c i d e n t axes. (3^C1 only) - 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 that the three p r i n c i p a l tensors may not be p a r a l l e l . The hyper f i n e and quadrupole tensors should 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 should both be dominated by the CIO bond. The g tensor axes however, may be governed more by the 0-0 bond and thus tend to a l i g n i t s e l f towards t h i s bond. The bond angle i n C100 has been determined 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° which would suggest an angle of from 0° - 20° f o r the angle between the g and A or Q tensors i n the molecular plane (by symmetry, the out of plane axes must be c o i n c i d e n t ) . A choice must now be made as to which component (x or y) i s to be d i r e c t e d along the common a x i s . Simulations f o r each choice were computed f o r an angle of r o t a t i o n of 5° and i t was immediately apparent that when the lowest g-value component was d i r e c t e d along the x molecular a x i s ( i e . the a x i s perpendicular to the C10 bond and i n the C100 plane) l a r g e changes i n the 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 of the high f i e l d components which correspond to 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 along the a x i s perpendicular to the molecular plane, q u i t e reasonable s p e c t r a r e s u l t e d when the angle between the tensors was w i t h i n the 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 simulated s p e c t r a l i n e p o s i t i o n s r e s u l t e d . By v a r y i n g the angle between the tensors and performing a l e a s t squares a n a l y s i s , the parameters i n Table 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 angle of 5°. The main e f f e c t of r o t a t i o n i s to reduce the TABLE 7.1 P r i n c i p a l Components of the Spin Hamiltonian Parameters f o r the C100 R a d i c a l . Hyperfine components Quadrupole components (cm" 1xl0 4) ( c m - 1 x l 0 4 ) 8 x 8 y g z A X A y A z QD QE KCIO, ( a ) 4 1.9983 2.0017 2.0130 4.9 6.7 .14.0 — — 1.9965 2.0035 2.0100 +4.3 +1.9 (±)16.8 ±6.8 ±.1 KCIO. ( b ) 4 1.9915 1.9987 2.0100 5.3 3.0 16.7 8.7 0. (c) Argon 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 ±.0002 ±.2 ±.2 (a) Ref. (126) (b) Ref. (124) (c) Ref. (35) (d) This work - a l l tensor axes p a r a l l e l . (e) This work - g tensor r o t a t e d by 5° from A and Q tensor frame. - 95 -i n t e n s i t y of the l i n e at 3390 G to a value more i n accord w i t h the 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 negative value had no observable e f f e c t on the simulated powder spectrum. The "allowed" l i n e p o s i t i o n s ( i e . the most intense l i n e s ) corresponding to H//x remained u n s h i f t e d and the i n t e n s i t i e s u n a l t e r e d . 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 of the "forbidden" t r a n s i t i o n s , of course, but the i n t e n s i t i e s of these t r a n s i t i o n s are too low to c o n t r i b u t e to the powder spectrum. Reversing the r e l a t i v e s i g n of the quadrupole coupling tensor however had a d e t r i m e n t a l e f f e c t on the spectrum, attempts to s h i f t the simulated l i n e s to correspond to the observed l i n e p o s i t i o n s were unsuccessful and a l l l e a s t squares f i t t i n g procedures produced high RMS e r r o r s . I t i s reasonably c e r t a i n then, that the r e l a t i v e s i g n s chosen are c o r r e c t f o r QD and A , A . The s i g n of A i s s t i l l some-x y z what u n c e r t a i n . I t i s unfortunate that the i s o t r o p i c spectrum of C100 could not be obtained s i n c e t h i s would remove the ambiguity of the 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 misleading method of a s s i g n i n g l i n e s to one of the three " l i n e shapes" discussed e a r l i e r can be i l l u s t r a t e d here. The two l i n e s marked by arrows i n F i g . 7.1 were assigned i n c o r r e c t l y by Adrian et 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 increased i n t e n s i t y of the center component was presumed to be from an overlap of the m^. = l / 2 ; - l / 2 l i n e s due to the quadrupole coupling decreasing t h e i r spacing. When the lineshape i s simulated, F i g . 7.4 Simulated EPR spectrum of the C100 r a d i c a l assuming the non-coincident a x i s system of Fig.7.2. - 97 -however t h i s l i n e i s e n t i r e l y missing from the 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 " of these two t r a n s i t i o n s ' i n t e n s i t i e s . With the t r a n s i t i o n s due to H a l i g n e d along the x p r i n c i p a l a x i s , an increased 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 appear w i t h that i n t e n s i t y i n the a c t u a l spectrum, again because of f o r t u i t o u s " c a n c e l l i n g " . However the couplings 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 to the observation of other t r a n s i t i o n s which defined t h i s c o u p l i n g . 7.3 I n t e r p r e t a t i o n of the Hamiltonian Parameters In a l l previous s t u d i e s , i t has been assumed that r a d i c a l s of the type X00 were IT type r a d i c a l s where the unpaired e l e c t r o n r e s i d e s i n a molecular o r b i t a l composed of p type o r b i t a l s perpen-d i c u l a r to the molecular plane. This has been l a r g e l y s u b s t a n t i a t e d (111 112) f o r H00 ' where accurate molecular 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 n a n attempt to p r e d i c t the ground s t a t e of the C100 r a d i c a l from CNDO/2 and INDO methods a v a i l a b l e , severe d i f f i c u l t i e s were encountered i n the handling of near degeneracies 2 of the f i l l e d valence 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 . For t h i s reason, the s p i n d e n s i t i e s and wave functi o n s were considered u n r e l i a b l e and could 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 of the a n i s o t r o p i c h y p e r f i n e tensor nor i n p r e d i c t i n g g tensor s h i f t s . (128^ 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 A" ground s t a t e . - 98 -Recently, 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 both 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 discrepancy as to the ground s t a t e of these r a d i c a l s 2 now e x i s t s . I t was shown that these two species are both of A 1 symmetry i n the ground s t a t e ( i e . the unpaired e l e c t r o n i s i n a a type o r b i t a l i n the molecular p l a n e ) . The i m p l i c a t i o n of t h i s c a l c u l a t i o n i s manifold and se r i o u s problems are posed i n attempt-i n g to i n t e r p r e t the hy p e r f i n e tensor and the g - s h i f t s . I f , as i n a l l previous work, the r a d i c a l i s assumed to have a T ground s t a t e , the 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 that the g tensor component l y i n g along the d i r e c t i o n perpendicular to the molecular plane would be c l o s e to f r e e s p i n (g g) and that 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 the l a r g e s t hyper-f i n e c oupling constant. Since, 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 are n e g l i g i b l e , t h i s component cannot l i e perpendicular to the maximum quadrupole component (QD). The quadrupole coupling tensor expected to be dominated by the CIO bond and QD should l i e along t h i s d i r e c t i o n and the hy p e r f i n e component assigned k^ should 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 . I t now remains f o r us to a s s i g n the d i r e c t i o n s of the remaining two hy p e r f i n e components and t h i s cannot be done on the b a s i s of the g - s h i f t s s i n c e n e i t h e r g tensor component can be considered to be clos e to g g . To account f o r the l a r g e h y p e r f i n e component along the bond, a la r g e s p i n p o l a r i z a t i o n of the CIO bond must be introduced as was done w i t h F00 . Fo 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 tensor i s (±6.78, -4 -1 ±7.58, +14.37) x 10 cm . The a x i s assignment of the x and y tensor components i s ambiguous at t h i s p o i n t . This tensor can be resolved i n t o the sum of two a x i a l tensors, one a x i a l about the y d i r e c t i o n and the other about the z d i r e c t i o n (Eqn. [6.11]). Since the s p i n d e n s i t y i n the T o r b i t a l along p y should be p o s i t i v e and the s p i n d e n s i t y i n the p z o r b i t a l on c h l o r i n e should be negative, the only s i g n choice and a x i s assignment compatible w i t h t h i s c h o i c e , i s f o r A z to be negative and f o r the s m a l l e s t h y p e r f i n e component to be o r i e n t e d along the x a x i s . T XX 6.8 -.25 7.05 T yy = 7.6 = .5 + 7.05 T zz -14.4 -.25 -14.10 [7.1] Note that t h i s w i l l a l s o r e q u i r e to be negative. This a n a l y s i s then p r e d i c t s that the s m a l l e s t g tensor component w i l l l i e along the y d i r e c t i o n ( g y = 1.9883). This 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 non-colinear tensor a n a l y s i s p r e v i o u s l y described although t h i s cannot be construed as supporting evidence f o r the non-c o l i n e a r i t y of the tensors. This l a r g e negative g - s h i f t perpendicular to the molecular plane 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 -center g tensor theory f o r a "ir r a d i c a l " and i t seems necessary to consider the c o n t r i b u t i o n s from the two center terms. 2 As mentioned e a r l i e r , a A' ground s t a t e has been proposed f o r t h i s r a d i c a l . 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 coupling tensor can be i n t e r p r e t e d using the approximation 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 . The l a r g e s p i n p o l a r i z a -t i o n of the a-bond, which was necessary i n the i r - r a d i c a l i n t e r p r e t a t i o n , 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 . Using Eqn. [6.9] and assuming that the s p i n d e n s i t y i n the a bond i s now p o s i t i v e , 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 center are p^ = .006; p z - .12. In 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 coupling tensor i s a l s o unequivocal, w i t h the h y p e r f i n e tensor component of i n t e r -mediate absolute magnitude (A y) o r i e n t e d perpendicular to the molecular plane. This 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 non-colinear axes s i n c e t h i s would r e q u i r e the y- component of the g tensor ( g y = 1.9983) to be o r i e n t e d perpendicular to the Cl-0 bond and i n the plane of the r a d i c a l . -4 -1 The s m a l l i s o t r o p i c h y p e r f i n e coupling (±3 x 10 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 the inner Is - 2s o r b i t a l s on CI would be necessary to cancel the Fermi contact term i n the 3s o r b i t a l . A l t e r n a t i v e l y , s i n c e the unpaired e l e c t r o n i s expected 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, i t may be that there i s very 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 of the h y p e r f i n e and g tensor i n t h i s r a d i c a l i s ambiguous and no c l e a r choice as to the ground s t a t e of the r a d i c a l - 101 -can be made on the b a s i s of these r e s u l t s . The determination of i s o t r o p i c c oupling constant would c e r t a i n l y remove any ambiguity of the choice of r e l a t i v e signs but t h i s would s t i l l not r e s o l v e the ground s t a t e dilemma and t h i s choice may not be p o s s i b l e from EPR r e s u l t s alone. This d e c i s i o n would be helped by a more accurate LCAO - MO - SCF c a l c u l a t i o n of the r e l a t i v e energies of the ground s t a t e and lowest e x c i t e d s t a t e s as a f u n c t i o n of geom e t r i c l con-f i g u r a t i o n and should 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 order to give a good.estimate of 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 of the ground s t a t e . At t h i s point i t may be of i n t e r e s t to consider the process of forming the C 1 0 0 r a d i c a l from the symmetrical C I O 2 r a d i c a l . A r k e l l and Schwager^ 1 2^ have proposed a mechanism which f i r s t i n v o l v e s the formation of a p a r t i a l 0 - 0 bond and a compressed C 1 0 0 bond angle. A s l i g h t r o t a t i o n of the molecule would a l l o w the bond angle to increase to a t t a i n a more s t a b l e s t r u c t u r e . This conversion i s l i k e l y to be enhanced by the "cage e f f e c t " which would r e s t r i c t a l l three atoms to a confined space. This process 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 of C I O 2 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) the ex c i t e d s t a t e l i e s very c l o s e to the ground s t a t e of C 1 0 2 . I t - 102 -has been observed 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 the C100 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^ centers formed are i r r a d i a t e d w i t h UV l i g h t . I f the c r y s t a l i s allowed to stand at 295 K the CIC^ molecule i s reformed w i t h about 70% y i e l d . The conversion between these two isomers i s thus only i n h i b i t e d by a thermal b a r r i e r . CHAPTER EIGHT F l u o r o s u l f i n y l R a d i c a l , FSO 8.1 Results and D i s c u s s i o n I t would appear that 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 (129) (130) (SG^) has not been s t u d i e d . Donovan e_t al_. and Okabe have 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 . Donovan e_t a l . found that 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 energized C1S0 r a d i c a l which may undergo f u r t h e r d i s s o c i a t i o n to y i e l d another c h l o r i n e atom and 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 . I t i s thought that 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 p h o t o d i s s o c i a t i o n . T h i o n y l f l u o r i d e , ( F 2 S O ) was d i l u t e d i n an argon or krypton m a t r i x (R:M - .1mm:20mm) and the mixture was photolyzed e i t h e r during or a f t e r d e p o s i t i o n w i t h UV sources of v a r y i n g wave lengths. P h o t o l y s i s of the mixture w i t h the r e l a t i v e l y low energy, high pressure mercury lamp f a i l e d to produce any EPR s i g n a l s . When a higher energy source such as a low pressure mercury lamp (A - 2537 A; 1849 A) or a v max hydrogen resonance lamp (^ m a x ~ 1215 A) was used, a reasonably intense EPR spectrum r e s u l t e d , which was due to two overlapping r a d i c a l - 104 -species. One of these species i s the methyl r a d i c a l whose EPR spectrum has been studied i n the i n e r t m a t r i c e s ^ ' . The formation of t h i s species i s due almost c e r t a i n l y to trac e i m p u r i t i e s i n t r o -duced during the sample pr e p a r a t i o n s i n c e these s i g n a l s i n v a r i a b l y appeared when samples other than F2SO were photolyzed w i t h the gas resonance lamps or the low pressure mercury lamp. St r i n g e n t p u r i f i c a t i o n procedures i n c l u d i n g vacuum d i s t i l l a t i o n of the t h i o n l y f l u o r i d e , baking the vacuum manifold f o r s e v e r a l days at 80°C and passing the matrix 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 to remove a l l traces of the i m p u r i t y , although the i n t e n s i t y of the impu 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 the second r a d i c a l species. The spectrum of t h i o n y l f l u o r i d e i n an argon matri x i s shown i n F i g . 8.1. Since the S-Obond i n F2SO i s l i k e l y to be much stronger than the S-F bond, p h o t o l y s i s w i l l most probably r e s u l t i n the l o s s of a f l u o r i n e atom to give the asymmetrical r a d i c a l FSO which should (128) be bent, s i n c e i t i s a nineteen e l e c t r o n r a d i c a l . This proposed decomposition product i s the only one which i s c o n s i s t e n t w i t h the observed EPR spectrum. I f more than one f l u o r i n e were contained i n the r a d i c a l , a much more complicated spectrum would r e s u l t due to the i n t e r a c t i o n of two n u c l e i w i t h nuclear s p i n 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 which e x h i b i t e d a x i a l symmetry. Rearrangement to the isomer, FOS, i s not considered l i k e l y s i n c e t h i s would place a la r g e s p i n d e n s i t y on a te 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 . A d d i t i o n a l - 105 -F i g . 8.1 Observed EPR spectrum of the FSO r a d i c a l i n an argon matrix at 4.2 K. - 106 -support for the structure FSO, comes from comparison of the observed ( 26) spectrum with that of the F00 radical in an argon matrix . The species FSO is valence isoelectronic with F00 and spin density distributions would not be expected to be greatly different. The hyperfine tensors should then be similar. The g tensor values would be quite different, however, because of the larger spin-orbit coupling constant for a sulfur atom. Because of these observations, i t is considered that the most likely conformation for the radical species is 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 in F00 Because of the rather large magnetic moment of a fluorine nucleus, there w i l l be a significant contribution to the total spin Hamiltonian from the nuclear Zeeman term. This term, while not affecting the allowed transitions in a f i r s t order approximation, w i l l cause shifts in the line positions of Am^  = ± 1 transitions which are normally "forbidden". The resonance fields of these "forbidden" transitions w i l l be in a region between the "allowed" transitions. If the intensities of these transitions i s large enough, to allow their detection, they provide the necessary information to determine the line pairing of the allowed transitions. The forbidden transitions can also be used to determine the relative signs of the hyperfine tensor components. If the powder lineshape is simulated with different choices for the relative signs, only one should agree with the observed lineshape. - 107 -Using the above g u i d e l i n e s , the observed spectrum can be analyzed. The two outermost l i n e s can be assigned to one p r i n c i p a l a x i s s i n c e no forbidden t r a n s i t i o n s are observed near the center of any other l i n e p a i r i n g scheme. I f another l i n e p a i r were chosen, conside 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 not expected from molecules of t h i s type. The l i n e p a i r i n g of the remaining two hy p e r f i n e m u l t i p l e t s i s not c l e a r . But t h i s can be resolved by comparing a computer simulated spectrum w i t h the observed spectrum. The Hamiltonian used to describe t h i s system i s that given i n Eqn. [2.23] (without the quadrupole term). I n i t i a l guesses were taken f o r the hy p e r f i n e and g tensor values and the p o l y c r y s t a l l i n e l ineshape was simulated. Several l i n e p a i r i n g schemes were chosen and a l l but one produced forbidden t r a n s i t i o n s which d i d not correspond w i t h the observed l i n e p o s i t i o n s . Having determined the l i n e p a i r i n g , 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 reasonable f i t was achieved w i t h the allowed l i n e p o s i t i o n s . The lineshape was then simulated w i t h the four p o s s i b l e r e l a t i v e s i g n combinations of the hyperfine tensor. Only one s i g n combination reproduced the observed lineshape ( F i g . 8.2). To f a c i l i t a t e the comparison of the simulated and observed s p e c t r a , the 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 to the s i m u l a t i o n f o r FSO. The experimentally determined g tensor and hy p e r f i n e tensor values are given i n Table 8.1. The observed values f o r F00 are a l s o given f o r comparison. F i g . 8.2 Computer simulated 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 of the s p i n Hamiltonian EPR parameters f o r the FSO r a d i c a l . S l g2 g 3 A l A 2 A 3 -1 4 (cm xlO ) 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 ( F 0 0 ( 2 6 ) ) The p r i n c i p a l d i r e c t i o n s are defined i n F i g . 3. TABLE 8.2 Ca l c u l a t e d (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 the FSO r a d i c a l 3p 3p 2p 2p 2p -3p 2p -3^ r z y z y y y z p^ .13 .24 -.023 .005 -.01 -.035 INDO/2 -.062 .013 - - p r e d i c t e d . - 1 1 0 -It should be mentioned that t h i s analysis assumes that the g and A tensors i n FSO are p a r a l l e l . Because of the large anisotropy i n the A. tensor, the allowed powder l i n e positions w i l l correspond to the f i e l d oriented along the p r i n c i p a l A axes and the g tensor w i l l be nondiagonal when measured i n the A tensor frame. Since the g tensor anisotropy i s very small, the o f f diagonal components w i l l be n e g l i g i b l e and the g and A tensor 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 hyperfine and g tensor components to the molecular axes cannot be determined from the p o l y c r y s t a l l i n e spectrum alone. To make th i s assignment, a comparison with t h e o r e t i c a l estimates of these quantities i s necessary. Unfortunately, the accurate LCAO-MO-SCF cal c u l a t i o n s needed for evaluating these values are not a v a i l a b l e f or the r a d i c a l species FSO and a more approximate MO c a l c u l a t i o n must be used. It has been shownv ' ' ' that CNDO/2 or INDO MO c a l c u l a t i o n s can be used for obtaining a reasonable estimate of the geometry of small molecules. If i t i s assumed that the bond lengths i n the r a d i c a l do not change s i g n i f i c a n t l y from the parent compound F 2 S O , the known F-S and S-0 bond lengths can be used i n determining the geometry of FSO. Molecular o r b i t a l c a l c u l a t i o n s were performed with various assumed angles of the FSO bond angles and a minimum i n the t o t a l energy was reached for the case with an angle of 1 2 0 ° . Both the CNDO/2 and INDO cal c u l a t i o n s predict that FSO should 2 be a "TT r a d i c a l " ( A" ground state) . This i s also consistent with - I l l -Walsh's c o r r e l a t i o n diagrams for nineteen electron r a d i c a l s 2 I t should be r e c a l l e d here that the assumed A" ground state of the F00 r a d i c a l i s somewhat questionable (Chapter Six) and may i n fact have a 2A' ground s t a t e . Because of the strong s i m i l a r i t i e s between the FSO and F00 r a d i c a l s , the ground state of FSO may also be doubtful. The i n t e r p r e t a t i o n which w i l l be followed here w i l l assume that FSO i s a ' V - r a d i c a l . It should be noted that an equally 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 given for a " a " ground state. It has been previously mentioned that the g-factor which i s oriented perpendicular to the molecular plane w i l l have a value close to that for the free electron. I t i s tempting then, to assign the tensor component g^ to t h i s d i r e c t i o n since i t has the smallest g - s h i f t but g^ and %^ could also be considered to be close to the free spin value. Derivations from g g along the d i r e c t i o n perpendicul to the molecular plane can be caused by the introduction of unpaired electron density into the i n plane o r b i t a l s through spin p o l a r i z a t i o n Because of the small g - s h i f t s observed for FSO, no axis assignment can be made on the basis of the g-values, and the assignment must be based on a q u a l i t a t i v e analysis of the hyperfine tensor. It was found i n the C100 r a d i c a l , that the largest hyperfine component must l i e along the CIO bond (Chapter Seven). This i s i n q u a l i t a t i v e agreement with the assignment i n F00 where the largest hyperfine component was assigned to the F-0 bond d i r e c t i o n . Because of the s i m i l a r i t y between the t o t a l hyperfine tensor i n F00 and that i n FSO, i t i s thought that the largest hyperfine coupling i n FSO should - 112 -a l s o l i e along the F-S bond. With t h i s assignment, the molecular d i r e c t i o n s of the remaining two p r i n c i p a l axes can be assigned. Returning to the a n a l y s i s of the hy p e r f i n e tensor f o r a " I T r a d i c a l " given i n Chapter S i x , the a n i s o t r o p i c part of the hy p e r f i n e tensor can be expressed as two a x i a l c o n t r i b u t i o n s , one from the p ^ - o r b i t a l and another from the p ^ - o r b i t a l along the F-S bond (Eqn. [6.11]). The a x i s system chosen places T along the F-S bond, T J zz ° yy perpendicular to the molecular plane, and T normal to the FS bond XX but i n the molecular plane ( F i g . 8.3). In t h i s a n a l y s i s , the same arguments that were used to analyse the a n i s o t r o p i c h y p e r f i n e tensor of the F00 r a d i c a l w i l l be employed. I t w i l l be r e c a l l e d that the s p i n d e n s i t y i n the p^ (TT) o r b i t a l , was taken to 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 the p z (a) o r b i t a l was taken to be negative due to the s p i n p o l a r i z a t i o n of the F-0 bond by the i r odd e l e c t r o n on the c e n t r a l oxygen. Using these p r e d i c t i o n s f o r the signs of the s p i n d e n s i t i e s i n FSO, and having already e s t a b l i s h e d that the maximum hyp e r f i n e component corresponds to ^ z z , the assignment of the tensor components T and T can be made as f o l l o w s : r xx yy T XX "28.46" ~-l.ll' " 36.23" T yy = 51.77 = 15.54 + 36.23 -4 x 10 cm T zz -80.23 -7.77 -72.46 _ - -This assignment a l s o p r e d i c t s that the s i g n of the i s o t r o p i c hyper--4 -1 f i n e coupling constant i s negative (-13.9 x 10 cm ). This was a l s o - 113 -F i g . 8.3 Molecular a x i s system f o r the FSO r a d i c a l . - 114 -found to be the 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 can y z be estimated from these two a x i a l tensors to be p = .013 and y = -.062. These values can be compared w i t h the s p i n d e n s i t i e s from an INDO/2 c a l c u l a t i o n on the FSO r a d i c a l (Table 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 not account f o r the d i p o l a r or overlap c o n t r i b u t i o n to 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 . These c o n t r i b u t i o n s can be estimated by c o n s i d e r i n g the one center, two center and overlap i n t e g r a l s given i n Appendix B. Using the INDO/2 s p i n d e n s i t i e s given i n Table 8.2, the 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 tensor i s (8.7, 15.2, -23.9) x 10 cm Although the numerical agreement w i t h the observed tensor i s very poor ( a l l values being lower than the observed values by a f a c t o r of about 3.6) the shape and r e l a t i v e signs of the tensor are 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 monochloride (S^Cl^) The i d e n t i f i c a t i o n of the t r a n s i e n t species and products formed i n the p h o t o l y s i s of s u l f u r c o n t a i n i n g compounds has been the subject of many spe 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. The y 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 acids has been found to give r i s e to r a d i c a l s where the unpaired e l e c t r o n i s l o c a l i z e d on a s u l f u r a t o m ( 1 3 1 ' 1 3 8 ' 1 3 9 ) . The p h o t o l y s i s of a l k y l t h i o l s (RSH) 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 ' 1^0) Wh-Q e p h o t o l y s i s of H 2S and d i s u l f a n e (^S,,) give 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 which i s very s i m i l a r , being dominated by a strong 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 or no h y p e r f i n e coupling which i s recognized as being c h a r a c t e r i s t i c of 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 intermediate by Johnson and S e t s e r ^ 1 ^ " ^ who stud i e d the i n f r a r e d chemiluminescence from the r e a c t i o n of hydrogen atoms w i t h s u l f u r monochloride (S^C^) . This r a d i c a l has al s o been suggested to 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 at 2974 - 3390 A i n the - 116 -f l a s h p h o t o l y s i s of S 0C1_ by Donovan e_t a l . (142) The primary process i n the p h o t o l y t i c decomposition has been suggested to be the homolytic f i s s i o n of the C1S-SC1 bond followed by r a d i c a l a t t a c k on the parent species In view of these proposals, i t i s thought that matrix i s o l a t i o n would provide an e x c e l l e n t means of i s o l a t i n g and i d e n t i f y i n g the r a d i c a l species formed i n the p h o t o l y t i c decomposition of S 2 C I 2 . 9.2 Results and Di s c u s s i o n S u l f u r monochloride ( S 2 C I 2 ) was d i l u t e d w i t h one of the three r a r e gas m a t r i c e s , neon, argon or krypton to a concentration of R:M -,1mm:20mm. The sample was i r r a d i a t e d during d e p o s i t i o n , w i t h a high pressure mercury lamp and EPR s i g n a l s were produced w i t h i n a short p e r i o d of time (^  10 min). I t was found that t h i s method produced the best y i e l d of the r a d i c a l , w h i l e d e p o s i t i o n of the sample followed by UV i r r a d i a t i o n produced somewhat l e s s intense s i g n a l s . Gradual warming of the matrix had no e f f e c t on the spectrum, producing only a gradual decrease i n the o v e r a l l i n t e n s i t y . 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 surface through 90° but no changes i n the l i n e i n t e n s i t i e s were observed. Upon (l) s 2 c i 2 hv *• 2C1S-(2) CIS- + S 2C1 2 - 117 -examining the target rod a f t e r the experiment, a bl a c k deposit had formed on the copper surface. A s u s p i c i o n arose that the r a d i c a l s formed during the 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 the copper surface and were c o n t r i b u t i n g to 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 obtained w i t h a s i l v e r p l a t e d target surface. A t y p i c a l spectrum i s shown i n F i g . 9 . 1 . The four c l o s e l y spaced low f i e l d l i n e s are expected f o r a c h l o r i n e c o n t a i n i n g species s i n c e the nuclear s p i n of 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 couplings are i n d i c a t i v e of a c h l o r i n e w i t h a sm a l l s p i n d e n s i t y ( c f . C 1 0 0 ) . The high f i e l d t r a n s i t i o n s are obviously not due to a simple 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 at l e a s t seven t r a n s i t i o n s are observed. The wide spacing of 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 of a very strong g tensor anisotropy. Before attempting to determine the s p i n Hamiltonian parameters, the p o s s i b l e decomposition products of C I 2 S 2 are considered. S 2 C I 2 has an S-S bond and a s t r u c t u r e s i m i l a r to ^ C^. The most l i k e l y i n i t i a l decomposition products are C 1 S S * and CIS* formed by the homolytic cleavage of the S-Cl and S-S bond r e s p e c t i v e l y . Two f a c t o r s are i n favour of the former process. Were the S-S bond broken, t h i s would lead to the diatomic species CIS- which, i n the n e g l i g i b l e c r y s t a l f i e l d of an i n e r t m a t r i x , would e x h i b i t a x i a l symmetry which i s c l e a r l y not compatible w i t h the observed spectrum. A l s o , i f the bond energies i n CF^SSCF^ are considered ^"^"^ , the C-S bond has a bond energy of 2 . 0 eV. as compared to 3 . 9 eV f o r the - 118 -F i g . 9.1 Observed EPR spectrum of the S 2 C I r a d i c a l i n an argon matrix at 4.2 K. - 119 -SS bond. I t i s expected that C1^2 w i H be q u i t e s i m i l a r i n t h i s respect and the S-S bond should then remain i n t a c t and f i s s i o n of the Cl-S bond would occur. This c o n t r a d i c t s the process suggested by Donovan e_t al_. who propose an SCI intermediate which sub-sequently a b s t r a c t s a c h l o r i n e atom from the parent S 2 C I 2 to form S C I 2 and C 1 S S . This process i s not considered l i k e l y here because of the low concentration of ^ C ^ and the r e l a t i v e l y short f l i g h t path between the spray o r i f i c e and the copper target 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 considered u n l i k e l y . There does however appear to be a broad u n d e r l y i n g resonance i n the spectrum which may be due to i m p u r i t i e s i n the S 2 C I 2 . I t i s reasonably c e r t a i n then, that the species can be assigned the s t r u c t u r e C 1 S S . In s u l f u r c o n t a i n i n g species of t h i s type, the h i g h l y a n i s o -t r o p i c g tensor dominates the s p e c t r a l p a t t e r n and wi t h many sm 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 , there i s u s u a l l y found to 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^, C 1 0 0 , C 1 C 0 ) and t h i s r a d i c a l should be no exception. Indeed, i f an attempt i s made to f i t the spectrum with only the Zeeman and hyp e r f i n e parameters, the agreement i s very poor i n the high f i e l d p o r t i o n of the spectrum where even i n c l u s i o n of the nuclear Zeeman terms cannot account f o r the observed seven l i n e p a t t e r n . The s p i n Hamiltonian f o r the system i n c l u d i n g quadrupole i s given by Eqn. [2.23]. I f the matrix elements of t h i s Hamiltonian are considered, i t becomes c l e a r that the quadrupole term QD has i t s maximum e f f e c t on those hyperfine components which - 120 -are orthogonal to the d i r e c t i o n of QD. The i n c l u s i o n of the quadrupole term w i l l a l t e r the expected four l i n e p a t t e r n of a s p i n 3/2 nucleus to an extent depending on the r e l a t i v e magnitudes of A and Q. A graphic i l l u s t r a t i o n of t h i s i s given by B l e a n e y ^ 7 ^ . I t i s c l e a r from the appearance of the spectrum i n F i g . 9.1 that the low f i e l d l i n e s appear r e l a t i v e l y unaffected by the quadrupole s i n c e they are almost e q u a l l y spaced and of n e a r l y equal i n t e n s i t y . Again, the matrix elements of the Hamiltonian show that the h y p e r f i n e component p a r a l l e l to the maximum quadrupole coupling should be a f f e c t e d the l e a s t by the quadrupole. Now the quadrupole coupling tensor should be dominated by the d i r e c t i o n of the CIO b o n d ^ 1 2 7 ^ and i t i s f o r t h i s reason that t h i s d i r e c t i o n i s assigned to the component e x h i b i t i n g the maximum g s h i f t . With t h i s i n i t i a l assignment s e v e r a l guesses were made at the magnitudes of the g, A and Q tensors (which are i n i t i a l l y assumed to have c o l i n e a r axes) and the powder lineshape was simulated using these parameters. Through t r i a l and e r r o r v a r i a t i o n , a reasonable f i t to the observed spectrum was obtained. This f i t was then r e f i n e d using a l e a s t squares f i t t i n g procedure on the observable t r a n s i t i o n s . When the 37, r e f i n e d f i t was obtained, the CI isotope was superimposed i n the 37 n a t u r a l abundance. This s i m u l a t i o n p r e d i c t e d peaks due to the CI isotope to 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 to detect these t r a n s i t i o n s , the region was scanned 155 times, w i t h the r e s u l t s of each scan being accumulated by a time averaging computer. The r e s u l t s of t h i s scan are shown i n the - 121 -i n s e t to 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 but the resonance between H and I i s l o s t i n the 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 of CI2S2 by e l e c t r o n d i f f r a c t i o n and the C1SS bond angle was found to be 108.2°. I f i t i s assumed that the bond angle does not change app r e c i a b l y on r a d i c a l formation, the r a d i c a l w i l l have a s t r o n g l y bent s t r u c t u r e . In t h i s case the A and Q tensors can be assumed to 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 . The g tensor, however, may be more determined by the S-S bond and may tend to have one p r i n c i p a l d i r e c t i o n defined by t h i s bond. From the l i m i t e d symmetry of C1SS, the d i r e c t i o n perpendicular to the molecular plane must n e c e s s a r i l y be common f o r one component of the three tensors. I t must be decided then which component should be assigned to t h i s d i r e c t i o n . Since one g tensor component was found to l i e very c l o s e to f r e e s p i n w h i l e the other two tensor components were s t r o n g l y s h i f t e d d ownfield, i t i s reasonable to suspect that C1SS i s a "TT type" r a d i c a l . T h i s , coupled w i t h the f a c t that the maximum h y p e r f i n e component i s a l s o along t h i s d i r e c t i o n and that there 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 strong evidence that t h i s i s the case. The assignment of the tensor components to the molecular axes of 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 perpendicular to the r a d i c a l plane ( y ) ; the intermediate g s h i f t i s i n the plane of the r a d i c a l and approximately perpendicular to the - 122 -CIS bond ( x ) ; the component w i t h the maximum g s h i f t i s p a r a l l e l to the CIS bond ( z ) . With t h i s assignment then, the angle between the g and A/Q tensors i n the plane of the r a d i c a l was v a r i e d w h i l e using the l e a s t squares a n a l y s i s to f i t the observed l i n e p o s i t i o n s . At an angle of about 10° between these tensor d i r e c t i o n s the best 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 achieved. This i s i n reasonable agreement w i t h the 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 angle of about 100°. The r e s u l t i n g parameters (diagonal i n t h e i r own frame) are compiled i n Table 9.1 and the simulated spectrum i s shown i n F i g . 9.2. The a x i s system i s described i n F i g . 9.3. The l i n e p o s i t i o n s were measured from the simulated spectrum and the r e s u l t s are given i n Table 9.2. The agreement i s seen to be b e t t e r than .4 gauss. The only discrepancy between the observed and c a l c u l a t e d spectrum i s that the i n t e n s i t i e s of the l i n e s on the high f i e l d s i d e of the sharp c e n t r a l t r a n s i t i o n are not e x a c t l y reproduced. This r e s u l t i s not r e a d i l y explained s i n c e the i n t e n s i t y p a t t e r n of the low f i e l d components i s w e l l reproduced. Since s e v e r a l " f orbidden" t r a n s i t i o n s were observed i n the high f i e l d p o r t i o n of the 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", these features were used as a c r i t e r i o n f o r determining the r e l a t i v e signs given i n Table 9.1. Simulations w i t h r e l a t i v e signs other than those shown produced a s i g n i f i c a n t l y poorer f i t to the observed spectrum. The c h l o r i n e h y p e r f i n e tensor f o r C1SS can be seen to be very a n i s o t r o p i c . This anisotropy can r e s u l t from the one center and two - 123 -F i g . 9.2 Computer simulated 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 Hamiltonian parameters to the molecular axes i n the S 9C1 r a d i c a l . - 125 -TABLE 9-1 Experimentally determined p r i n c i p a l values of the s p i n Hamiltonian parameters of the S 2 C I r a d i c a l . § 1 g 2 S 3 A x A 2 A 3 QD QE - 1 4 - 1 4 (cm xlO ) (cm xlO ) 2.0019 2.0225 2.0384 -5.9 +1.3 +3.5 +5.65 -.1 (-.0002) (-.0002) (-.0002) (-.2) (-.2) (±.2) (-.2) (-.2) The p r i n c i p a l d i r e c t i o n s of the tensor components are shown i n F i g . 9.3. TABLE 9.2 Comparison of experimental and c a l c u l a t e d values f o r the EPR spectrum of the S 2C1 i n argon. Peak Observed p o s i t i o n C a l c u l a t e d p o s i t i o n (gauss) (gauss) A 3314.2 3314.2 B 3317.9 3317.8 C 3321.4 3321.3 D 3325.0 3325.0 E 3343.8 3343.5 F 3348.0 3347.7 G 3363.6 3363.6 H 3369.5 3369.2 I 3374.3 3374.6 J 3379.6 3379.6 K 3386.2 3385.9 L 3389.7 3389.7 M 3396.5 3396.7 - 126 -center c o n t r i b u t i o n s to the c h l o r i n e h y p e r f i n e 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 the Cl-S sigma bond or a combination of both. The f o l l o w i n g a n a l y s i s shows that the c o n t r i b u t i o n from two center terms i s l i k e l y to be s m a l l . Using the method of Appendix B, the two center 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 Cl-S bond length of 2.057 A and an e f f e c t i v e nuclear charge of 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 of S "CI S S "CI s i n t e g r a l s of the type <x3p |0 |x3p > and < x 3pJo J x 3 > were -4 -1 z found to be (-.26, - .16, .42) x 10 cm and (-.48, -.48, .96) x -4 -1 10 cm r e s p e c t i v e l y . Even i f the s p i n d e n s i t y on the c e n t r a l s u l f u r were reasonably l a r g e , these i n t e g r a l s would not c o n t r i b u t e s i g n i f i c a n t l y . I t i s reasonable to neglect a l l two center 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 tensor can be decomposed according to Eqn. [6.11] and the two a x i a l tensors are T XX +1.62 +2.37 "±..75 ' T yy = ± 5 . 4 8 = ± 4 . 7 3 + ± . 7 5 T zz +3.87 +2.37 +1.50 _ _ _ _ (Again, t h i s a n a l y s i s assumes that 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 the c h l o r i n e 3p^ o r b i t a l and negative s p i n d e n s i t y i n the 3p (which would be required by s p i n p o l a r i z a t i o n ) . - 127 -This 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 the assignment of the s m a l l e s t p r i n c i p a l value of the hy p e r f i n e coupling constant (A^) to the d i r e c t i o n perpendicular to the CIS bond and i n the molecular 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 the above r e s o l u t i o n are CI CI p3p y = .04 and p3p z = -.01. The s p i n d e n s i t i e s p r e d i c t e d from the CI CI INDO/2 c a l c u l a t i o n s are p3p = .002 and p3p = -.04. The numerical X z agreement i s rat h e r poor and the INDO/2 r e s u l t s would r e q u i r e the 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 to l i e along the CIS bond which i s c l e a r l y incompatible w i t h the observed r e s u l t s . The c a l c u l a t i o n s ' then, tend to overestimate the core p o l a r i z a t i o n w h i l e de-emphasizing the 3 p-spin d e n s i t y on c h l o r i n e . The Fermi contact term i s p r e d i c t e d S to be p o s i t i v e (p3g- = .0002) and s m a l l , suggesting that the inner s o r b i t a l s on c h l o r i n e are being p o l a r i z e d by the 3 s - e l e c t r o n d e n s i t y l e a d i n g to an o v e r a l l p o s i t i v e core p o l a r i z a t i o n . The quadrupole coupling constant f o r C1SS i s a l s o of some i n t e r e s t . The observed values of the quadrupole c o u p l i n g constant correspond to a pure quadrupole resonance of 33.9 MHz which i s i n f a i r agreement w i t h the observed quadrupole resonance of 35.6 and 35.99 MHz f o r c h l o r i n e i n the parent $ 2 C ^ 2 • T n e quadrupole c o u p l i n g constant can be estimated 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 around the c h l o r i n e nucleus approximations. The f i e l d gradient 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 simple one center approximation (127,146) as occ V = e £ P..q L! [8.1] zz —^' 11 11 1 - 128 -where P i s the bond order matrix or t o t a l d e n s i t y matrix and «ii = < + l ^T1- I V [8-2] where 0 and r are the angle and d i s t a n c e between the e l e c t r o n and the nucleus. The quadrupole coupling constant can be w r i t t e n as e 2Qq = °f] P..e 2Q C 1q C?: [8-3] z v i i at 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 the value 109.75 MHz (36.6 x 10 cm ). Using the r e l a t i o n s h i p [2.20] t h i s can be expressed i n terms of the quadrupole c o u p l i n g constants QD and QE. Using these a p p r o x i -mations, the estimated quadruple c o u p l i n g constants are tabulated i n Table 9.3. The r e s u l t s w h i l e only f a i r i n agreement w i t h the observed value tend to confirm the s i g n choice of QD as being negative along the Cl-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 of the CI quadrupole coupling constant i n C1S 9 T o t a l e l e c t r o n d e n s i t y QD QE i n CI 3p o r b i t a l s . _, , Z (cm xlO ) 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) Using Benson and Hudson para 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 Reactions w i t h SO^ 10.1 I n t r o d u c t i o n The r e a c t i o n of SC^ w i t h various molecular and atomic species has been the subject of many k i n e t i c s t u d i e s i n the l a s t decade mainly because of i t s involvement i n many of the chemical r e a c t i o n s o c c u r r i n g i n the upper atmosphere and a l s o because of i t s i n d u s t r i a l s i g n i f i c a n c e . 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 chemical or photochemical processes and the r e a c t i o n mechanisms which are proposed are g e n e r a l l y complex and remain somewhat u n c e r t a i n . G e n e r a l l y , the intermediates involved cannot be i d e n t i f i e d , and t h e i r existence can only be i n f e r r e d from an a n a l y s i s of the products. The k i n e t i c s of the r e a c t i o n between hydrogen atoms and SC^ have been determined using 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 methyl and e t h y l r a d i c a l s w i t h SG^ has been followed at various temperatures i n the gas p h a s e - ^ 3 ) > r e s u l t s of these f i n d i n g s i n d i c a t e that complex r e a c t i o n paths are followed and i t has been suggested that the f i r s t step i n the r e a c t i o n 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 the r e a c t i o n between trapped hydrocarbon polymers and S C ^ ^ " ^ , the r e s u l t s i n d i c a t i n g hydrocarbon-sulphonyl r a d i c a l formation. More r e c e n t l y , Adrian et a l . ^ ^ ^ ^ have obtained the NaSO^ r a d i c a l species by c o - d e p o s i t i o n of a beam of sodium atoms w i t h a beam of 1% SC^ i n argon and have determined the a n i s o t r o p i c components of the g and A tensors. Morton 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 out an EPR study of the photochemical r e a c t i o n of h y p o f l u o r i t e s w i t h compounds of t e t r a v a l e n t sulphur. In p a r t i c u l a r , when a h y p o f l u o r i t e was photolysed i n the presence of SC^, a d d i t i o n of both the R0-and F* fragments to SC^ was observed to give the ROSC^ and FSC^ r a d i c a l s p e c i e s . In a l l cases only the i s o t r o p i c g and A tensor values were reported. The EPR spectra described here were obtained when hydrogen atoms, f l u o r i n e atoms and methyl 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 krypton or 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 hy p e r f i n e tensors from the w e l l resolved s p e c t r a w i l l be analysed i n terms of non c o i n c i d e n t g and A tensors. Reactions of the type suggested above occur i n the case of hydrogen and f l u o r i n e atoms. Methyl r a d i c a l s a l s o react but the true nature of the adduct i s u n c e r t a i n . While these r e s u l t s may not be d i r e c t l y a p p l i c a b l e to the k i n e t i c s i n the gas phase, they do demonstrate that r a d i c a l species of the type RSC^ are v i a b l e intermediates. - 132 -10.2 Results and D i s c u s s i o n 10.2.1 Reactions of H Atoms w i t h S n2 An HI/S02/Kr mixture was photolyzed f o r approximately 15 minutes. During t h i s period a broad s i g n a l w i t h unresolved s t r u c t u r e appeared centered on g = 2 as w e l l as the expected H atom s i g n a l s separated by about 506 gauss. Continued i r r a d i a t i o n r e s u l t e d i n an increase i n i n t e n s i t y of these two s i g n a l s . The mat r i x was then allowed to warm to about 30 K. During the warm-up a weak p a i r of t r i p l e t s appeared, separated by about 110 gauss and g r a d u a l l y increased i n i n t e n s i t y as the sample temperature increased. At about 30 K, the krypton matrix began d i f f u s i n g from the d e p o s i t i o n surface 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 that i s o t r o p i c motion of the species had begun. The sample was then recooled to 4.2 K. The i s o t r o p i c doublet again s p l i t i n t o a w e l l resolved 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 that a s i n g l e species w i t h orthorhombic symmetry had formed. The sample was again allowed to warm and the i n t e n s i t y of these l i n e s were observed to increase i n d i c a t i n g a f u r t h e r r e a c t i o n was o c c u r r i n g . I t now remains to i d e n t i f y the r a d i c a l species formed. The photochemistry of SO2 has been w e l l s t u d i e d and d i s s o c i a t i o n of SO2 i n t o SO and oxygen atoms i s known not to occur u n t i l 2 1 8 0 A ( 7 7 ) which i s w e l l above the energy s u p p l i e d by the high pressure mercury lamp. The most l i k e l y r e a c t i o n which can occur then i s the a t t a c k of H atoms on the SO2 molecule. Since the r e a c t i o n i s not observed to occur at 4.2 K but only on warming, - 1 3 3 -4 J 25 G a'bl Observed EPR spectrum of the HSO^ r a d i c a l i n a krypton matrix at 4.2 K. - 134 -the H atoms are supposed to d i f f u s e through the m a t r i x and react on encountering an SC^ molecule. There are two p o s s i b l e p o s i t i o n s f o r a t t a c k , e i t h e r at the sulphur 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 112 gauss, i n d i c a t e s that there i s a sub-s t a n t i a l s p i n d e n s i t y i n the hydrogen Is 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 attached to the center c o n t a i n i n g the unpaired e l e c t r o n . The asymmetric form would place the hydrogen too f a r from the unpaired e l e c t r o n to give an i s o t r o p i c c o upling of the s i z e observed. INDO c a l c u l a t i o n s have been performed f o r these two isomeric s t r u c t u r e s , using the known s t r u c t u r a l parameters f o r S 0 2 ^ ~ ^ and assumed bond lengths f o r HS and OH of 1 . 3 3 A and . 9 9 A. They show that the unpaired e l e c t r o n i s concentrated on the s u l f u r and that 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 ten 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 assigned then as the symmetrical form H S O 2 . 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 being achieved when the HS bond was.45° below the S 0 2 plane ( F i g . 1 0 . 2 ) . I t i s thus very l i k e l y that the g and A tensors i n t h i s r a d i c a l w i l l be non-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 account. Since there are only s i x l i n e p o s i t i o n s observable i n the powder spectrum (any forbidden t r a n s i t i o n s w i l l be hidden i n the broad c e n t r a l envelope), there i s i n s u f f i c i e n t data a v a i l a b l e to determine the angle between the tensors. There i s a l s o the a d d i t i o n a l - 135 -F i g . 10.2 R e l a t i o n of the s p i n Hamiltonian parameters molecular axes i n the HS0 o r a d i c a l . to the - 136 -problem, inherent 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, of determining the p a i r i n g of l i n e s and a s s i g n i n g the corresponding p r i n c i p a l d i r e c t i o n s of the tensors. F o r t u n a t e l y 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). This was achieved by not a l l o w i n g the sample to warm to the point where i s o t r o p i c motion began, but simply warming enough to allow some d i f f u s i o n of the H atoms. I t i s q u i t e probable that the SG^ molecules are deposited 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 with s i m i l a r t r i a t o m i c molecules (NC^ , C l O ^ , NF 2 ). I f 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 to the 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 the d i f f u s i n g hydrogen atoms may not destroy t h i s p a r t i a l o r i e n t a t i o n . I t would be expected that i n the pyramidal type s t r u c t u r e of H S G ^ , the o r b i t a l c o n t a i n i n g the unpaired e l e c t r o n on s u l f u r would be d i r e c t e d along the pyramidal a x i s and thus c o n s t i t u t e a "unique" 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 c l o s e to the perpendicular from the rod face, then a marked change i n the i n t e n s i t y of the 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 should be observable on r o t a t i o n of the rod face by 90° such that 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 to the magnetic f i e l d . Such a change i n i n t e n s i t y does indeed occur, w i t h the cc' 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 the i n t e n s i t i e s of the other two components decrease. On the ba s i s of t h i s o bservation the l i n e p a i r cc' i s e s t a b l i s h e d and we ass i g n to i t the d i r e c t i o n of the pyramidal a x i s . This assignment w i l l s h o r t l y F i g . 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 surface by 90°. - 138 -be f u r t h e r corroborated by an a n a l y s i s of the g tensor. A problem now a r i s e s of determining the p r i n c i p a l g and A tensor values f o r t h i s d i r e c t i o n s i n c e the g and A tensors w i l l undoubtedly be non-co i n c i d e n t and i t i s not evident which tensor w i l l dominate the EPR spectrum. Since HSG^ has symmetry, the a x i s perpendicular to the symmetry plane must be a common a x i s f o r both the g and A tensors, w h i l e the remaining two p r i n c i p a l axes of these tensors do'not n e c e s s a r i l y have to be c o i n c i d e n t . I t was shown i n Chapter Four, that when the d i f f e r e n c e ( i n gauss) between the two components of the A tensor, which are i n the molecular symmetry plane, i s of the same order of magnitude as the d i f f e r e n c e ( i n gauss) between the corresponding g tensor components, then the l i n e p o s i t i o n s observed i n the powder spectrum do not n e c e s s a r i l y correspond to the case where the 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 tensor axes. Using an assumed angle of 20° ( F i g . 10.2) f o r r o t a t i n g the A-frame out of the g-frame (the reason f o r t h i s choice of angle w i l l be explained s h o r t l y ) , i t was p o s s i b l e to determine the f i e l d o r i e n t a t i o n which would produce l i n e p o s i t i o n s which correspond to the observed l i n e p o s i t i o n s . A l e a s t squares a n a l y s i s of the observed powder l i n e p o s i t i o n s was then performed to a r r i v e at the p r i n c i p a l components of the g and A tensors. This was c a r r i e d out f o r the two p o s s i b l e choices f o r the l i n e p a i r i n g of the remaining four powder t r a n s i t i o n s and a l s o f o r the two p o s s i b l e choices of a x i s assignment s i n c e one set of axes w i l l l i e i n the - 139 -rot a t e d frame w h i l e the other s et (g and A i n F i g . 10.2) are 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 tensors 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 tensors w i t h the r e s u l t that o f f diagonal components of the g tensor could be considered n e g l i g i b l e and the g values measured would be w i t h i n experimental e r r o r the p r i n c i p a l values. The o f f diagonal components of the A tensor are s i g n i f i c a n t and are dependent on the s i z e of the angle chosen between the g and A tensors. In the event that the chosen angle i s out by ± 10° -4 -1 the e r r o r i n the p r i n c i p a l values would be no more than .5 x 10 cm The r e s u l t s of t h i s a n a l y s i s are summarized i n Table 10.1. The hype r f i n e tensors have been separated i n t o i s o t r o p i c c o u p l i n g and the a n i s o t r o p i c components. The p o l y c r y s t a l l i n e s p e c t r a which are simulated using these parameters ( F i g . 10.4) assuming a 20° angle between the g and A tensors i n the x,z plane, w i l l o bviously appear i d e n t i c a l ( n e g l e c t i n g of course the unobserved forbidden t r a n s i t i o n s ) and the agreement between the s i m u l a t i o n and the observed spectrum i s e x c e l l e n t . To determine i f any of these four p o s s i b l e choices 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 species might be e n l i g h t e n i n g . R a d i c a l s of t h i s type that have been p r e v i o u s l y observed are H C 0 ^ 7 \ and FCO^O) a n ( j they e x h i b i t the l a r g e i s o t r o p i c c oupling which i s c h a r a c t e r i s t i c of a h i g h l y bent a r a d i c a l . The HISK^^"^ r a d i c a l which i s valence i s o e l e c t r o n i c w i t h HSO^ has been found to be only s l i g h t l y bent and th e r e f o r e has a sm 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 . Morton^"'^ has st u d i e d the r a d i c a l s formed i n i r r a d i a t e d ammonium hypophosphite and has i d e n t i f i e d one species as HPO2 which - 140 -Hi 2 5 6 >i 10.4 Computer simulated EPR spectrum of the HSO^ r a d i c a assuming the non-coincident a x i s system of F i g . 10 TABLE 10.1 P r i n c i p a l Values f o r the Spin Hamiltonian : Parameters f o r the HS0 2 R a d i c a l . Hyperfine components f -1 (cm x 4 10 ) l i n e p a i r 8 y A X A y A z T. ISO T X T y T z x; z 2 .0028 2.0071 2.0082 ±103.6 ±101.0 ±109.8 ±104.8 +1.2 +3.8 ±5.0 ba 1;ab * 2 .0028 2.0065 2.0090 ±104.1 ±103.1 ±107.3 ±104.8 + .7 +1.7 ±2.4 bb 1;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 t * Ref. 18 (HP0 2) t L i n e p a i r s r e f e r to F i g . 10.1 - 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 to e x h i b i t s i m i l a r c h a r a c t e r i s t i c s . In HPO^ the unpaired e l e c t r o n has been shown to occupy a a type o r b i t a l on phosphorous d i r e c t e d along the pyramidal a x i s . From the 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 of the Zeeman and hydrogen h y p e r f i n e tensor was e s t a b l i s h e d to be 27° and the d e v i a t i o n from p l a n a r i t y of the molecule to be about 60° - i e . the angle between the H-P bond and the PG^ plane. I t was on t h i s b a s i s that the angle between the g and A tensors 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 the angle between the HS bond and the SC^ plane as determined from the INDO c a l c u l a t i o n s ) . I t i s noted that i n HPO2 the d i r e c t i o n of the pyramidal a x i s corresponds to the minimum g - s h i f t from g g and that the g tensor i s n e a r l y a x i a l about t h i s d i r e c t i o n . The H-P bond d i r e c t i o n corresponds to the 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 t h i s a x i s . The assigned p r i n c i p a l tensors i n the a x i s system s i m i l a r to F i g . 10.2 are given i n Table 10.1 f o r comparison. By s t r i c t analogy w i t h HPO2 we have taken the b a s i c c h a r a c t e r -i s t i c s and a p p l i e d them to the HSO2 r a d i c a l . In a d d i t i o n to the evidence from p a r t i a l o r i e n t a t i o n , the assignment of the cc' l i n e p a i r as being a s s o c i a t e d w i t h the pyramidal a x i s d i r e c t i o n i s based on the observation that t h i s i s a l s o the p a i r which e x h i b i t s the minimum g - s h i f t . Attempts to f i t the spectrum w i t h l i n e p a i r s other than cc' r e s u l t e d i n g-values which were much higher than ge» I f the near a x i a l i t y of the g and A tensors 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) are to 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 are c l o s e r to being 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 the d i r e c t i o n of maximum A i s along the H-S bond i n the former as i s the case w i t h HPG^. This analogy cannot be c a r r i e d too f a r however, because of the d i f f e r e n t c r y s t a l environments experienced i n the two cases, the 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 rare gas matrix. In an attempt to r e s o l v e the discrepancy a r i s i n g from the l i n e p a i r i n g , an experiment was performed using HI enriched to about 10% i n DI. Unfortunately the decreased couplings of the deuterium species caused the l i n e s to l i e completely w i t h i n the broad c e n t r a l a b s o r p t i o n . Experiments performed at a higher microwave frequency would a i d the determination of the l i n e p a i r i n g due to the increased s i g n i f i c a n c e of the g tensor anisotropy. To confirm the assignment of the tensor o r i e n t a t i o n and the l i n e p a i r i n g a t h e o r e t i c a l estimate of the EPR parameters i s necessary. The anisotropy of the g tensor i s very small and t h e o r e t i c a l e s t i m a t i o n of the g - s h i f t s from the r e l a t i v e l y poor INDO wavefunctions would not be r e l i a b l e . Since the MO c a l c u l a t i o n s show that HSO2 i s a a r a d i c a l , 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 to p o s i t i v e s p i n d e n s i t y 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 the hydrogen i s o r b i t a l of .3 which represents an a p p r o x i --4 -1 mate i s o t r o p i c h y p e r f i n e coupling of ^  139 x 10 cm i n f a i r agree-ment w i t h the observed values. The l a r g e i s o t r o p i c coupling i n d i c a t e s 2 that the ground s t a t e i s A' as t h i s would provide the necessary mixing between the A' o r b i t a l s on s u l f u r and that on hydrogen. I t i s - 144 -reasonable t h e r e f o r e to assume that the major c o n t r i b u t i o n to the anisotropy i n the hydrogen h y p e r f i n e tensor w i l l a r i s e from d i r e c t c o n t r i b u t i o n s of the unpaired e l e c t r o n d e n s i t y i n the s u l f u r 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 i n t e r a c t i o n . The molecular o r b i t a l s i n HSC^ can be represented as a l i n e a r combination of A' symmetry o r b i t a l s , composed of s-, p - , and p- o r b i t a l s where X z the z a x i s r e f e r s to the H-S bond d i r e c t i o n and the x a x i s i s perpendicular to t h i s and i n the symmetry plane. Since the p-o r b i t a l s on s u l f u r are of A" symmetry, they cannot mix e f f i c i e n t l y w i t h the A' o r b i t a l s and t h e i r c o n t r i b u t i o n to the t o t a l tensor w i l l be neglected. The s p i n p o l a r i z a t i o n w i l l a l s o c o n t r i b u t e to the o v e r a l l tensor but i t s e f f e c t w i l l be neglected i n the c a l c u l a -t i o n . The s m a l l c o n t r i b u t i o n from the oxygen o r b i t a l s w i l l a l s o be neglected. The d i p o l a r i n t e r a c t i o n i s represented by the two center i n t e g r a l s <x3p S|0 H |x3pS> and <x3p S |o H |x3pS>. These were c a l c u l a t e d X 01 Oi X Z QLQL Z using a S l a t e r 3p-atomic o r b i t a l i n a manner described i n Appendix B. An e f f e c t i v e nuclear charge of 5.45 was chosen f o r s u l f u r and an average H-S bond length was chosen from a f a m i l y of HS-type o — compounds to be 1.33 A. For c a l c u l a t i o n s on HPG^ a P-H bond length o of 1.54 A and an e f f e c t i v e nuclear charge of 4.8 f o r phosphorous were chosen. The i n t e g r a l s f o r HSO^ are given i n Table 10.2 and show that the form of the d i p o l a r tensor w i l l be s m all and negative i n the x and y d i r e c t i o n s and l a r g e r and p o s i t i v e i n the z (bond) d i r e c t i o n . S i m i l a r c a l c u l a t i o n s on HP0„ i n d i c a t e the same shape f o r - 145 -TABLE 10.2 Pr e d i c t e d A n i s o t r o p i c Hyperfine Tensor Components f o r HS0 9 <3p x|0 H|3p x> -.03 -7.32 +7.35 p 3 ? x = .154 <3p z|0 H|3p z> -10.8 -10.8 +21.6 p3p^ = .122 z T o t a l -1.32 -2.45 +3.77 - 146 -the tensor. Since HPC^ and HSO^ are i s o e l e c t r o n i c , the s p i n d e n s i t y d i s t r i b u t i o n s should 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 that the 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 s u l f u r Z. X 2 and phosphorous were lower by ^  10% i n HSC^ wh i l e the hydrogen s-den s i t y i s higher i n HSO2 by ^  25% which i s again c o n s i s t e n t w i t h the observed couplings. Using the known d i p o l a r tensor f o r HPO2 the s p i n d e n s i t i e s i n the 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 the values given by the 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 the d i p o l a r tensor f o r HSO2 was c a l c u l a t e d . The c a l c u l a t e d tensor f o r HSO2 i s seen to f i t c l o s e l y to choices (a) and (b), w h i l e not agreeing w i t h the 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 are of course dependent on the bond lengths chosen f o r each species and a l s o on the values of the o r b i t a l exponents. I t i s p o s s i b l e that b e t t e r o r b i t a l exponents may be chosen and that the average bond lengths chosen are not accurate, but the general shape of the tensor w i l l not 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 are s i g n i f i c a n t enough to all o w the d i p o l a r tensors (a) and (b) to be chosen over (c) and (d). A choice between (a) and (b) may not be s i g n i f i c a n t due to the sm a l l d i f f e r e n c e s between the tensors. 10.2.2 Reaction of F l u o r i n e Atoms w i t h SO? Mixtures of CF^OF and SO2 i n argon were subjected to i r r a d i a t i o n w i t h a high pressure mercury lamp. ( I n i t i a l l y a low - 147 -pressure mercury lamp was thought necessary but produced no s i g n a l . ) A r e l a t i v e l y complex and intense absorption was observed centered about g = 2. This i n i t i a l spectrum has not been analyzed but i s presumably due to CF^O r a d i c a l . Continued i r r a d i a t i o n produced weak absorptions i n the outer wings composed of a p a i r of t r i p l e t s centered about g = 2 ( F i g . 10.5). The most notable f e a t u r e i s the very l a r g e coupling e x h i b i t e d by the outer p a i r of l i n e s of about 267 gauss. The general shape of the spectrum i n d i c a t e s that the species formed contains f l u o r i n e i n a p o s i t i o n i n which i t possesses considerable s p i n d e n s i t y . I t i s very l i k e l y that the species formed i s F S O 2 i n a r e a c t i o n s i m i l a r to that which produced H S O 2 The lower s o f t e n i n g point of argon has presumably allowed the r e a c t i o n to proceed without the warming which was necessary w i t h krypton matrix used f o r H S O 2 , the s o f t e n i n g e f f e c t being produced by the r e l a t i v e l y high IR output of the high pressure lamp. To confirm the assignment of the r a d i c a l species as F S O 2 , s u l f u r y l f l u o r i d e ( S O 2 F 2 ) was i r r a d i a t e d i n an argon matrix w i t h a hydrogen resonance lamp and y i e l d e d a very complex spectrum w i t h s e v e r a l species present ( F i g . 10.6). One species which seems to be i n v a r i a b l y i n cluded i n a l l experiments using a hydrogen resonance lamp i s the CH~. r a d i c a l . The complete removal of a l l organic traces from the sample gases and contaminants introduced from s m a l l undetected leaks i s extremely d i f f i c u l t . The other r a d i c a l species present i s due to contamination of the s u l f u r y l f l u o r i d e by t h i o n y l f l u o r i d e . 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 melti n g p o i n t s - 148 -- 149 -F i g . 10.6 Observed EPR spectrum of the F SO2 r a d i c a l i n an argon matrix at 4.2 K (formed by the UV p h o t o l y s i s of F 2 S 0 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 technique v i r t u a l l y i m p o s s ible. The r a d i c a l species formed corresponds e x a c t l y to that i n pure F 2 S O and has been assigned to the r a d i c a l species FSO which i s considered a d e t a i l i n Chapter E i g h t . The remaining r a d i c a l species i n the F 2 S O 2 mixture corresponds e x a c t l y to that observed i n C F 2 O F / S O 2 mixtures. The l o s s of f l u o r i n e from F 2 S O 2 i s ener-g e t i c a l l y more favourable than l o s s of an oxygen which would a l s o produce a more complicated powder p a t t e r n than observed due to the i n t e r a c t i o n of two equivalent f l u o r i n e s . On t h i s b a s i s , r a d i c a l species i s assigned as F S O 2 . The sample was allowed to rewarm i n order to o b t a i n the i s o t r o p i c c o u p l i n g but only a gradual decrease i n the i n t e n s i t y was observed u n t i l the sample was 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 . The sample was 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 d e t e c t a b l e 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 observed. Again as w i t h H S O 2 , there i s the ambiguous choice of l i n e p a i r i n g and tensor 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 be made. I t i s reasonable to assume that the two outer components of the spectrum, (a) and (c') are 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 molecule as otherwise unreasonable g-values 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 . A l s o s i n c e F S O 2 would be expected to 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 coupling should be i n the molecular plane. INDO c a l c u l a t i o n s do indeed 2 i n d i c a t e that F S O 2 has a A' ground s t a t e . I t might a l s o be noted that Walsh ^ -'^ p r e d i c t s that F P 0 „ , which i s i s o e l e c t r o n i c w i t h F S 0 „ - 151 -should be non planar. Refinements on the molecular geometry using the s t r u c t u r a l parameters of F2S0-2''^^ i n d i c a t e s that the F-S bond i s about 25° from the SG^ plane. The g and A tensors w i l l most l i k e l y be non-coincident i n t h i s case as w e l l ( F i g . 10.7). Using the same arguments as were used f o r HS02» the angle between g and A tensors has been assumed to be 10°. Since the anisotropy of the A tensor i s very much l a r g e r than the g-anisotropy, the powder l i n e s observed are due to the f i e l d being o r i e n t e d along the p r i n c i p a l A tensor axes and only the " e f f e c t i v e " g-values can be measured. The o f f diagonal components of the g tensor w i l l be small however, and the non c o l i n e a r i t y of the tensors may be neglected without severe e r r o r , but f o r completeness, the tensors w i l l be assumed non c o i n c i d e n t . Least-squares f i t t i n g of the powder l i n e p o s i t i o n s r e s u l t e d i n the values i n Table 10.3 which are again represented as a se p a r a t i o n of the i s o t r o p i c and a n i s o t r o p i c components. The lineshape i n F i g . 10.8 was simulated using the parameters f o r tensor (a) s i n c e there are again four p o s s i b l e tensor choices each of which w i l l e x a c t l y simulate the 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 to 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 oupling of 132 x 10 cm and an i s o t r o p i c g-value of 2.0026. This i s i n e x c e l l e n t agreement w i t h the i s o t r o p i c values reported f o r t h i s species by Morton and P r e s t o n ' " ^ of 130 to 134 x -4 -1 10 . cm f o r the h y p e r f i n e tensor and an i s o t r o p i c g value of 2.0026. - 152 -A z g z F i g . 10.7 R e l a t i o n of the s p i n Hamiltonian parameters to the molecular axes in. the FS0„ r a d i c a l . - 153 -TABLE 10.3 P r i n c i p a l Components of the Spin Hamiltonian Parameters f o r the FS0„ R a d i c a l . Hyperfine components (cm xlO ) l i n e p a i r g x g y g z A X A y A z T. ISO T X T y T z x; 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 ±.2 f Line p a i r s r e f e r to F i g . 3. - 155 -This a l s o agrees remarkably w e l l w i t h the 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 of .005 which gives an i s o t r o p i c hyper--4 -1 f i n e c o u p l i n g of 130 x 10 cm The anisotropy of the f l u o r i n e h y p e r f i n e tensor w i l l undoubtedly be dominated by i t s own molecular o r b i t a l s and a f f e c t e d to a smaller extent by the anisotropy introduced by the c o n t r i b u t i o n from the neighbouring s u l f u r o r b i t a l s . The 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 not be considered nor w i l l the c o n t r i b u t i o n from the oxygen p-o r b i t a l s . The a n i s o t r o p i c tensor can be represented by a form s i m i l a r to those of Eqn. [6.7]. The f i r s t three terms i n the expression are the one center c o n t r i b u t i o n using the INDO s p i n d e n s i t i e s . The c o n t r i b u t i o n of the one center term gives the a n i s o t r o p i c tensor shown i n Table 10.4. The combination of the two center terms has been evaluated s e p a r a t e l y to i l l u s t r a t e that these c o n t r i b u t i o n s are much l e s s than the one center terms, and that a one center c a l c u l a t i o n gives 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 tensor i s then p r e d i c t e d to have the major component p a r a l l e l to the F-S bond and the intermediate component perpendicular to the molecular plane of symmetry. This then allows a choice to be made between the four axes and l i n e p a i r i n g choices i n Table 10.3. Only the case (a) f i t s the observed tensor adequately. Had the s p i n d e n s i t i e s f o r F S O 2 not been a v a i l a b l e , the treatment using 2 2 Eqn. [6.9] would have p r e d i c t e d the same r e s u l t s (c = .01, c = .1) (ta k i n g i n t o account that the two center terms are neglected) but no choice could have been made between cases (a) and (d). - 156 -TABLE 10.4 Pre d i c t e d A n i s o t r o p i c Hyperfine Components f o r the F S 0 2 r a d i c a l . F i "F 2p 0 r x 1 a F "F 2p 0 r z a 3 P S | 0 F *x a 3 P V r z ' a 3 P S | 0 F *x1 a 3 P S | 0 F  r z 1 a 2 P F> x 3PS> X 2p F> r x 5.87 -.11 .18 -1.28 3.61 y -2.94 -58.70 -58.7 -.47 ,18 .65 3.61 -2.94 117.4 .58 -.37 .63 -7.23 F P2p, P2p. P3p P3p„ = .005 = .1 = .09 -.02 „S F = -.02 P3p x2p x p3p 2p = .05 c z c z S = .111 XX S = -.244 zz T o t a l -50.4 -57.6 108.7 - 1 i n " 4 cm xlO - 157 -10.2.3 Reaction of methyl r a d i c a l s w i t h SO^ A mixture of CH.JI/SO2/A . 1mm:.. 1mm: 10mm) at 4.2K photolyzed w i t h a high pressure mercury lamp. I n i t i a l l y , an intense spectrum which was due to methyl r a d i c a l s was observed and no other secondary species could be detected. On a l l o w i n g the m a t r i x to 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 K, a weak, broad.secondary r a d i c a l species was detected which overlapped the methyl r a d i c a l spectrum. The i r r a d i a t i o n of CH^I/A or SO2/A mixtures 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 only 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 of 2.042, 2.010 and 2.002. The l i n e at g = 2.010 overlapped s t r o n g l y w i t h a methyl r a d i c a l h y p e r f i n e component and t h i s g-value i s some-what more un c e r t a i n than the other two components. There are s e v e r a l products which might be formed 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 a nuclear s p i n I = 5/2 and would be expected to produce a h y p e r f i n e p a t t e r n i f a d d i t i o n to SO2 occurred. The outer l i n e component at g = 2.042 was not observed i n the p h o t o l y s i s of HI/SO2 mixtures and i t i s thus u n l i k e l y that t h i s species i s due to i o d i n e atom a d d i t i o n . 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 migrate through the rare gas l a t t i c e at higher temperatures and to react w i t h the S0 o molecules - 158 -F i g . 10.9 Observed EPR spectrum of the r a d i c a l species formed on UV p h o t o l y s i s of a CH I/SO /A mixture at 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 with the a d d i t i o n o c c u r r i n g at the s u l f u r or oxygen atoms. I f the a d d i t i o n were to occur at the s u l f u r atom, a g tensor s i m i l a r to that observed f o r HSC>2 and FSO^ would be expected. The s p i n d e n s i t y i n t h i s symmetrical a d d i t i o n r a d i c a l would be l a r g e l y concentrated 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 ( 6 8 ) couplings which are 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 here, the symmetrical 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 methyl r a d i c a l were to occur at the oxygen of SC^ to form the asymmetrical r a d i c a l CH^OSO. In t h i s case, the unpaired e l e c t r o n may have an appreciable s p i n d e n s i t y on the t e r m i n a l oxygen atom which could produce a strong 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 protons would a l s o be expected to be very s m a l l i n t h i s case. The present experimental evidence i s not strong enough to unequivocally 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 species 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^ mixtures would e s t a b l i s h whether the observed l i n e s are due to a g f a c t o r anisotropy and would confirm 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 Ch l o r i n e Dioxide, ClO^ 11.1 I n t r o d u c t i o n C h l o r i n e d i o x i d e (CIC^) i s one of the 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 respect i t becomes a r e l a t i v e l y easy compound to study by EPR si n c e i t s formation through chemical r e a c t i o n or p h o t o l y s i s i s unnecessary. There have been many extensive EPR st u d i e s on CIC^ . . (161-167) , . . ..,(126,168-170) , . i n s o l u t i o n and i n the s o l i d s t a t e and a l s o . . . * (171,172) i n the p o l y c r y s t a l l i n e s t a t e adsorbed on surfaces or (123) d i s s o l v e d i n a frozen solvent . Only one of these s t u d i e s has considered the l a r g e quadrupole c o u p l i n g of the c h l o r i n e nucleus j . u - . v * .(173,174) Extensive microwave st u d i e s have a l s o been performed and the a n i s o t r o p i c h y p e r f i n e , Zeeman and quadrupole tensors are thus known f o r the gas phase and from EPR f o r the s o l i d s or gla s s e s . A study of t h i s species i n a non-polar matrix would thus provide an e x c e l l e n t study f o r comparison w i t h C I O 2 i n the " f r e e " gas s t a t e . The paramagnetic property of ClO^ permits the use of extremely low concentrations of C I O 2 i n the trapping m a t r i x thus a l l o w i n g the wide sep a r a t i o n of neighbouring paramagnetic c e n t e r s , and thereby decreasing any i n t e r a c t i o n s w i t h nearby C I O 2 molecules. I t has been - 161 -shown i n st u d i e s i n v o l v i n g the trapping of atoms i n i n e r t m a t r i c e s , that 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 the rare gas matrix to produce a c h a r a c t e r i s t i c s h i f t i n the Zeeman and hyp e r f i n e tensors (8,9,13,14,66) _ , . . . ._ (66) The theory developed to e x p l a i n these s h i f t s has not been extended to trapped paramagnetic molecules and semi-q u a l i t a t i v e arguments based on the general theory 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 or krypton matrix to a concentration of R;M ^ .1mm:300mm. This d i l u t i o n was found to give e x c e p t i o n a l l y w e l l resolved s p e c t r a w i t h no appr e c i a b l e broadening due to s p i n - s p i n coupling of nearby CIC^ neighbours. 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 to the f l a t face of the rod on which the sample i s deposited. F i g . 11.2 shows the e f f e c t of r o t a t i n g the d e p o s i t i o n surface by 90°. Large changes i n the i n t e n s i t i e s of the various l i n e components are i n d i c a t i v e of the phenomenon of p a r t i a l o r i e n t a t i o n , which has been wi d e l y observed . , _ . . . (14,19,34,76) i n many cases where r a d i c a l s are trapped i n the ra r e gases The e f f e c t of p a r t i a l o r i e n t a t i o n w i l l be discussed i n more d e t a i l l a t e r . From the e l e c t r o n i c spectrum of C I C ^ ' 7 " ^ , the ground s t a t e has 2 been e s t a b l i s h e d to be B^ i n which the unpaired 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 w i t h respect to r e f l e c t i o n i n the molecular plane. C1C>2 i s thus a " T f-type" - 162 -F i g . 11.1 Experimental EPR spectrums of CIC^ i n an argon matrix at 4.2 K. H i s p a r a l l e l to the rod face. - 163 -F i g . 11.2 Experimental EPR spectrum of ClO^ i n an argon matrix. H q i s perpendicular to the rod face. - 164 -r a d i c a l and should 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^ species w i t h 19 e l e c t r o n s i n the valence 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 to occupy a b^ o r b i t a l and a l s o suggests that the molecule i s s t r o n g l y bent and t h i s i s confirmed 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) ^ ^ e theory of u r a d i c a l s would then r e q u i r e that the s m a l l e s t s h i f t i n the g f a c t o r should be f o r the d i r e c t i o n p a r a l l e l to the T o r b i t a l i n which the e l e c t r o n r e s i d e s and that t h i s d i r e c t i o n should a l s o e x h i b i t the maximum hyp e r f i n e c o u p l i n g . 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 that 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 molecule. Measurement of the h y p e r f i n e c o u p l i n g -4 -1 and g value f o r t h i s d i r e c t i o n leads to values of 64.52 x 10 cm and 53.7 x 10 ^cm ^ f o r the h y p e r f i n e of " ^ C l and " ^ C l r e s p e c t i v e l y and a g value of 2.0025. The h y p e r f i n e components are c l o s e to the expected r a t i o of 1:83 which i s expected from the r a t i o of the magnetic moments and the i n t e n s i t y r a t i o s of the two isotopes are 35 37 c l o s e to the expected r a t i o of .76:.24 ( CI: C I ) . From the above 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 to the assignment of t h i s com-ponent of the G and A tensors to the d i r e c t i o n perpendicular to the molecular plane which i s i n agreement w i t h previous i n t e r p r e t a -t i o n s . In 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 defined as f o l l o w s : the x a x i s i s perpendicular to the molecular plane; the 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 the z a x i s i s along the b i s e c t o r of the symmetry a x i s ( F i g . 11.3). For - 165 -F i g . 11.3 Molecular a x i s system f o r C I O 2 (x a x i s i s perpendicular to the molecular plane and H i s the f i e l d d i r e c t i o n ) . - 166 -convenience a l l polar angles w i l l be defined w i t h the angle 0 being measured from the x a x i s and the angle cp being measured from the y a x i s . The tensor components of the c e n t r a l region of the spectrum ( F i g . 11.4) where the f i e l d i s approximately p a r a l l e l to the y and z a x i s must now be assigned. This becomes a r a t h e r complex task because of the strong overlap of the 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 to be expected that "forbidden" t r a n s i t i o n s (Am^ . = ±1, ±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 region because of the i n t e r a c t i o n of the e l e c t r i c f i e l d gradient w i t h the quadrupole moment of c h l o r i n e and the nuclear Zeeman i n t e r a c t i o n ^ " ^ ^ . In ge n e r a l , the most intense l i n e s i n t h i s r e gion are a c t u a l l y the "forbidden" t r a n s i t i o n s s i n c e the Am^ = ±1 l i n e s reach t h e i r maximum i n t e n s i t y i n the region 7O°<0$9O° and the Am^ . = ±2 t r a n s i t i o n s (56) reach 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 order e f f e c t of the nuclear Zeeman or quadrupole coupling (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 the Am^ . = 0 t r a n s i t i o n are 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 of the hy p e r f i n e components or quadrupole components can be obtained. However, s i n c e the m a j o r i t y of l i n e s observed i n the c e n t r a l region of the spectrum a r i s e from "forbidden" t r a n s i t i o n s which w i l l show f i r s t order s h i f t s i n t h e i r r e l a t i v e 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 , the assignment of the r e l a t i v e signs of the hy p e r f i n e and quadrupole components can be e s t a b l i s h e d . - 167 -Experimental 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 -Using the s i g n convention assigned by Byberg and a p p r o x i -mate Hamiltonian parameters measured from the observed s p e c t r a , the simulated spectrum was computed using the complete Hamiltonian (Eqn. [2.23]). P l o t s of f i e l d vs. angle ( F i g . 11.5) 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 three p r i n c i p a l planes, were drawn and compared with the powder p a t t e r n which they simulated. I t i s obvious, from the appearance of F i g . 11.5 that 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 complicated by the occurrance of "angular a n o m a l i e s " ^ 5 6 ^ which occur only 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 "angular anomalies" are absent.) The powder l i n e s were then assigned 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 angle (0,<f>) which corresponded to the minimum changes i n f i e l d w i t h respect to angle ( e i t h e r an angular 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 ) . A l e a s t squares f i t t i n g procedure was then performed on the Hamiltonian parameters. A f t e r each refinement, the f i e l d vs. angle diagram was again p l o t t e d and t h i s procedure c y c l e d . A f t e r successive c y c l i n g , a reasonable f i t to the observed spectrum was obtained assuming a random d i s t r i -b u t i o n f o r the molecular o r i e n t a t i o n ( F i g . 11.6). The i n t e n s i t i e s of the random s i m u l a t i o n do not reproduce the observed i n t e n s i t i e s of the spectrum when H q i s e i t h e r p a r a l l e l or perpendicular to the rod face. This i s because of the p r e v i o u s l y mentioned phenomenon of p a r t i a l o r i e n t a t i o n . 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 discussed. 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 face) the x - 169 -- 170 -F i g . 11.6 Computer simulated EPR spectrum of C IO2 using a completely 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 are seen to be much weaker than i n the perpendicular o r i e n t a t i o n , w h i l e the converse i s true f o r the y and z components. Since i t i s e s t a b l i s h e d that the x component has the 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 that i n the perpendicular o r i e n t a t i o n , there are more molecules o r i e n t e d w i t h t h e i r x axes p a r a l l e l to the magnetic f i e l d than i n the p a r a l l e l o r i e n t a t i o n . This suggests that the CIG^ molecules are p r e f e r e n t i a l l y o r i e n t e d w i t h t h e i r molecular plane p a r a l l e l to the rod su r f a c e . Since the x components do not completely disappear i n the p a r a l l e l o r i e n t a t i o n , any f u n c t i o n d e s c r i b i n g the o r i e n t a t i o n d i s t r i b u t i o n of the molecules w i t h respect to the rod face cannot go to zero i n the p a r a l l e l o r i e n t a t i o n . 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 to that used by Kasai e_t_ al_. to account f o r p a r t i a l o r i e n t a t i o n of trapped r a d i c a l s . Since p a r t i a l o r i e n t a t i o n a f f e c t s only the l i n e i n t e n s i t i e s and not the l i n e p o s i t i o n s , a new set of i n t e n s i t i e s T' can be defined by T'(0,<j>) = T(0,cp)P(a) where T(0,cj)) are the 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 p r o b a b i l i t i e s between l e v e l s |mm> 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 the angle between the rod su r f a c e and the r a d i c a l plane. When the magnetic f i e l d i s perpendicular to the rod fac e , the angles 0 and a become eq u i v a l e n t . However, when the rod - 172 -i s r o t a t e d by 90° so that the rod face i s p a r a l l e l to the magnetic 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 ^ where N i s a n o r m a l i z i n g constant, x = cosa and Q(x) = P ( a ) . This i n t e g r a l was evaluated n u m e r i c a l l y f o r a given f u n c t i o n of P ( a ) . From t r i a l and e r r o r s i m u l a t i o n , f o r the two o r i e n t a t i o n s , the d i s t r i b u t i o n f u n c t i o n 1 - .38 (0^6<T T/2 rad.) was found to best describe the system ( F i g s . 11.7 - 11.9). I t was found that only the perpendicular o r i e n t a t i o n s was h i g h l y s e n s i t i v e to the d i s t r i b u -t i o n f u n c t i o n chosen. The agreement between the simulated and observed spe c t r a i s s a t i s f a c t o r y but a refinement of the d i s t r i b u t i o n f u n c t i o n was 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 the system and 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 molecules about an a x i s perpendicular to the molecular plane may be necessary. S i m i l a r a n a l y s i s procedures were c a r r i e d out w i t h the CIC^ trapped i n neon and krypton matrices. The appearance of the s p e c t r a are e s s e n t i a l l y s i m i l a r except f o r s l i g h t changes i n the l i n e p o s i t i o n s of several components and corresponding s h i f t s i n the g values. The r e s u l t s are presented i n Table 11.1. The s p e c t r a f o r CIC^ trapped i n neon and krypton are s l i g h t l y d i f f e r e n t from that of s i t e I and s i t e I I i n argon. To o b t a i n an ,0 o - 173 -F i g . 11.7 Computer simulated EPR spectrum of C I O 2 using 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 cosO. H i s p a r a l l e l to the rod face. - 174 -F i g . 11.8 Computer simulated EPR spectrum of CIC^ (expanded 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). - 175 -11.9 Computer simulated EPR spectrum of C I O 2 using 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 Q i s perpendicular to the rod face. X TABLE 11.1 EPR parameters f o r c h l o r i n e d i o x i d e . g. A A i s o x y 4 -1 .(xlO cm ) xso QD QE ( x l O 4 ) (cm" 1) Ref. 2.0036 2.0183 2.0088 2.0015 2.0016 2.01667 2.01214 to t o to 2.00245 2.01614 2.01154 2.002 2.015 2.013 2.0022 2.0159 2.0125 2.0022 2.0157 2.0125 2.0023 2.0159 2.0125 2.0026 2.0164 2.0131 ±0.0002 ±0.0002 ±0.0002 2.0102 +68.3 +14.6 +10.8 14.45 ±65.9 ±69.84 +10.21 +10.8 2.0101 to to to ±64.28 +8.34 +6.24 2.010 ±69.13 +12.38 +10.62 15.48 ±66.76 +10.91 +9.33 ±65.86 +10.88 +9.55 ±64.52 +10.91 +9.33 ±64.23 +9.69 +8.15 ±0.3 ±0.3 ±0.3 15.21 ±0.3 ±2.95 168 123 169 173 ±0.2 ±3.02 Argon I I * ±0.5 ±2.63 Neon* ±0.4 ±2.66 Argon I * ±0.5 ±2.63 K r y p t o n * ±0.3 ±2.83 ±0.2 ±0.2 * T h i s work. - 177 -accurate measurement of the l i n e p o s i t i o n s i n Ne, Kr and Ar, the usua l 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 of l e s s than one gauss are concerned and the resonance p o s i t i o n of proton l i n e from the 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 the magnetic f i e l d . Instead, a s m a l l c r y s t a l of DPPH was d i s s o l v e d i n benzene and the copper rod l i g h t l y coated and allowed to dry. The experiments i n a l l three matrices were then repeated 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 standard. An attempt was made to o b t a i n a completely random spectrum i n argon by a l l o w i n g the sample to slo w l y warm. No motional narrowing of the l i n e s was observed up to about 30 K at which point the o v e r a l l i n t e n s i t y of the spectrum began decreasing. In s e v e r a l such attempts however, the sample was allowed to warm to about 25 K and then r a p i d l y cooled again to 4.2 K. Upon annealing 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 completely l o s t and s l i g h t narrowing of the l i n e components was observed along w i t h the appearance of a second trapping s i t e ( 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 oupling constant than that o r i g i n a l l y observed (Table 11.1). On r o t a t i n g the rod by 90° from that shown i n F i g . 11.10, the x component feature due to 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 increased i n i n t e n s i t y ) but the s i t e I I x-component i n t e n -s i t i e s were unaffected by the r o t a t i o n . On rewarming, a gradual decrease i n the 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 increase i n the i n t e n s i t y of the type I I s i t e which i n d i c a t e s - 178 -F i g . 11.10 Observed EPR spectrum of C I O 2 i n an argon matrix 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 conversion from type I to type I I s i t e s but the type I s i t e could not be completely annealed out and p e r s i s t e d u n t i l the sample deposit was l o s t due to the warmup. The same warmup procedure was t r i e d w i t h Kr and Ne matrices but no m u l t i p l e trapping s i t e s were observed, however, p a r t i a l o r i e n t a t i o n was present to about the same extent as i n argon. 11.3 The Hamiltonian Parameters Since the h y p e r f i n e , quadrupole and Zeeman tensors are l i k e l y c o i n c i d e n t f o r CIO,-,, there i s only the question of a s s i g n i n g the tensor values obtained to the p r i n c i p a l d i r e c t i o n s i n the 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 to e s t a b l i s h t h i s , Consider f i r s t the g tensor. The character t a b l e f o r symmetry shows that L x transforms l i k e the B 2 r e p r e s e n t a t i o n . The theory f o r g s h i f t s (Eqn. [6.15]) w i l l then only a l l o w L x to couple the ground s t a t e w i t h an e x c i t e d s t a t e of A,, symmetry. The molecular o r b i t a l f o r an A 2 s t a t e i s composed of anti-bonding o r b i t a l s centered mainly on the t e r m i n a l oxygens. 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 °1 °2 cp. = (C" X - C l) X A 2 x x px Since L I x^O, L cannot couple, the A„ s t a t e w i t h the B 1 ground state; the g s h i f t f o r t h i s d i r e c t i o n should be zero as was e a r l i e r described and the x a x i s then corresponds w i t h the minimum g s h i f t - 180 -(Ag = +.0002). According to Walsh's c o r r e l a t i o n diagram f o r AB^ 2 2 2 1 2 systems, the ground s t a t e can be w r i t t e n as (..3b2la2^a^2b^; B^). The o r d e r i n g of the f i r s t three 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 accurate LCAO-MO-SCF c a l c u l a t i o n s t o be E(A 0-B.) 2 E(B„-B1) > E(A -B.). Now the g s h i f t s f o r g and g 2 1 2 1 1 1 y z are 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 that the e x c i t e d s t a t e s mixing 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 unpaired e l e c t r o n 1 2 2 o r b i t a l . Consider 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 that L transforms l i k e the B., r e p r e s e n t a t i o n y 1 2 2 and w i l l thus mix s t a t e s whose symmetry i s A^. Since the A^ s t a t e l i e s lowest i n energy i t i s expected that t h i s s t a t e w i l l g i ve r i s e to a strong p o s i t i v e g s h i f t . transforms as A 2 and w i l l couple 1 2 2 2 2 2 only s t a t e s of B 2 symmetry (. . . 3b2la24a^2b^; B 2 ) • Since the B 2 2 s t a t e i s of s l i g h t l y greater energy than the A^ s t a t e a smaller g s h i f t i s expected. The a x i s assignment i s then g^ = 2.0159 (Ag = +.0137) and = 2.0125 (Ag = +.0102). This assignment i s i n agree-ment w i t h the previous i n t e r p r e t a t i o n s . The r e l a t i v e signs of the h y p e r f i n e and quadrupole tensors can now be e s t a b l i s h e d . From a simple one center argument, the a n i s o -t r o p i c h y p e r f i n e coupling tensor should have a maximum value when the f i e l d i s o r i e n t e d along the y (TT) a x i s and the s p i n d e n s i t y i n t h i s o r b i t a l should be p o s i t i v e . Having made t h i s choice, the only remaining s i n g choice f o r A^ and A^ to both be negative, s i n c e t h i s i s the only combination which w i l l give the observed i s o t r o p i c - 181 -(161—167) s p l i t t i n g . The temperature v a r i a t i o n of the i s o t r o p i c c o u p l i n g was found to be very s m a l l a n d thus there i s no ambiguity i n the r e l a t i v e s i g n choice. The s i g n of the quadrupole coupling can now be determined experimentally. The l i n e p o s i t i o n s f o r a l l four p o s s i b l e s i g n choices f o r QD and QE were c a l c u l a t e d and the spectrum was simulated. Only one s i g n choice f i t t e d the observed spectrum w e l l and that s i g n choice was w i t h QD and QE of 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 h y p e r f i n e c o u p l i n g tensor can be estimated using the method of Chapter S i x f o r I T r a d i c a l s (Eqn. [6.10]). The parameters used i n the c a l c u l a t i o n s were a bond lengths of 1.471 A and a bond angle of 117.6° ' 178) ^ ^ would be expected, the main c o n t r i b u t i o n to the a n i s o t r o p i c tensor comes from the one center term and i s a x i a l about the y a x i s . Smaller c o n t r i b u t i o n s from the two center and overlap i n t e g r a l tend to make the a x i a l tensor, n o n - a x i a l (Table 11.2). The unpaired e l e c t r o n i n the b^ o r b i t a l can a l s o p o l a r i z e the e l e c t r o n s i n the inner a^ o r b i t a l on c h l o r i n e comprised of 3s- and 3p z~ atomic o r b i t a l s . This s p i n p o l a r i z a t i o n can be approximated by i n c l u d i n g a term CI CI CI p3p < x3p 0 v3p >. The e f f e c t of t h i s i n c l u s i o n i s seen to *o r a ' aa 1 'a be small (Table 11.2). The t o t a l a n i s o t r o p i c tensor agrees w e l l w i t h the experimental values (+49.75, -25.65, -24.10) but p r e d i c t s that |A |<|A^| a f a c t which i s not i n agreement w i t h the experimental. The d i f f e r e n c e i s small however and could be correct e d i f s l i g h t l y more s p i n p o l a r i z a t i o n were introduced. A recent "ab i n i t i o " SCF - 182 -TABLE 11.2 C a l c u l a t e d h y p e r f i n e 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 using INDO/2 method. Spin d e n s i t i e s A A A xx yy zz CI p3prr 0.39 48.49 -24.24 -24.24 0 p2p-rr 0.31 0.19 0.25 -0.44 Cl-0 p2P7r3p7r -0.34 -3.05 +1.5 1.56 p3pa 0.0033 -0.2 -0.2 0.4 T o t a l (gauss) 42.55 -20.94 -21.61 ( c m - 1 x l 0 4 ) 39.77 -19.70 -20.30 - 183 -c a l c u l a t i o n has been performed on ClO^ where the h y p e r f i n e anisotropy was c a l c u l a t e d to be 31G, (.0029cm "*") f o r the p -d i r e c t i o n . 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- overlap was considered, but c o n t r i b u t i o n s from the two center terms and s p i n p o l a r i z a t i o n were neglected. 11.4 M a t r i x E f f e c t s When atoms or s m a l l molecules are trapped i n an i n e r t m a t r i x , i t i s not unusual to observe m u l t i p l e trapping s i t e s . These were f i r s t observed f o r the hydrogen atoms trapped i n argon, neon and (8) krypton matrices . Each atom would be expected to r e f l e c t the character of i t s p a r t i c u l a r environment and indeed i n argon and krypton, three d i s t i n c t p a i r s of hype r f i n e l i n e s were observed, as opposed to the expected one p a i r , and each possessed s l i g h t l y d i f f e r e n t h y p e r f i n e and g tensor values. These couplings 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 being due to hydrogen atoms trapped i n t e t r a h e d r a l , octahedral or 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) tra p p i n g s i t e s have a l s o been observed f o r other atoms ' and a l s o f o r molecules i n various matrices. The trapping s i t e s have been a t t r i b u t e d to e i t h e r i n t e r s t i t i a l or s u b s t i t u t i o n a l s i t e s , w i t h the l a r g e r atoms occupying 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 that 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 radius of a CIO2 molecule 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 of 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 radius of about .78 A f o r the octahedral 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 fr e e radius of about 1.88 A and could conceivably accommodate the CIC^ molecule w i t h only a moderate l a t t i c e d i s t o r t i o n . When the CIC^ mixture i s i n i t i a l l y condensed, there w i l l very l i k e l y be considerable s t r a i n s i n the l a t t i c e s t r u c t u r e and l a t t i c e defects are e s p e c i a l l y prevalent to form s i n c e (89' the m a t r i x i s being condensed w e l l below one-half i t s m e l t i n g p o i n t In these defect s i t e s , the l a t t i c e order i s e s s e n t i a l l y i n t a c t , but l o c a l d i s t o r t i o n s of the 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 to " a t t r a c t " an impurity atom during c r y s t a l g r o w t h . I t i s f e l t that s i n c e there i s only one s i t e observed when the matrix i s condensed ( s i t e I ) , that these l a t t i c e defects form the major trapping s i t e . I f the CIG^ molecules are 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 required on condensation and t h i s prospect seems rath e r u n l i k e l y . When the matrix i s allowed to warm g r a d u a l l y the matrix w i l l begin to s o f t e n and rearrangement of the c r y s t a l s t r u c t u r e w i l l take p l a c e , r e l i e v i n g any s t r a i n s imparted on condensation. On r e c o o l i n g the matrix to 4.2 K, the second t r a p p i n g s i t e appears i n d i c a t i n g that p a r t i a l r e o r d e r i n g of the c r y s t a l s t r u c t u r e has indeed taken place and to a considerable extent s i n c e the " s i t e I I " s i g n a l i s more intense than the corresponding " s i t e I " s i g n a l s . The r e d u c t i o n i n i n t e n s i t y of the 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 surface i s r o t a t e d by 90° and the corresponding increase i n the y and z components, i n d i c a t e s that the 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 not l o s t on annealing. The i n t e n s i t y of the s i t e two x components i s unaltered by the r o t a t i o n and i t can thus be i n f e r r e d that the molecules i n t h i s s i t e are e s s e n t i a l l y randomly o r i e n t e d and are surrounded i s o t r o p i c a l l y by matrix atoms. This would be the case i f the molecules were to occupy a s u b s t i t u t i o n a l s i t e i n the matrix s i n c e there 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 the completely symmetric environment of the 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 that i s observed f o r the 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 the theory o u t l i n e d i n Chapter F i v e . The l a t t i c e defects would be expected to have a l e s s symmetrical environment and consequently have a l a r g e r space between the matrix atoms. This would have the e f f e c t of pe r t u r b i n g the molecular o r b i t a l s on CIC^ to a l e s s e r extent than the s u b s t i t u t i o n a l s i t e . 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 contract 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 to an increase i n the hy p e r f i n e coupling constant. There were no m u l t i p l e trapping s i t e s observed when ClO^ was trapped i n neon or krypton matrices. Annealing of neon i s v i r t u a l l y impossible due to i t s low melti n g p o i n t and annealing i n krypton produced no second s i t e s . The powder l i n e p o s i t i o n s were, however, d i f f e r e n t f o r each matrix. As can be seen from Table 11.1, the hyp e r f i n e values decrease w i t h an increase i n matrix s i z e . This can be q u a l i t a t i v e l y accounted f o r by the theory i n Chapter F i v e . As the matrix s i z e i n c r e a s e s , the average distance between the 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 the o r b i t a l s on the matrix atom - 186 -w i l l i n c r e a s e . This w i l l lead to a r e d u c t i o n i n the P a u l i forces 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 increase i n the van der Waals i n t e r a c t i o n . Since the P a u l i forces are r e p u l s i v e and the van der Waals forces 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 decrease i n the s p i n d e n s i t y which i n t u r n w i l l decrease 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 h y p e r f i n e coupling 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 greater than that i n neon. Since the CIC^ i s l i k e l y trapped i n a l a t t i c e defect i n neon (which should have l e s s f r e e space than one i n argon) any h y p e r f i n e coupling greater than that 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 t h i s l a r g e h y p e r f i n e s h i f t f o r s i t e I I i n argon that leads us to p o s t u l a t e the s u b s t i t u t i o n a l t r a p p i n g s i t e . The 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 simply c o n s i d e r i n g the P a u l i and van 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 tend to increase w i t h an increase i n matrix s i z e . Since the p - e l e c t r o n i n c h l o r i n e w i l l induce a small 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, there w i l l be a small s p i n - o r b i t coupling from the matrix atom. I t may be that 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 c o n t r i b u t e to give an o v e r a l l p o s i t i v e g s h i f t or that the energies of the e x c i t e d s t a t e s are decreased s l i g h t l y which would give r i s e to an o v e r a l l p o s i t i v e g s h i f t . Comparison of the r e s u l t s i n Table 11.1 show a s i g n i f i c a n t d i f f e r e n c e between the Hamiltonian parameters of C10 9 i n the r a r e - 187 -gases and those i n the s i n g l e c r y s t a l environment. This i s not unexpected s i n c e the 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 to be s u b s t a n t i a l , such f i e l d s of course being much smaller f o r the i n e r t matrices. L a t t i c e v i b r a t i o n s i n the i n e r t matrices at 4.2 K would a l s o be expected to be minimal and 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 hyp e r f i n e components that are observed at higher 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 not f u l l y understood but i t appears to depend on s e v e r a l f a c t o r s ^ ' 1 8 ^ . I t would appear that the formation of defect s i t e s i s an important f a c t o r s i n c e when the CIG^ i s trapped i n a s u b s t i t u t i o n a l s i t e , there i s no p a r t i a l o r i e n t a t i o n e f f e c t . 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Herzberg i n " E l e c t r o n i c Spectra of Polyatomic Molecules" (D. van Nostrand Co. Inc., P r i n c e t o n , New J e r s e y ) . 176. A.H. Cl a r k and B. Beagley, J . Chem. S o c , (A), 46 (1970). 177. R.F. C u r l , J.L. Kinsey, J . C Baker, D.H. B a i r d , G.R. B i r d , R.F. Heidelberg, T.M. Sudgen, D.R. Jenkins and C N . Kenney, Phys. Rev., 121, 1119 (1961). - 199 -178. R.F. C u r l , R.F. Heidelberg and J.L. Kinsey, Phys. Rev., 125, 1993 (1962). 179. D.C. McCain and W.E. Palke, J . Chem. Phys., 56_, 4957 (1972). 180. D.W. Pashely, Adv. Phys., 14, 327 (1965). 181. W. Weltner, J r . , Adv. i n High Temp. Chem., 2, 85 (1969). 182. P. K o t t i s and R. Lefebvre, J . Chem. Phys., 39, 393 (1963). - 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 outlined here i s based (182) on the theory of Lefebvre and has been extended to include the nuclear Zeeman i n t e r a c t i o n Expanding Eqn. [2.48] i n terms of the d i r e c t i o n cosines of Eqn. [2.43] we have n . J ' T - T )}) c . = \<i>\ha (g (s + s ) - £G-1(IT + i . ab 1 a 1 x x f—i. N i i J = l J J " i/2<yg y(S + - S") - E G N ( I 1 -+ 1 > z s z - x ^ ' v i 2 [ A - 1 ] where = g ^ / B ^ This can be further expanded by s u b s t i t u t i n g the form of the state vectors i|> , ty, into the above equation as follows: a b -S+l - I . -I -S - I , -I . <\\**]\>-L £ 1 - £ n £ Z n G*(m;,mi • m'=S m' =1 , m' =1 m =S-1 iru =1 , mT =1 1 s I - i l I n s I-, 1 I n I n I n x <p(m ,m' • •-m')<j> (m ,m , • • *m )G(m ,m • • 'm ) 6m'. ,m + 1 S X X S X X S J- — X S S n " n I n h x 6m' ni •••m: ,mT {S(S+1) - m (m + 1 ) } I I- I I s s 1 n n L, JZ G ( m s + 1> m-[- ' • •mI ,a)G(m .m^. • •-m ,b) x m =S-1 m,. m_ I n I n s 1^ I 1 n x {S(S+1) - m (m [A. 2 ] - 201 -and similarly -S - I . -I I, 1 I n * * |S"|*.> = £ E G ( m s ' m T * " ' m T •'.a)G(m'+l>m * • •m]. ,b) x a m'=S-l m„ =1, mT =1 I n I n x (S(S+1) - (m'+Dm'}^ [A.3] s s -S - I , -I !*a' Sz ' V = ^ ^ £U m s G ( m s ' m l " * m l » a > G ( m s » ° I • " m i ' b ) m =S mT =1, mT =1 I n I n [A.4] s I, • 1 I n 1 n The nuclear Zeeman operators are equivalently defined -S - I , -I =1 -I V S " l ^ l n I -V 1 m i " ^ l m l = I n 1 r r+1 n * G (m ,mT •••m_ ,mT +l,m_ •••m ,a) x s l . l . l •«• . i 1 1 r-1 r r+1 n x G(m ,m_ :",m_ ,*"mT ,b){I (I +1) - m_ (m +1)} s l . I i r r i i 1 r n r r 2 S "I I -I m =S m =1 m =l - i m =i m = I • L i -L I r I r+1 T ~ G ^ m s , m i '°'mi " " m I » a) 1 r n [A.5] - 202 -••"V . " j +l,m -•••mT ,b){I (I +l)-m_ (mT +1)} 1 r-1 r r+1 n r r I r \ [A.6] -s - i x -I <* a |i> b > - E E m =S m_ = s I I n * mT G (m ,m •••m_ ,a)G(m ,mT • •-m " l , m l = I n r - 1 'n 8 Xn I I n [A.7] The integrals can be evaluated for the a,b transitions involved since the G's are simply the coefficients of the eigenfunctions which are determined by diagonalizing the spin Hamiltonian at the resonance f i e l d . Defining j=l J J P y = -i/2[g {<4< a|S +-S-|VB>} - £ Gj{<¥ |I+-IT-|? >}] j=l J J P Z - ^ < * a l s J V } " E ^ a ' ^ I V 1 [A'8] w e h a v e T a b = |rP x + l y P Y + l z P z | 2 [A. 9] where P X » P Y a n d P z w i l 1 b e complex functions of the coefficients G. - 203 -Expanding [A.9] we have Tab = ^ ^ V 2 + < C < P X ) 2 ) + 2 1 x i ; ^ P X ) ^ ( P Y ) + < t ( p x ) ^ ( p Y ) + 2I;IZ(IR(Px)(R(PZ) +€(P X)C (P Z)) + iy 2(fK (p y ) 2 + C ( P Y ) 2 ) 2ri Z(«\(P Y)iR(p z) +C(P Yxr ; (p z )) + i z ( i ^ p z ) 2 +C(P Z) 2) [A.io] where |r\ and <D are the real and complex parts of P. Substituting for the direction cosines from Eqn. [2.43] and averaging over a l l n as in Eqn. [2.45] the following expression is obtained 2 ' 2 2 2 1 ' T . = C (sin 9 cos <p + sin cf>) + C (cos 6 sin2<p) + C (sin20 coscb) aD xx xy xz ' 2 2 ' ? ' + C (sin20 sin <)> + cos cf>) + C (sin20 sincb) + C (cos 0 ) yy yz zz [A.11] where 0 = 0 + 90° always. (0 and 0 are as defined in Fig. 2.3) The coefficients A^ to A^ of Eqn. [2.49] are defined by A_ C • A_ = C jAy- = C 1 xx 2 xy 6 zz 2 2 where C = ( (PY ) + (PY ) ) etc. X X A A When 0 = 0°; 0' =90° (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 is no nuclear Zeeman interaction, [A.11] is equivalent to the expression given in Eqn. [2.45]. - 205 -APPENDIX B The theory f o r the magnetic d i p o l e i n t e r a c t i o n between a proton and an unpaired 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 derived by McConnell 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 to 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 at the proton. As was pointed out by M and S, the theory which was used to approximate the a n i s o t r o p i c h y p e r f i n e coupling was derived f o r a C-H fragment but t h i s could be g e n e r a l i z e d to an A-X fragment i f the appropriate atomic o r b i t a l s on center A are considered. The d e r i v a t i o n of M & S was co r r e c t e d by P i t z e r e_t al_. ^ "^^ f o r terms which were neglected. 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 which were co r r e c t e d by Barf i e l d ' ^ 2 ^ . A complete l i s t of the i n t e g r a l s f o r a 2p atomic o r b i t a l on center A can be found i n B a r f i e l d ' s paper. Because the b a s i c method f o r the e v a l u a t i o n of the i n t e g r a l s , given 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 given here and the equations used by M & S w i l l be referenced d i r e c t l y . The d i p o l a r i n t e r a c t i o n of i n t e r e s t here i s between a nucleus X and an unpaired e l e c t r o n i n a 3p atomic o r b i t a l on center A. The two center i n t e g r a l <x3p I0^ Ix3p > i s the e a s i e s t to evaluate and y 1 aa 1 r y ~X w i l l be considered f i r s t . 0 i s the d i p o l a r operator defined i n aa Eqn. [6.3] and the a x i s system i s the same as that chosen i n Chapter S i x . (The odd e l e c t r o n i n center A i s i n a 3p y o r b i t a l perpendicular to the A-X bond; the A-X d i r e c t i o n defines the z a x i s and the x a x i s - 206 -i s mutually orthogonal to 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 defined y l^i—y 2 - p / 3 o . i Jp = 8 I p e sxn0 sinep y \ 3 . 5T T [ B . l ] where K = Z/a where Z i s the e f f e c t i v e nuclear charge of center A o and p = Kr where r i s the vect o r from.the center A to the e l e c t r o n . Since the angular part of the 3p^ atomic o r b i t a l i s the same as the 2py atomic o r b i t a l , the i n t e g r a t i o n over the angular part w i l l be the 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 the center X as where i s the s p i n d e n s i t y i n the u o r b i t a l on center A. The i n t e g r a l can be w r i t t e n as as defined i n M & S (Eqn. 12). Ev a l u a t i n g the angular part of the i n t e g r a l , the f o l l o w i n g equation s i m i l a r to M & S Eqn. 20 w i l l r e s u l t . [B.2] [B.3] 2a 6 -2p/3 p e i 2a 8 -2p/3 P e d p - 207 --16a 3 3 -2p/3 J j , 2 -- I p e dp t + P cos0 cos2tp ^2a J 1 3 r°° 15 i r 2 a 6 -2p/3, 6 0 a ^ n P 6 d p + 8 a J r ° 3 -2p/3, j n J ^ P d dpj [B.4] KR where a = 2— and R i s the 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 ) are the Legendre polynomials defined by M.& S. I f t h i s i n t e g r a l on p i s evaluated, the r e s u l t i s 1/R" n 189 . \ 64 a4 . 376 a 3 a 184 a 2 , 68 a , 163 252 1 j + < + + H + h 5a ( 405 405 45 5 5 5a , 189 -4a/3 +77 r ( l - 3 c o s 2 8 ) + 1/R" 189 10a' 64 a 5 , 32 a 4 , 88 a 3 ,. 112 a 2 112 a + + — — + 3645 1215 135 45 45 + 84 + 126 + 189 -4a/3 5a 10a 2-(1 -cos 0) cos2tj) [B.5] The e v a l u a t i o n of the i n t e g r a l <x3p |0 |x3p > i s done i n an analogous Z OtOu z manner. S u b s t i t u t i n g the S l a t e r o r b i t a l X3p z =| 2K~ 3?5TT 2 -2p/3 , p e cosf [B . 6 ] i n t o Eqn. 12 of M & S, an equation i d e n t i c a l to M & S Eqn. 17 i s obtained. I f the i n t e g r a t i o n of these equations i s c a r r i e d out over cp w i t h the 3p z o r b i t a l s , and then the i n t e g r a t i o n over 0 i s performed, the i n t e g r a l w i l l have the form. - 208 -<x3p 0 x3p > = -2K' 3§5 p^Ccose) 2a ( l / 3 a + 2,_ 5, 6 -2p/3, p /5a )p e dp - 16 3 - 2 p / 3 J 15 p e d p | a [B.7] Performing the i n t e g r a t i o n on p, the f o l l o w i n g formula i s obtained. 1/R- , . 378 ( 1024 a7 . 256 a 6 ^ 512 a 5 J 32 a 4 x 1232 a 3 5a 98415 10935 3645 45 405 , 488 a . 468 a . 341 . 504 378 / -4a/3 T -t- -t- + + — — > e 45 15 5a 5a ( 1 - 3 cos 20) [B.8] The term 1024 a 98415 i s the c o r r e c t i o n term added to t h i s i n t e g r a l 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 ^ i s z^r~ f ^ where f(R) i s the square of the r a d i a l part of the S l a t e r o r b i t a l , evaluated at r = R (p = KR). These i n t e g r a l s , along w i t h the 2p i n t e g r a l s tabulated by B a r f i e l d ' ^ 2 ^ were programmed f o r an IBM 360 computer. 1 

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