UBC Theses and Dissertations

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UBC Theses and Dissertations

Electronic spectroscopy by electron impact Tam, Wing-cheung 1974

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ELECTRONIC SPECTROSCOPY BY ELECTRON IMPACT by WING-CHEUNG TAM B.Sc. ( G e n . ) , U n i v e r s i t y o f Hong Kong (1970) . A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n t h e Department o f CHEMISTRY We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA J u l y , 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 the r equ i r emen ts 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 agree 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 tudy . 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 pu rposes may be g r a n t e d by the Head o f my Department or 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 Chemistry 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 July 22, 1974 i i . ABSTRACT The d e s i g n and c o n s t r u c t i o n o f a h i g h - r e s o l u t i o n , l o w - e n e r g y and v a r i a b l e - a n g l e e l e c t r o n i m p a c t s p e c t r o m e t e r has e n a b l e d t h e s t u d y o f t h e i n t e r a c t i o n between a low en e r g y monochromatic e l e c t r o n beam and a s e r i e s o f atoms and m o l e c u l e s . O p t i c a l l y f o r b i d d e n t r a n s i t i o n s have been s t u d i e d f o r a r g o n and neon. The Rydberg t r a n s i t i o n s i n atoms and s m a l l m o l e c u l e s have a l s o been i n v e s t i g a t e d . The "vacuum u l t r a v i o l e t s p e c t r a " ( e l e c t r o n i m p a ct s p e c t r a ) o b t a i n e d f o r some o r g a n i c m o l e c u l e s such as t h e a l k y l d e r i v a t i v e s o f w a t e r and c a r b o n y l compounds have been i n t e r p r e t e d i n terms o f Rydberg t r a n s i t i o n s . S u b s t i t u e n t e f f e c t s on Rydberg o r b i t a l e n e r g i e s and i o n i z a t i o n p o t e n t i a l s a r e d i s c u s s e d u s i n g T a f t a* v a l u e s . i i i . TABLE OF CONTENTS Page CHAPTER I : INTRODUCTION 1 CHAPTER I I : THEORY OF INELASTIC ELECTRON SCATTERING 4 2.1. E l e c t r o n - H y d r o g e n Atom S c a t t e r i n g 4 2.2. A p p r o x i m a t e T h e o r e t i c a l Methods 6 2.3. F i r s t Born A p p r o x i m a t i o n 7 2.4. L i m i t Theorem o f G e n e r a l i s e d O s c i l l a t o r S t r e n g t h . 9 2.5. Low Energy E l e c t r o n S c a t t e r i n g 13 CHAPTER I I I : EXPERIMENTAL DEVICES 16 3.1. E l e c t r o n Guns 16 3.2. E l e c t r o n Lenses 19 3.3. E l e c t r o n Energy A n a l y s e r s 26 3.3.1. G e n e r a l a s p e c t s 26 3.3.2. Th e o r y o f t h e 127° a n a l y s e r 28 3.3.3. Energy r e s o l u t i o n o f t h e 127° a n a l y s e r . . . 33 3.3.4. D e f l e c t i o n v o l t a g e f o r t h e 127° a n a l y s e r . 36 3.3.5. A n a l y s e r s and t h e space c h a r g e p r o b l e m . . . 38 CHAPTER IV: APPARATUS AND PERFORMANCE 41 4.1. The S p e c t r o m e t e r 41 4.2. A G a s - t i g h t , R o t a t a b l e C o l l i s i o n Chamber 48 4.3. E l e c t r o n i c s and E l e c t r o n D e t e c t i n g System 52 4.4. Vacuum System and Gas H a n d l i n g 56 CHAPTER V: OPTICALLY FORBIDDEN TRANSITIONS 59 5.1. O p t i c a l S e l e c t i o n R u l e s 59 i v . Page 5.2. E l e c t r o n Impact E x c i t a t i o n o f O p t i c a l l y F o r b i d d e n T r a n s i t i o n s 62 5.2.1. Energy dependence 63 5.2.2. A n g u l a r dependence 65 5.3. O p t i c a l l y F o r b i d d e n T r a n s i t i o n s i n Argon and Neon 67 5.3.1. Argon 69 5.3.2. Neon 81 CHAPTER V I : MOLECULAR RYDBERG STATES 85 6.1. G e n e r a l A s p e c t s 85 6.2. Rydberg S t a t e s o f Hydrogen C y a n i d e 88 6.2.1. A s s i g n m e n t o f Rydberg s e r i e s 89 6.2.2. Dependence o f t h e sp e c t r u m on impact e n e r g y ... 94 CHAPTER V I I : ELECTRON IMPACT SPECTRA OF SOME ALKYL DERIVATIVES OF WATER AND RELATED COMPOUNDS 98 7.1. I n t r o d u c t i o n 98 7.2. Water, Methanol and D i m e t h y l E t h e r 99 7.3. E t h y l e n e O x i d e 106 7.4. E t h y l , I s o p r o p y l and t - B u t y l A l c o h o l s 108 7.5. D i e t h y l E t h e r and T e t r a h y d r o f u r a n 114 7.6. E f f e c t o f A l k y l S u b s t i t u t i o n on EIS 118 CHAPTER V I I I ELECTRONIC SPECTRA OF SOME CARBONYL COMPOUNDS BY ELECTRON IMPACT SPECTROSCOPY 122 8.1. I n t r o d u c t i o n 123 8.2. S a t u r a t e d A l d e h y d e s . . . ; 123 8.2.1. Formaldehyde and a c e t a l d e h y d e 123 8.2.2. P r o p i o n a l d e h y d e and i s o b u t y r a l d e h y d e 128 8.2.3. Rydberg and v a l e n c e a s s i g n m e n t s 134 8.2.4. E f f e c t o f a l k y l s u b s t i t u e n t s 135 V. 8.3. S a t u r a t e d Ketones 137 8.3.1. Ac e t o n e and 2-butanone 137 8.3.2. H i g h e r ketones 146 8.3.3. E f f e c t o f a l k y l s u b s t i t u e n t s 149 8.4. U n s a t u r a t e d Compounds 151 8.4.1. P r o p e n a l ( a c r o l e i n ) 151 8.4.2. Met h y l v i n y l ketone 158 CHAPTER IX: CONCLUSION 161 REFERENCES: 163 APPENDIX: PHOTOELECTRON SPECTRA OF SOME ALDEHYDES AND KETONES 169 VI . LIST OF FIGURES F i g u r e Page 1. E l e c t r o n l e n s e s 21 2. C h a r a c t e r i s t i c s o f e l e c t r o n l e n s e s 24 3. 127° c y l i n d r i c a l a n a l y s e r f i e l d 29 4. Diagrams t o i l l u s t r a t e c a l c u l a t i o n o f t h e energy r e s o l u t i o n o f 127° a n a l y s e r 34 5. S c h e m a t i c d i a g r a m o f t h e e l e c t r o n s p e c t r o m e t e r 42 6. E l a s t i c s c a t t e r i n g i n h e l i u m a t 30 eV 47 7. R o t a t a b l e , g a s - t i g h t c o l l i s i o n chamber 50 8. The c o n t r o l c i r c u i t d i a g r a m 54 9. E l e c t r o n i m p a ct s p e c t r a f o r 3p -> 4s e x c i t a t i o n o f argon a t 30 eV 70 10. R e l a t i v e d i f f e r e n t i a l c r o s s s e c t i o n f o r the f o r m a t i o n o f m e t a s t a b l e a r g o n ( 3 P2) a t 30 eV 71 11. R e l a t i v e d i f f e r e n t i a l c r o s s s e c t i o n f o r e x c i t a t i o n t o t h e 4s s t a t e s o f argon a t 30 eV 72 12. D i f f e r e n t i a l c r o s s s e c t i o n r a t i o s f o r e x c i t a t i o n t o t h e 4s s t a t e s o f a r g o n a t 30 eV 74 13. E l e c t r o n impact s p e c t r a f o r 3p -> 4p e x c i t a t i o n o f argon a t 30 eV 75 14. E l e c t r o n impact s p e c t r a f o r 3p 4p e x c i t a t i o n o f argon a t 30 eV 77 15. R e l a t i v e d i f f e r e n t i a l c r o s s s e c t i o n f o r t h e e x c i t a t i o n t o t h e 4p s t a t e s o f argon 78 16. D i f f e r e n t i a l c r o s s s e c t i o n r a t i o s f o r e x c i t a t i o n t o 4p s t a t e s o f argon a t 30 eV 80 17. E l e c t r o n i m p a ct s p e c t r u m o f neon a t 70 eV and 2° s c a t t e r i n g a n g l e 82 18. Energy dependence o f t h e r e l a t i v e d i f f e r e n t i a l s c a t t e r i n g c r o s s s e c t i o n f o r t h e 3p' (J=0) s t a t e o f neon 84 v i i . F i g u r e Page 19. E l e c t r o n impact s p e c t r a o f HCN 90 20. R e l a t i v e i n t e n s i t i e s o f some t r a n s i t i o n s i n t h e e l e c t r o n impact spectrum o f HCN 95 21. E l e c t r o n i m p a c t s p e c t r a o f H 90, CH-.0H and CHJ3CH.> a t 100 eV, 2° ? . f f 101 22. E l e c t r o n i m p a ct s p e c t r u m o f e t h y l e n e o x i d e a t 50 eV, 2° 107 23. E l e c t r o n i m p a c t s p e c t r a o f e t h y l , i s o p r o p y l and t -t - b u t y l a l c o h o l s a t 100 eV, 2° 110 24. E l e c t r o n impact s p e c t r a o f d i e t h y l e t h e r and t e t r a h y d r o f u r a n a t lOOeV, 2° 115 25. E f f e c t o f a l k y l s u b s t i t u t i o n on Rydberg term v a l u e s and f i r s t i o n i z a t i o n p o t e n t i a l s i n a l k y l d e r i v a t i v e s o f wa t e r 119 26. E l e c t r o n impact s p e c t r u m o f a c e t a l d e h y d e a t 100 eV, 2° 126 27. E l e c t r o n impact s p e c t r a o f a c e t a l d e h y d e , p r o p i o n -a l d e h y d e and i s o b u t y r a l d e h y d e a t 100 eV, 2° 130 28. E f f e c t o f a l k y l s u b s t i t u t i o n on Rydberg term v a l u e s and and f i r s t i o n i z a t i o n p o t e n t i a l s i n a l d e h y d e s 136 29. E l e c t r o n impact s p e c t r a o f CH^COCH^ and CH.X0C oH c a t 100 eV, 2° ....... 139 30. E l e c t r o n impact s p e c t r a o f t h e f i r s t two bands o f C H 3 C 0 C 2 H 5 a t 30, 70 and 100 eV 145 31. E l e c t r o n impact s p e c t r a o f (CH 3) 2CHCH 2C0CH 3, ( C H 3 ) 2 C H C 0 C H 3 and ( C H 3 ) 3 C C 0 C H 3 a t 100 eV, 2° 147 32. E f f e c t o f a l k y l s u b s t i t u t i o n on Rydberg term v a l u e s and f i r s t i o n i z a t i o n p o t e n t i a l s i n k e t o n e s 150 33. E l e c t r o n impact s p e c t r a o f p r o p e n a l and methyl v i n y l ketone a t 100 eV, 2° ". 152 34. Energy l e v e l s and e l e c t r o n i c t r a n s i t i o n s i n p r o p e n a l . . 157 o 35. 584 A p h o t o e l e c t r o n s p e c t r a o f CH^CHO, CH-CH ?CH0 and (CH 3) 2CHCH0 T .... 170 36. 584 A p h o t o e l e c t r o n s p e c t r a o f CH 30CH 3, CH 3CH 2C0CH 3 ( C H 3 ) 2 CHCH 2C0CH 3, ( C H 3 ) 2 C H C 0 C H 3 , ( C H 3 ) 3 C C 0 C H 3 and CH 0 = CHC0CH,. 172 v i i i . L IST OF PLATES P l a t e Page 1. The S p e c t r o m e t e r 43 2. The g a s - t i g h t , r o t a t a b l e c o l l i s i o n chamber 51 3. The c o m p l e t e e x p e r i m e n t a l arrangement 57 i x . L IST OF TABLES T a b l e Page 1. O p t i c a l s e l e c t i o n r u l e s i n a t o m i c s p e c t r a 60 2. Rydberg t r a n s i t i o n s i n HCN 91 3. E l e c t r o n i c t r a n s i t i o n s i n w a t e r , methanol and d i m e t h y l e t h e r 102 4. Rydberg s e r i e s i n e t h y l e n e o x i d e 109 5. E l e c t r o n i c t r a n s i t i o n s i n e t h y l , i s o p r o p y l and t - b u t y l a l c o h o l s I l l 6. E l e c t r o n i c t r a n s i t i o n s i n d i e t h y l e t h e r and t e t r a h y d r o f u r a n 117 7. Rydberg t r a n s i t i o n s i n a c e t a l d e h y d e 129 8. E l e c t r o n i c t r a n s i t i o n s i n p r o p i o n a l d e h y d e and i s o b u t y r a l d e h y d e 133 9. Rydberg t r a n s i t i o n s i n a c e t o n e 142 10. Rydberg t r a n s i t i o n s i n 2-butanone 144 11. E l e c t r o n i c t r a n s i t i o n s i n m ethyl i s o b u t y l k e t o n e , m e t h y l i s o p r o p y l k e t o n e and m e t h y l t - b u t y l k e t o n e . . 148 12. Rydberg t r a n s i t i o n s i n p r o p e n a l 154 13. Rydberg t r a n s i t i o n s i n m e t h y l v i n y l ketone 159 14. I o n i z a t i o n p o t e n t i a l s f o r some c a r b o n y l compounds.. 174 X. ACKNOWLEDGEMENTS I would l i k e t o e x p r e s s my d e e p e s t g r a t i t u d e t o my r e s e a r c h s u p e r v i s o r , P r o f e s s o r C. E. B r i o n , f o r h i s s u p p o r t , a s s i s t a n c e and i n v a l u a b l e a d v i c e t h r o u g h o u t t h e c o u r s e o f t h i s work, as w e l l as h i s deep and genuine c o n c e r n f o r h i s s t u d e n t s . I would a l s o l i k e t o thank my c o l l e a g u e s , Mr. Gordon R. Wi g h t , Mr. S. Tong Lee and Mr. Derek S. C. Yee f o r h e l p f u l d i s c u s s i o n s and u n s e l f i s h a s s i s t a n c e on many o c c a s i o n s . S p e c i a l t hanks a r e due t o Mr. Yee f o r h i s a s s i s t a n c e i n r u n n i n g t h e p h o t o e l e c t r o n s p e c t r a o f many compounds s t u d i e d . I w i s h t o acknowledge g r a t e f u l l y t h e s t a f f o f t h e m e c h a n i c a l and e l e c t r o n i c w orkshops, e s p e c i a l l y M e s s r s . J . Wyngaarden, E. Gomm, M. Vagg, J . Shim, D. C a t t and K. S. Au f o r c o n s t r u c t i o n and maintenance o f t h e a p p a r a t u s , and t h e i l l u s t r a t o r s Mr. F. R o b e r t s and Mr. A. S e n z a k i f o r making up many b e a u t i f u l d i a g r a m s . I thank t h e N a t i o n a l R e s e a r c h C o u n c i l o f Canada f o r generous f i n a n c i a l s u p p o r t and t h e 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 f o r a U.B.C. Graduate F e l l o w s h i p . 1. CHAPTER I  INTRODUCTION In t h e f o l l o w i n g p r o c e s s : X + e ^ E ^ -> X* + e 2 ( E 2 ) where an atom o r m o l e c u l e X i s bombarded by an e l e c t r o n e-j w i t h e n e r g y E-j g r e a t e r than t h e energy E between t h e ground s t a t e and an e x c i t e d * s t a t e X , t h e i n c i d e n t e l e c t r o n i s i n e l a s t i c a l l y s c a t t e r e d . In so d o i n g i t s u f f e r s an energy l o s s E-j - E 2 w h i c h i s equal t o E . I f t h e i n c i d e n t e l e c t r o n e nergy E-j i s s u f f i c i e n t l y h i g h , s c a t t e r i n g o f t h e i n c i d e n t m o n o e n e r g e t i c beam o f e l e c t r o n s r e s u l t s i n an e n e r g y l o s s s p e c t r u m , w i t h a d i s c r e t e e n e r g y l o s s i n t h e beam c o r r e s p o n d i n g t o e v e r y a c c e s s i b l e e nergy s t a t e i n t h e t a r g e t . The f i r s t measurement o f t h e en e r g y l o s s s u f f e r e d by e l e c t r o n s i n c o l l i s i o n w i t h atoms and m o l e c u l e s was made by Franck and H e r t z [ 1 ] i n 1914 i n a m u l t i p l e c o l l i s i o n e x p e r i m e n t and was used t o o b t a i n i n f o r m a t i o n about t h e e l e c t r o n i c e nergy l e v e l s o f t h e t a r g e t . However, t h e use o f energy l o s s measurements i n e l e c t r o n m o l e c u l e c o l l i s i o n s as a s p e c t r o s c o p i c t e c h n i q u e was q u i t e l i m i t e d due t o e x p e r i m e n t a l d i f f i c u l t i e s . The l a s t two decades have seen a r e s u r g e n c e o f i n t e r e s t i n t h i s f i e l d r e s u l t i n g f r o m t h e more s o p h i s t i c a t e d e l e c t r o n i c and e l e c t r o n o p t i c a l t e c h n i q u e s w h i c h have s i n c e been d e v e l o p e d . The method o f energy l o s s e l e c t r o n s p e c t r o s c o p y ( o r e l e c t r o n i m p a c t s p e c t r o s c o p y ) has now proved t o be a h i g h l y v e r s a t i l e t o o l f o r t h e i n v e s t i g a t i o n o f e x c i t a t i o n by e l e c t r o n i m p a c t . P a s t a c h i e v e m e n t s and c u r r e n t developments a r e d i s c u s s e d i n 2. r e c e n t r e v i e w s [ 2 , 3 , 4 ] . The energy l o s s s p e c t r a have been s t u d i e d w i t h t h e o b j e c t i v e o f i d e n t i f y i n g b oth o p t i c a l l y f o r b i d d e n and a l l o w e d t r a n s i t i o n s and o f d i s c o v e r i n g Rydberg s t a t e s and a u t o i o n i z i n g s t a t e s i n t h e c o n t i n u a . A t h i g h i m p a c t e n e r g i e s and s m a l l s c a t t e r i n g a n g l e s , d i p o l e terms a r e dominant, and as a r e s u l t , t h e s c a t t e r i n g i n t e n s i t y i s s t r o n g l y peaked about t h e f o r w a r d d i r e c t i o n . Under t h e s e c o n d i t i o n s t h e f a i r l y s t r i n g e n t s e l e c t i o n r u l e s g o v e r n i n g o p t i c a l t r a n s i t i o n s a r e f o l l o w e d . A t l o w e r e l e c t r o n impact e n e r g i e s ( a p p r o x i m a t e l y below 50 eV) a v a r i e t y o f o p t i c a l l y f o r b i d d e n t r a n s i t i o n s may be i n d u c e d and f o r h e l i u m i t has been shown [ 5 , 6 ] t h a t t h e d i f f e r e n t i a l c r o s s s e c t i o n s have a d i f f e r e n t a n g u l a r b e h a v i o u r f r o m t h o s e w h i c h a r e e l e c t r i c d i p o l e a l l o w e d . Two o f t h e more common t y p e s o f o p t i c a l l y f o r b i d d e n p r o c e s s e s o b s e r v e d by low e n e r g y e l e c t r o n i m p a ct a r e s p i n exchange and t h e e x c i t a t i o n o f symmetry f o r b i d d e n ( e l e c t r i c q u a d r u p o l e ) bands. Many o f t h e normal o p t i c a l s e l e c t i o n r u l e s can be broken by s u i t a b l e c h o i c e o f i n c i d e n t e l e c t r o n e n e r g y and s c a t t e r i n g a n g l e . By a n a l o g y w i t h the a b s o r p t i o n o f l i g h t quanta i n o p t i c a l s p e c t r o s c o p y , e l e c t r o n e n e r g y l o s s e s a r e "ab s o r b e d " i n e l e c t r o n i m p a c t s p e c t r o s c o p y ( E I S ) . Some o f t h e r e l a t i v e m e r i t s o f EIS and o p t i c a l s p e c t r o s c o p y have been d i s c u s s e d i n r e c e n t r e v i e w s [ 3 , 6 ] . From an e x p e r i m e n t a l s t a n d p o i n t , t h e r e a r e advantages t o t h e use o f EIS i n t h e vacuum u l t r a v i o l e t w i t h r e g a r d t o r e s o l u t i o n , i n t e n s i t y and t h e a v a i l a b i l i t y o f a continuum o f ener g y . In t h e energy range above 10 eV i n t e n s e c o ntinuum l i g h t s o u r c e s do not e x i s t , w i t h t h e e x c e p t i o n o f s y n c h r o t r o n r a d i a t i o n which i s a t p r e s e n t o n l y o f l i m i t e d a v a i l a b i l i t y . However, i t i s w e l l known [ 7 ] t h a t 3. the i n t e r a c t i o n o f a f a s t e l e c t r o n w i t h a m o l e c u l a r t a r g e t r e s u l t s i n t h e c r e a t i o n o f a v i r t u a l photon f i e l d . T h us, i n u s i n g an e l e c t r o n i m p a c t s p e c t r o m e t e r t h e energy l o s s s i m i l a t e s t h e photon e n e r g y . T h i s q u a n t i t a t i v e r e l a t i o n s h i p between f a s t e l e c t r o n i m p a c t and p h o t o a b s o r p t i o n has r e c e n t l y been d e m o n s t r a t e d i n t h e d e t e r m i n a t i o n o f a b s o l u t e o p t i c a l o s c i l l a t o r s t r e n g t h s by an e l e c t r o n i m p a c t t e c h n i q u e [ 8 ] . A l s o , f u r t h e r i n f o r m a t i o n about t h e e x c i t e d s t a t e s can be o b t a i n e d t h r o u g h t h e i r dependence on i n c i d e n t e l e c t r o n e n e r g i e s and s c a t t e r i n g a n g l e s . Un-ambiguous i d e n t i f i c a t i o n o f e x c i t e d s t a t e s can be a c h i e v e d i n many c a s e s . E I S , as a means o f s t u d y i n g quantum s t a t e s o f n e u t r a l s ( i . e . bound s t a t e s ) i s c o m p l i m e n t a r y t o p h o t o - e l e c t r o n s p e c t r o s c o p y (PES) where i o n i c s t a t e s a r e s t u d i e d . W i t h t h e ad v e n t o f t h e l a t t e r as a c o n v e n i e n t and a c c u r a t e method t o d e t e r m i n e t h e v a r i o u s i o n i z a t i o n p o t e n t i a l s o f m o l e c u l e s , t h e c o m b i n a t i o n o f t h e s e two methods can be used t o e l u c i d a t e new Rydberg s e r i e s and t o d e t e r m i n e o r b i t a l symmetries f r o m quantum d e f e c t s and measured t e r m v a l u e s [ 9 , 1 0 ] . T h i s p r o c e d u r e has now been a p p l i e d t o l a r g e r m o l e c u l e s o f c h e m i c a l i n t e r e s t . 4. CHAPTER I I  THEORY OF INELASTIC ELECTRON SCATTERING 2 . 1 . E l e c t r o n - H y d r o g e n Atom S c a t t e r i n g . The t h e o r y f o r t h e s i m p l e s t case o f t h e e l e c t r o n i m p a ct e x c i t a t i o n o f a t o m i c hydrogen w i l l be d e v e l o p e d f i r s t and t h e n g e n e r a l i s e d t o more c o m p l i c a t e d s y s t e m s . The work i n v o l v e d i n o b t a i n i n g a c c u r a t e t h e o r e t i c a l e x c i t a t i o n c r o s s s e c t i o n s i s so f o r m i d a b l e t h a t no e x a c t s o l u t i o n s f o r t h e l o w e s t s t a t e s o f a t o m i c h y d r o g e n , t h e 2s and 2p, have been o b t a i n e d . V a r i o u s degrees o f a p p r o x i m a t i o n must be i n t r o d u c e d . M o i s e i w i t s c h & Smith [ 1 1 ] have g i v e n t h e f o l l o w i n g t r e a t m e n t f o r t h e c a s e o f e l e c t r o n -hydrogen atom s c a t t e r i n g . C o n s i d e r a system composed o f two e l e c t r o n s denoted by 1, 2 moving i n t h e coulomb f i e l d o f a p r o t o n assumed t o have i n f i n i t e mass. The S c h r t i d i n g e r e q u a t i o n f o r t h i s s y s t e m i s : [-£ "i2 + '22'-^-fJ+4"EJf<?i*f2) = 0 <2J) where r - j , a r e t h e p o s i t i o n v e c t o r s o f e l e c t r o n s 1, 2 r e f e r r e d t o t h e p r o t o n as o r i g i n ; r ^ i s t h e i n t e r e l e c t r o n d i s t a n c e ; Ey i s t h e t o t a l e n e rgy o f t h e system. Y ( r - j , r 2 ) , t h e t o t a l wave f u n c t i o n c h a r a c t e r i s i n g t h e two e l e c t r o n s , can be e x p r e s s e d i n terms o f t h e o r t h o n o r m a l s e t o f hydrogen atom wave f u n c t i o n s ^ n ( r ) s a t i s f y i n g t h e e q u a t i o n where E n a r e t h e a s s o c i a t e d e i g e n - e n e r g i e s . I f we assume 5. Hrvr2) ^ V V y V (2-3) where t h e symbol S denotes a summation o v e r t h e d i s c r e t e s t a t e s and an i n t e g r a t i o n o v e r t h e continuum s t a t e s . S u b s t i t u t i n g (2.3) i n t o ( 2 . 1 ) , m u l t i p l y i n g b oth s i d e s by ij> ( r - j ) and i n t e g r a t i n g w i t h r e s p e c t t o r - j , t h e r e s u l t i s *2 + O F n <V = WK ( W - W ' V - t f l . (2-4) where V ( r r r 2 ) = ( e 2 / r ] 2 ) - ( e 2 / r 2 ) (2.5) i s t h e i n t e r a c t i o n energy between t h e i n c i d e n t e l e c t r o n 2 and a hydrogen atom composed o f e l e c t r o n 1 and t h e p r o t o n . The wave number k n i s g i v e n by k n 2 = (2m/0 2) ( E j - E n ) (2.6) Suppose e l e c t r o n 2 impinges upon a hydrogen atom i n t h e ground I s s t a t e (denoted by s u b s c r i p t 1 ) , t h e d i r e c t i o n o f i n c i d e n c e b e i n g g i v e n by t h e wave v e c t o r T<-|, t h e n t h e a s y m p t o t i c b e h a v i o u r o f t h e f u n c t i o n F n ( r ) f o r l a r g e r t a k e s t h e form F n ( r ) * exp ( 1 ^ . r ) 6 n l + r " 1 exp ( i l y ) fn(e,<|>) (2.7) where fn(e,<f>) i s t h e s c a t t e r i n g a m p l i t u d e c o r r e s p o n d i n g t o t h e e x c i t a t i o n o f t h e n t h s t a t e o f t h e hydrogen atom, and e, <f> a r e t h e p o l a r a n g l e s o f r r e f e r r e d t o t h e d i r e c t i o n o f i n c i d e n c e as p o l a r a x i s . 6^ i s t h e K r o n e c k e r d e l t a . I n t r o d u c i n g t h e Green's f u n c t i o n G(r,r\,) f o r a f r e e p a r t i c l e s a t i s f y i n g t h e e q u a t i o n ( v 2 + k n 2 ) G ( r , r 2 ) = 6 ( r - r 2 ) , (2.8) i t can be shown t h a t 6. F n ( r " ) = exp ( 1 ^ . * ) 6 n l + $ f f & ( r f 2 h * $ } ) V ( r ^ ) x f ( r 1 r 2 ) dr-jdr 2 (2.9) I f G ( r , r ? ) i s chosen t o have t h e form (2.10) F n ( r ) has t h e c o r r e c t a s y m p t o t i c form as i n ( 2 . 9 ) . Now f o r l a r g e r , k I r - r 0 K k r - £ . r„ n 1 / 1 n n / (2.11) where l< n i s a wave v e c t o r i n t h e d i r e c t i o n o f r , then x V ( r r r 2 ) v ( r l f r 2 ) dr]dr2 (2.12) The d i f f e r e n t i a l c r o s s s e c t i o n f o r t h e e x c i t a t i o n t o t h e n t h s t a t e o f a hydrogen atom i s g i v e n i n terms o f t h e s c a t t e r i n g a m p l i t u d e f n(e,<t>h c o r r e s p o n d i n g t o an i n c i d e n t e l e c t r o n s c a t t e r e d t h r o u g h a n g l e s e,<|> by t h e f o r m u l a 2.2.Approximate T h e o r e t i c a l Methods V a r i o u s a p p r o x i m a t i o n s have been r e v i e w e d by M o i s e i w i t s c h and Smith [11] i n some d e t a i l . Many quantum t h e o r e t i c a l c a l c u l a t i o n s o f e x c i t a t i o n c r o s s s e c t i o n s have been made. For h i g h impact e n e r g i e s , weak c o u p l i n g a p p r o x i m a t i o n s , which n e g l e c t t h e c o u p l i n g from t h e i n i t i a l t o t h e f i n a l s t a t e s , and t o a l l o t h e r s t a t e s , a r e s u i t a b l e . The f i r s t Born a p p r o x -l n ( e , * ) = ( y k ^ i y e , * ) ! 2 (2.13) w h i l e t h e t o t a l c r o s s s e c t i o n t a k e s t h e form (2.14) 7. i m a t i o n , and a m o d i f i e d f o r m , t h e Bethe a p p r o x i m a t i o n , a r e w i d e l y used and a r e e f f e c t i v e a t h i g h and moderate impact e n e r g i e s . A more c o m p l i c a t e d weak c o u p l i n g a p p r o x i m a t i o n i s t h a t o f t h e d i s t o r t e d wave, whi c h r e p r e s e n t s t h e f r e e e l e c t r o n by f u n c t i o n s d e s c r i b i n g i t s m o t i o n i n t h e s t a t i c f i e l d o f t h e atom b e f o r e and a f t e r e x c i t a t i o n . F o r e x c i t a t i o n p r o c e s s e s i n w h i c h t h e r e i s an i m p o r t a n t c o n t r i b u t i o n from e l e c t r o n exchange, t h e Born-Oppenheimer a p p r o x i m a t i o n , w h i c h n e g l e c t s c e r t a i n f i r s t o r d e r terms i n t h e i n t e r a c t i o n e n e r g y , g i v e l e s s s a t i s f a c t o r y r e s u l t s than t h e Ochkur a p p r o x i m a t i o n which i s a l s o s i m p l e r t o a p p l y . S t r o n g c o u p l i n g a p p r o x i m a t i o n s a r e a p p l i c a b l e a t l o w e r e l e c t r o n e n e r g i e s . These i n c l u d e t h e m o d i f i e d Bethe a p p r o x i m a t i o n , t h e impact parameter method and t h e u n i t a r i s e d Born a p p r o x i m a t i o n . The e x a c t r e s o n a n c e a p p r o x i m a t i o n a p p l i e s t o c a s e s where t h e l e v e l t o be e x c i t e d i s v e r y c l o s e i n energy t o t h e s t a t e b e f o r e e x c i t a t i o n . When t h e c o u p l i n g between t h e i n i t i a l and f i n a l s t a t e s i s weak, but t h a t t o a t h i r d s t a t e i s s t r o n g , one can use t h e c l o s e c o u p l i n g a p p r o x i m a t i o n . The s e m i -c l a s s i c a l p e r t u r b a t i o n - i m p a c t parameter t r e a t m e n t , sometimes c a l l e d t h e " d i p o l e a p p r o x i m a t i o n " has a l s o proved v a l u a b l e . 2 . 3 . F i r s t Born A p p r o x i m a t i o n . T h i s a p p r o x i m a t i o n , t h e s i m p l e s t o f a l l , assumes t h a t t h e i n c i d e n t e l e c t r o n i n t e r a c t s o n l y s l i g h t l y w i t h the t a r g e t atom, so t h a t i t s wave f u n c t i o n may be c l o s e l y a p p r o x i m a t e d by t h e p l a n e wave exp (ik-j . r ) w h i c h would be the c o r r e c t f u n c t i o n i n t h e absence o f a l l i n t e r a c t i o n s . T h i s s h o u l d be v a l i d when t h e speed o f the i n c i d e n t e l e c t r o n i s g r e a t i n c o m p arison w i t h t h a t o f t h e e l e c t r o n i n t h e t a r g e t atom. T h i s i s 8. e s s e n t i a l l y e q u i v a l e n t t o t h e r e q u i r e m e n t t h a t k-ja>>!, where a i s t h e range o f t h e e l e c t r o n - a t o m i n t e r a c t i o n . S u b s t i t u t i n g Y ( r r r 2 ) = e x p ( i ^ . r" 2) * ( f , ) (2.15) i n t o t h e r i g h t hand s i d e o f (2.12) y i e l d s t h e f i r s t Born a p p r o x i m a t i o n to t h e s c a t t e r i n g a m p l i t u d e V9'*) = ^ | ? / e x P f i ( t l - V • M V n l ( V d ? 2 ( 2 - 1 6 ) where V n l ( r ~ 2 ) =fy* (^) V ( r ^ ) ^ (r})dr} (2.17) D e n o t i n g t h e momentum change o f t h e i n c i d e n t e l e c t r o n by t h e v e c t o r tft, where t = t-j - t^, and u s i n g Bethe's i n t e g r a l exp (il£.r2) 4TT » • * , = -o exp ( i t . r , ) (2.18) 1 2| K 1 t h e s c a t t e r i n g a m p l i t u d e can be e x p r e s s e d i n t h e s i m p l e r f o r m f n ( K ) = - ( 2 m e 2 / t f 2 K 2 ) / * n * ( r ) exp ( i i t . r ) ^ ( r ) d r (2.19) wh i c h depends o n l y on K i n t h e f i r s t Born a p p r o x i m a t i o n w i t h t h e term a r i s i n g f r o m e l e c t r o n - p r o t o n i n t e r a c t i o n v a n i s h i n g here because o f t h e o r t h o g o n a l i t y o f t h e a t o m i c wave f u n c t i o n . I t may be shown t h a t t h e s e hypotheses a r e p r a c t i c a l l y v a l i d i f t h e energy t r a n s f e r r e d t h r o u g h t h e c o l l i s i o n complex t o t h e t a r g e t i s s m a l l compared t o t h a t o f t h e i n c i d e n t p a r t i c l e ; more p r e c i s e l y , i t s h o u l d be v a l i d when t h e energy o f t h e i m p i n g i n g p a r t i c l e s i s such t h a t i t s v e l o c i t y i s a t l e a s t f i v e t o seven t i m e s t h a t o f t h e o r b i t a l e l e c t r o n , o f w h i c h t h e energy i s o f t h e o r d e r o f 10 - 15 eV. From t h a t p o i n t o f v i e w , t h e Born a p p r o x i m a t i o n s h o u l d h o l d f o r e l e c t r o n s h a v i n g e n e r g i e s o f t h e o r d e r o f 150 eV o r more. At equal s p e e d s , t h e Born a p p r o x i m a t i o n i s l i k e l y t o be b e t t e r s a t i s f i e d f o r n e u t r a l p a r t i c l e s t h a n f o r e l e c t r o n s 9. o r i o n s . 2 . 4 . L i m i t Theorem o f G e n e r a l i s e d O s c i l l a t o r S t r e n g t h . The f o l l o w i n g d e r i v a t i o n i s e s s e n t i a l l y t h a t due t o L a s s e t t r e [ 1 2 ] . Combining e q u a t i o n s (2.13) and (2.16) and g e n e r a l i s i n g t o t h e c a s e o f an e l e c t r o n e x c i t i n g a s c a t t e r e r from s t a t e 1 t o s t a t e 2, t h e d i f f e r e n t i a l c r o s s s e c t i o n i s g i v e n by P 2 k 9 | CC ^ (^ n ~ ^p) • ^ * 9 ! 1 2 = p ~ k j I JJ V x e *1*2 d ^ d x ( 2 > 2 0 ) where ^ - j , a r e t n e e i g e n f u n c t i o n s f o r t h e s c a t t e r e r i n i t s i n i t i a l and f i n a l s t a t e ; K^j and Ki<2 a r e t h e momenta o f t h e c o l l i d i n g e l e c t r o n b e f o r e and a f t e r s c a t t e r i n g ; V i s t h e p o t e n t i a l e nergy o f t h e i n c i d e n t e l e c t r o n i n t h e f i e l d o f t h e s c a t t e r e r ; dft d e s i g n a t e s an element o f t h e volume f o r t h e c o l l i d i n g e l e c t r o n and dx i s a c o m p o s i t e volume element f o r t h e s c a t t e r e r , whose c e n t r e o f mass i s f i x e d . In c a s e s o f atoms, Bethe [ 7 ] showed t h a t t h e i n t e g r a t i o n o v e r t h e i n c i d e n t e l e c t r o n c o - o r d i n a t e , ft, can be c a r r i e d o u t , s i n c e t h e i n t e r -a c t i o n p o t e n t i a l i s t h e sum o f t h e a c t u a l p o t e n t i a l e n e r g i e s o f t h e i n c i d e n t e l e c t r o n w i t h each a t o m i c e l e c t r o n and w i t h t h e n u c l e u s . A f t e r i n t e g r a t i o n , t h e d i f f e r e n t i a l c r o s s s e c t i o n i n a t o m i c u n i t s , i s g i v e n by 4 k 2 ee CT12 = F ~ ' ~ 4 ( 2 ' 2 ] ) u K i r where K ( t = £•] - 1<2) i s t h e magnitude o f t h e momentum t r a n s f e r K 2 = k ^ + k 2 2 - 2 k ] k 2 cos e (2.22) w i t h 9 b e i n g t h e s c a t t e r i n g a n g l e . The q u a n t i t y e i s g i v e n by 10. / * 1 N * r s * The Born-Oppenheimer a p p r o x i m a t i o n t o e x p r e s s t ^ , ^ as p r o d u c t s o f t h e e l e c t r o n i c and n u c l e a r s t a t e f u n c t i o n s has been a p p l i e d . The terms depending on n u c l e a r c o - o r d i n a t e s v a n i s h due t o o r t h o g o n a l i t y ( s e e r e f . 1 3 ) . Here r" s i s t h e p o s i t i o n v e c t o r o f t h e s t h a t o m i c e l e c t r o n and t h e summation e x t e n d s o v e r a l l such e l e c t r o n s . The i n t e g r a t i o n e x t e n d s o v e r a t o m i c e l e c t r o n s o n l y and t h e e x p r e s s i o n i s o n l y v a l i d f o r i n e l a s t i c s c a t t e r i n g . When t h e momentum t r a n s f e r K i s s m a l l , t h e e x p o n e n t i a l i n (2.23) can be expanded i n t o a power s e r i e s and i n t e g r a t e d term by term t o o b t a i n 4k r e 2 2 ff12 = k^" [ ~ ^ ~ + ( £ 2 ' 2 e l e 3 ) + ( e 3 2 " 2 e 2 e 4 + 2 e l 2 e 5 ) K + J (2.24) When t h e H a m i l t o n i a n f u n c t i o n i s r e a l , i t i s alw a y s p o s s i b l e t o choose r e a l e i g e n f u n c t i o n s , l e a d i n g t o a s e r i e s c o n t a i n i n g o n l y even powers o f K. In ( 2 . 2 4 ) , t h e c o e f f i c i e n t s a r e g i v e n by I t i s a c o n v e n t i o n t o t a k e t h e z - a x i s o f t h e c o - o r d i n a t e system as p a r a l l e l t o t so t h a t t . r* s = K z § . The q u a n t i t y e ^  i s o b v i o u s l y t h e m a t r i x element o f t h e e l e c t r i c d i p o l e moment ( z-component). The c r o s s s e c t i o n tends towards p r o p o r t i o n a l i t y w i t h under c o n d i t i o n s such t h a t K i s smal1. 2 The magnitude o f K can be w e l l a p p r o x i m a t e d by 2 K 2 = 8 E [ s i n 2 (|) + (^j J when f < 0.1 (2.26) E = E - W/2, w i t h E equal t o t h e k i n e t i c e n ergy o f t h e i n c i d e n t e l e c t r o n 11. 2 _ and W i s t h e e x c i t a t i o n e nergy. K i s a minimum when 9 = 0 and E l a r g e , t h e o n l y term o f s i g n i f i c a n t magnitude i s t h e f i r s t term on t h e r i g h t o f e q u a t i o n ( 2 . 2 4 ) . A l s o , under t h e s e c o n d i t i o n s , k 2 ~ k-j, so a 1 2 * r| e l 2 < 2- 2 7) W T h i s a p p r o x i m a t e f o r m u l a v a n i s h e s when e-j v a n i s h e s , and t o t h i s d e g r e e o f a c c u r a c y , o p t i c a l s e l e c t i o n r u l e s h o l d . However, from ( 2 . 2 4 ) , a ^ 2 does not c o m p l e t e l y v a n i s h even when e-j = 0 u n l e s s e 2 = 0 a t t h e same t i m e . A l l o w e d t r a n s i t i o n , w i t h e-j f 0, have c r o s s s e c t i o n s w h i c h a r e e s s e n t i a l l y p r o p o r t i o n a l t o E, whereas t h e f o r b i d d e n t r a n s i t i o n s (E-J = 0, e 2 f 0) have a c r o s s s e c t i o n i ndepednent o f E (E b e i n g v e r y l a r g e i n each c a s e ) . Hence f o r l a r g e enough E", t h e c r o s s s e c t i o n o f d i p o l e f o r b i d d e n t r a n s i t i o n s i s n e g l i g i b l e compared t o d i p o l e a l l o w e d t r a n s i t i o n s . T h e r e f o r e , i t can be c o n c l u d e d from t h e Born A p p r o x i m a t i o n t h a t o p t i c a l s e l e c t i o n r u l e s h o l d most a c c u r a t e l y a t 9 = 0 when E i s l a r g e . The r e l a t i o n between e x c i t a t i o n by e l e c t r o n impact and by a b s o r p t i o n o f r a d i a t i o n can be made more p r e c i s e by i n t r o d u c t i o n o f t h e c o n c e p t o f g e n e r a l i s e d o s c i l l a t o r s t r e n g t h f i r s t employed by Bethe [ 7 ] . The g e n e r a l i s e d o s c i l l a t o r s t r e n g t h f-| 2 f o r e x c i t a t i o n between d i s c r e t e 1 e v e l s 1, 2 i s d e f i n e d by f 1 2 ( K 2 ) = h ( K ) | 2 (2.28) K where z i s d e f i n e d b e f o r e i n ( 2 . 2 3 ) . By c o m p a r i s o n w i t h t h e f i r s t Born a p p r o x i m a t i o n c r o s s s e c t i o n CT^2 i n ( 2 . 2 1 ) , i t i s o b v i o u s t h a t f ^ 2 can be e x p r e s s e d i n terms o f a ^ 2 as f 1 2 = 7 \ K S 2 <2'29> 12. E q u a t i o n s (2.28) and (2.29) have been used more o r l e s s as e q u i v a l e n t d e f i n i t i o n s o f t h e g e n e r a l i s e d o s c i l l a t o r s t r e n g t h . The e q u i v a l e n c e r e s t s on t h e v a l i d i t y o f t h e Born a p p r o x i m a t i o n , because (2.21) i s o b t a i n e d u s i n g a plane-wave r e p r e s e n t a t i o n o f t h e p e r t u r b i n g e l e c t r o n . A t e l e c t r o n e n e r g i e s where t h e Born a p p r o x i m a t i o n i s no l o n g e r v a l i d , i t i s u s e f u l t o d e f i n e an e f f e c t i v e o s c i l l a t o r s t r e n g t h F ^ 2 such t h a t when put i n t o (2.29) i n p l a c e o f f 1 2 i t w i l l g i v e t h e c o r r e c t c r o s s s e c t i o n . F-j2 c a n be d e r i v e d from measured c r o s s s e c t i o n as f o l l o w s : F 1 2 ( E 1 ' K ) = £ i^" ^ 1 2 ( 2 > 3 0 ) w h i c h depends on t h e i n c i d e n t e l e c t r o n e nergy E^. Measurement o f F-|2 as a f u n c t i o n o f energy s h o u l d g i v e i n f o r m a t i o n about t h e v a l i d i t y o f t h e Born a p p r o x i m a t i o n a t low e n e r g i e s . As t h e en e r g y i n c r e a s e s i n t o t h e r e g i o n where t h e Born a p p r o x i m a t i o n i s v a l i d , F ^ 2 t e n d s towards f - j 2 and i s ind e p e n d e n t o f ene r g y . When t h e Born a p p r o x i m a t i o n i s v a l i d and a-j 2 from (2.24) i s s u b s t i t u t e d i n t o (2 .29) , i t i s o b v i o u s t h a t as K -* 0 2 fi2 = ! r2 *2 ? p - •• 2 < . <2-31> 2 However t h e q u a n t i t y 2We^  i s p r e c i s e l y e q u a l , i n atomic' u n i t s , t o t h e o p t i c a l o s c i l l a t o r s t r e n g t h f , whi c h c h a r a c t e r i s e s e m i s s i o n and a b s o r p t i o n o f r a d i a t i o n . Hence 1 im f = f as K 2 •*• 0 o Even when t h e Born a p p r o x i m a t i o n does not h o l d a t l a r g e r v a l u e s o f K, i t was shown by L a s s e t t r e e t a l . [13] t h a t t h e l i m i t o f t h e g e n e r a l i s e d o s c i l l a t o r s t r e n g t h , when e x t r a p o l a t e d i n t o t h e n o n - p h y s i c a l r e g i o n o f z e r o momentum t r a n s f e r i s t h e o p t i c a l o s c i l l a t o r s t r e n g t h f . T h i s i s 13. q u i t e i n d e p e n d e n t o f t h e Born a p p r o x i m a t i o n . T h e r e f o r e , one may o b t a i n o p t i c a l t r a n s i t i o n p r o b a b i l i t i e s f r o m e l e c t r o n i m p act d a t a even a t low e n e r g i e s i f one has an a b s o l u t e c a l i b r a t i o n o f impact c r o s s s e c t i o n s . A l t e r n a t i v e l y , one can v a l i d l y o b t a i n a b s o l u t e c r o s s s e c t i o n f o r i n e l a s t i c e l e c t r o n impact c o l l i s i o n s ( a t l e a s t f o r e l e c t r i c - d i p o l e - a l l o w e d p r o c e s s e s ) by n o r m a l i s i n g t h e v a l u e o f t h e c r o s s s e c t i o n , e x t r a p o l a t e d t o K = 0 , t o an a v a i l a b l e v a l u e o f f from o p t i c a l d a t a . o r The argument p r e s e n t e d above i s d e v e l o p e d s p e c i f i c a l l y f o r t h e c a s e o f atoms. In m o l e c u l e s , i f t h e e i g e n f u n c t i o n s a r e s e p a r a b l e i n t o e l e c t r o n i c and n u c l e a r f u n c t i o n s i n t h e u s u a l way, t h e n i t can be shown [14 ] t h a t e q u a t i o n (2.21) i s v a l i d , w i t h e g i v e n by an e q u a t i o n s i m i l a r t o (2.23) but w i t h t h e e i g e n f u n c t i o n s b e i n g t h o s e f o r t h e m o l e c u l a r e l e c t r o n s . Even i f t h e e x c i t e d s t a t e wave f u n c t i o n s a r e n o n - s e p a r a b l e , t h e same f o r m u l a e a r e v a l i d when s t a t e 1 i s t h e ground s t a t e and s t a t e 2 i s an e x c i t e d s t a t e l y i n g s e v e r a l v o l t s above t h e ground s t a t e , so t h a t t h e y do n o t p e r t u r b each o t h e r . The r e s u l t o f t h i s l i m i t i n g t h e o r y i s t h a t one can o b t a i n t h e c r i t e r i a f o r a l l o w e d and f o r b i d d e n t r a n s i t i o n s . C o n s i d e r i n g t h e e f f e c t i v e g e n e r a l -i s e d o s c i l l a t o r s t r e n g t h F d e f i n e d i n (2.30) K^Q F = 2W[e-j [ f o r an a l l o w e d t r a n s i t i o n „ N F = 0 f o r a f o r b i d d e n t r a n s i t i o n . 2.5.Low Energy E l e c t r o n S c a t t e r i n g . I n many c a s e s , t h e f i r s t Born a p p r o x i m a t i o n has been s u c c e s s f u l i n e x p l a i n i n g t h e d i f f e r e n t i a l c r o s s s e c t i o n f o r e l e c t r o n i c e x c i t a t i o n o f atoms and m o l e c u l e s by e l e c t r o n i m p a c t a t h i g h e n e r g i e s (E-,> ^ 150 eV) 14. and s m a l l s c a t t e r i n g a n g l e s (e< ^ 1 5 ° ) . + T h i s i s t h e r e g i o n where a s t u d y o f t h e a s s u m p t i o n s b e h i n d t h e f i r s t Born a p p r o x i m a t i o n l e a d s one t o e x p e c t i t t o be most v a l i d , a l t h o u g h t h e q u a n t i t a t i v e v a l i d i t y o f t h e t h e o r y depends on t h e p a r t i c u l a r n a t u r e o f t h e t r a n s i t i o n . F o r example L a s s e t t r e [ 1 5 ] , g u i d e d i n p a r t by e x p e r i m e n t a l r e s u l t s [ 1 6 ] , t h e o r e t i c a l l y showed t h a t t h e d e v i a t i o n f r o m t h e f i r s t B o rn a p p r o x i m a t i o n a t a g i v e n k i n e t i c e n e r g y o f impact can be more a p p r e c i a b l e f o r a t r a n s i t i o n between s t a t e s w i t h t h e same s p e c t r o s c o p i c d e s i g n a t i o n t h a n f o r a t r a n s i t i o n between s t a t e s w i t h d i f f e r e n t d e s i g n a t i o n s . A t l o w e r impact e n e r g i e s , l e s s t h a n say t e n t i m e s t h e e x c i t a t i o n e n e r g y , t h e f i r s t Born a p p r o x i m a t i o n i s no l o n g e r v a l i d i n g e n e r a l . The problem o f c a l c u l a t i n g c r o s s s e c t i o n s under t h e s e c o n d i t i o n s i s d i f f i c u l t and r e l i a b l e r e s u l t s can o n l y be o b t a i n e d , i f a t a l l , by e m p l o y i n g much more e l a b o r a t e a n a l y t i c a l and c o m p u t a t i o n a l p r o c e d u r e s . I t i s not p o s s i b l e t o r e p l a c e t h e c l e a r - c u t p r o c e d u r e o f t h e Born a p p r o x i m a t i o n by one o f comparable g e n e r a l i t y and d e f i n i t e n e s s . The Born a p p r o x i m a t i o n n e g l e c t s t h e e f f e c t o f e l e c t r o n exchange, d i s t o r t i o n o f s c a t t e r i n g - e l e c t r o n wave f u n c t i o n s and p o l a r -i s a t i o n o f t h e t a r g e t by t h e incoming e l e c t r o n . V a r i o u s methods have been d e v i s e d t o t a k e t h e s e e f f e c t s i n t o a c c o u n t . A s u r v e y o f t h e a n a l y t i c a l t h e o r y f o r s l o w e l e c t r o n c o l l i s i o n i s g i v e n by Massey and Burhop [ 1 7 ] . The r e l a t i v e i m p o r t a n c e o f t h e t h r e e e f f e c t s named above depend on i n d i v i d u a l t r a n s i t i o n s and i t seems t h a t no t h e o r e t i c a l scheme o f c a l c u l a t i o n has a g e n e r a l a p p l i c a b i l i t y . A t l o w e r impact e n e r g i e s near t h e e x c i t a t i o n t h r e s h o l d , t h e phenomena o f r e s o n a n c e s c a t t e r i n g i s dominant. "Resonances" a r e a l s o c a l l e d + For r e f e r e n c e s , see R i c e e t a l . , Phys. Rev. A 5_ (1972) 762. 15. "compound s t a t e s " o r "temporary n e g a t i v e i o n s " . T h e i r o c c u r r e n c e , a t more o r l e s s w e l l - d e f i n e d e n e r g i e s when e l e c t r o n s s c a t t e r f r o m atoms and m o l e c u l e s , i s due t o t h e f o r c e f i e l d o f t h e s c a t t e r e r b e i n g s u f f i c i e n t -l y a t t r a c t i v e t o h o l d t h e f r e e e l e c t r o n f o r a t i m e l o n g compared w i t h t h e normal t i m e o f passage t h r o u g h t h e s c a t t e r i n g r e g i o n . These " r e s o n a n c e s " can be viewed as n o n - s t a t i o n a r y ( s h o r t - l i v e d ) s t a t e s o f an atom o r m o l e c u l e . In s h a r p c o n t r a s t t o s t a t i o n a r y s t a t e s , " r e s o n a n c e s " decay by t h e e m i s s i o n o f e l e c t r o n s r a t h e r t h a n p h o t o n s . They r e s u l t i n f i n e s t r u c t u r e s i n c r o s s s e c t i o n s c o r r e s p o n d i n g t o d i f f e r e n t e x i t c h a n n e l s . The t h e o r e t i c a l problem a s s o c i a t e d w i t h r e s o n a n c e s i n e l e c t r o n - a t o m and e l e c t r o n - m o l e c u l e s c a t t e r i n g has been r e v i e w e d by T a y l o r [ 1 8 ] and by N i c o l a i d e s [ 1 9 ] . S c h u l z [ 2 0 ] has r e c e n t l y g i v e n a s y s t e m a t i c d i s c u s s i o n o f t h e s p e c t r o s c o p y o f r e s o n a n c e s . 16. CHAPTER I I I EXPERIMENTAL DEVICES 3 . 1 . E l e c t r o n Guns. The e s s e n t i a l f u n c t i o n s o f an e l e c t r o n impact s p e c t r o m e t e r a r e t h e p r o d u c t i o n o f an e n e r g y - s e l e c t e d beam o f e l e c t r o n s and t h e a n a l y s i s o f the energy d i s t r i b u t i o n o f t h e s c a t t e r e d e l e c t r o n s w i t h v a r i a t i o n o f t h e impact energy and t h e s c a t t e r i n g a n g l e . The s o u r c e o f e l e c t r o n s i s u s u a l l y a t h e r m i o n i c c a t h o d e i n an e l e c t r o n gun. Depending on t h e i n d i v i d u a l e x p e r i m e n t s , e l e c t r o n beams o f a s p e c i f i c e n e r g y , c r o s s s e c t i o n , a n g u l a r d i v e r g e n c e and minimum c u r r e n t may be r e q u i r e d . E l e c t r o n guns c a n n o t always be d e s i g n e d t o meet a l l t h e s e r e q u i r e m e n t s , e s p e c i a l l y f o r t h e minimum c u r r e n t , s i n c e t h e r e a r e p h y s i c a l laws w h i c h p l a c e s t r i n g e n t l i m i t s on t h e maximum o b t a i n a b l e c u r r e n t once o t h e r beam pa r a m e t e r s a r e f i x e d . The f o l l o w i n g a n a l y s i s has been g i v e n by Simpson [ 2 1 ] . I f an e l e c t r o n beam o f energy E i s t o pass t h r o u g h two a p e r t u r e s o f d i a m e t e r 2 r Q s e p a r a t e d by a d i s t a n c e £ . t h e r e a r e two fundamental l i m i t s on t h e c u r r e n t t h a t can be t r a n s m i t t e d . The f i r s t i s due t o space c h a r g e , w h i c h l i m i t s t h e maximum c u r r e n t o f e l e c t r o n s w i t h e nergy E ( e V ) , i n t h e p r e s e n c e o f a s t r o n g enough c o l l i m a t i n g m a g n e t i c f i e l d ( s o t h a t t h e r a d i u s o f t h e s p i r a l p ath i s smallerthan t h e beam r a d i u s ) t o be I = 3 5 E 3 / 2 ( p A ) (3.1) max v ' v ' I f t h e r e i s no m a g n e t i c f i e l d , t h e t r a n s m i t t e d c u r r e n t i s maximum a t an optimum convergence a n g l e Y = t a n " 1 - 2 ^ 0 - and t h e space c h a r g e f o r c e s p r e a d s 17. t h e beam so t h a t a t t h e c e n t r e o f t h e space t h e beam becomes a d i s c o f d i a m e t e r 2 r Q / 2 . 3 5 and a l l e l e c t r o n s move p a r a l l e l t o t h e a x i s . The maximum c u r r e n t i s t h e n I m a x = 3 8 . 5 E 3 / 2 ( 2 r 0 / 0 2 = 3 8 . 5 E 3 / 2 t a n 2 Y (uA) (3.2) The second l i m i t i s based on t h e H e l m h o l t z - L a g r a n g e theorem w h i c h s t a t e s t h a t f o r any two c o n j u g a t e p l a n e s (such t h a t one i s t h e image o f t h e o t h e r ) s e p a r a t e d by a n o n - a b s o r b i n g o p t i c a l p a t h /E"i dx-j s i n e-j = /E~2 d x 2 s i n e 2 (3.3) where E.., dx. and e. ( i = 1,2) a r e t h e e l e c t r o n e n e r g y , d i f f e r e n t i a l l e n g t h e l ement and a n g l e o f co n v e r g e n c e i n t h e p l a n e i . S i n c e c u r r e n t i s c o n s e r v e d i n a n o n a b s o r b i n g c h a n n e l and i f J ^ i s t h e c u r r e n t d e n s i t y l] = J ] d x ^ = J 2 d x 2 2 = I 2 (3.4) E q u a t i o n s (3.3) and (3.4) can be combined t o g i v e R l °1 J 2 _ R 2 1 s i n E 2 s i n e 2 E 2 w h i c h e x p r e s s e s t h e c o n s e r v a t i o n o f " R i c h t s t r a h l w e r t " o r " b r i g h t n e s s " R-. When t h i s r e l a t i o n i s a p p l i e d between t h e p l a n e s o f t h e s m a l l e s t d i a m e t e r and t h e c a t h o d e a t a t e m p e r a t u r e T p r o d u c i n g a M a x w e l l i a n d i s t r i b u t i o n o f e l e c t r o n e n e r g i e s , t h e maximum c u r r e n t d e n s i t y t h a t can be t r a n s m i t t e d i s r e 2 -J 2 max " J c a t h o d e L1 + F T s i n 2 e 2 (3.6) where k i s t h e Boltzmann's c o n s t a n t . T h i s l i m i t on e l e c t r o n beam b r i g h t -ness i s r e a l l y a consequence o f t h e th e r m a l e nergy o f t h e e m i t t e d e l e c t r o n s , I n t h e case o f beams used i n e l e c t r o n m i c r o s c o p y , beam w e l d i n g and 18. e l e c t r o n d i f f r a c t i o n , w i t h an energy o f above 10 KeV, s p o t s i z e < 1mm _3 and convergence a n g l e < 10 r a d , t h e guns a r e b r i g h t n e s s l i m i t e d . A t v o l t a g e s between 10 KeV and 300 eV, p a r t i c u l a r l y a t h i g h c o n v e r g e n c e a n g l e , t h e guns a r e u s u a l l y space c h a r g e d o m i n a t e d . Below 300 eV, t h e space c h a r g e i n f r o n t o f t h e c a t h o d e d e c r e a s e s t h e c a t h o d e b r i g h t n e s s and r e n d e r s t h e guns b r i g h t n e s s l i m i t e d a g a i n . As p o i n t e d o u t by Simpson, i t i s i m p o r t a n t t o n o t e t h a t t h e space c h a r g e l i m i t depends o n l y on t h e r a t i o o f d i m e n s i o n s and n o t on t h e i r m a g n i t u d e , and hence f o r t h e same co n v e r g e n c e a n g l e t h e maximum c u r r e n t i s i n d e p e n d e n t o f t h e s i z e o f t h e beam. The b r i g h t n e s s , on t h e o t h e r hand, depends i n v e r s e l y on t h e beam d i a m e t e r . Hence a change o f p h y s i c a l d i m e n s i o n o f t h e gun w i l l a l t e r t h e r e l a t i v e i m p o r t a n c e o f t h e s e two l i m i t s . The e l e c t r o n gun employed i n t h i s work i s a s i m p l e t h r e e element gun c o n s i s t i n g o f an i n d i r e c t l y heated c a t h o d e f o l l o w e d by a g r i d and an anode. The p o t e n t i a l d i s t r i b u t i o n near t h e cathode p l a y s a dominant r o l e . T h i s depends on t h r e e p a r a m e t e r s : ( a ) t h e d i s t a n c e between t h e cathode and t h e g r i d , (b) t h e g r i d a p e r t u r e and i t s t h i c k n e s s and ( c ) t h e g r i d v o l t a g e and p o l a r i t y w i t h r e s p e c t t o t h e c a t h o d e . The p o s i t i o n o f t h e " c r o s s - o v e r " , where t h e t r a j e c t o r i e s o f t h e e l e c t r o n f r o m t h e c a t h o d e i n t e r c e p t t h e a p e r t u r e a x i s , n o r m a l l y l i e s between t h e c a t h o d e and t h e anode, but can be moved f u r t h e r from them by v a r y i n g t h e g r i d v o l t a g e and p o l a r i t y . The g r i d v o l t a g e a l s o c o n t r o l s t h e beam i n t e n s i t y . I t seems t h a t t h e e l e c t r o n s o u r c e i s t h e weakest and most unpred-i c t a b l e p a r t o f t h e whole e l e c t r o n s p e c t r o m e t e r , and t h e r e i s no c o m p l e t e l y s a t i s f a c t o r y s o l u t i o n t o t h i s problem. In t h i s work, d i r e c t l y h e ated c a t h o d e s c o n s i s t i n g o f t u n g s t e n and rhenium f i l a m e n t s were f i r s t t r i e d , 19. but t h e y t e n d t o move when h e a t e d . K u y a t t [ 2 2 ] r e p o r t s t h e s u c c e s s f u l use o f t u n g s t e n h a i r p i n s o f about 0.005" d i a m e t e r w h i c h have been p r e -c o n d i t i o n e d . A rhenium r i b b o n r e q u i r e d l a r g e h e a t i n g c u r r e n t s 6A) and t h e performance o f t h e s p e c t r o m e t e r was p e r t u r b e d by space c h a r g e and/or m a g n e t i c f i e l d e f f e c t o f t h e gun. I n d i r e c t l y h e ated c a t h o d e s p o s s e s s m e c h a n i c a l s t a b i l i t y but t h e i r l i f e t i m e i s dependent on t h e n a t u r e o f gases t o w h i c h t h e y a r e exposed. A F r e n c h C.S.F. t y p e CI 10 i n d i r e c t l y h e a ted c a t h o d e has worked q u i t e w e l l w i t h i n e r t gases and has a l i f e t i m e o f about 6 months. However, performance w i t h o r g a n i c m o l e c u l e s such as a l c o h o l s , e t h e r s and c a r b o n y l compounds i s n o t s a t i s f a c t o r y i n t h a t t h e e m i s s i o n decays r a p i d l y a f t e r t h e i n i t i a l a c t i v a t i o n . A n o t h e r draw-back t o t h e s e c a t h o d e s i s t h e i r expense $ 2 0 0 ). W i t h o r g a n i c m o l e c u l e s , a compromise has been f o u n d by u s i n g a c o m b i n a t i o n o f RCA o x i d e c a t h o d e s w i t h P h i l i p s Elmet h e a t e r s . These c a t h o d e s a r e s l i g h t l y m a g n e t i c and a r e v e r s a l o f t h e d i r e c t i o n o f t h e h e a t e r c u r r e n t causes a change i n t h e f o c u s s i n g v o l t a g e o f t h e energy a n a l y s e r s . However, t h i s i s t o l e r a b l e and t h e low c o s t o f t h e s e c a t h o d e s and h e a t e r s p e r m i t s f r e q u e n t r e p l a c e m e n t . The u l t i m a t e s o l u t i o n t o t h i s problem o f s h o r t c a thode l i f e i s t o d e s i g n a d i f f e r e n t i a l l y pumped system t o i s o l a t e t h e gun from t h e t a r g e t gas. 3 . 2 . E l e c t r o n L e n s e s . E l e c t r o n s move t h r o u g h an e l e c t r i c f i e l d i n an a n a l o g o u s f a s h i o n t o the passage o f l i g h t r a y s t h r o u g h a medium o f c o n t i n u o u s l y v a r i a b l e r e f r a c t i v e i n d e x . E l e c t r o n s may be r e f l e c t e d , r e f r a c t e d and f o c u s s e d . A c r o s s a boundary s e p a r a t i n g two e q u i p o t e n t i a l r e g i o n s o f p o t e n t i a l s V Q and V-|, " S n e l l ' s Law" h o l d s i n t h e form 20. JT^ s i n 0 Q = s i n e ] (3.7) where e Q and a r e t h e a n g l e s t h a t t h e e l e c t r o n beam makes w i t h t h e normal on e i t h e r s i d e o f t h e boundary. Hence /V may be used as a " r e f r a c t i v e i n d e x " , w i t h V = 0 when e l e c t r o n s a r e a t r e s t . A s i m p l e e l e c t r o n l e n s u s u a l l y t a k e s t h e f o r m o f two c i r c u l a r c y l i n d e r s on two c i r c u l a r a p e r t u r e s o f d i a m e t e r D ke p t a t d i f f e r e n t p o t e n t i a l s and a t a d i s t a n c e A a p a r t . The l e n s a c t i o n can be e x p l a i n e d by c o n s i d e r i n g t h e e q u i p o t e n t i a l s u r f a c e between two c y l i n d e r s o f equal d i a m e t e r a t a s h o r t d i s t a n c e a p a r t ( F i g u r e l a ) . The e l e c t r o n path i s smo o t h l y c u r v e d i n s t e a d o f c o n s i s t i n g o f s t r a i g h t l i n e f r a g m e n t s . A r a y p a r a l l e l t o t h e a x i s f r o m t h e l e f t e x p e r i e n c e s a c o n v e r g e n t a c t i o n i n p a s s i n g t h r o u g h t h e l e f t p a r t o f t h e l e n s because t h e g r a d i e n t o f t h e p o t e n t i a l has a component d i r e c t e d towards the a x i s . In p a s s i n g t h r o u g h t h e r i g h t hand p a r t , t h i s r a y e x p e r i e n c e s a d i v e r g e n t a c t i o n because t h e r a d i a l component o f t h e p o t e n t i a l g r a d i e n t i s d i r e c t e d o u t w a r d s . Thus when t h e e q u i p o t e n t i a l s u r f a c e i s convex as approached by t h e e l e c t r o n s i n t h e d i r e c t i o n o f  i n c r e a s i n g p o t e n t i a l , t h e a c t i o n i s c o n v e r g e n t . C o n v e r s e l y , when t h e e q u i p o t e n t i a l s u r f a c e i s c o n c a v e , t h e a c t i o n i s d i v e r g e n t . S i n c e e l e c t r o n s move more s l o w l y i n t h e c o n v e r g e n t r e g i o n than i n t h e d i v e r g e n t r e g i o n , t h e c o n v e r g e n t e f f e c t a l w a y s exceeds t h e d i v e r g e n t e f f e c t . E l e c t r o n l e n s e s a r e much more v e r s a t i l e than o p t i c a l l e n s e s because t h e i r s t r e n g t h can be changed by s i m p l y c h a n g i n g e l e c t r o d e p o t e n t i a l s i n s t e a d o f h a v i n g t o move l e n s components r e l a t i v e t o one a n o t h e r . The t h i c k l e n s t e r m i n o l o g y i s u s u a l l y used i n e l e c t r o n l e n s e s . W i t h r e f e r e n c e t o F i g u r e l b , t h e two r a y s t h a t l e a v e and e n t e r t h e l e n s p a r a l l e l t o t h e a x i s r e s p e c t i v e l y , a r e known as t h e f i r s t and second " p r i n c i p a l 21. a) V| < V 2 Thick-k-iib tiTiniiioIopy. K.R* Spangenberg, Vacuum Tubes. McGraw H i l l , N.Y. 19 Z f 8 c) v 1 < v 2 0.01" D D = 1 / S " A / D = 1 4.5D- -H 6.5 D— H F i g u r e 1. E l e c t r o n l e n s e s . 22. r a y s " . F o r l e n s e s w i t h i n i t i a l and f i n a l g r a d i e n t s o f p o t e n t i a l t h a t a r e z e r o , t h e i n i t i a l and f i n a l p o r t i o n s o f t h e r a y s w i l l be s t r a i g h t l i n e s . The p r i n c i p a l r a y s s e r v e t o d e f i n e t h e c a r d i n a l p o i n t s and f o u r t h i c k l e n s p a r a m e t e r s . I f t h e i n i t i a l and f i n a l s t r a i g h t p o r t i o n s o f t h e two p r i n c i p a l r a y s and extended u n t i l t h e y i n t e r s e c t , t h e i n t e r s e c t i o n s o c c u r a t what a r e known as t h e " p r i n c i p a l p l a n e s " and H,,. In a l m o s t a l l c a s e s both p r i n c i p a l p l a n e s l i e on t h e f o r e s i d e (low v o l t a g e s i d e ) o f t h e l e n s . F u r t h e r m o r e , t h e y a r e c r o s s e d , i . e . t h e second p r i n c i p a l p l a n e l i e s i n f r o n t o f t h e f i r s t p r i n c i p a l p l a n e . A f o c a l l e n g t h i s d e f i n e d as t h e d i s t a n c e f r o m t h e p r i n c i p a l p l a n e o f t h e l e n s t o t h e p o i n t a t w h i c h t h e c o r r e s p o n d i n g p r i n c i p a l r a y c r o s s e s t h e a x i s o f t h e l e n s ( t h e f o c a l p o i n t s ) . T h e r e a r e two f o c a l l e n g t h s , ( u s u a l l y d i f f e r e n t ) , one on each s i d e o f t h e l e n s and t h e y a r e d e s i g n a t e d by t h e symbol f . The d i s t a n c e from t h e f o c a l p o i n t t o t h e r e f e r e n c e p l a n e M, u s u a l l y t h e m i d - p l a n e o r e l e c t r o d e j u n c t i o n , i s i n d i c a t e d by t h e symbol F. f - j , f 2 , F-j, F^ a r e c a l l e d t h e c a r d i n a l c h a r a c t e r i s t i c s o f t h e t h i c k l e n s and a r e s u f f i c i e n t t o d e s c r i b e t h e l e n s c o m p l e t e l y . These p a r a m e t e r s can e i t h e r be f ound e x p e r i m e n t a l l y o r by c a l c u l a t i o n . The o b j e c t and image d i s t a n c e s a r e u s u a l l y measured r e l a t i v e t o t h e m i d - p l a n e and a r e d e n o t e d by P and Q r e s p e c t i v e l y . One s i g n c o n v e n t i o n a d o p t e d i s t o put t h e d i s t a n c e P on t h e low e nergy s i d e o f t h e l e n s . A c o n v e n i e n t r e l a t i o n t o use f o r d e t e r m i n a t i o n o f P o r Q when e i t h e r i s known i s t h e NEWTON RELATION, w h i c h s t a t e s t h a t (P - (Q - F 2 ) = f 1 f 2 (3.8) The v a l u e s f o r f - j , f g , F-p F 2 a r e a v a i l a b l e i n the l i t e r a t u r e , e.o. [ 2 3 , 2 4 ] . Spangenberg [23] has c o n v e r t e d t h e f 1 , f 2 , F^, F 2 c u r v e s t o 23. c u r v e s o f P and Q w i t h t h e m a g n i f i c a t i o n M as a pa r a m e t e r . An example i s shown i n F i g u r e 2. These diagrams a r e v e r y c o n v e n i e n t f o r d e s i g n work when t h e o b j e c t s and images a r e r e a l . When v i r t u a l images o r o b j e c t s a r e i n v o l v e d , t h e f o c a l p r o p e r t i e s need t o be used. M a g n i f i c -a t i o n o f t h e l e n s can e a s i l y be c a l c u l a t e d from t h e f o l l o w i n g r e l a t i o n s : l i n e a r m a g n i f i c a t i o n M a n g u l a r m a g n i f i c a t i o n m In t h e p r e s e n t work, 127 degr e e c y l i n d r i c a l d e f l e c t i o n a n a l y s e r s a r e used t o energy a n a l y s e an e l e c t r o n beam w h i c h i s r e c t a n g u l a r i n c r o s s - s e c t i o n . T h e r e f o r e , i n t h e p r e s e n t s p e c t r o m e t e r , t h e l e n s e s employ l o n g s l i t s i n s t e a d o f c i r c u l a r a p e r t u r e s . In some ways, t h i s s l i t l e n s can be t h o u g h t o f as a s e r i e s o f o v e r l a p p i n g a p e r t u r e l e n s e s a l o n g i t s l e n g t h . By making t h e s l i t s l o n g enough, u n d e s i r a b l e end-e f f e c t s can be a v o i d e d . These s l i t l e n s e s ( c f . c y l i n d r i c a l l e n s e s i n the o p t i c a l a n a l o g u e ) have found t o f u n c t i o n v e r y w e l l as d e c e l e r a t o r s and a c c e l e r a t o r s g i v i n g a w e l l - d e f i n e d f o c u s . To a n a l y s e t h e performance o f t h e e l e c t r o n s p e c t r o m e t e r , i t i s e s s e n t i a l t o e s t i m a t e t h e s i z e o f t h e v i r t u a l s l i t s a t t h e e n t r a n c e p l a n e o f t h e energy a n a l y s e r . From t h i s , t h e r e s o l u t i o n and o t h e r d e s i g n p a rameters can be c a l c u l a t e d . The d i m e n s i o n s o f t h e l e n s a r e shown i n F i g u r e I c . The c a r d i n a l p a r a m e t e r s i n u n i t s o f D ( w i d t h o f t h e l e n s s l i t ) g i v e n by Read [ 2 4 ] a r e used i n t h e f o l l o w i n g sample c a l c u l a t i o n s f o r P *„A M _ w i d t h o f r e a l s l i t n _ c cn. a n d " w i d t h o f v i r t u a l s l i t g i v e n Q " 6 ' 5 D : Q - F 2 f l f 2 ' " P - F 1 (3.9) P " F l _ f l f 2 Q - F 2 (3.10) 6f 2r The focal lengths/and/' am! foe;:! distances F and /•"' of the two-clement coaxial cylinder lens of unit diameter and 01 separation. The primed values refer to the high potential side of the lens D.W.O. Heddle, J. Phys. E Cylinder lens (c/y£»=0 1) 100, , . , 10 100 PID Values of object distance /'anil image ilistaiuv CJ expressed in terms of Jens diameter I) for the iwo-element coaxial cylinder lens of D/10 separation. Lines or constant voltage ratio and of constant magnification measured in the direction from low to high potential are shown 2 (1969) 10if6 F i g u r e 2. C h a r a c t e r i s t i c s o f e l e c t r o n l e n s e s . 25. V V 1 = 6 f l = 2 , 1 f 2 = 5 , 1 F l = 3 , 7 F 2 = 3 , 0 (P - 3.7) (6.5 - 3.0) = 2.1 x 5.1 = 10.7 (P - 3.7) = 10.7/3.5 = 3 . 0 P = LL M = TO = °' 7 0 V 2 / V l = 7 f-| = 1-7 f 2 = 4.6 F 1 = 3.1 F 2 = 2.6 (P - 3.1) (6.5 - 2.6) = 1.7 x 4.6 = 7.8 (P - 3.1) = 7.8/3.9 = 2.0 p = jy. M = FfJ = ° - 8 5 V 2 / V ] = 8 f 1 = 1.5 f 2 = 4.3 F 1 = 2.9 F 2 = 2.2 (P - 2.9) (6.5 - 2.2) = 1.5 x 4.3 = 6.5 (P - 2.9) = 6.5/4.3 = 1.5 P = 4.4 M = |4 = 1.00 = 1.5 ===== V 2/V ] = 9 f 1 = 1.4 f 2 = 4.0 F 1 = 2.7 F 2 = 2.0 (P - 2.7) (6.5 - 2.0) = 1.4 x 4.0 = 5.6 (P - 2.7) = 5.6/4.5 = 1.2 P = J L £ M = 14 = 1 ,17 From t h e s e c a l c u l a t i o n s , t h e optimum r e t a r d a t i o n r a t i o f o r t h e f i x e d d i s t a n c e s o f P = 4.5 D and Q = 6.5 D i s V 2/V 1 = 8. E x p e r i m e n t a l l y i t was found t h a t t h e l e n s e s o p e r a t e d b e s t w i t h a r e t a r d a t i o n r a t i o o f 7. Under t h e s e c o n d i t i o n s t h e m a g n i f i c a t i o n M i s l e s s t h a n u n i t y , meaning t h a t t h e w i d t h o f t h e v i r t u a l s l i t i s l a r g e r t h a n t h e p h y s i c a l s l i t . T h i s would somewhat degrade t h e r e s o l u t i o n o f t h e s p e c t r o m e t e r . 26. 3 . 3 . E l e c t r o n Energy A n a l y s e r s . 3.3.1. G e n e r a l a s p e c t s . The s t u d y o f e l e c t r o n s c a t t e r i n g phenomena r e q u i r e s t h e s u c c e s s f u l use o f t e c h n i q u e s o f b o t h e n e r g y monochromation and e n e r g y a n a l y s i s o f e l e c t r o n s . R e t a r d i n g t e c h n i q u e s o f v a r i o u s t y p e s have now been l a r g e l y r e p l a c e d by t i m e o f f l i g h t , m a g n e t i c and e l e c t r i c d e f l e c t i o n t e c h n i q u e s . Of t h e s e the use o f e l e c t r i c d e f l e c t i o n a n a l y s e r s i s t h e most w i d e s p r e a d . A d e t a i l e d a n a l y s i s o f t h e energy s e l e c t i o n o f e l e c t r o n s has been g i v e n by Hasted [ 2 5 ] . Momentum a n a l y s i s o f c h a r g e d p a r t i c l e s i n m a g n e t i c f i e l d s have been q u i t e e x t e n s i v e l y used f o r $-ray s p e c t r o m e t e r s , but t h e problem o f f r i n g e and s t r a y m a g n e t i c f i e l d s a f f e c t i n g n e i g h b o u r i n g p a r t s o f t h e e x p e r i m e n t i s u n f a v o u r a b l e f o r h i g h - r e s o l u t i o n , l o w - e n e r g y s t u d i e s as i n EIS e x p e r i m e n t s e m p l o y i n g d o u b l e a n a l y s e r s and more complex e l e c t r o n o p t i c s . On t h e o t h e r hand, e l e c t r o s t a t i c f i e l d s a r e e a s i l y produced and s h i e l d e d from f r i n g e e f f e c t s . There a r e two g e n e r a l t y p e s o f e l e c t r o s t a t i c e l e c t r o n e nergy a n a l y s e r s , namely, r e t a r d i n g a n a l y s e r s and d e f l e c t i o n a n a l y s e r s . R e t a r d i n g a n a l y s e r s o n l y measure t h e normal component o f e l e c t r o n v e l o c i t y and hence u s u a l l y e x h i b i t a l i m i t e d e n e r g y r e s o l v i n g power u n l e s s s p e c i a l p r o v i s i o n s a r e made, e.g. s p h e r i c a l g r i d s [ 2 6 ] and t h e use o f s p e c i a l l e n s e s [ 2 7 ] . The i n t e g r a l s t o p p i n g c u r v e s p r oduced a r e p a r t i c u l a r l y u s e f u l f o r m e a s u r i n g r e l a t i v e t r a n s i t i o n p r o b a b i l i t i e s but a r e l e s s s a t i s f a c t o r y f o r a c c u r a t e measurement o f e l e c t r o n e n e r g i e s u n l e s s e l e c t r o n i c c u r v e d i f f e r e n t i a t i o n i s employed. The r e t a r d i n g p o t e n t i a l d i f f e r e n c e (RPD) t e c h n i q u e [ 2 8 ] f o r t h e p r o d u c t i o n o f a pseudo-mono-e n e r g e t i c e l e c t r o n beam, has r e c e n t l y been improved and automated. T h i s can now g i v e a r e s o l u t i o n as low as 0.01 eV [ 2 9 ] when used c a r e f u l l y . I t 27. i s u s u a l l y used w i t h t h e t r a p p e d e l e c t r o n t e c h n i q u e [ 3 0 ] t o s t u d y e l e c t r o n impact s p e c t r a , e s p e c i a l l y near t h r e s h o l d . E l e c t r o s t a t i c a n a l y s e r s o f t h e d e f l e c t i o n t y p e produce a d i f f e r e n t i a l s pectrum which i s g e n e r a l l y more amenable t o s p e c t r o s c o p i c i n t e r p r e t a t i o n . I n t e g r a t i o n o f t h e d i f f e r e n t i a l s i g n a l r e a d i l y g i v e s r e l a t i v e t r a n s i t i o n p r o b a b i l i t i e s . S a r - e l [ 3 1 ] a f t e r i n v e s t i g a t i n g t h e r e l a t i v e m e r i t o f s e v e r a l t y p e s o f d e f l e c t i o n a n a l y s e r s , a s s i g n e d t h e h i g h e s t f i g u r e o f m e r i t t o t h e c y l i n d r i c a l m i r r o r a n a l y s e r . T h i s can c o l l e c t e l e c t r o n s a t a l l p o l a r a n g l e s from a p o i n t s o u r c e , but t h e r e a r e d i f f i c u l t i e s i n d e s i g n i n g c o m p a t i b l e e l e c t r o n l e n s systems s u i t a b l e f o r use i n E I S . M a g n e t i c f i e l d n e u t r a l i z a t i o n o v e r a l a r g e volume i s p a r t i c u l a r l y i m p o r t a n t . The c o n c e n t r i c h e m i s p h e r i c a l a n a l y s e r , f i r s t d e s c r i b e d by P u r c e l l [ 3 2 ] , has t h e advantage o f d o u b l e f o c u s s i n g and easy c o u p l i n g t o most s a t i s f a c t o r y s t r o n g l y d e c e l e r a t i n g and a c c e l e r a t i n g l e n s as w e l l as zoom l e n s e s w i t h c i r c u l a r symmetry. Simpson and c o - w o r k e r s [ 3 3 , 3 4 ] , and a l s o L a s s e t t r e and c o - w o r k e r s [ 3 5 ] have produced c o n c e n t r i c h e m i s p h e r i c a l a n a l y s e r s o f advanced d e s i g n f o r e x t e n s i v e s t u d y o f E I S . An a l t e r n a t i v e form o f e l e c t r o -s t a t i c d e v i c e i s t h e 127° e l e c t r o s t a t i c v e l o c i t y s e l e c t o r i n t r o d u c e d by C l a r k e [ 3 6 ] and improved by Marmet and Kerwin [ 3 7 ] . T h i s t y p e i s used i n t h e p r e s e n t work and a d e t a i l e d a c c o u n t w i l l be g i v e n l a t e r . A u n i f o r m e l e c t r o s t a t i c f i e l d between two p a r a l l e l p l a t e s a l s o s e r v e s as a e l e c t r o -s t a t i c a n a l y s e r [ 3 8 ] . The n e c e s s i t y o f c o l l i m a t i n g t h e beam p a r a l l e l a l o n g a p a t h a x i s making an a n g l e o f 45° w i t h t h e p l a t e s i s t h e main d i s a d v a n t -age, but t h e beam e n t e r s t h e a n a l y s e r t h r o u g h an e q u i p o t e n t i a l s u r f a c e , so no f r i n g e f i e l d c o r r e c t i o n i s n e c e s s a r y , c o n t r a r y t o most o t h e r a n a l y s e r s . Combined e l e c t r o s t a t i c and m a g n e tic f i e l d s a r e a l s o s u i t a b l e f o r 28. e l e c t r o n e nergy a n a l y s i s . U s i n g c r o s s e d e l e c t r o s t a t i c and m a g n e t i c f i e l d s , i n t h e p a t t e r n o f t h e c l a s s i c a l Wien f i l t e r [ 3 9 ] , a r e s o l u t i o n o f b e t t e r t h a n 0.01 eV has been a c h i e v e d . A new t y p e o f c r o s s - f i e l d a n a l y s e r , w i t h 0.02 eV r e s o l v i n g power, i n w h i c h the e l e c t r o n s pass down th e l i n e s o f f o r c e i n h e l i c a l p a t h s has been r e p o r t e d by S t a m a t o v i c and S c h u l z [40] ( t r o c h o i d a l e l e c t r o n monochromator). P r e s e n t l y , t h i s i s o n l y used f o r monochromation and not f o r t h e a n a l y s i s o f e l e c t r o n beams. With f u r t h e r d e v e l o p m e n t , t h i s s i m p l e d e v i c e s h o u l d f i n d wide a p p l i c a t i o n , e s p e c i a l l y when an a x i a l m a g n e t i c f i e l d i n t h e s o u r c e r e g i o n i s d e s i r a b l e . 3.3.2. Theory o f t h e 127° a n a l y s e r . As shown i n F i g u r e 3, c o n s i d e r a two d i m e n s i o n a l , r a d i a l e l e c t r o -~* A s t a t i c f i e l d E = -^j r , where r i s t h e r a d i a l u n i t v e c t o r . I f an e l e c t r o n o f mass m and c h a r g e -e i s i n j e c t e d n o r m a l l y ( a l o n g QP) i n t o t h i s f i e l d a t t h e p o i n t P, t h e n f o r a g i v e n v a l u e o f t h e f i e l d c o n s t a n t A, t h e r e e x i s t s a s p e c i f i c v a l u e o f t h e e l e c t r o n v e l o c i t y V where t h e e l e c t r o n w i l l d e s c r i b e c i r c u l a r m o t i o n i n t h e f i e l d ( o r b i t 1 ). The r e q u i r e m e n t f o r t h i s o r b i t ( w i t h r a d i u s r ) i s 2 eE = e £ = ^ ( c e n t r i f u g a l f o r c e ) (3.11) i . e . V = ( e A / m ) 1 ^ (3.12) To i n v e s t i g a t e t h e f o c u s s i n g p r o p e r t i e s o f such a f i e l d , c o n s i d e r t h e o r b i t o f an e l e c t r o n p r o j e c t e d i n t o t h e f i e l d a t t h e p o i n t P a t an a n g l e a t o t h e normal and w i t h v e l o c i t y v . The a c c e l e r a t i o n a e x p e r i e n c e d by t h e e l e c t r o n can be r e s o l v e d i n t o a r a d i a l and a t a n g e n t i a l component F i g u r e 3. 127° c y l i n d r i c a l a n a l y s e r f i e l d . 30. >r-i$-r{&Y (3-13) VFH") <3J4) 2 2 2 and a r + a^ = |a| . I f v^ i s t h e component o f t h e e l e c t r o n v e l o c i t y p e r p e n d i c u l a r t o f , t h e n f o r an i n f i n i t e s i m a l t i m e d i s p l a c e m e n t d t , d<j> = v x d t / r , so t h a t <p & • ? * • ( 3 - ' 5 ) F o r t h e case o f a c e n t r a l f i e l d under i n v e s t i g a t i o n , a, = 0 and so from ( 3 . 1 4 ) , ^  ( r 2 d r | - ) v a n i s h e s . ^ c i t " = c o n s t a n t = n f o r a l l t (3.16) where h = r 2^  at = ~ = V o c o s a (3-17) r = r Q o Changing t h e in d e p e n d e n t v a r i a b l e f r o m t t o $ v i a r e l a t i o n ( 3 . 1 6 ) d _ d d4> _ h d /- , R x d t d* d t " r ? d<j> ^ ' l o ; Now d e f i n i n g a new v a r i a b l e u = t h e n d r 1 du _ 1 h du . du 1 Q \ d t ~ " TJ2* d t " " u ? F2" d j " " 1 1 d* 1 ' } d 2 r _ d _ ( . d u \ _ h d _ / . d u \ d t ? " d t ^' n dcp y " F 7 d* \J n d^/ 1 _ h 2 d 2 u _ . 2 2 d 2 u 9 n v From e q u a t i o n s ( 3 . 1 3 ) and ( 3 . 1 6 ) a _ . 2 , 2 d 2 u „ h 2 _ . 2 2 f d 2 u .,1 r , 9 1 , a r " " h u d ? ? — r ?T " " h u ^ + u j ( 3 . 2 1 ) S i n c e f o r c e = mass x a c c e l e r a t i o n a _ u 2 M 2 [ d 2 u , „] _ e A a r " " h u |_dF U J ~ ~ m r . 2 , 2 f d 2 u . „1 _ Aeu h u \W j " ~nT ( 3 . 2 2 ) i . e . r I n t r o d u c i n g t h e v a r i a b l e y = {j- = (3.22) becomes S l Z + v = .,Ae.. - „Ae_ dt|>2 mh2un2y mj^v o2cos2ajj^y _e Jo i - e - d 2 X + y = £ i 2 v d<j)< where c = Ae = , v = y mv^COS^a V Zcos^a 1 C V COSa 0 ' 0 ~ ' 0 " The d i f f e r e n t i a l e q u a t i o n (3.23) i s t o be s o l v e d s u b j e c t e d t o t h e boundary c o n d i t i o n s ; a t <j> = 0 y = 1 ( i .e. r =' r ) and (3.23) (3.24) dy_ _ d _ dd; ~ d<j> = _ 1 r _ r 1 ' . d r o r Q * d<|> 1 d r r_ d* r=r. r o > d r r o v o C O S a ' d t - VoSina _ . - - — — — — = t a n a r=r v o C 0 S a o (3.25) F o l l o w i n g Hughes and R o j a n s k y [ 4 1 ] , a p p r o x i m a t e s o l u t i o n s o f t h i s d i f f e r e n t i a l e q u a t i o n a r e , f o r a n g l e s +a and - a +a : y-, = c + (1 - c ) cos /2~<f> - - ta n a s i n /2~c|> 1 /2* -a y 9 = c + (1 - c ) cos /2~<f> + - t a n a s i n /2<j> (3.26) F o r two e l e c t r o n s o f equal v e l o c i t y , one e n t e r i n g a t an a n g l e +a and the o t h e r a t -a, t h e p o s i t i o n o f r e f o c u s o c c u r s where t h e two o r b i t s c r o s s , i . e . y-| = y 2 , i n whi c h c a s e t h e term t a n a s i n /2<t> v a n i s h e s and Jit? = 0, T T , 2TT, . . . . e t c . The o r b i t s c r o s s f o r t h e f i r s t t i m e a t <fr = + e = i f / ^ " = 127° 17' (3.27) Note t h a t t h i s a n g l e i s inde p e n d e n t o f a 32. t > A y = ( c 1 - c ) (1 - cos /2(f)) (3.28) The second f a c t o r t o be i n v e s t i g a t e d i s t h e s p a t i a l s e p a r a t i o n o f two e l e c t r o n s , e n t e r i n g n o r m a l l y but w i t h s l i g h t l y d i f f e r e n t v e l o c i t i e s . When a = 0 y-j = c + (1 - c ) cos /2<f> y 2 = c' + (1 - c') cos /2<()] The s e p a r a t i o n o f t h e i r o r b i t s ( i . e . t h e d i s p e r s i o n ) w i l l be g r e a t e s t when Ay i s a maximum, i n w h i c h c a s e = - (c - c') /2 s i n /2<fr = 0 (3.29) T h i s a l s o g i v e s = T T / / 2 = 127° 17'. T h i s t r e a t m e n t shows t h a t t h e a n g l e 127° 17' i s t h e optimum p o s i t i o n t o i n t e r c e p t t h e e l e c t r o n beam i n a c y l i n d r i c a l e l e c t r o s t a t i c a n a l y s e r . The r e s o l v i n g power, d g , i s d e f i n e d as r Q - r , where r Q i s t h e r a d i u s o f t h e c i r c u l a r p a t h i n w h i c h an e l e c t r o n o f v e l o c i t y V w i l l t r a v e l , w h i l e r i s t h e r a d i u s v e c t o r a t $ = <j>e o f t h e p a t h o f an e l e c t r o n i n c i d e n t n o r m a l l y ( i . e . a = 0) w i t h v e l o c i t y v Q . A t <j> = f e f y = c + (1 - c ) (- 1) = 2c - 1 !o = 2 c _ ^ r = ^ ^ d e = r Q _ r = v £ 2 But f r o m ( 3 . 2 4 ) , c = V / v Q and i f @ = (V - v ) / V « 1 d e = 2 6 r o * 2gr (1 - 23) = (23 - 4 g 2 ) r (3.30) 1+23 0 °= where h i g h e r powers o f 3 a r e n e g l e c t e d . The d e v i a t i o n from p e r f e c t r e - f o c u s s i n g , s g , i s t h e s e p a r a t i o n a t <(> = <() o f t h e t w i n path o f t h e e l e c t r o n s e n t e r i n g t h e e l e c t r i c f i e l d a t a n g l e s ±a w i t h r e s p e c t t o t h e normal QP, f r o m t h e p a t h o f t h e e l e c t r o n e n t e r i n g a l o n g QP, a l l e l e c t r o n s h a v i n g t h e same v e l o c i t y V. A second a p p r o x i m a t i o n t o t h e s o l u t i o n o f (3.23) has t o be 33. used. N e g l e c t i n g h i g h e r powers o f a , s e = 4 a 2 r Q / 3 (3.31) The d e v i a t i o n i s towards t h e i n s i d e o f t h e c i r c l e o f r a d i u s r . 3.3.3. Energy r e s o l u t i o n o f t h e 127° a n a l y s e r . I t i s now p o s s i b l e t o c a l c u l a t e t h e range o f v e l o c i t i e s v w h i c h can pass t h r o u g h t h e a n a l y s e r . I f 6 = (V - v)/V i s s m a l l , where V i s d e f i n e d as i n e q u a t i o n (3.12) d e = (2e - 4 e 2 ) r Q = 2 s r o (3.32) L e t s-| and s 2 be t h e h a l f - w i d t h s o f t h e e n t r a n c e and e x i t s l i t s r e s p e c t i v e l y , t h e n t h e i n t e r v a l o f r a d i a l d i s t a n c e s a r e , f o r e n t r a n c e s l i t : ( r Q - S p r Q + s ^ ; e x i t s l i t : ( r Q - s 2 , r Q + s 2 ) . C o n s i d e r an i n f i n i t e l y narrow e l e c t r o n s o u r c e p l a c e d a t r Q i n t h e e n t r a n c e s l i t . An e l e c t r o n o f v e l o c i t y V w i l l f o l l o w a c i r c u l a r p a t h o f r a d i u s r , but an e l e c t r o n o f a d i f f e r e n t v e l o c i t y w i l l have a d i f f e r e n t r a d i u s v e c t o r f a t t h e e x i t s l i t , assuming a l l e l e c t r o n s e n t e r t h e f i e l d n o r m a l l y . A t t h e edges o f t h e e x i t s l i t r - r Q = + s 2 , and f r o m (3.32) s s s y- - 2 3 ^ 2F = 1 - f = ^ v = V ( l (3.33) 0 0 0 s 2 T h e r e f o r e , e l e c t r o n s w i t h i n t h e v e l o c i t y range V (1 ± p— ) can pass o t h r o u g h w i t h equal p r o b a b i l i t y i f t h e v e l o c i t y d i s t r i b u t i o n i s assumed t o be u n i f o r m o v e r t h a t s m a l l r a n g e . T h i s d i s t r i b u t i o n i s shown as t h e s o l i d l i n e r e c t a n g l e i n F i g u r e 4b. F o r a n o t h e r s i m i l a r s o u r c e l o c a t e d a t r Q + x (where | x j < f s - j | ) i n t h e e n t r a n c e s l i t , e l e c t r o n s w i t h v e l o c i t y a) 34. r0~ s 2 x «*— r 0 +s 2 ,V B c) int. V X~+S-| F i g u r e 4. S2 v r«s—H V - ± L_v 2r0 v X = -S-j Diagram t o i l l u s t r a t e t h e c a l c u l a t i o n o f t h e energy r e s o l u t i o n o f 127° a n a l y s e r . 35. V e n t e r i n g n o r m a l l y w i l l emerge a t t h e p o i n t r Q + x i n t h e e x i t s l i t ( F i g u r e 4 a ) . To c a l c u l a t e t h e v e l o c i t i e s o f t h e e l e c t r o n s t h a t come thr o u g h a t t h e edge A, i t i s noted t h a t t h e r a d i a l d i s t a n c e o f t h e p o i n t r Q + x fr o m A i s ( r Q + x) - ( r - s 2 ) = s 2 + x. v f l s0 + x s0 + x 1 - = VA = V ( 1 " ~Tr > ( 3 ' 3 4 ) o o The r a d i a l d i s t a n c e o f t h e p o i n t r Q + x from t h e o t h e r edge B i s ( r Q + x ) - ( r Q + s 2 ) = - ( s 2 - x) and so v p s 9 - X s0 - x 1 - / - " - T r - + T r — ) ( 3 - 3 5 ) o o Thus e l e c t r o n s w i t h i n t h e v e l o c i t y r a n g e [ S0 + X S/j — X "1 (I--|F->, vo + ) 0 o J can be t r a n s m i t t e d w i t h equal p r o b a b i l i t y . The v e l o c i t y d i s t r i b u t i o n i s s t i l l a r e c t a n g l e o f base w i d t h V ( s 2 / r Q ) , but t h e c e n t r e l i n e i s d i s p l a c e d by V ( x / 2 r Q ) t o t h e low v e l o c i t y s i d e i f x> 0 ( F i g u r e 4b, d o t t e d l i n e r e c t a n g l e ) . I f x i s t h e n c o n s i d e r e d t o v a r y c o n t i n u o u s l y f r o m 0 t o s-|, t h e v e l o c i t y d i s t r i b u t i o n r e c t a n g l e s c o n t i n u e t o move towards t h e low v e l o c i t y s i d e u n t i l t h e c e n t r e o f t h e r e c t a n g u l a r d i s t r i b u t i o n i s d i s p l a c e d by V ( s - | / 2 r Q ) from V. The same h o l d s f o r t h e h i g h v e l o c i t y s i d e ( F i g u r e 4 c ) . The r e s u l t a n t d i s t r i b u t i o n can be found by a d d i n g up a l l t h e s e r e c t a n g l e s . Case 1 s-| ^ s 2 The r e s u l t a n t i s a t r i a n g l e w i t h semi-base w i d t h e q u a l t o s 1 + s 2 — 2 ^ V, w h i c h i s p r e c i s e l y t h e h a l f - w i d t h o f t h e v e l o c i t y o 36. d i s t r i b u t i o n . V 2r0 ^  V " ^ 7 " ( 3-3 6 ) Case 2. s-j > S2 The r e s u l t a n t i s a t r a p e z i u m w i t h upper and l o w e r ^ b a s e e q u a l t o s l s ? s l + s ? 2r V a n d 2r V r e s p e c t i v e l y . 0 0 The h a l f w i d t h o f t h e v e l o c i t y d i s t r i b u t i o n i s I 2 r 0 2r o J r Q A V i , s, A E i , 2s, LZ- = JL L 2 . = L (3 37) M r E r U . J / ) 0 a o_ So i f t h e w i d t h s o f t h e e n t r a n c e and e x i t s l i t s a r e e q u a l , t h e e x p r e s s i o n f o r e n ergy r e s o l u t i o n i s A E l/2 _ s l i t w i d t h _ w / 3 3 8 \ E ~ mean r a d i u s r ' ' a 0 where A E i / 2 i s t h e f u l l w i d t h a t h a l f maximum (FWHM) o f t h e energy d i s t r i b u t i o n and E g i s a n a l y s i n g energy. E l e c t r o n s o f f i n i t e e n t r a n c e a n g l e a , but i d e n t i c a l v e l o c i t i e s V, a r e not a l l f o c u s e d a t one p o i n t 2 a t <(> = <J>ej but a t p o i n t s s e p a r a t e d a t a d i s t a n c e s g = 4a r Q / 3 (Eq. (3.31)) The r e s o l u t i o n , i n c l u d i n g a n g u l a r e f f e c t s , i s t h e r e f o r e L±k-*r + W (3.39) E. r o J 3.3.4. D e f l e c t i o n v o l t a g e f o r t h e 127° a n a l y s e r . The p o t e n t i a l f u n c t i o n between two c o n c e n t r i c c y l i n d e r s o f r a d i i a and b (a < b) i s 37. V ( r ) = B l n r + C (where B, C a r e c o n s t a n t s ) (3.40) A t r = b V(b) = B l n b + C r = a V ( a ) = B I n a + C V(b ) - V ( a ) = B ln(£) P - V ( b ) - V ( a ) _ Vab . . u B " l n ( b / a ) " TnlbTiT ( 3 - 4 1 ) V . The e l e c t r i c f i e l d t i s t h e r e f o r e , tw,~\ • — l n ( b / a ) r In o r d e r f o r an e l e c t r o n w i t h v e l o c i t y V, ( k i n e t i c e n ergy = 1/2m\l = eW) t o t r a v e l i n a c i r c u l a r p a t h o f r a d i u s r Q m V 2 V 3 h o II F = — v ab e _ 2ew " r Q =? TnTBTaT ' r Q " r Q where both V a ^ and W a r e e x p r e s s e d i n v o l t s . V a b = 2W l n(b/a) (3.42) For t h e p r e s e n t e x p e r i m e n t , b = 2" a = 1", t h e n Vab = (21n2^ W = 1 , 3 9 W In o r d e r t h a t e l e c t r o n s w i t h t h e d e s i r e d e n e r g y to be a n a l y s e d w i l l t r a v e l a l o n g t h e c i r c l e w i t h r a d i u s r , t h e p o t e n t i a l d i f f e r e n c e s V(b) - V ( r Q ) and V ( r Q ) - V(a) must be t i e d at a f i x e d r a t i o (to be d e t e r m i n e d below) so t h a t V ( r Q ) = W, t h e energy at w h i c h e l e c t r o n s a r e a n a l y s e d . From (3.40) V(b) - V ( r ) = B l n b - B l n r Q = B l n ( b / r Q ) V ( r Q ) - V(a) = B l n r Q - B l n a = B l n ( r Q / a ) 38. V o u t V ( b ) - v ( r 0 ) l n ( b / r Q ) l o g ( b / r o ) V — = V ( r Q ) - V(a) = l n ( r 0 / a ) = l o g ( r 0 / a ) ( 3 ' 4 3 ) In t h e p r e s e n t e x p e r i m e n t a = 1" b = 2" r = 1.5" o v o u t 1°g( 4/3) 0 - 1 2 4 5 Y — = l o g ( 3 / 2 ) = 0TT76 * ~T 3.3.5. A n a l y s e r s and t h e space c h a r g e problem. The 127° a n a l y s e r can be used t o produce a beam o f low energy monochromatic e l e c t r o n s f r o m a t h e r m i o n i c s o u r c e . To be u s e f u l f o r most e x p e r i m e n t s r e q u i r i n g a monochromatic beam, a s e l e c t o r must be c a p a b l e o f _8 p a s s i n g c u r r e n t s o f t h e o r d e r o f ^ 10 amp w i t h an energy d i s t r i b u t i o n o f l e s s t h a n 0.1 eV FWHM. The problem a r i s e s t h a t w i t h r e l a t i v e l y h i g h c u r r e n t and low e n e r g y , t h e e l e c t r o n beam i n t h e s e l e c t o r p r o d u ces a space c h a r g e w h i c h d i s t o r t s t h e i n t e r n a l f i e l d and i n c r e a s e s t h e d i s t r i b u t i o n w i d t h . Marmet and Kerw i n [ 37] i n t r o d u c e d an i m p o r t a n t b r e a k t h r o u g h t o t h e space c h a r g e problem by r e p l a c i n g t h e f i e l d - f o r m i n g c y l i n d r i c a l m e t a l e l e c t r o d e s by a 90% t r a n s p a r e n t t u n g s t e n g r i d mesh. S o l i d m e tal p l a t e s ( c a t c h e r e l e c t r o d e s ) h e l d a t a p o s i t i v e p o t e n t i a l were p l a c e d o u t s i d e t h e g r i d s . Those e l e c t r o n s w h i c h caused space c h a r g e by r e f l e c t i o n f rom t h e s o l i d f i e l d - f o r m i n g p l a t e s a t u n d e s i r e d e n e r g i e s c o u l d t h e n pass t h r o u g h t h e g r i d s and be removed from t h e w o r k i n g r e g i o n . C o a t i n g t h e c a t c h e r e l e c t r o d e s w i t h low e l e c t r o n r e f l e c t i v i t y m a t e r i a l ( s u c h as benzene s o o t o r " e l e c t r o n v e l v e t " [ 3 7 ] ) f u r t h e r r e d u c e d t h e space c h a r g e . A b e t t e r s o l u t i o n t o t h i s space c h a r g e problem i s t o o p e r a t e t h e a n a l y s e r w i t h " v i r t u a l s l i t s " - i . e . w i t h o u t h a v i n g r e a l , p h y s i c a l s l i t s 39. a t t h e f o c a l p l a n e s . From ( 3 . 3 8 ) , i t i s noted t h a t t h e energy r e s o l u t i o n o f t h e a n a l y s e r i s i n v e r s e l y p r o p o r t i o n a l t o t h e a n a l y s i n g e n e r g y . T h e r e f o r e , e l e c t r o n s s h o u l d e n t e r t h e a n a l y s e r a t t h e l o w e s t p o s s i b l e e n e r g y , which i s u s u a l l y below t h e e nergy o f i n t e r e s t i n most e x p e r i m e n t s . To compensate f o r t h i s , a d e c e l e r a t i o n - a n a l y s i s - r e a c c e l e r a t i o n c o n f i g u r a t i o n i s a d o p t e d . T h i s i n v o l v e s t h e use o f e l e c t r o n l e n s e s . A beam o f e l e c t r o n s e n t e r s t h e p h y s i c a l s l i t p l a c e d a t t h e o b j e c t p l a n e o f t h e r e t a r d i n g l e n s w h i c h i s h e l d a t a h i g h e r p o t e n t i a l . The p h y s i c a l e n t r a n c e s l i t i s then imaged by t h e r e t a r d i n g l e n s onto t h e e n t r a n c e f o c a l p l a n e o f t h e a n a l y s e r a t a l o w e r p o t e n t i a l t o f o r m a v i r t u a l s l i t . S i m i l a r l y , the v i r t u a l e x i t s l i t a t t h e e x i t f o c a l p l a c e i s t h e image o f the p h y s i c a l s l i t p l a c e d a t t h e h i g h e r p o t e n t i a l s i d e o f t h e r e a c c e l e r -a t i n g l e n s . The advantages o f u s i n g v i r t u a l s l i t s a r e : (1) By p l a c i n g t h e p h y s i c a l s l i t s a t h i g h e r p o t e n t i a l s , e l e c t r o n s w h i c h a r e s c a t t e r e d from s l i t edges and l o s e a s i g n i f i c a n t p a r t o f t h e i r e n e r g y a r e p r e v e n t e d f r o m e n t e r i n g t h e s e l e c t o r t o c a u s e c o m p l i c a t i o n s . (2) The e l e c t r o n beam e n t e r i n g t h e a n a l y s e r can be c a r e f u l l y c o l l i m a t e d t o match th e c h a r a c t e r i s t i c s o f t h e e l e c t r o s t a t i c d e f l e c t o r . Hence unwanted e l e c t r o n s a r e r e d u c e d t o a minimum, and no s u r f a c e c o a t i n g o r g r i d i s needed t o r e d u c e t h e d e l e t e r i o u s e f f e c t s o f a l a r g e number o f e x t r a n e o u s e l e c t r o n s . The " v i r t u a l s l i t " c o n f i g u r a t i o n w i t h e l e c t r o n o p t i c s has been used w i t h many h e m i s p h e r i c a l a n a l y s e r d e s i g n s . One o f t h e p u rposes o f t h e p r e s e n t work i s t o b u i l d and t e s t a g r i d l e s s 127° a n a l y s e r u s i n g e l e c t r o n l e n s e s and v i r t u a l s l i t s . P a v l o v i c e t a l . [ 4 2 ] have r e c e n t l y r e p o r t e d a s i m i l a r d e v i c e w i t h e l e c t r o n l e n s e s but u s i n g r e a l s l i t s . I t now seems w e l l 40. e s t a b l i s h e d t h a t g r i d s a r e not r e q u i r e d f o r e f f i c i e n t o p e r a t i o n o f 127° c y l i n d r i c a l a n a l y s e r s . 41. CHAPTER IV  APPARATUS AND PERFORMANCE 4.1.The S p e c t r o m e t e r An energy s e l e c t e d beam o f e l e c t r o n s i s f o r m e d , s c a t t e r e d and a n a l y s e d i n the a p p a r a t u s shown s c h e m a t i c a l l y i n F i g u r e 5. P l a t e 1 i s a photograph o f t h e s p e c t r o m e t e r . E l e c t r o n s a r e produced i n a space c h a r g e l i m i t e d e l e c t r o n gun e m p l o y i n g an i n d i r e c t l y h e a t e d c a t h o d e . The s p e c t r o m e t e r works on the p r i n c i p l e o f v i r t u a l s l i t s a t t h e e n t r a n c e and e x i t p l a n e s o f t h e a n a l y s e r s . T h i s p r i n c i p l e was f i r s t a p p l i e d t o c i r c u l a r a p e r t u r e s and images by K u y a t t and Simpson [ 3 4 ] . We have a p p l i e d t h e s e i d e a s t o s l i t geometry. The e l e c t r o n beam forms a r e a l o b j e c t a t h i g h e nergy ( t y p i c a l l y 70 eV) wh i c h i s f o c u s s e d onto t h e f o c a l p l a n e o f t h e monochromator u s i n g a 7:1 r e t a r d i n g l e n s . S i m i l a r l e n s e s a r e l o c a t e d a t the i n p u t and e x i t o f both monochromator and a n a l y s e r . The l e n s p a r a m e t e r s , a d a p t e d t o s l i t geometry, have been t a k e n f r o m t h e c a l c u l a t i o n s o f Read [ 2 4 ] f o r c i r c u l a r a p e r t u r e two element l e n s e s . The l e n s o p e r a t i n g p o t e n t i a l s a r e found t o c o r r e s p o n d q u i t e c l o s e l y t o t h e c a l c u l a t e d v a l u e s . The l e n s e l e m e n t s c o n s i s t o f a p a i r o f r e c t a n g u l a r s l i t s 0.125" by 1", spaced 0.1251" a p a r t . The o b j e c t s l i t i s 0.010" i n w i d t h and was o r i g i n a l l y l i m i t e d t o 0.25" i n l e n g t h . However, burns on the a n g u l a r s t o p i n t h e e x i t arm o f t h e monochromator i n d i c a t e a s h a r p l i n e f o c u s o v e r t h e f u l l 1" h e i g h t o f t h e l e n s e l e m e n t s t h u s s u g g e s t i n g t h a t a l o n g s l i t may be s a t i s f a c t o r i l y t r e a t e d as a " s t a c k " o f c i r c u l a r a p e r t u r e s . A m a g n i f i c a t i o n o c c u r s i n t h e r e t a r d i n g l e n s g i v i n g a v i r t u a l image c a l c u l a t e d t o be 0.012" w i d e . The low en e r g y s i d e o f t h e l e n s i n c o r p o r a t e s a Herzog c o r r e c t i o n [ 4 3 ] m a t c h i n g i t t o the i n p u t o f t h e COLLISION CHAMBER P l a t e 1. The S p e c t r o m e t e r . 44. monochromator. The 127 d e g r e e , c y l i n d r i c a l monochromator has a mean r a d i u s o f 1.5 i n c h e s w i t h an i n t e r e l e c t r o d e a n n u l a r s p a c i n g o f 1". The h e i g h t o f the monochromator i s 4" t o m i n i m i z e end e f f e c t s . The s p e c t r o -meter i s f a b r i c a t e d from c o p p e r , w h i l e a l l s l i t s and a p e r t u r e s a r e o f molybdenum. S l i t s 2, 3, 6, 7 s e r v e as s t o p s t o l i m i t t h e a n g u l a r d i v e r g e n c e o f t h e beam. In t h i s way unwanted e l e c t r o n s a r e r e d u c e d t o a minimum and the g r i d s t r u c t u r e used i n e a r l i e r monochromators [ 3 7 ] i s not needed. To f u r t h e r r e d u c e background s c a t t e r i n g t h e s u r f a c e s o f t h e d e f l e c t i n g e l e c t r o d e s a r e c o a t e d w i t h benzene s o o t . In the e a r l y s t a g e s o f t h i s work, t a r g e t gas i s a l l o w e d t o e n t e r t h e c i r c u l a r c o l l i s i o n chamber as a q u a s i - m o l e c u l a r beam, formed by a 50V q u a r t z c a p i l l a r y a r r a y . The a n a l y s e r , i d e n t i c a l i n c o n s t r u c t i o n t o the monochromator, i s mounted on a r o t a t a b l e c i r c u l a r p l a t f o r m a l l o w i n g t h e s e l e c t i o n o f any d e s i r e d s c a t t e r i n g a n g l e between -30 and +100 degrees w i t h an a c c u r a c y o f t1/^0. An a n g u l a r r e s o l u t i o n o f < 1° ( a t h a l f maximum) i s o b s e r v e d i n agreement w i t h c a l c u l a t i o n s based on t h e geometry o f t h e s y s t e m . P l a t e s Qi»2»3>u and 5 a r e p a i r s o f h o r i z o n t a l and v e r t i c a l d e f l e c t i o n p l a t e s w h i c h t o g e t h e r w i t h t h e p a i r s o f s p l i t p l a t e s a r e used t o a l i g n the e l e c t r o n beam t h r o u g h the s p e c t r o m e t e r . The mean e l e c t r o n e nergy i n both a n a l y z e r s i s 10 eV w h i l e t h e d e s i r e d e l e c t r o n impact energy i s a p p l i e d t o t h e c o l l i s i o n chamber ( w i t h r e s p e c t t o t h e c a t h o d e ) . The p r i m a r y beam p r o f i l e and t h e e n e r g y l o s s s p e c t r u m a r e o b t a i n e d by a p p l y i n g a ramp v o l t a g e between t h e a n a l y s e r and the monochromator. A t optimum performance p r i m a r y beam i n t e n s i t i e s measured w i t h a v i b r a t i n g r e e d e l e c t r o m e t e r a t the e x i t o f the a n a l y s e r a r e a p p r o x i m a t e l y 1 0 " 1 0 amp. a t a FWHM o f ^  20 meV i n each a n a l y s e r . The vacuum chamber i s s u r r o u n d e d by a hydrogen 45. a n n e a l e d mumetal s h i e l d w i t h f i n e f i e l d t r i m m i n g i n t h e v e r t i c a l d i r e c t i o n b e i n g e f f e c t e d by a p a i r o f c o i l s . I n p r a c t i c e i t has been found t h a t t h e s p e c t r o m e t e r e x h i b i t s optimum p e r f o r m a n c e ( f o r r e s o l u t i o n and i n t e n s i t y ) w i t h a r e s i d u a l m a g n e t i c f i e l d o f ^ 200 m i l l i g a u s s p a r a l l e l t o t h e c y l i n d r i c a l a x i s . The r e a s o n f o r t h i s i s as y e t n o t f u l l y u n d e r s t o o d , a l t h o u g h i t i s p r o b a b l e t h a t t h e p r i n c i p a l e f f e c t i s an i n c r e a s e d d i s p e r s i o n i n t h e en e r g y a n a l y s e r s r e s u l t i n g i n a t y p e o f c u r v e d 'Wien f i l t e r ' . The optimum r e s o l v i n g power (0.020 eV FWHM) o b t a i n e d i s 3 t o 4 t i m e s g r e a t e r t h a n t h a t c a l c u l a t e d f o r a p u r e l y e l e c t r o s t a t i c c y l i n d r i c a l a n a l y s e r o f t h e same d i m e n s i o n s and o p e r a t e d a t t h e same mean e l e c t r o n e nergy (10 e V ) . The ma g n e t i c f i e l d p e r t u r b a t i o n o f t h e e l e c t r o n t r a j e c t o r y i n the s c a t t e r i n g chamber i s l e s s than t h e a n g u l a r r e s o l u t i o n e x c e p t a t v e r y low s c a t t e r e d e l e c t r o n e n e r g i e s . Energy l o s s s p e c t r a a r e r e c o r d e d u s i n g a channel e l e c t r o n m u l t i p l i e r and c o n v e n t i o n a l p u l s e c o u n t i n g t e c h n i q u e s . S p e c t r a a r e d i s p l a y e d d i r e c t l y on a c h a r t r e c o r d e r o r a r e a c c u m u l a t e d i n a m u l t i -c h a n n e l a n a l y s e r . A t l a r g e s c a t t e r i n g a n g l e s t h e c o u n t r a t e s a r e u s u a l l y r a t h e r l o w , r e s u l t i n g i n i n c o n v e n i e n t l y l o n g c o l l e c t i o n t i m e s f o r c o m p l e t e energy l o s s s p e c t r a . C o n s e q u e n t l y , d i f f e r e n t i a l c r o s s s e c t i o n s f o r t h e e x c i t a t i o n o f v a r i o u s s t a t e s have g e n e r a l l y been d e t e r m i n e d by s e t t i n g t h e energy l o s s t o t h e r e q u i r e d v a l u e ( u s i n g t h e f o r w a r d s c a t t e r i n g spectrum) and r e c o r d i n g t h e c o u n t r a t e as a f u n c t i o n o f a n g l e . A t each a n g l e t h e n e t c o u n t r a t e i s o b t a i n e d by background s u b t r a c t i o n . Energy l o s s i s measured u s i n g a d i g i t a l v o l t m e t e r . Energy s c a l e s have been s e t u s i n g p r o m i n e n t peaks i n t h e s p e c t r u m o r by s e t t i n g t h e e l a s t i c s c a t t e r e d peak a t E = 0. Measurements t a k e n a t d i f f e r e n t s c a t t e r i n g a n g l e s 46. c o r r e s p o n d t o d i f f e r e n t s c a t t e r i n g volumes. C o n s e q u e n t l y , t h e i n t e n s i t y o b t a i n e d a t a p a r t i c u l a r a n g l e 8 i s m u l t i p l i e d by s i n 6 t o g i v e a r e l a t i v e d i f f e r e n t i a l c r o s s s e c t i o n . The e r r o r due t o t h e s i n e c o r r e c t i o n i s ^ 1% a t 5 d egrees and becomes n e g l i g i b l e a t l a r g e r s c a t t e r i n g a n g l e s . The performance o f t h e i n s t r u m e n t has been t e s t e d by comparing w i t h p r e v i o u s e x p e r i m e n t a l and t h e o r e t i c a l e l e c t r o n s c a t t e r i n g d a t a f o r h e l i u m . LaBahn and C a l l a w a y [ 4 4 ] have c a l c u l a t e d t h e d i f f e r e n t i a l c r o s s s e c t i o n f o r e l a s t i c e l e c t r o n - h e l i u m s c a t t e r i n g a t c o l l i s i o n e n e r g i e s i n t h e range 1-95 eV and a t a s e l e c t i o n o f s c a t t e r i n g a n g l e s from 0° - 180°. F i g u r e 6 shows o u r e x p e r i m e n t a l r e s u l t s compared t o t h e c a l c u l a t e d c u r v e a t 30 eV impact energy o v e r t h e a n g u l a r range (-30° t o +100°) o f o u r i n s t r u m e n t . We have n o r m a l i z e d e x p e r i m e n t and t h e o r y a t an a n g l e o f 10 d e g r e e s . I t i s a p p a r e n t t h a t our d i s t r i b u t i o n o f e l a s t i c a l l y s c a t t e r e d e l e c t r o n s i s s y m m e t r i c a l about 0° i n d i c a t i n g t h a t no s i g n i f i c a n t , s p u r i o u s f i e l d g r a d i e n t s o c c u r i n the s c a t t e r i n g p l a n e . The d i f f e r e n t i a l c r o s s s e c t i o n cannot be d e t e r m i n e d w i t h c o n f i d e n c e a t a n g l e s l e s s than 10° due t o p o s s i b l e i n t e r f e r e n c e from m i n o r components i n the p r i m a r y e l e c t r o n beam. The l a r g e s t s t a t i s t i c a l e r r o r i s about 2%. Over t h e a n g u l a r range 10° - 45° t h e agreement o f t h e two c u r v e s i s s a t i s f a c t o r y . Beyond 45° c a l c u l a t i o n i s c o n s i s t e n t l y h i g h e r t h a n o u r e x p e r i m e n t a l v a l u e . I t i s not known how a c c u r a t e t h e c a l c u l a t i o n s a r e a t l a r g e s c a t t e r i n g a n g l e s . LaBahn and C a l l a w a y [ 4 4 ] have compared t h e i r c a l c u l a t e d v a l u e s w i t h t h e a b s o l u t e e x p e r i m e n t a l d a t a o f G i b s o n and D o l d e r [ 4 5 ] and s t a t e t h a t t h e i r c a l c u l a t i o n s a g r e e b e s t w i t h t h e s m a l l a n g l e d a t a and t e n d t o be somewhat h i g h e r t h a n e x p e r i m e n t e s p e c i a l l y a t l a r g e a n g l e s . In v i e w o f t h i s and t h e o v e r a l l agreement, a n g u l a r d i s c r i m i n a t i o n e f f e c t s i n o u r (0 ; 1 i 1 1 1 1 1 1 1 1 1 1 j 1—— -30° -20° -10° CP IO° 2 0 ° 3 0 ° 4 0 ° 5 0 ° 6 0 ° 7 0 ° 8 0 ° 9 0 ° 100° S C A T T E R I N G A N G L E 8 F i g u r e 6. E l a s t i c s c a t t e r i n g i n h e l i u m a t 30 eV. 48. i n s t r u m e n t a r e e x p e c t e d t o be s m a l l . Kuppermann e t a l [ 5 , 6 ] have i n v e s t i g a t e d t h e i n e l a s t i c d i f f e r e n t i a l s c a t t e r i n g c r o s s s e c t i o n s f o r t h e e x c i t a t i o n o f o p t i c a l l y a l l o w e d and f o r b i d d e n t r a n s i t i o n s by e l e c t r o n impact on h e l i u m . In p a r t i c u l a r t h e t r a n s i t i o n s f r o m t h e ground ( U S ) s t a t e t o 2 3 S , 2 ^ , 2 3 P and 2lP s t a t e s were s t u d i e d . We have r e p e a t e d t h e s e measurements a t 44 eV impact e nergy and s a t i s f a c t o r y agreement f o r i n t e n s i t y r a t i o s i s o b s e r v e d i n com p a r i s o n w i t h t h e d a t e o f Kuppermann e t a l . 4.2.A G a s - t i g h t , R o t a t a b l e C o l l i s i o n Chamber. In ; a l l o w i n g t h e t a r g e t gas t o e n t e r an open c o l l i s i o n r e g i o n as a q u a s i - m o l e c u l a r beam formed by a m u l t i c h a n n e l a r r a y , t h e ambient p r e s s u r e i n t h e a p p a r a t u s had t o be r a i s e d as h i g h as l x l O _ i + t o r r t o g a i n s u f f i c i e n t s e n s i t i v i t y . Under t h e s e c o n d i t i o n s a maximum c o u n t r a t e o f 600 c. p . s . was o b t a i n e d f o r e x c i t a t i o n t o t h e s t a t e o f argon (11.83 eV) a t an impact e nergy o f 70 eV and 2° s c a t t e r i n g a n g l e . The r e p l a c e m e n t o f an open c o l l i s i o n r e g i o n by a gas t i g h t chamber ( w i t h t h e e x c e p t i o n o f e n t r a n c e and e x i t s l i t s ) n o t o n l y a l l o w s a h i g h e r t a r g e t p r e s s u r e but a l s o p e r m i t s a l o w e r ambient p r e s s u r e i n the r e s t o f t h e s p e c t r o m e t e r . T h i s i s o f p a r t i c u l a r i m p o r t a n c e w i t h r e g a r d t o t h e e f f e c t i v e e l i m i n a t i o n o f s c a t t e r i n g by gas m o l e c u l e s i n t h e e l e c t r o n a n a l y s e r s . In e x i s t i n g e l e c t r o n s p e c t r o m e t e r s gas t i g h t c o l l i s i o n r e g i o n s have u s u a l l y been a c h i e v e d e i t h e r by o b l i q u e l y s p l i t t i n g t h e c y l i n d r i c a l c o l l i s i o n chamber [ 4 6 ] r e s u l t i n g i n a c o m p l i c a t e d s c a t t e r i n g geometry o r by t h e use o f b e l l o w s [34,35,47] w h i c h may e x h i b i t p r oblems o f f l e x i b i l i t y and a l s o o f a ch a n g i n g i n s i d e c o n f i g u r a t i o n w i t h r e g a r d t o main beam r e f l e c t i o n s . Foo e t a l . [ 4 8 ] were a b l e t o a v o i d t h e s e problems by u s i n g 49. a c o l l i s i o n chamber c o n s i s t i n g o f i n t e r l e a v i n g vanes but t h i s arrangement l i m i t e d t h e s c a t t e r i n g a n g l e t o a range o f -1° t o +70°. L a r g e r v a r i a t i o n would have c a u s e d o v e r l a p w i t h t h e e n t r a n c e s l i t and l o s s o f gas t i g h t n e s s . The f o l l o w i n g s e c t i o n d e s c r i b e s t h e d e s i g n and c o n s t r u c t i o n o f a gas t i g h t c o l l i s i o n chamber t o r e p l a c e t h e m o l e c u l a r beam t a r g e t used i n the e a r l i e r s t a g e s o f t h i s work. A v a r i a t i o n i n s c a t t e r i n g a n g l e f r o m -30° t o +100° i s a c h i e v e d and i s l i m i t e d o n l y by t h e s i z e and s p a c i n g o f t h e e l e c t r o n a n a l y s e r s . T h i s c o l l i s i o n chamber a l o n e i s shown i n P l a t e 2 and F i g u r e 7 shows a s c h e m a t i c d i a g r a m o f i t . The h a t c h e d p o r t i o n s a r e s l o t s ( 0.2" w i d e ) c u t i n a c y l i n d r i c a l b r a s s s h e l l . I n c i d e n t e l e c t r o n s e n t e r t h r o u g h a molybdenum s l i t , A, (0.01" x 0.2").which i s f i x e d t o t h e main c y l i n d e r . The e x i t s l i t , B, (0.10" x 0.2") i s mounted on a m o v a b l e c a r r i a g e , C, t r a v e l l i n g on r a i l s c o n c e n t r i c w i t h t h e main c y l i n d e r above and below t h e s l o t . T h i s c a r r i a g e i s c o u p l e d d i r e c t l y t o t h e t u r n t a b l e so t h a t i t moves s y n c h r o n o u s l y w i t h t h e a n a l y s e r used f o r d e t e c t i o n o f t h e s c a t t e r e d e l e c t r o n s . A l o n g s t r i p o f b r a s s shim s t o c k (0.004" t h i c k n e s s x 0.75" w i d t h ) i s s o l d e r e d t o t h e back o f t h e c a r r i a g e , C, and f i t s s n u g l y i n t o a t h i n gap between the r a i l s and t h e main c y l i n d e r . The b r a s s shim a c t s as a b l i n d w h i c h e f f e c t i v e l y c l o s e s t h e s l o t w herever t h e e x i t s l i t may be w i t h i n the a n g u l a r range (-30° t o +100°). S m a l l c u t s , D and E a r e made i n t h e r a i l s t o a l l o w t h e shim t o s l i d e o u t . S u i t a b l e s t o p s and g u i d e s a r e i n s t a l l e d on e i t h e r s i d e so t h a t the shim c u r l s backwards t h u s p r e v e n t i n g i t f r o m c o n t a c t i n g o t h e r p a r t s o f t h e s p e c t r o m e t e r on r o t a t i o n . Gas can now o n l y e f f e c t i v e l y l e a k t h r o u g h t h e two s l i t s ( 0 . 0 1 " x 0.2") and t h i s r e s u l t s i n a 2 0 0 0 - f o l d r e d u c t i o n SCATTERED ELECTRONS COUPLING TO "TURNTABLE BRASS SHIM RAIL INCIDENT ELECTRONS O N E I N C H F i g u r e 7. I t o t a t a b l e , g a s - t i g h t c o l l i s i o n chamber. o P l a t e 2. The g a s - t i g h t , r o t a t a b l e c o l l i s i o n chamber. 52. i n open a r e a o f t h e c o l l i s i o n r e g i o n . U s i n g t h i s c o l l i s i o n chamber a c o u n t r a t e o f 5000 c.p.s. was o b t a i n e d f o r e x c i t a t i o n t o t h e s t a t e o f a r g o n ( a t 70 eV, 2°) w h i l e t h e ambient p r e s s u r e i n t h e vacuum chamber was 1 x 1 0 " 5 t o r r . T h i s r e p r e s e n t s an o r d e r o f magnitude i n c r e a s e i n s i g n a l w i t h a t e n - f o l d d e c r e a s e i n . a m b i e n t p r e s s u r e when compared w i t h the p r e v i o u s arrangement w i t h a p s e u d o - m o l e c u l a r beam. The re d u c e d gas c o n s u m p t i o n i s o f i m p o r t a n c e where s m a l l o r e x p e n s i v e samples a r e used. F u r t h e r m o r e t h e p r e s e n c e o f a narrow e x i t s l i t i n t h e c o l l i s i o n chamber d e c r e a s e s t h e a c c e p t a n c e a n g l e o f t h e e l e c t r o n a n a l y s e r f o r s c a t t e r e d e l e c t r o n s . U s i n g t h e m o l e c u l a r beam t h e w i d t h o f an i n e l a s t i c -a l l y s c a t t e r e d peak i s about 0.020 eV w i d e r t h a n t h e p r i m a r y t r a n s m i t t e d peak due t o t h e d i f f e r e n c e i n a c c e p t a n c e a n g l e s . However, w i t h t h e narrow e x i t s l i t i n t h e new c o l l i s i o n chamber, t h e w i d t h s o f t h e two peaks a r e now s i m i l a r . The 130 degree a n g u l a r range i n t h e p r e s e n t s y s t e m i s a l i m i t s e t by t h e g e o m e t r i c a l arrangement and p h y s i c a l s i z e o f t h e o t h e r p a r t s o f t h e e x i s t i n g s p e c t r o m e t e r . I f t h e d i s t a n c e between t h e c o l l i s i o n chamber and t h e en e r g y s e l e c t o r s were t o be i n c r e a s e d and/or t h e geometry and p h y s i c a l s i z e o f t h e a n a l y s e r s changed, t h i s d e s i g n o f c o l l i s i o n chamber would a l l o w an a n g u l a r v a r i a t i o n a t l e a s t t w i c e as g r e a t . Such a d e s i g n s h o u l d p r o v e u s e f u l n o t o n l y i n e l e c t r o n s c a t t e r i n g but a l s o f o r pho t o -e l e c t r o n a n g u l a r d i s t r i b u t i o n s t u d i e s as w e l l as i n o t h e r t y p e s o f cha r g e d p a r t i c l e s p e c t r o s c o p y . 4 . 3 . E l e c t r o n i c s and E l e c t r o n D e t e c t i n g System. The v o l t a g e s u p p l i e s and c o n t r o l c i r c u i t r y f o r t h e p r e s e n t e l e c t r o n 53. s p e c t r o m e t e r a r e shown i n F i g u r e 8. A l m o s t a l l v o l t a g e s a r e p r o v i d e d by low impedance r e g u l a t e d power s u p p l i e s . R i p p l e p r o b l e m s , f r e q u e n t l y e n c o u n t e r e d when many commercial power s u p p l i e s a r e o p e r a t e d i n a f l o a t e d mode above ground p o t e n t i a l can be s o l v e d by al w a y s f l o a t i n g t h e power s u p p l i e s on t o p o f o t h e r power s u p p l i e s , n e v e r on t o p o f a r e s i s t o r network. In t h i s way, t h e r e i s no problem i f power s u p p l i e s a r e o b t a i n e d w h i c h a r e d e s i g n e d f o r f l o a t i n g o p e r a t i o n and have v e r y low e f f e c t i v e impedances. R i p p l e o c c u r s when power s u p p l i e s a r e f l o a t e d on a moderate impedance ( s a y , a r e s i s t o r n e t w o r k ) coming t h r o u g h t h e c i r c u i t formed by the t r a n s f o r m e r i n t e r w i n d i n g c a p a c i t a n c e ^ i n s e r i e s w i t h t h e 60 Hz power l i n e and t h e impedance from t h e power s u p p l y t o ground. A l e s s e f f e c t i v e s o l u t i o n i s t o p l a c e a l a r g e c a p a c i t o r a c r o s s t h e impedance t o g r o u n d , e.g. between one t e r m i n a l F o f t h e f i l a m e n t power s u p p l y and ground as i n t h e c i r c u i t d i a g r a m . However, t h i s u n f o r t -u n a t e l y produces s e v e r e damping e f f e c t s when v o l t a g e s a r e r a p i d l y scanned. The use o f b a t t e r i e s i s a s i m p l e and i n e x p e n s i v e s o l u t i o n w i t h t h e a v a i l a b i l i t y o f l o n g l i f e m e rcury and a l k a l i n e c e l l s as w e l l as r e -c h a r g e a b l e b a t t e r i e s . However, one drawback o f t h i s i s t h a t b a t t e r i e s do not have l o n g term s t a b i l i t y and t h e v o l t a g e s tend t o d r i f t when da t a a c q u i s i t i o n o v e r a l o n g p e r i o d o f t i m e i s r e q u i r e d . The c o n t r o l c i r c u i t r y shown i s d e s i g n e d so t h a t a l l power s u p p l i e s a r e e i t h e r grounded one s i d e o r f l o a t e d d i r e c t l y on t o p o f a n o t h e r power s u p p l y . V a r i a b l e v o l t a g e s a r e o b t a i n e d by remote r e s i s t a n c e programming o f l K n per v o l t . The v a l u e o f t h e programming r e s i s t o r s a r e shown i n the b l o c k r e p r e s e n t i n g t h e power s u p p l y . V o l t a g e a d j u s t m e n t s a r e p o s s i b l e u s i n g v e r n i e r - d r i v e p o t e n t i o m e t e r s . The cathode o f t h e e l e c t r o n gun. i s F i g u r e 8. The c o n t r o l c i r c u i t d iagram. 55. h e l d a t t h e p o t e n t i a l o f t h e f i l a m e n t c e n t r e - t a p ( F C T ) , w h i c h i s n e g a t i v e w i t h r e s p e c t t o ground. The p o l a r i t y o f t h e g r i d v o l t a g e o f the e l e c t r o n gun i s n o r m a l l y k e p t n e g a t i v e w i t h r e s p e c t t o the c a t h o d e , but i t can be s w i t c h e d o v e r t o p o s i t i v e p o l a r i t y i f n e c e s s a r y . The v o l t a g e s t o t h e d e f l e c t o r p l a t e s Q 1 t o 5 and t h e s p l i t p l a t e s (see F i g u r e 5) a r e s u p p l i e d by du a l power s u p p l i e s and g a n g e d - p o t e n t i o m e t e r s w i r e d so t h a t t h e v o l t a g e can be scanned c o n t i n u o u s l y from p o s i t i v e t o n e g a t i v e w i t h o u t a r e v e r s i n g s w i t c h . The p o l a r i t y o f t h e i n n e r - e l e c t r o d e s o f t h e s e l e c t o r and t h e a n a l y s e r a r e p o s i t i v e w i t h r e s p e c t t o t h e i r c o r r e s p o n d i n g o u t e r - e l e c t r o d e s . The f o c u s v o l t a g e s (Focus 1 & 2) a r e p r o v i d e d by du a l power s u p p l i e s t r a c k e d i n t h e r a t i o o f 5 : 7 and t h e c e n t r e - t a p s a r e t i e d t o t h e l o w - p o t e n t i a l s i d e o f the l e n s e lements so t h a t e l e c t r o n s t o be a n a l y s e d t r a v e l a l o n g t h e c o r r e c t p a t h (see s e c t i o n 3.3.4.). The c o l l i s i o n chamber (CC) can be s w i t c h e d e i t h e r t o g r o u n d , t o a v a r i a b l e power s u p p l y o r t o a K e i t h l e y e l e c t r o m e t e r t o measure t h e e l e c t r o n c u r r e n t coming out o f t h e s e l e c t o r . Many wo r k e r s o p e r a t e 127° s e l e c t o r s by s c a n n i n g t h e v o l t a g e a c r o s s t h e r a d i a l p l a t e s . T h i s changes t h e f i e l d s t r e n g t h f o r d i f f e r e n t e n e r g y e l e c t r o n s and produces a r e s o l v i n g power which i s a f u n c t i o n o f e l e c t r o n energy. A f u r t h e r d i s a d v a n t a g e i s t h a t t h e e l e c t r o n e n e r g y must be c a l c u l a t e d from t h e g e o m e t r i c d i m e n s i o n s o f t h e a n a l y s e r as i n s e c t i o n 3.3.4 and t h i s may e x p l a i n t h e s c a t t e r o f i o n i z a t i o n p o t e n t i a l v a l u e s [49] o b s e r v e d i n PES. A more s a t i s f a c t o r y p r o c e d u r e i s t o r e a c c e l e r a t e a l l e l e c t r o n s w h i c h have l o s t e n e r g y due t o c o l l i s i o n t o t h e same en e r g y p r i o r t o t h e i r e n t r y t o t h e a n a l y s e r which i s t h e n o p e r a t e d a t a f i x e d e nergy r e s o l u t i o n . T h i s i s a c c o m p l i s h e d by a p p l y i n g a v a r i a b l e b u c k i n g 56. and s c a n n i n g v o l t a g e ( F i g u r e 8) between S ( t h e h i g h - p o t e n t i a l e l ement o f l e n s 1) w h i c h i s h e l d a t ground p o t e n t i a l and A ( t h e h i g h - p o t e n t i a l element o f l e n s 2 ) . These two el e m e n t s a r e shown c r o s s - h a t c h e d i n F i g u r e 5. T h i s v o l t a g e can be scanned o v e r a range o f 10 v o l t s by a m o t o r - d r i v e n p o t e n t i o m e t e r programming a power s u p p l y o r swept by an e l e c t r o n i c ramp, a m p l i f i e d by t h e ramp a m p l i f i e r , o p e r a t i n g s y n c h r o u s l y w i t h a m u l t i c h a n n e l a n a l y s e r . A c l o s e d - e n d c h a n n e l e l e c t r o n m u l t i p l i e r ( M u l l a r d B419AL) i s used f o r e l e c t r o n d e t e c t i o n . P r i o r t o measurement o f s c a t t e r e d e l e c t r o n s , i t i s n e c e s s a r y t o m o n i t o r t h e main beam and tune t h e s p e c t r o m e t e r . The i n t e n s i t y o f t h e main beam 1 0 " 1 0 amp) i s t o o i n t e n s e f o r t h e c h a n n e l t r o n to d e t e c t u s i n g t h e c o u n t i n g mode. I n s t e a d , t h e c h a n n e l t r o n i s used as a Faraday cage c o u p l e d t o a v i b r a t i n g r e e d e l e c t r o m e t e r f o r t h i s p u r p o s e . To d e t e c t t h e s c a t t e r e d e l e c t r o n s , t h e c h a n n e l t r o n i s used i n t h e c o u n t i n g mode f o r b e t t e r s e n s i t i v i t y . A p o s i t i v e h i g h v o l t a g e o f ^ 3KV i s a p p l i e d t o i t s o u t p u t w h i l e t h e i n p u t i s h e l d a t about 100 V above ground. S i n c e o n l y r e l a t i v e c r o s s s e c t i o n a r e measured, t h e a c t u a l v a l u e f o r d e t e c t i o n e f f i c i e n c y i s not i m p o r t a n t and no c a l i b r a t i o n has been made. The c o u n t i n g equipment i s c o n v e n t i o n a l , c o m p r i s i n g o f a p r e a m p l i f i e r , an a m p l i f i e r and d i s c r i m i n a t o r . A s c a l e r , r a t e m e t e r o r m u l t i c h a n n e l a n a l y s e r may be used as o u t p u t d e v i c e . 4.4.Vacuum System and Gas H a n d l i n g . A p i c t u r e o f the complete e x p e r i m e n t a l arrangement i s shown i n P l a t e 3. The vacuum chamber h o u s i n g t h e e l e c t r o n s p e c t r o m e t e r c o n s i s t s o f an a l u m i n i u m tube 16" i n h e i g h t and 16" i n o u t s i d e d i a m e t e r . The w a l l i s 1 / 2 " t h i c k and both open ends a r e p o l i s h e d . T h i s t u b e s i t s on a v i t o n 0 - r i n g ( w i t h o u t g r e a s e ) i n a groove c u t i n a 17" d i a m e t e r a l u m i n i u m base P l a t e 3. The complete e x p e r i m e n t a l arrangement. 58. f l a n g e on w h i c h t h e e l e c t r o n s p e c t r o m e t e r i s l o c a t e d . The t o p o f t h e chamber i s c l o s e d w i t h an a l u m i n i u m l i d c a r r y i n g an a i r i n l e t v a l v e and an i o n i z a t i o n guage head. The vacuum s e a l i s e f f e c t e d by a v i t o n 0 - r i n g h e l d i n a groo v e c u t i n t h e l i d . S i n c e n e i t h e r screws n o r b o l t s a r e u s e d , t h e vacuum chamber i s e a s i l y demountable. When b a k i n g i s n o t n e c e s s a r y t h i s t y p e o f system i s v e r y c o n v e n i e n t , p a r t i c u l a r l y i f f r e q u e n t a c c e s s t o t h e s p e c t r o m e t e r i s r e q u i r e d ( e . g . r e p l a c i n g guns, c l e a n i n g s l i t s e t c . ) . A t r a n s p a r e n t p l e x i g l a s s window ( h e l d by b o l t s and a v i t o n 0 - r i n g ) on one s i d e o f t h e chamber a l l o w s d i r e c t o b s e r v a t i o n o f t h e s c a t t e r i n g a n g l e . E l e c t r i c a l c o n n e c t i o n s a r e made v i a c e r a m i c o c t a l - s e a l s o r f e e d - t h r o u g h s s o l d e r e d i n t o b r a s s f l a n g e s w h i c h a r e t h e n b o l t e d on t o t h e a l u m i n i u m base f l a n g e and s e a l e d w i t h v i t o n 0 - r i n g s . The vacuum i s produced by a NRC 6" d i f f u s i o n pump ( u s i n g C o n v a l e x 10 o i l ) and r o t a r y pump arrangement w i t h a l i q u i d n i t r o g e n c o l d t r a p and wat e r b a f f l e between t h e main chamber and t h e d i f f u s i o n pump. The t y p i c a l vacuum w i t h o u t gas sample i n t h e c o l l i s i o n chamber i s ^  3 x 1 0 ~ 7 t o r r as measured by a Vecco i o n i z a t i o n gauge. A d u a l i n l e t system a l l o w i n g m i x i n g o f gases has been c o n s t r u c t e d . One s y s t e m , f o r c o r r o s i v e gases and o r g a n i c c h e m i c a l s , i s made up o f s t a i n l e s s s t e e l t u b e s and v a l v e s w i t h t e f l o n s e a l s w h i l e t h e o t h e r system f o r n o n - c o r r o s i v e g a s e s , c o n s i s t s o f b r a s s p a r t s w i t h v i t o n 0 - r i n g s . The gas f l o w i s r e g u l a t e d by a Granv.il 1e;-Phi 11 i p s s e r i e s 203 v a r i a b l e l e a k , w h i c h can be bypassed i f l o w ; v o l a t i l i t y l i q u i d s o r s o l i d s a r e s t u d i e d . A i l i q u i d n i t r o g e n c o l d t r a p between t h e main m a n i f o l d o f t h e s a m p l i n g system and t h e r o t a r y pump p r e v e n t s c h e m i c a l s from g e t t i n g i n t o t h e pump o i l . 59. CHAPTER V  OPTICALLY FORBIDDEN TRANSITIONS 5 . 1 . O p t i c a l S e l e c t i o n R u l e s . There a r e s e v e r a l o p i n i o n s as t o t h e d e f i n i t i o n o f a l l o w e d and f o r b i d d e n t r a n s i t i o n ; t he f o l l o w i n g i s a p r a c t i c a l t e r m i n o l o g y s u g g e s t e d by G a r s t a n g [ 5 0 ] : In a t o m i c s p e c t r o s c o p y , a l l t r a n s i t i o n s w h i c h v i o l a t e t h e r i g o r o u s s e l e c t i o n r u l e s f o r e l e c t r i c d i p o l e r a d i a t i o n i n f r e e atoms a r e termed f o r b i d d e n t r a n s i t i o n s . T h i s c a t e g o r y i n c l u d e a l l m a g n e t i c d i p o l e and e l e c t r i c q u a d r u p o l e t r a n s i t i o n s , two quantum p r o c e s s e s , e l e c t r i c d i p o l e r a d i a t i o n e n f o r c e d by p e r t u r b a t i o n s e x t e r n a l t o t h e atom, and e l e c t r i c d i p o l e t r a n s i t i o n s caused by t h e a t o m i c n u c l e u s . E l e c t r i c d i p o l e t r a n s i t -2 I r i o n s w h i c h v i o l a t e o n l y c e r t a i n a p p r o x i m a t e s e l e c t i o n r u l e s ( e . g . 4s ;>0 - 4s4p P.j i n Ca I , w h i c h v i o l a t e s t h e r u l e AS= 0) a r e n o t c a l l e d f o r b i d d e n t r a n s i t i o n s . I n m o l e c u l a r s p e c t r o s c o p y a l l t r a n s i t i o n s w h i c h v i o l a t e any s e l e c t i o n r u l e , whether r i g o r o u s o r n o t , a r e c a l l e d f o r b i d d e n . Thus i n t e r c o m b i n -3 1 a t i o n s ( e . g . n - z) a r e i n c l u d e d among f o r b i d d e n m o l e c u l a r t r a n s i t i o n s . In p o l y a t o m i c m o l e c u l e s , t r a n s i t i o n s made p o s s i b l e by v i b r o n i c i n t e r -a c t i o n a r e a l s o i n c l u d e d among f o r b i d d e n t r a n s i t i o n s . In atoms, t h e s e l e c t i o n r u l e s f o r e l e c t r i c d i p o l e , m a g n e t i c d i p o l e and e l e c t r i c q u a d r u p o l e t r a n s i t i o n s a r e l i s t e d i n T a b l e 1, t a k e n f r o m G a r s t a n g [ 5 0 ] . The s e l e c t i o n r u l e s ( 1 ) , (2) and (3) a r e r i g o r o u s i n t h e absence o f n u c l e a r p e r t u r b a t i o n and two quantum p r o c e s s e s . R u l e (4) E l e c t r i c d i p o l e M a g n e t i c d i p o l e E l e c t r i c q u a d r u p o l e (1) AJ = 0, ± 1 (0 0) (2) AM = 0, ± 1 (3) P a r i t y change ( 4 ) One electron jump Al = ± 1 (5) AS = 0 (6) AL = 0, ± 1 (0 •<+* 0) AJ = 0, ± 1 (0 ^ 0) AM = 0, ± 1 No p a r i t y change No electron jump Al = 0 An = 0 AS = 0 AL = 0 AJ = 0, ± 1, ± 2 (0 0, 1/2 V 2 . 0 -AM = 0, ± 1, ± 2 No p a r i t y change One o r no e l e c t r o n jump Al = 0, ± 2 AS = 0 AL = 0, ± 1, ± 2 (0 +t* 0, 0 1) 1) T a b l e 1 S e l e c t i o n R u l e s i n A t o m i c S p e c t r a , 61. h o l d s o n l y when 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 s n e g l i g i b l e , and r u l e s (5) and ( 6 ) h o l d o n l y f o r LS c o u p l i n g . T r a n s i t i o n s due t o v i o l a t i o n o f a p p r o x i m a t e s e l e c t i o n r u l e s (4) - (6) a r e not u s u a l l y termed " f o r b i d d e n " . In d i a t o m i c m o l e c u l e s , t h e g e n e r a l s e l e c t i o n r u l e s f o r e l e c t r i c d i p o l e t r a n s i t i o n s a r e : (1) I f J i s t h e t o t a l a n g u l a r momentum AJ = 0, ± 1 (but n o t 0 +-> 0) T h i s i s a s t a n d a r d r u l e o f g e n e r a l v a l i d i t y f o r any a t o m i c system. (2) P o s i t i v e (+) terms combine o n l y w i t h n e g a t i v e (-) te r m s . (3) F o r i d e n t i c a l n u c l e i , symmetric ( s ) terms combine o n l y w i t h symmetric terms and a n t i s y m m e t r i c ( a ) terms w i t h a n t i s y m m e t r i c . (4) F o r n u c l e i o f e q u a l c h a r g e ( b u t n o t n e c e s s a r i l y o f equal mass) even (g) e l e c t r o n i c s t a t e s combine o n l y w i t h odd (u) e l e c t r o n i c s t a t e s . B e s i d e s t h e s e , t h e r e a r e o t h e r r u l e s w h i c h a r e v a l i d o n l y f o r c e r t a i n c a s e s o f c o u p l i n g , e.g. Hund's c a s e s ( a ) o r ( b ) . D e t a i l s can be f o u n d i n [ 5 0 ] . There a r e t h r e e t y p e s o f f o r b i d d e n t r a n s i t i o n s i n m o l e c u l e s : ( i ) Those w h i c h a r e r i g o r o u s l y f o r b i d d e n f o r e l e c t r i c d i p o l e t r a n s i t -i o n s , a r i s i n g f r o m h i g h e r m u l t i p o l e s . They a r e much weaker t h a n a l l o w e d e l e c t r i c d i p o l e t r a n s i t i o n s and i n p r a c t i c e , i t i s f o u n d t h a t o n l y , m a g n e t i c d i p o l e s and e l e c t r i c q u a d r u p o l e t r a n s i t i o n s need t o be c o n s i d e r e d . The s e l e c t i o n r u l e s a r e g i v e n i n [ 5 0 ] . ( i i ) Those w h i c h v i o l a t e a p p r o x i m a t e s e l e c t i o n r u l e s , u s u a l l y caused by s p i n - o r b i t c o u p l i n g o r r o t a t i o n a l - e l e c t r o n i c i n t e r a c t i o n . ( i i i ) Those r i g o r o u s l y f o r b i d d e n f o r f r e e m o l e c u l e s b u t w h i c h become a l l o w e d as a r e s u l t o f e x t e r n a l p e r t u r b i n g i n f l u e n c e s , such as e x t e r n a l 62. f i e l d s , c o l l i s i o n w i t h o t h e r m o l e c u l e s and a r e known as e n f o r c e d d i p o l e t r a n s i t i o n s . These u s u a l l y o c c u r i n h i g h p r e s s u r e g a s e s . F o r p o l y a t o m i c m o l e c u l e s , t h e i n t e n s i t y o f an e l e c t r o n i c band i n the s p e c t r u m i s p r o p o r t i o n a l t o t h e s q u a r e o f t h e t r a n s i t i o n d i p o l e moment. To a f i r s t a p p r o x i m a t i o n , t h i s may be c a l c u l a t e d w i t h t h e n u c l e i i n t h e i r e q u i l i b r i u m p o s i t i o n . F o r many o f t h e more s y m m e t r i c a l m o l e c u l e s , however, symmetry c o n s i d e r a t i o n s impose a z e r o v a l u e f o r t h e e q u i l i b r i u m d i p o l e moment. I n such c a s e s , weak t r a n s i t i o n s may s t i l l be o b s e r v e d . These v i b r o n i c t r a n s i t i o n s a r e due t o m i x i n g o f t h e w a v e - f u n c t i o n s o f c e r t a i n v i b r a t i o n a l s t a t e s . .During t h e s e v i b r a t i o n s , t h e d i p o l e moment w i l l have non-zero i n s t a n e o u s v a l u e s , a l t h o u g h t h e a v e r a g e v a l u e w i l l s t i l l be z e r o . V i b r o n i c i n t e r a c t i o n may a l s o g i v e a p p r e c i a b l e c o n t r i b -u t i o n s t o t h e band i n t e n s i t y o f w e a k l y a l l o w e d t r a n s i t i o n s . A n o t h e r c l a s s o f weak t r a n s i t i o n s a r i s e s from s p i n - o r b i t i n t e r a c t i o n , w h i c h a l l o w s f i n i t 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 s t a t e s o f d i f f e r e n t m u l t i p l i c i t i e s . 5 . 2 . E l e c t r o n Impact E x c i t a t i o n o f O p t i c a l l y F o r b i d d e n T r a n s i t i o n s . I t has been mentioned i n s e c t i o n 2 . 4 . t h a t o p t i c a l s e l e c t i o n r u l e s h o l d q u i t e a c c u r a t e l y f o r e l e c t r o n s c a t t e r i n g a t z e r o a n g l e and r e l a t i v e l y h i g h impact e n e r g i e s (> 100 e V ) . A t t h e s e e n e r g i e s , o p t i c a l l y f o r b i d d e n t r a n s i t i o n s a r e e i t h e r e x t r e m e l y weak o r as i n t h e c a s e o f s p i n - f o r b i d d e n t r a n s i t i o n s , u s u a l l y n o t seen a t a l l . Many o f t h e normal s e l e c t i o n r u l e s , however, can be broken by j u d i c i o u s c h o i c e o f i n c i d e n t e nergy and s c a t t e r i n g a n g l e . Through t h e mechanism o f e l e c t r o n exchange e x c i t a t i o n , low energy e l e c t r o n s ( w i t h i n a few t e n s o f e l e c t r o n v o l t s 63. o f t h e e x c i t a t i o n t h r e s h o l d ) can be q u i t e e f f e c t i v e i n c a u s i n g t r a n s i t i o n s between s t a t e s o f d i f f e r e n t s p i n m u l t i p l i c i t y , w h i c h a r e h i g h l y f o r b i d d e n i n o p t i c a l s p e c t r o s c o p y i n t h e absence o f a p p r e c i a b l e s p i n - o r b i t c o u p l i n g . T h i s i n v o l v e s t h e i n t e r c h a n g e o f t h e i n c i d e n t e l e c t r o n and a bound e l e c t r o n In a d d i t i o n , t h e p r o b a b i l i t y o f p r o d u c i n g t r a n s i t i o n s w h i c h a r e o p t i c a l l y symmetry f o r b i d d e n can be d r a m a t i c a l l y i n c r e a s e d by u s i n g low en e r g y e l e c t r o n s . 5.2.1. Energy dependence. Enhancement o f o p t i c a l l y f o r b i d d e n t r a n s i t i o n s a t l o w e r impact e n e r g i e s can be e x p l a i n e d as f o l l o w s : When t h e Born a p p r o x i m a t i o n h o l d s , t h e g e n e r a l i z e d o s c i l l a t o r s t r e n g t h from (2.28) i s f = 2Wee*/K and t h e m a t r i x , element e i s , f o r i n i t i a l and f i n a l s t a t e s , s e = o ^ l f e 1 ^ * ! ^ (5.1) z s i s t h e z- c o - o r d i n a t e (which i s t a k e n t o be t h e d i r e c t i o n o f t h e momentum t r a n s f e r v e c t o r K) o f t h e s e l e c t r o n i n t h e s c a t t e r e r . On expandi n g e as a power s e r i e s i n K, e = f j i K ) * ^ where e £ = 1, ^ l l S z ^ l ^ (5.2) Then e-j i s t h e m a t r i x element o f t h e e l e c t r i c d i p o l e moment. I f a t r a n s i t i o n i s o p t i c a l l y a l l o w e d and K i s v e r y s m a l l , = 2 W | E l | 2 (5.3) I f e-j = 0 but ££ + 0, t h e n a t s m a l l v a l u e s o f K ( n e g l e c t i n g h i g h e r o r d e r powers o f K) f 2 = 2W|e 2| 2K 2 (5.4) 2 2 2 2 S i n c e z = 1 / 3 r + (z - 1/3r ) , t h e q u a n t i t y c9 can be e x p r e s s e d as 64. T h i s i s u s u a l l y r e f e r r e d t o as t h e m a t r i x element o f t h e e l e c t r i c q u a d r u p o l e moment and any t r a n s i t i o n i n w h i c h = 0 and £2^0 has been c a l l e d an e l e c t r i c q u a d r u p o l e t r a n s i t i o n . In o p t i c a l s p e c t r o s c o p y o n l y t h e second term i n (5.5) a r i s e s i n c o n s i d e r i n g t h e i n t e n s i t y o f t h e e l e c t r i c q u a d r u p o l e t r a n s i t i o n s . There i s no o p t i c a l a n a l o g u e o f t h e f i r s t t e r m . The l ^ S -»- 2^S t r a n s i t i o n i n h e l i u m i s an example o f a t r a n s i t i o n i n w h i c h t h e second term v a n i s h e s but t h e f i r s t does n o t , w h i l e the L y m a n - B i r g e - H o p f i e l d bands o f ^ p r o v i d e an example i n which o n l y t h e f i r s t t erm v a n i s h e s . I t has been shown i n e q u a t i o n (2.27) f o r v e r y s m a l l K a t z e r o s c a t t e r i n g a n g l e and h i g h i m p a c t e n e r g y , t h e c r o s s s e c t i o n f o r d i p o l e t r a n s i t i o n s ( a d ) h = 8 £ l 2 E/W2 (5.6) Under s i m i l a r c o n d i t i o n s , f o r e l e c t r i c q u a d r u p o l e t r a n s i t i o n s ( a q ) h = 4 e 2 2 (5.7) whi c h i s i n d e p e n d e n t o f t h e i m p a c t e n e r g y . The r a t i o ( a q ) h / ( o d ) h = W 2 e 2 2 / ( 2 E e i 2 ) (5.8) i s o b v i o u s l y i n c r e a s i n g w i t h d e c r e a s e i n i m p a c t e n e r g y and hence f o r b i d d e n t r a n s i t i o n s a r e enhanced r e l a t i v e t o t h e a l l o w e d ones. The s u b s c r i p t h emphasises t h e c o n d i t i o n o f h i g h impact e n e r g i e s . A t l o w e r impact e n e r g i e s , t h e s i t u a t i o n can o n l y be d i s c u s s e d somewhat q u a l i t a t i v e l y . I f t h e e x c i t a t i o n e n e r g y o f t h e q u a d r u p o l e and the d i p o l e t r a n s i t i o n i n q u e s t i o n a r e not v e r y d i f f e r e n t from each o t h e r , the r a t i o o f t h e i r c r o s s s e c t i o n s a t low impact e n e r g i e s ( a q ) j / ( a ( j ) a is» by e q u a t i o n (2.30) q u a l i t a t i v e l y s i m i l a r t o ( F q ) ^ / ( F d ) £ , t h e r a t i o o f t h e 65. e f f e c t i v e g e n e r a l i s e d o s c i l l a t o r s t r e n g t h s . Due t o t h e l i m i t i n g t h e o r y o f g e n e r a l i s e d o s c i l l a t o r s t r e n g t h s g i v e n i n s e c t i o n 2.4, (F )„ and g *• ( F j ) ^ may n o t d i f f e r d r a s t i c a l l y f r o m t h e i r v a l u e ( F q ) h and ( F ^ ) ^ a t h i g h i m p a c t e n e r g i e s ( i . e . s u f f i c i e n t l y s m a l l K ) . A t h i g h i m p a c t e n e r g i e s F approaches t h e g e n e r a l i s e d o s c i l l a t o r s t r e n g t h f , w h i c h i n t u r n t e n d s t o t h e o p t i c a l o s c i l l a t o r s t r e n g t h s f when K ten d s t o z e r o . Thus Thus f r o m e q u a t i o n ( 5 . 8 ) , t h e r e l a t i v e enhancement o f t h e e l e c t r i c q u a d r u p o l e t r a n s i t i o n s a t l o w e r i n c i d e n t e n e r g i e s i s a g a i n e x p e c t e d . E l e c t r o n impact s p e c t r a , a t z e r o s c a t t e r i n g a n g l e and d i f f e r e n t i n i t i a l k i n e t i c e n e r g i e s , a r e u s u a l l y s t r i k i n g l y s i m i l a r as f a r as r e l a t i v e i n t e n s i t i e s o f e l e c t r i c d i p o l e a l l o w e d t r a n s i t i o n s a r e c o n c e r n e d . T h i s has been i l l u s -t r a t e d by S k e r b e l e and L a s s e t t r e [ 5 1 ] , where t h e y compared t h e i r s p e c t r a o f N 2 a t 90 eV w i t h t h a t o f G e i g e r and Sch r t t d e r [ 5 2 ] a t 25 KeV. The e f f e c t o f impact e n e r g y on r e l a t i v e i n t e n s i t i e s o f o p t i c a l l y f o r b i d d e n t r a n s i t i o n s has been d i s c u s s e d by B r i o n and O l s e n [ 5 3 ] . O p t i c a l l y f o r b i d d e n t r a n s i t i o n s become more and more p r o m i n e n t i n t h e s p e c t r a when t h e impact e n e r g y i s l o w e r e d towards t h r e s h o l d . 5.2.2. A n g u l a r dependence. Kuppermann e t a l . [ 5 , 6 ] have made e x t e n s i v e s t u d i e s o f e l e c t r o n s c a t t e r i n g by h e l i u m atoms and some s m a l l m o l e c u l e s a t low e n e r g i e s and v a r i a b l e s c a t t e r i n g a n g l e . They o b s e r v e d d i f f e r e n t a n g u l a r dependence o f e l e c t r o n s i n e l a s t i c a l l y s c a t t e r e d f r o m h e l i u m a s s o c i a t e d w i t h t r a n s i t i o n s 3 1 3 1 t o t h e 2 S, 2 S, 2 P and 2 P s t a t e s . These a n g u l a r dependence c u r v e s have 66. been used t o check t h e p e r f o r m a n c e o f t h e p r e s e n t s p e c t r o m e t e r (see s e c t i o n 4.1.). Kuppermann e t a l . [ 5 , 6 ] have proposed a q u a l i t a t i v e t h e o r e t i c a l j u s t i f i c a t i o n o f a d i f f e r e n c e i n t h e a n g u l a r dependences as f o l l o w s . The n a t u r e o f t h e i n t e r a c t i o n g i v i n g r i s e t o t h e l ^ S -> 2V t r a n s i t i o n ( o r any o p t i c a l l y a l l o w e d t r a n s i t i o n ) i s t h e c o u l o m b i c r e p u l s i o n between the i n c o m i n g e l e c t r o n and t h e a t o m i c e l e c t r o n . T h i s i s a r e l a t i v e l y l o n g - r a n g e d f o r c e and so s m a l l a n g u l a r d e f l e c t i o n s , c o r r e s p o n d i n g t o l a r g e impact p a r a m e t e r s , w i l l c o n t r i b u t e t o t h e d i f f e r e n t i a l c r o s s s e c t i o n , y i e l d i n g a s t r o n g l y : f o r w a r d - p e a k e d d i s t r i b u t i o n o f s c a t t e r e d e l e c t r o n s . On t h e o t h e r hand, f o r a s p i n exchange p r o c e s s such as t h a t 1 3 i n v o l v e d i n t h e V S 2 P t r a n s i t i o n , t h e i n c i d e n t e l e c t r o n must a p p r o a c h the t a r g e t w i t h r e l a t i v e l y s m a l l i n c i d e n t e nergy and i m p a ct p a r a m e t e r t o a l l o w t h e much s h o r t e r range exchange p r o c e s s t o o c c u r . Under t h e s e c o n d i t i o n s , t h e s c a t t e r e d e l e c t r o n p a r t l y " f o r g e t s " where t h e i n c i d e n t e l e c t r o n comes from and i s e m i t t e d more i s o t r o p i c a l l y . More q u a n t i t a t i v e l y , t h e e l e c t r o n p l u s t a r g e t s c a t t e r i n g can be t r e a t e d as i f i t were due t o an e f f e c t i v e c e n t r a l f i e l d p o t e n t i a l . S i n c e t h e r a n g e o f t h e i n t e r a c t i o n l e a d i n g t o e x c i t a t i o n v i a a d i r e c t mechanism i s much l a r g e r t h a n t h a t l e a d i n g t o e x c i t a t i o n v i a exchange, many more p a r t i a l waves c o n t r i b u t e t o t h e d i f f e r e n t i a l c r o s s s e c t i o n because t h e phase s h i f t f o r t h e nth p a r t i a l wave i s p r o p o r t i o n a l t o ( r „ „ ) 2 l + ^ a t low enough e n e r g y , where max r i s t h e e f f e c t i v e r a n g e . S i n c e t h e d i f f e r e n t i a l c r o s s s e c t i o n i s max g i v e n by ° ( M ) = ^1 J ^ + l ) n / £ ( c o s e ) | 2 (5.9) and f r o m t h e n a t u r e o f t h e Legendre p o l y n o m i a l s P 0 ( c o s e ) , t h e more 67. p a r t i a l waves t h a t a r e i n c l u d e d , t h e more s h a r p l y peaked towards e - 0° can be t h e d i f f e r e n t i a l c r o s s s e c t i o n . As a r e s u l t , i t i s e x p e c t e d t h a t t h e a n g u l a r d i s t r i b u t i o n o f e l e c t r o n s s c a t t e r e d a f t e r c a u s i n g d i r e c t e x c i t a t i o n i s more f o r w a r d peaked t h a n t h a t o f t h o s e e l e c t r o n s c a u s i n g e x c i t a t i o n v i a an exchange mechanism. T h i s i s a g e n e r a l phenomenen q u i t e i n d e p e n d e n t o f t h e s p e c i f i c atom o r m o l e c u l e b e i n g e x c i t e d . Kuppermann e t a l . [ 5 , 6 ] c l a i m e d t h a t measurements o f e l e c t r o n impact d i f f e r e n t i a l c r o s s s e c t i o n o r t h e i r r a t i o s as a f u n c t i o n o f s c a t t e r i n g a n g l e can be used t o c h a r a c t e r i s e and i d e n t i f y s i n g l e t - t r i p l e t ( s p i n -f o r b i d d e n ) t r a n s i t i o n s . F o r example, t h e 11.87 eV t r a n s i t i o n o f Ng has been d i s c u s s e d i n [ 6 ] , where a s e t o f g e n e r a l i z a t i o n s based on e m p i r i c a l r e s u l t s i s a l s o g i v e n . A f u r t h e r p o i n t t o m e n t i o n about th e a n g u l a r dependence o f i n t e n s i t y i s t h a t t h e r e l a t i v e v i b r a t i o n a l band i n t e n s i t i e s w i t h i n a g i v e n e l e c t r o n i c band a r e c o n s t a n t [ 3 5 ] . That t h e s e r e l a t i v e i n t e n s i t i e s a r e p r o p o r t i o n a l t o t h e r e s p e c t i v e Franck-Condon f a c t o r s seems t o i m p l y t h a t t h e c r o s s s e c t i o n f o r e x c i t a t i o n o f t h e n t h e l e c t r o n i c , v t h v i b r a t i o n a l s t a t e o f t h e m o l e c u l e can be e x p r e s s e d i n t h e form a n v ( E ' 9 ) ^ n v V E ' e ) ( 5 J 0 ) where G i s t h e F r a n c k Condon f a c t o r a s s o c i a t e d w i t h t h e (00) -> (nv) nv e l e c t r o n i c - v i b r a t i o n a l t r a n s i t i o n and X n ( E , e ) i s a f u n c t i o n o f e n e r g y , a n g l e and e l e c t r o n i c s t a t e . T h i s f a c t can be u t i l i z e d t o d i s t i n g u i s h peaks due t o one e l e c t r o n i c t r a n s i t i o n from t h o s e o f a n o t h e r . 5 . 3 . O p t i c a l l y F o r b i d d e n T r a n s i t i o n i n Argon and Neon. I t i s the purpose o f t h e p r e s e n t work t o i n v e s t i g a t e i n e l a s t i c 6 8 . e l e c t r o n s c a t t e r i n g by a r g o n and neon atoms as a f u n c t i o n o f energy and s c a t t e r i n g a n g l e w i t h p a r t i c u l a r r e g a r d t o t h e o p t i c a l l y i n a c c e s s i b l e s t a t e s . I t i s a l s o o f i n t e r e s t t o e x p l o r e t h e e x t e n t t o w h i c h c o r r e l a t i o n s d i s c u s s e d by Kuppermann e t a l . [ 5 , 6 ] f o r h e l i u m can be a p p l i e d t o t h e h e a v i e r r a r e g a s e s . Helium i s t h e o n l y r a r e gas i n w h i c h R u s s e l l - S a u n d e r s (L-S) c o u p l i n g i s e x h i b i t e d . . The s p i n o r b i t s p l i t t i n g w h i c h i n c r e a s e s w i t h a t o m i c w e i g h t i n t h e s e r i e s neon, a r g o n , k r y p t o n and xenon, r e s u l t s i n j - j ( o r j - 1 ) c o u p l i n g [ 5 4 ] . The m e t a s t a b l e s t a t e s ( 3 P 2 > 3 P Q ) + » o f a rgon a r e o f i n t e r e s t as energy s o u r c e s f o r Penning i o n i z a t i o n [ 5 5 , 5 6 ] and f i n d a p p l i c a t i o n i n t h e G.L.C. argon i o n i z a t i o n d e t e c t o r . The meta-s t a b l e s t a t e s have not been s p e c i f i c a l l y s t u d i e d by energy l o s s s p e c t r o s -copy a l t h o u g h a 5 0 eV spec t r u m ( a t 1 5 ° ) r e p o r t e d by L a s s e t t r e e t a l . [ 3 5 ] shows some p o s s i b l e m i n i m a l c o n t r i b u t i o n f r o m t h e s e e x c i t a t i o n s . E x c i t -a t i o n f u n c t i o n s f o r m e t a s t a b l e argon r e p o r t e d by Olmstead e t a l . [ 5 7 ] and a l s o be L l o y d e t a l . [ 5 8 ] a r e s h a r p l y peaked i n t h e r e g i o n o f 3 0 eV i n d i c a t i n g t h a t i m p a ct e n e r g i e s o f 3 0 eV s h o u l d be o p t i m a l f o r such a s t u d y w h i l e t h e h e l i u m t r i p l e t s t a t e e x p e r i m e n t s [ 5 , 6 ] s u g g e s t t h a t i t 3 3 would be u s e f u l t o l o o k a t A r ( P 2 , P Q ) e x c i t a t i o n a t l a r g e r s c a t t e r i n g a n g l e s . ? 6 7 5 E x c i t a t i o n o f t h e t y p e -ns np -*• ns np (n + l ) p i n a r g o n and neon a r e symmetry f o r b i d d e n but a r e e a s i l y o b s e r v e d by low en e r g y e l e c t r o n impact [ 3 5 , 5 3 , 5 9 ] . W i t h i n t h i s band t h e r e a r e a t o t a l o f t e n J s t a t e s [ 6 0 ] a l t h o u g h some o f t h e s e may be e f f e c t i v e l y d i s c o u n t e d s i n c e t h e y would r e q u i r e o c t u p o l e t r a n s i t i o n s . The c l o s e s p a c i n g i n each o f t h e + u s u a l l y so d e s i g n a t e d d e s p i t e s p i n o r b i t c o u p l i n g . 69. (n + 1 )s and (n + 1)p bands n e c e s s i t a t e s t h e use o f a h i g h r e s o l u t i o n e l e c t r o n monochromator and a n a l y s e r . 5 . 3 . 1 . Argon. We have l o o k e d f o r t h e p r e s e n c e o f t h e m e t a s t a b l e s t a t e s ( P 2 Q ) o f a r g o n i n t h e en e r g y l o s s s p e c t r a u s i n g l ow i m p a c t e n e r g y and l a r g e s c a t t e r i n g a n g l e as s u g g e s t e d by t h e e x c i t a t i o n f u n c t i o n [ 5 7 , 5 8 ] and a l s o by e a r l i e r e l e c t r o n s c a t t e r i n g s t u d i e s [ 6 1 , 3 5 , 5 3 , 5 9 ] . F i g u r e 9 shows t h e e n e r g y l o s s s p e c t r a o f a r g o n a t 3 0 eV f o r s e l e c t e d s c a t t e r i n g a n g l e s i n t h e range 5 ° - 2 5 ° . The e n e r g y s c a l e i s e s t a b l i s h e d w i t h r e f e r e n c e t o th e o p t i c a l l y a l l o w e d peaks [ 6 0 ] 3 P ] and 1 P ] a t 1 1 . 6 2 eV and 1 1 . 8 3 eV 3 r e s p e c t i v e l y . The P 2 l e v e l a t 1 1 . 5 5 eV f i r s t a p p e a r s as a s h o u l d e r on 3 t h e low en e r g y s i d e o f t h e P-j ( 1 1 . 6 2 eV) peak w i t h t h e i n t e n s i t y o f th e m e t a s t a b l e peak r e l a t i v e t o t h e o p t i c a l l y a l l o w e d peak i n c r e a s i n g as t h e s c a t t e r i n g a n g l e i n c r e a s e s . Two d i s t i n c t peaks a r e o b s e r v e d a t 3 l a r g e r a n g l e s . The PQ peak a t 1 1 . 7 2 eV i s much l e s s i n t e n s e t h a n t h e 3 P 2 ( a p p r o x i m a t e l y an o r d e r o f magnitude l e s s ) as has been o b s e r v e d i n Penning i o n i z a t i o n e l e c t r o n s p e c t r o s c o p y u s i n g m e t a s t a b l e a r g o n atoms [ 5 5 ] . However, ( F i g u r e 9 ) a s m a l l peak can be seen (most c l e a r l y a t 1 5 ° and 2 0 ° ) between t h e o p t i c a l l y a l l o w e d s t a t e s . The r e l a t i v e d i f f e r -e n t i a l c r o s s s e c t i o n f o r p r o d u c t i o n o f t h e P 2 s t a t e i s shown as a f u n c t i o n o f s c a t t e r i n g a n g l e i n F i g u r e 1 0 w h i c h shows a maximum between 1 0 ° and 1 5 ° and t h e n d e c r e a s e s q u i t e r a p i d l y t o 6 0 ° beyond w h i c h t h e r a t e o f d e c r e a s e i s q u i t e s m a l l . The e r r o r b a r s show t h e s t a t i s t i c a l e r r o r s i n v o l v e d . The d i f f e r e n t i a l c r o s s s e c t i o n f o r t h e P 2 s t a t e i s compared t o t h o s e f o r 1 P ] ( 1 1 . 8 3 eV) and 3 P 1 ( 1 1 . 6 2 eV) i n F i g u r e 11 70. Energy Loss eV F i g u r e 9. E l e c t r o n impact s p e c t r a f o r 3p -* 4s e x c i t a t i o n o f a t 30 eV. 71. F i g u r e 10. R e l a t i v e d i f f e r e n t i a l c r o s s s e c t i o n f o r t h e f o r m a t i o n o f m e t a s t a b l e a rgon ( 3 P 9 ) a t 30 eV. 72. SCATTERING ANGLE 9 F i g u r e 11. R e l a t i v e d i f f e r e n t i a l c r o s s s e c t i o n f o r e x c i t a t i o n t o t h e 4s s t a t e s o f a r g o n a t 30 eV. 73. ( n o t e l o g a r i t h m i c s c a l e ) . The o p t i c a l l y a l l o w e d t r a n s i t i o n s a r e , as e x p e c t e d , s t r o n g l y peaked i n t h e f o r w a r d d i r e c t i o n and d e c r e a s e m o n o t o n i c a l l y a t l a r g e r a n g l e s . The r a t i o s o f i n t e n s i t i e s o f v a r i o u s t r a n s i t i o n s t o t h o s e f o r t h e o p t i c a l l y a l l o w e d ^P-j e x c i t a t i o n a r e shown 3 1 (on a l o g s c a l e ) i n F i g u r e 12. As e x p e c t e d , t h e P^/ P^ r a t i o ( o p t i c a l 3 1 t r a n s i t i o n s ) i s e s s e n t i a l l y i s o t r o p i c . Whereas t h e V^J P^ r a t i o i n c r e a s e s by one o r d e r o f magnitude from 2° t o 30° where i t r e a c h e s a l o c a l maximum b e f o r e d e c r e a s i n g t o a f l a t minimum a t 55°. A t h i g h e r a n g l e s t h e r a t i o i n c r e a s e s s l o w l y a g a i n . T h i s b e h a v i o u r i s q u i t e d i f f e r e n t from t h a t f o r any o p t i c a l l y f o r b i d d e n t r a n s i t i o n i n h e l i u m [ 5 , 6 ] and p r e sumably r e f l e c t s t h e d i f f e r e n t c h a r a c t e r due t o j j c o u p l i n g . + 6 1 Some members o f t h e p a r i t y f o r b i d d e n m u l t i p l e t s -3p ( S Q ) -»• 5 2 -3p ( P 3 / i . )4p appear i n energy l o s s s p e c t r a a t l o w e r impact e n e r g i e s . The s p e c t r a r e p o r t e d by L a s s e t t r e e t a l . [ 3 5 ] a t 50 eV (0° and 15°) show f o u r peaks a t 13.09, 13.17, 13.30 and 13.48 eV. Each o f t h e f i r s t t h r e e bands i n v o l v e s a J = 2 t r a n s i t i o n w h i c h i s e l e c t r i c q u a d r u p o l e a l l o w e d ( d i p o l e f o r b i d d e n ) . The f o u r t h peak i n v o l v e s a s t a t e w i t h J = 0 and so has t h e same term symbol as the ground s t a t e . Such a t r a n s i t i o n , s i m i l a r t o t h e I ^ S Q 2^SQ t r a n s i t i o n i n h e l i u m , i s a l l o w e d i n e l e c t r o n i m p a c t . A t 50 eV L a s s e t t r e e t a l . [35] d i d not o b s e r v e t h e J = 1 s t a t e [60] a t 12.91 eV w h i c h has been r e p o r t e d i n t h e t h r e s h o l d spectrum o f a r g o n by B r i o n and 01 sen [ 5 3 ] . F i g u r e 13 shows t h e r e l e v a n t p a r t o f t h e e n ergy l o s s s p e c t r u m o f a rgon a t 30 eV a t s c a t t e r i n g a n g l e s from 2° t o + Two s e r i e s o f l i n e s d e s i g n a t e d n l , n l 1 o c c u r i n t h e s p e c t r a o f t h e r a r e gases l a r g e r than h e l i u m due t o t h e s p i n - o r b i t s p l i t t i n g o f t h e i o n c o r e . F o r a f u l l e r d i s c u s s i o n o f t h i s n o t a t i o n see r e f e r e n c e s 54 and 60. Ar, 3 0 eV SCATTERING ANGLE 6 90° F i g u r e 12. l i f f e r ' s n t i a l c r o s s s e c t i o n r a t i o s f o r e x c i t a t i o n t o t h e 4s s t a t e s o f argon a t 30 eV. F i g u r e 13. E l e c t r o n impact s p e c t r a f o r 3p -*• 4p e x c i t a t i o n o f argon a t 30 eV. 76. 25°. The energy s c a l e i s f i x e d u s i n g t h e J = 0 l e v e l a t 13.48 eV [ 6 0 ] . A t r a n s i t i o n i s c l e a r l y o b s e r v e d a t 12.91 eV. F i g u r e 14 shows t h e same energy l o s s s p e c t r a a t 50 eV and i t i s a p p a r e n t t h a t t h e r e l a t i v e i n t e n s i t y o f t h e 12.91 eV peak has d e c r e a s e d such t h a t i t i s b a r e l y d i s c e r n a b l e . An i n t e r e s t i n g f e a t u r e i n t h e s e s p e c t r a i s t h e b e h a v i o u r , w i t h s c a t t e r i n g a n g l e s , o f t h e r e l a t i v e i n t e n s i t y o f t h e J = 0 peak a t 13.48 eV. A t 50 eV t h e J = 0 l e v e l g i v e s t h e most i n t e n s e peak a t 2° b u t , as has a l s o been o b s e r v e d by L a s s e t t r e , [ 3 5 ] i t s i n t e n s i t y r e l a t i v e t o t h e J = 2 s t a t e s d e c r e a s e s v e r y r a p i d l y when th e s c a t t e r i n g a n g l e i s i n c r e a s e d t o 15°. However, a t h i g h e r s c a t t e r i n g a n g l e s we have o b s e r v e d t h a t t h e r e l a t i v e i n t e n s i t y o f t h e J = 0 l e v e l r i s e s a g a i n becoming comparable t o t h e J = 2 s t a t e s a g a i n a t 25°. S i m i l a r f e a t u r e s a r e o b s e r v e d a t 30 eV ( f i g u r e 13) where t h e J = 0 r e l a t i v e i n t e n s i t y d e c r e a s e s t o 10° b e f o r e i n c r e a s i n g a g a i n and becoming t h e most i n t e n s e peak i n t h e band a t 25°. The r e l a t i v e d i f f e r e n t i a l c r o s s s e c t i o n s f o r t h e e x c i t a t i o n o f s e v e r a l 4p s t a t e s o f argon a r e shown i n F i g u r e 15 a t s c a t t e r i n g a n g l e s , i n t h e range 5° - 90°. A t 30 eV t h e d i f f e r e n t i a l c r o s s s e c t i o n f o r t h e J = 0 t r a n s i t i o n (13.48 eV) shows a minimum a t about 10° b e f o r e i n c r e a s i n g r a p i d l y t o a s h a r p maximum a t 30° beyond w h i c h i t d e c r e a s e s more g e n t l y t o a minimum a t 70°. A t h i g h e r a n g l e s the c r o s s s e c t i o n r i s e s a g a i n . F o r t h e same t r a n s i t i o n a t 50 eV (see i n s e r t i n F i g u r e 15) t h e c r o s s s e c t i o n i s s h a r p l y peaked i n t h e f o r w a r d d i r e c t i o n b e f o r e d e c r e a s i n g v e r y r a p i d l y t o a near z e r o minimum between 15° and 20°. A s e c o n d , b r o a d e r maximum i s o b s e r v e d a t about 45°. A s l o w i n c r e a s e i s t h e n o b s e r v e d a t h i g h e r a n g l e s . Ar 50 eV 10° i — I — i — i — r 130 i — i — i — i — r 133 136 15° 4 .1 • V : •V :-.v.- t-J* 1 3 2 I 20° m A 25° i — r 1—I—I—I—I— T 1 130 133 136 Energy Loss eV F i g u r e 14. E l e c t r o n impact s p e c t r a f o r 3p -»• 4p e x c i t a t i o n o f a r g o n a t 50 eV. 8Ch 7 0 H SCATTERING ANGLE 9 F i g u r e 15. R e l a t i v e d i f f e r e n t i a l c r o s s s e c t i o n s f o r t h e e x c i t a t i o n t o t h e 4p s t a t e s o f a r g o n . 79. The J = 1 s t a t e a t 12.91 eV has a r e l a t i v e l y s m a l l c r o s s s e c t i o n . The a n g u l a r b e h a v i o u r , shown i n F i g u r e 15 i s q u i t e d i f f e r e n t from t h a t o f t h e J = 0 s t a t e . A f l a t maximum e x i s t s between 10° and 15°. A f t e r p a s s i n g t h r o u g h a minimum a t 45° a second s h a l l o w maximum i s o b s e r v e d a t 60° b e f o r e t h e c r o s s s e c t i o n a g a i n d e c r e a s e s s l o w l y t o 90°. T h i s a n g u l a r b e h a v i o u r r u l e s o u t t h e p o s s i b i l i t y t h a t t h e 12.91 eV peak c o u l d be due t o a n i t r o g e n i m p u r i t y . N i t r o g e n has a s t r o n g o p t i c a l l y a l l o w e d band a t 12.93 eV wh i c h i s s t r o n g l y peaked i n t h e f o r w a r d d i r e c t i o n . The r e l a t i v e d e c r e a s e i n i n t e n s i t y o f t h e 12.91 peak i n g o i n g from 30 eV t o 50 eV i s a l s o f u r t h e r e v i d e n c e t h a t t h e t r a n s i t i o n i s an o p t i c a l l y f o r b i d d e n p r o c e s s i n a r g o n . The r e l a t i v e c r o s s s e c t i o n ( F i g u r e 15) f o r t h e t r a n s i t i o n a t 13.09 eV, a l t h o u g h more i n t e n s e , shows q u a l i t a t i v e l y t h e same b e h a v i o u r as t h e J = 1 s t a t e . Two l o c a l maxima and one minimum a r e o b s e r v e d ( a t d i f f e r e n t a n g l e s from t h o s e i n t h e J = 1 p e a k ) . A c c o r d i n g t o Moore [60] t h e r e a r e two l e v e l s c l o s e t o t h i s e n e r g y , due t o J = 3 and J = 2 s t a t e s . S i n c e t h e ground s t a t e o f argon has J = 0, a t r a n s i t i o n t o t h e J = 3 s t a t e would i n v o l v e A J = 3. Such an o c t u p o l e t r a n s i t i o n m i g h t be e x p e c t e d t o be r e l a t i v e l y i m p r o b a b l e and on t h i s b a s i s we may r e g a r d t h e 13.09 eV peak as due t o a s i n g l e t r a n s i t i o n t o t h e J = 2 l e v e l . F i g u r e 16 shows (on a l o g s c a l e ) t h e r a t i o s o f t h e i n t e n s i t i e s o f th e J = 0 and J = 1 s t a t e s t o t h a t o f t h e o p t i c a l l y a l l o w e d s t a t e (11.83 e V ) . L a r g e u n d u l a t i o n s a r e o b s e r v e d i n t h e r a t i o s . S i n c e t h e d i f f e r e n t i a l c r o s s s e c t i o n f o r t h e o p t i c a l l y a l l o w e d t r a n s i t i o n i s s t r i c t l y d e c r e a s i n g maxima and minima a r e much more a c c e n t u a t e d i n t h e r a t i o p l o t and t h e y may not o c c u r a t t h e same a n g l e s as i n t h e d i f f e r e n t i a l Ar, 3 0 e V 0 0 10° 2 0 ° 3 0 ° AO° 5 0 ° 6 0 ° 7 0 ° 8 0 ° 9 0 ° SCATTERING ANGLE 0 F i g u r e 16. D i f f e r e n t i a l c r o s s s e c t i o n r a t i o s f o r e x c i t a t i o n t o 4p s t a t e s o f argon a t 30 eV. 81. c r o s s s e c t i o n s . 5.3.2. Neon. L i t t l e work has been r e p o r t e d on t h e e l e c t r o n i m p a c t e x c i t a t i o n o f neon i n c o n t r a s t t o t h e o t h e r r a r e g a s e s h e l i u m and a r g o n . B r i o n and O l s e n [ 5 3 ] have shown a t h r e s h o l d e x c i t a t i o n s p e c t r u m o f neon and Foo [4 8 ] has measured medium r e s o l u t i o n e n e r g y l o s s s p e c t r a o f neon a t 34 eV and 100 eV a t s c a t t e r i n g a n g l e s o f 0° and 45°. H i g h e r r e s o l u t i o n i s n e c e s s a r y f o r t h e s t u d y o f neon due t o t h e c l o s e l y s p a c e d e n e r g y l e v e l s . [ 6 0 ] . F i g u r e 17 shows an en e r g y l o s s s p e c t r u m o f neon we have o b t a i n e d a t 70 eV and 2° s c a t t e r i n g a n g l e . The l o w e s t e n e r g y , o p t i c a l l y a l l o w e d 5 2 s t a t e s due t o t h e -2p ( P 3 / , )3s c o n f i g u r a t i o n s a r e c l e a r l y r e s o l v e d '2 > / 2 a t 16.67 and 16.85 and t h e n e x t Rydberg s e r i e s members a t 19.69 and 19.78 eV can a l s o be seen. The f i r s t member o f t h e -2p nd s e r i e s o c c u r s a t 20.0 eV w h i l e peaks a t h i g h e r e n e r g i e s can be a t t r i b u t e d p r i m a r i l y t o 5 5 f u r t h e r s t a t e s o f t h e t y p e -2p ns and -2p nd. Ten p o s s i b l e s t a t e s e x i s t due t o t h e c o n f i g u r a t i o n s -2p ( P 3^ ^ )3p and a r e e x p e c t e d t o o c c u r i n t h e en e r g y range 18.3 eV - 19.0 eV. A broad hump and a s h a r p e r peak a r e o b s e r v e d i n t h i s r e g i o n i n F i g u r e 17. The s h a r p peak a t 18.97 eV i s due t o t h e 3 p ' ( J = 0) s t a t e w h i l e t h e broad hump encompasses e i g h t s t a t e s w i t h J v a l u e s v a r y i n g f r o m 0 t o 3. A s m a l l peak t o t h e low energy s i d e o f t h i s broad band i s j u s t d i s c e r n a b l e and may be a t t r i b u t e d t o t h e 3p(0 = 1) s t a t e a t 18.38 eV. T h i s peak a p p e a r s more p r o m i n e n t l y a t a lo w e r i m p a c t energy (36 eV ) . T h i s s t a t e i s a n a l o g o u s t o t h e 12.91 eV 3 3 l e v e l i n a r g o n ' d i s c u s s e d e a r l i e r i n t h i s paper. The ?2> PQ m e t a s t a b l e s t a t e s o f neon were n o t r e s o l v e d i n t h i s work. 3s,3s' 3p,3p' 4s,4s',3d • i i \ i i 170 180 19.0 20.0 21.0 22.0 Energy Loss eV F i g u r e 17. E l e c t r o n impact s p e c t r a o f neon a t 70 eV and 2° s c a t t e r i n g a n g l e . We have a l s o d e t e r m i n e d t h e r e l a t i v e d i f f e r e n t i a l c r o s s s e c t i o n f o r t h e w e l l r e s o l v e d 3 p ' ( J = 0) s t a t e a t 18.97 eV a t impact e n e r g i e s o f 36, 56, 80 and 100 eV ( F i g u r e 1 8 ) . A t t h e h i g h e r impact e n e r g y , 100 eV, t h e c r o s s s e c t i o n d e c r e a s e s r a p i d l y f r o m 5° t o 10°. A near z e r o minimum i s o b s e r v e d a t about 30°. A broad maximum ap p e a r s a t 50° and t h e c u r v e f a l l s t o z e r o a g a i n beyond 80°. As t h e impact e n e r g y i s d e c r e a s e d t h e c r o s s s e c t i o n d e c r e a s e s more g e n t l y f r o m 5° t o 10°. F i n a l l y a t 36 eV a maximum ap p e a r s a t 10°. I t seems l i k e l y t h a t t h e c r o s s s e c t i o n i s s h a r p l y peaked i n t h e f o r w a r d d i r e c t i o n a t h i g h impact e n e r g i e s and t h a t t h e maximum i s s h i f t i n g t o h i g h e r s c a t t e r i n g a n g l e s as th e i m p a ct energy i s r e d u c e d . The p o s i t i o n o f t h e f i r s t minimum behaves s i m i l a r l y . T h i s b e h a v i o u r was a l s o o b s e r v e d i n the c a s e o f argon (see the p r e v i o u s s e c t i o n ) where t h e c r o s s s e c t i o n f o r t h e 3 p ' ( J = 0) s t a t e was s t u d i e d a t 30 eV and 50 eV. The e r r o r b a r s a r e q u i t e l a r g e beyond t h e second maximum ( F i g u r e 18) but w i t h i n e x p e r i m e n t a l e r r o r t h e c u r v e s a t 56 eV and 80 eV s t i l l show an upward t r e n d w h i c h i s c h a r a c t e r i s t i c i n t h e c a s e o f t h e J = 0 s t a t e o f a r g o n . S t u d i e s o f t h e h e a v i e r r a r e gases may h o p e f u l l y b r i n g a b out t h e use o f t h e a n g u l a r b e h a v i o u s o f t h e c r o s s s e c t i o n t o c h a r a c t e r i z e t h e J v a l u e s o f e x c i t e d s t a t e s i n a t o m i c s p e c t r o s c o p y . The f a c t t h a t t h e c r o s s s e c t i o n o f J = 0 s t a t e s becomes more and more i s o t r o p i c as t h e impact energy i s l o w e r e d can be e x p l a i n e d by t h e c o n t r i b u t i o n o f t h e exchange mechanism r e l a t i v e t o t h a t o f d i r e c t e x c i t a t i o n . A t h i g h e r i m p a c t e n e r g i e s exchange e f f e c t s s h o u l d be s m a l l and t h e c r o s s s e c t i o n more f o r w a r d peaked so t h a t t h e h e i g h t o f t h e second maximum i s r e l a t i v e l y s m a l l . As t h e impact energy i s l o w e r e d e x c i t a t i o n v i a exchange becomes i n c r e a s i n g l y i m p o r t a n t and t h e f i r s t and second maxima become comparable i n i n t e n s i t y . 8 0° 10° 20° 30° 40° 50° 60° 70° 80° 90° SCATTERING ANGLE 9 Energy dependence o f t h e r e l a t i v e d i f f e r e n t i a l s c a t t e r i c r o s s s e c t i o n f o r t h e 3p' ( J = 0) s t a t e o f neon. 85. CHAPTER VI  MOLECULAR RYDBERG STATES 6.1.General A s p e c t s . A t y p i c a l m o l e c u l e w i t h a s e t o f o c c u p i e d v a l e n c e s h e l l m o l e c u l a r o r b i t a l s (M.O.) ty. has a c o r r e s p o n d i n g s e t o f v i r t u a l v a l e n c e s h e l l o r b i t a l s Beyond t h e v a l e n c e s h e l l , t h e r e a r e s e t s o f M.O.'s whi c h i n t h e LCAO a p p r o x i m a t i o n i s composed o f a t o m i c o r b i t a l s (A.O.) o f h i g h e r p r i n c i p a l quantum number ( t h e Rydberg A.O.'s, R * ) . These h i g h e r M.O.'s a r e more and more l i k e A.O.'s and t h e r e f o r e g i v e r i s e t o Rydberg s e r i e s o f e l e c t r o n i c s t a t e s whose l i m i t c o r r e s p o n d s t o t h e co m p l e t e removal o f t h e e l e c t r o n c o n s i d e r e d , i . e . t o an i o n i z a t i o n l i m i t o f t h e m o l e c u l e . S p e c t r o s c o p i s t s c o n t i n u e t o use a t o m i c - l i k e d e s c r i p t i o n o f the Rydberg o r b i t a l s as i f t h e c o r e p o t e n t i a l s were s p h e r i c a l s y m m e t r i c . The e nergy o f Rydberg s t a t e s formed by e x c i t a t i o n o f a s i n g l e e l e c t r o n t o a Rydberg o r b i t a l can be w e l l a p p r o x i m a t e d by t h e Rydberg f o r m u l a : where A i s t h e i o n i z a t i o n l i m i t , R i s t h e Rydberg c o n s t a n t ( = 13.61 e V ) , n i s t h e p r i n c i p a l quantum number o f t h e e l e c t r o n and <5 i s t h e Rydberg c o r r e c t i o n (quantum d e f e c t ) . F o r m o l e c u l e s b u i l t up from f i r s t row atoms, 6 i s s m a l l ( ^  0.1) f o r s t a t e s d e r i v e d f r o m nd e l e c t r o n s , somewhat l a r g e r (0.3 - 0.5) f o r np e l e c t r o n s and a p p r e c i a b l y l a r g e r (0.9 - 1.2) f o r ns e l e c t r o n s [ 6 2 ] . L i n d h o l m [ 9 ] has shown how quantum d e f e c t s can be used t o f a c i l i t a t e t h e i n t e r p r e t a t i o n o f Rydberg s e r i e s o b s e r v e d i n e l e c t r o n impact 8 6 . s p e c t r o s c o p y . T h i s method u t i l i s e s t h e a c c u r a t e v a l u e s o f i o n i z a t i o n p o t e n t i a l s t h a t have become a v a i l a b l e f r o m p h o t o e l e c t r o n s p e c t r o s c o p y . L i n d h o l m [ 9 ] d i d n o t q u i t e a g r e e w i t h t h e r a n g e o f quantum d e f e c t v a l u e s g i v e n above [ 6 2 ] and che p r e s e n t e d a t a b l e o f t y p i c a l e x p e r i m e n t a l quantum d e f e c t s f o r s m a l l m o l e c u l e s . U s i n g a t e n t a t i v e v a l u e o f quantum d e f e c t [ 9 ] , t h e energy o f the Rydberg t r a n s i t i o n can r e a d i l y be e s t i m a t e d and compared w i t h t h a t f o r an e x p e r i m e n t a l l y o b s e r v e d peak i n t h e s p e c t r u m . S i n c e t h e e l e c t r o n s i n Rydberg o r b i t a l s c o n t r i b u t e v e r y l i t t l e t o m o l e c u l a r b o n d i n g , t h e v i b r a t i o n a l s t r u c t u r e ( o r F r a n c k Condon e n v e l o p e ) a s s o c i a t e d w i t h a Rydberg e x c i t a t i o n must c l o s e l y r e s e m b l e t h e p h o t o e l e c t r o n band towards w h i c h i t would c o n v e r g e . An example i n t h e c a s e o f i s o c y a n i c a c i d HNCO has been g i v e n by R o b i n [ 6 3 ] . In an a n a l y s i s , one can u s u a l l y s t a r t w i t h a s t r o n g band a t low e n e r g y and w i t h a knowledge o f t h e i o n i z a t i o n p o t e n t i a l f r o m PES, t h e c a l c u l a t e d quantum d e f e c t can be compared w i t h t h e e x p e c t e d v a l u e s . T h i s p r o c e d u r e can o f t e n be used t o d e t e r m i n e whether t h e band i s t h e f i r s t member o f a Rydberg s e r i e s o r a v a l e n c e s h e l l t r a n s i t i o n . Term v a l u e s [63,64,65] a r e a l s o u s e f u l i n t h e i n t e r p r e t a t i o n o f e l e c t r o n i m p a c t s p e c t r a . H a r s h b a r g e r e t a l . [ 6 5 ] have d e f i n e d t h e term v a l u e o f an e x c i t e d s t a t e [ty. ,R) i n w h i c h an e l e c t r o n i s promoted from a m o l e c u l a r o r b i t a l ijj. t o R as t h e i o n i z a t i o n p o t e n t i a l o f the i/^.M.O. minus t h e if;.. -> R e x c i t a t i o n e n e r g y . W i t h o u t a p p r o x i m a t i o n , t h i s i s t h e i o n i z a t i o n p o t e n t i a l , o r t h e b i n d i n g e n e r g y , o f t h e Rydberg o r b i t a l . F o r a g i v e n p r i n c i p a l quantum number n, t h e d i s c u s s i o n o f t h e term v a l u e i s e q u i v a l e n t t o a d i s c u s s i o n o f 6 i n t h e Rydberg f o r m u l a , f o r t h e term v a l u e i s R/(n - <s) . H a r s h b a r g e r e t a l . [ 6 5 ] have a l s o f o u n d t h a t t h e t e r m v a l u e o f t h e (T|;. ,R) Rydberg c o n f i g u r a t i o n i n a g i v e n m o l e c u l e i s 87. v e r y n e a r l y i n d e p e n d e n t o f t h e o r i g i n a l o r b i t a l s i p.. I n a s e r i e s o f a l k y l a t e d compounds such as a l c o h o l s , k e t o n e s , o l e f i n s and amines, i t has been f o u n d t h a t as a l k y l a t i o n p r o c e e d s , t h e 3s te r m v a l u e d e c r e a s e s from ^ 5 eV t o a l i m i t o f 2.7 eV. The 3p and 3d term v a l u e s a r e more c o n s i s t e n t t h r o u g h o u t the a l k y l s e r i e s , w i t h v a l u e s o f a p p r o x i m a t e l y 2.5 and 1.6 eV r e s p e c t i v e l y . The unexpected f a c t t h a t i n t h e l i m i t o f l a r g e a l k y l g r o u p s , t h e 3s term v a l u e i s i n d e p e n d e n t o f t h e c e n t r a l g r o u p , has been e x p l a i n e d by Ro b i n [ 6 3 , 6 6 ] . U s i n g t h e i o n i z a t i o n p o t e n t i a l s as d e t e r m i n e d by PES, t h e bands i n the s p e c t r a can be s e p a r a t e d i n t o t h o s e w h i c h have the s p e c i f i c term v a l u e s (Rydberg t r a n s i t i o n s ) and t h o s e t h a t do n o t ( v a l e n c e s h e l l t r a n s i t i o n s ) . R o b i n [63,66] has p o i n t e d o u t t h a t p h y s i c a l l y , a m o l e c u l a r . R y d b e r g o r b i t a l i s d i s t i n g u i s h e d f r o m a v a l e n c e s h e l l o r b i t a l by i t s c o n s i d e r a b l y l a r g e r s i z e and so i t i s more s u s c e p t i b l e t o o u t s i d e p e r t u r b a t i o n s . He fou n d t h a t s p e c t r a due t o v a l e n c e s h e l l t r a n s i t i o n s , were i n d e p e n d e n t o f p r e s s u r e (up t o P = 100 atm.) whereas Rydberg t r a n s i t i o n s show an asymmetric b r o a d e n i n g t o h i g h e r f r e q u e n c y under h i g h p r e s s u r e c o n d i t i o n s . I t has a l s o been found t h a t Rydberg t r a n s i t i o n s can be e l i m i n a t e d by r u n n i n g t h e o p t i c a l s p e c t r a i n a condensed phase ( i . e . as a . s o l u t i o n o r as a p o l y c r y s t a l l i n e f i l m [ 6 7 ] ) # A n o t h e r u s e f u l c r i t e r i o n i s t h a t t h e o s c i l l a t o r s t r e n g t h per d e g r e e . o f s p a t i a l d e g e n e racy i n Rydberg t r a n s i t i o n s seems not t o exceed 0.08 i n m o l e c u l e s c o n s t r u c t e d from f i r s t row atoms. A l t e r n a t i v e l y , i n e l e c t r o n i m p a c t , a minimum s h o u l d e x i s t i n t h e g e n e r a l i s e d o s c i l l a t o r s t r e n g t h as a f u n c t i o n o f t h e sq u a r e o f momentum t r a n s f e r f o r a Rydberg t r a n s i t i o n , whereas t h a t f o r a v a l e n c e t r a n s i t i o n s h o u l d m o n o t o n i c a l l y d e c r e a s e t o z e r o w i t h t h e square o f momentum t r a n s f e r 88. [ 6 8 , 6 9 , 7 0 ] . A s t u d y o f t h e a n g u l a r b e h a v i o u r o f a t r a n s i t i o n s h o u l d t h e r e f o r e c l a r i f y an a s s i g n m e n t . 6.2.Rydberg S t a t e s o f Hydrogen C y a n i d e . The near UV o p t i c a l a b s o r p t i o n s p e c t r u m o f hydrogen c y a n i d e has been s t u d i e d by s e v e r a l a u t h o r s . H i l g e n d o r f f [ 7 1 ] o b s e r v e d a s y s t e m o f weak bands between 6.2 - 7.3 eV w h i l e H e r z b e r g and Innes [ 7 2 ] e x t e n d e d t h i s system and made a d e t a i l e d i n v e s t i g a t i o n o f t h e f i n e s t r u c t u r e o f t h e bands f o r both HCN and DCN. Four band systems have been f o u n d i n t h e r e g i o n 6.2 - 9.2 eV. The upper s t a t e s c o r r e s p o n d i n g t o two o f t h e s e a, i i i t r a n s i t i o n s a r e d e s i g n a t e d A A" and B A" [ 7 2 ] . The t h i r d band, w i t h ^ "I upper s t a t e C A' was b r i e f l y d e s c r i b e d by H e r z b e r g [ 6 2 ] and t h i s t r a n s i t i i s c l a i m e d t o be much s t r o n g e r t h a n t h e A - X and B - X t r a n s i t i o n s . The f o u r t h band has not been d i s c u s s e d and t h e symmetry o f t h e upper s t a t e D, i s not known. The vacuum UV a b s o r p t i o n spectrum o f HCN was f i r s t - s t u d i e d by P r i c e [ 7 3 ] and l a t e r by P r i c e and Walsh [ 7 4 ] . A l t h o u g h s t r o n g d i f f u s e • bands were found a t e n e r g i e s h i g h e r t h a n 11 eV no a n a l y s i s was made arid no Rydberg s e r i e s have been i d e n t i f i e d f rom o p t i c a l s p e c t r a . Thus, no s p e c t r o s c o p i c i o n i z a t i o n p o t e n t i a l i s a v a i l a b l e [ 6 2 ] , a l t h o u g h i o n i z a t i o n p o t e n t i a l s o f HCN have r e c e n t l y been d e t e r m i n e d by p h o t o e l e c t r o n s p e c t r o -scopy [ 7 5 ] . R e p o r t e d i n t h i s s e c t i o n i s t h e e l e c t r o n i m p a c t energy l o s s s p e c t r u m o f HCN (which i s c l o s e l y r e l a t e d t o t h e vacuum UV a b s o r p t i o n ) . T h i s s t u d y has a l s o been prompted by t h e work o f F r o s t e t a l [ 7 5 ] who, by co m p a r i s o n w i t h t h e p h o t o e l e c t r o n spectrum o f HCP, have pr o p o s e d a r e a s o n a b l e i n t e r p r e t a t i o n o f t h e p h o t o e l e c t r o n s p e c t r u m o f HCN. On t h i s b a s i s t h e f i r s t two i o n i z a t i o n p o t e n t i a l s o f HCN a t 1-3.61 arid 14.00 eV 89. r e s p e c t i v e l y can be used t o f a c i l i t a t e t h e i n t e r p r e t a t i o n o f t h e e l e c t r o n impact s p e c t r u m . The e l e c t r o n i c c o n f i g u r a t i o n o f HCN and o u t e r o r b i t a l e n e r g i e s o f HCN [ 7 5 ] a r e ( l a ) 2 ( 2 a ) 2 ( 3 a ) 2 ( 4 a ) 2 ( 5 a ) 2 ( H ) 4 . -14.00, -13.61 eV I t has been c l a i m e d [ 7 5 ] t h a t t h e c o m p l i c a t e d s t r u c t u r e i n t h e f i r s t p h o t o -2 e l e c t r o n band i s due t o v i b r o n i c i n t e r a c t i o n s o f t h e two i o n i c s t a t e s X Ji 2 and A i a r i s i n g f r o m t h e i o n i z a t i o n o f t h e l i r and t h e 5a e l e c t r o n s r e s p e c t i v e l y , The e l e c t r o n i m p a ct spectrum o f HCN a t 50 eV impact e n e r g y and 2° s c a t t e r i n g a n g l e ( F i g u r e 19b) s e r v e s as an example t o i l l u s t r a t e s p e c t r u m a n a l y s i s u s i n g quantum d e f e c t s and term v a l u e s as d i s c u s s e d i n t h e l a s t s e c t i o n s . On t h i s b a s i s most bands can be a r r a n g e d i n t o Rydberg s e r i e s ( T a b l e 2) u s i n g t h e i o n i z a t i o n p o t e n t i a l s o b s e r v e d by PES [ 7 5 ] . The d e r i v e d quantum d e f e c t s a r e c o n s i s t e n t w i t h t h o s e f o r s m a l l m o l e c u l e s c o n t a i n i n g H, C, N, 0 as t a b u l a t e d i n r e f . 9. I t i s a l s o n o t e d (see T a b l e 2) t h a t t h e term v a l u e s o f t h e Rydberg l e v e l s a r e e s s e n t i a l l y i n d e p e n d e n t o f t h e i n i t i a l o r b i t a l f r o m w h i c h t h e e l e c t r o n was e x c i t e d as has been o b s e r v e d i n o t h e r t y p e s o f m o l e c u l e [ 6 4 , 6 5 ] . 6.2.1. A s s i g n m e n t o f Rydberg s e r i e s . 1 TT ->- nsa We p o s t u l a t e t h e f i r s t member (n = 3) o f t h i s s e r i e s o c c u r s as two v i b r a t i o n a l bands a t 10.20 ( B ) and 10.43 eV ( C ) . The v i b r a t i o n a l s p a c i n g 2 o f about 0.23 eV compares w e l l w i t h t h e v i b r a t i o n a l s p a c i n g o f t h e X n i o n i c s t a t e , 0.228 eV o b s e r v e d i n PES [ 7 5 ] . The t e r m v a l u e o f t h e 10.20 eV ( B ) band w i t h r e s p e c t t o t h e ITT I.P. i s 3.41 eV and fr o m t h i s t h e c a l c u l a t e d quantum d e f e c t i s 1.00. U s i n g t h i s , we p r e d i c t t h e n = 4,5,6 members t o o c c u r a t about 12.09, 12.76 and 13.06 eV. Peaks a s s i g n a b l e t o A30ev, 2' CO ZD >-< Ql C D CC < >-CO LU I-\ 50 eV, 2° lTr-»-np |7TH»-nS j / . r— | i | i | r 100 eV , 10 "1 ""| 1 8 i r 9 10 II 12 ENERGY LOSS (eV) 13 90. F i g u r e 19. E l e c t r o n impact s p e c t r a o f HCN. 91. PEAK OBSERVED ENERGY(eV) TERM VALUE(eV) ASSIGNMENT CALCULATED EHERGY(eV) C A L C U L A T E : QUANTUM DEFECT B C 10.20) 10.43 / 3.41 l-rr -» 3so lir -* 3sc + v 3 1.00 D E F G 10.G4 ) 10.73 | 10.82 ) 10.88 3.36 5a 3s 5= •* 3sc + v 2 5a -*• 3sc + 2v2 5a -*• 3sa + v 3 0.99 II I 10.93 11.06 2.68 2.55 In -> 3pa lTT -*• 3pTT 0.75 0.69 J K 11.42 11.54 2.58 2.46 5a •*• 3po 5a -*• 3pn n.32 n . 4 5 . L M 11.80 11.95 1.81 1.66 l ir -> 3da In -> 3dir 0.26 0.14 N 12.07 1.54 l-rr -v 4sa 12.09 0 12.30 1.31 In -> 4sc + v 3 In 4pc In •* 4pn 12.30 12.33 12.37 P 12.48 1.52 5~ •+ 4sc 12.50 Q 12.57 1.C4 l-rr 4dc 12.64 R 12.77 1.23 • Q.84 5= •*• 4pa 5a •*• 4pn In •*• 5sc 12.72 12.76 12.76 S 12.99 0.62 1.01 In -* 5sc + v'3 5a -> 4da 12. £9 13.03 T 13.09 0.52 0.91 In ->• 6sa 5o 4dn 13.06 13.08 U 13.18 0.82 5a -*• 5sa 13.16 Respective I.P. can be obtained by adding the. term value to the t r ans i t i on energy. Table 2 Rydberg t rans i t ions in HCN. [ 92. t h e s e t r a n s i t i o n s a r e o b s e r v e d i n t h e s p e c t r u m a t 12.07 ( N ) , 12.77 (R) and 13.09 eV ( T ) . Two o t h e r peaks a t 12.30 (0) and 12.99 eV ( S ) can be a s s i g n e d as t h e n = 4 and n = 5 s t a t e s accompanied b y v i b r a t i o n a l quantum (C = N s t r e t c h ) . 5a -* nsa . S i n c e the term v a l u e s o f Rydberg l e v e l s have been o b s e r v e d t o be i n d e p e n d e n t o f t h e i n i t i a l o r b i t a l o f t h e e l e c t r o n s e x c i t e d [ 6 4 , 6 5 ] we. e x p e c t t h e 5c -> 3so t r a n s i t i o n t o o c c u r a t a b out 3.4 eV below t h e 2nd I.P. (14.00 e V ) . T h e r e f o r e , we a s s i g n t h e i n f l e x i o n a t 10.64 eV (D) t o be t h e (000) member o f t h i s band. The peak a t 10.73 eV (E) c o r r e s p o n d s t o t h e (010) member w h i l e t h e two s m a l l peaks a t 10.82 (F) and 10.88 eV (G) on the p l a t e a u f o l l o w i n g t h i s may c o r r e s p o n d t o t h e (020) and (001) members. The v i b r a t i o n a l s p a c i n g f o r v 2 and d e t e r m i n e d f r o m EIS (0.09 and 0.24 eV r e s p e c t i v e l y ) i s c o n s i s t e n t w i t h v a l u e s f o r t h e A E i o n i c s t a t e , v i z . 0.100 and 0.255 eV o b s e r v e d i n PES by F r o s t e t a l [ 7 5 ] , The quantum d e f e c t c a l c u l a t e d f r o m t h e 10.64 eV (D) t r a n s i t i o n i s 0.99 and f r o m t h i s v a l u e o f t h e quantum d e f e c t , t h e peaks a t 12.48 (P) and 13.18 eV (U) a r e a s s i g n e d t o be n = 4 and n = 5 members o f t h i s s e r i e s . The e n e r g i e s e x p e c t e d from c a l c u l a t i o n a r e shown i n T a b l e 2. V i b r a t i o n a l s t r u c t u r e accompanying t h e s e two s t a t e s i s n o t o b s e r v e d i n o u r s p e c t r u m , l i r ^ npq and npu The most i n t e n s e f e a t u r e i n t h e s p e c t r u m o c c u r s a t 11.06 eV. ( I ) I t s term v a l u e w i t h r e s p e c t t o t h e f i r s t I.P. (13.61 eV) i s 2.55 eV. ;We c a l c u l a t e t h e quantum d e f e c t t o be 0.69, w h i c h i s c o n s i s t e n t w i t h a 3p upper s t a t e . A s m a l l s t e p o c c u r s a t 10.93 eV (H) ( t e r m v a l u e 2.68) and t h i s g i v e s a quantum d e f e c t o f 0.75. The quantum d e f e c t s f o r t h e 3pa and 93. 3p-rr Rydberg l e v e l s i n t h e i s o e l e c t r o n i c m o l e c u l e N 2 a r e 0.67 and 0.60 [9 ] . I t i s r e a s o n a b l e t o assume t h a t i n HCN t h e 3pa quantum d e f e c t i s a l s o g r e a t e r t h a n t h e 3PTT quantum d e f e c t . T h e r e f o r e f e a t u r e s a t 10.93 eV (H) and 11.06 ey ( I ) a r e a s s i g n e d ITT -> 3pg and In 3pir Rydberg t r a n s i t i o n s r e s p e c t i v e l y . U s i n g t h e s e v a l u e s o f quantum d e f e c t s , t h e n = 4 members a r e e x p e c t e d a t 12.33 and 12.37 eV and t h e t r a n s i t i o n s 1 -r  ->• 4po and 1 TT -* 4pir may have c o n t r i b u t i o n s t o t h e peak a t 12.30 eV (0) p r e v i o u s l y a s s i g n e d as 1 TT -> 4scr + v 3 . The n = 5 members e x p e c t e d a t about 12.87 eV p r o b a b l y o v e r l a p w i t h o t h e r s t a t e s and a r e n o t r e s o l v e d i n t h e spe c t r u m . 5p ->- npa & np-rr By s u b t r a c t i n g t h e 3pa term v a l u e (see T a b l e 2) o f ^  2.7 eV f r o m the second I.P. (14.0 e V ) , t h e 5a'-*- 3p t r a n s i t i o n i s e x p e c t e d a t a- '11.3 eV. T h e r e f o r e t h e s t e p a t 11.42 eV ( J ) may be a s s i g n e d t o t h i s t r a n s i t i o n and t h e peak n e x t t o i t at-11.54, eV (K) i s a s s i g n e d t h e 5a •-*• 3pw t r a n s i t i o n . The two 5a -»• 4p t r a n s i t i o n s p r o b a b l y o v e r l a p and c o n t r i b u t e t o t h e peak a t 12.77 eV ( R ) . 1 TT -> nd & 5a nd Two s m a l l peaks a t 11.80 (L) and 11.95 eV (M) have t e r m v a l u e s o f 1.81 and 1.66 eV r e s p e c t i v e l y w . r . t . t h e f i r s t I.P. (13.61 e V ) . The quantum d e f e c t s c a l c u l a t e d a r e 0,26 and 0.14 r e s p e c t i v e l y and t h e s e seem t o be c o n s i s t e n t w i t h 3da and 3d?r upper s t a t e s r e s p e c t i v e l y . U s i n g t h e s e v a l u e s f o r quantum d e f e c t s , t h e f e a t u r e a t 12.57 eV (Q) i s a s s i g n e d t o t h e t r a n s i t i o n ITT 4da. The t r a n s i t i o n , 1 TT -»- 4dir, e x p e c t e d a t 12.70 eV, i s not a p p a r e n t i n t h e spe c t r u m . S u b t r a c t i n g l r 8 eV from 14.00 eV (2nd I . P . ) , t h e 5a -> 3da t r a n s i t i o n i s e x p e c t e d a t ^  12.2 eV. The spectrum a t t h i s e nergy shows no e v i d e p c e 94. o f any t r a n s i t i o n s . The 5a •> 3du t r a n s i t i o n i s e x p e c t e d a t 12.34 eV. T h i s , i f o c c u r r i n g , i s b u r i e d under t h e 12.30 eV peak (0) a s s i g n e d t o 1 IT -* 4so + v^. The 5a -> 4da and 5a -> 4dn t r a n s i t i o n s a r e e x p e c t e d a t 13.03 and 13.08 eV and t h e s e would a l s o be o v e r l a p p e d by t h e lir 5sa + and ITT -> 6sa t r a n s i t i o n s . I t i s t h e r e f o r e n o t c e r t a i n f r o m o u r s p e c t r u m whether the 5a -> nd s e r i e s a c t u a l l y makes a s i g n i f i c a n t c o n t r i b -u t i o n . 6.2.2. Dependence o f t h e s p e c t r u m on i m p a c t e n e r g y . We have s t u d i e d t h e s p e c t r a a t 100, 50 and 30 eV i m p a c t e n e r g y and 2° s c a t t e r i n g a n g l e ( F i g u r e 19a, b and c ) . The f i r s t f e a t u r e i n t h e s p e c t r a i s a broad band m a x i m i s i n g a t about 8.9 eV. T h i s band does n o t f i t any Rydberg a s s i g n m e n t and i s p r o b a b l y a v a l e n c e t r a n s i t i o n c o r r e s p o n d -i n g t o t h e D - X t r a n s i t i o n mentioned by H e r z b e r g [ 6 2 ] . The symmetry o f the upper s t a t e i s not known, nor i s t h i s t r a n s i t i o n d e s c r i b e d i n any d e t a i l . The r e l a t i v e i n t e n s i t y o f t h i s band, w i t h r e s p e c t t o the lir ->• 3s Rydberg s t a t e a t 10.20 eV, ( B ) , i n c r e a s e s as t h e i m p a c t energy i s d e c r e a s e d f r o m 100 eV t o 30 eV. (See F i g u r e 2 0 ) . T h i s i s d i f f e r e n t from th e b e h a v i o u r o f t h e r e l a t i v e i n t e n s i t i e s o f o t h e r Rydberg s t a t e s , e.g. 5a + 3sa + v 2 a t 10.73 eV ( E ) , lir + 3p-rr a t 11.06 eV ( I ) and 5o -> 3PTT a t 11.54 eV (K) w i t h r e s p e c t t o t h e lir + 3sa t r a n s i t i o n a t 10.20 eV ( B ) , i n w h i c h c a s e s t h e r e l a t i v e i n t e n s i t y i n c r e a s e s w i t h i n c r e a s i n g i m p a c t energy. ( F i g u r e 2 0 ) . T h i s i n d i c a t e s t h a t t h e energy dependence o f t h e r e l a t i v e c r o s s - s e c t i o n o f t h i s v a l e n c e s t a t e i s v e r y d i f f e r e n t from t h a t o f t h e Rydberg s t a t e s . I t a p p e a r s t h a t t h e r e l a t i v e i n t e n s i t y o f t h i s f i r s t band i n o u r spectrum shows a b e h a v i o u r w h i c h i s c h a r a c t e r i s t i c o f a f o r b i d d e n t r a n s i t i o n . I n t h e c a s e o f l i n e a r p o l y a t o m i c m o l e c u l e s w i t h U I 1 1 1 1 1 1 1 T 1 20 30 40 50 60 70 80 90 100 ELECTRON IMPACT ENERGY (eV) tn i g u r e 20. R e l a t i v e i n t e n s i t i e s o f some t r a n s i t i o n s i n the e l e c t r o n impact spectrum o f HCN. 96. a ^ E + ground s t a t e , t h e group t h e o r e t i c a l t r e a t m e n t o f Goddard e t a l . [ 7 6 ] p r e d i c t s t h e t r a n s i t i o n from t h e \ + ground s t a t e t o a z" ( l i n e a r ) upper s t a t e t o be f o r b i d d e n i n e l e c t r o n i m p a c t f o r a x i a l s c a t t e r i n g (0° o r 180° s c a t t e r i n g a n g l e ) . On t h i s b a s i s i t i s p o s s i b l e t h a t t h e D band c o r r e s p o n d s t o a l i n e a r s t a t e . From F i g u r e 19c i t can be seen t h a t t h e i n t e n s i t y o f the 8.9 eV band r e l a t i v e t o t h e ITT -* 3sa band a t 10.20 eV i n c r e a s e s v e r y r a p i d l y when t h e s c a t t e r i n g a n g l e i s i n c r e a s e d from 2 t o 10 d e g r e e s . T h i s b e h a v i o u r f u r t h e r s u p p o r t s t h e s u g g e s t i o n t h a t t h e 8.9 eV band i s due t o a f o r b i d d e n t r a n s i t i o n o f t h e t y p e d i s c u s s e d by Goddard e t a l . [ 7 6 ] . The energy l o s s r e g i o n beyond 11.6 eV shows an i n t e r e s t i n g dependence on impact energy. W h i l e a s e r i e s o f peaks a s s i g n a b l e t o Rydberg s t a t e s a r e o b s e r v e d a t 50 eV impact e n e r g y , t h e y a p p a r e n t l y have a much s m a l l e r c r o s s s e c t i o n a t an impact energy o f 30 eV. O n l y two s m a l l peaks a r e o b s e r v e d a t 12.30 and 12.53 eV on t o p o f a d e c r e a s i n g c o n t i n u u m . These two t r a n s i t i o n s may c o r r e s p o n d t o t h e ITT -* 4pTr and ITT ->• 4da t r a n s i t i o n s r e s p e c t i v e l y . On t h e o t h e r hand, when t h e impact energy i s i n c r e a s e d t o 100 eV, some o f t h e peaks become broadened and merge i n t o a broad hump. F o r example, t h e 11.95 (M) and 12.07 (N) eV peaks become a broad peak and t h e two peaks a t 12.57 eV (Q) and 12.77 (R) eV a r e n o t so d i s t i n c t l y s e p a r a t e d when t h e impact energy i s i n c r e a s e d from 50 eV t o 100 eV. In g e n e r a l , t h e r e l a t i v e i n t e n s i t y o f t h e u n d e r l y i n g continuum i n c r e a s e s a t h i g h e r i m p a c t e n e r g i e s . The b r o a d e n i n g o f some o f t h e peaks may be due t o changes i n r e l a t i v e c r o s s - s e c t i o n w i t h change i n impact energy o r due t o t h e f a c t t h a t t h e c r o s s s e c t i o n f o r p r e d i s s o c i a t i o n o f t h e m o l e c u l e s i n c r e a s e s a t a h i g h e r i m p a c t e n e r g y . As t h e i m p a c t 97. energy i s i n c r e a s e d t o approach t h e o p t i c a l l i m i t , t h e peaks may become so broad t h a t a c o m p l e t e l y d i f f u s e s p e c t r u m r e s u l t s , as has been r e p o r t e d i n o p t i c a l work [ 7 4 ] . 98. CHAPTER V I I ELECTRON IMPACT SPECTRA OF SOME ALKYL DERIVATIVES OF WATER AND RELATED COMPOUNDS 7 . 1 . I n t r o d u c t i o n . In t h i s s t u d y , t he e l e c t r o n i m p a ct e n e r g y l o s s s p e c t r a o f some a l k y l d e r i v a t i v e s o f w a t e r and r e l a t e d compounds a r e r e p o r t e d . A l t h o u g h most o f t h e s e compounds have been s t u d i e d i n t h e gas phase by UV s p e c t r o s c o p y o r by p h o t o e l e c t r o n s p e c t r o s c o p y ( P E S ) , o n l y w a t e r [77-81] and methanol [ 6 4 ] have energy l o s s e l e c t r o n i m p a ct s p e c t r a r e p o r t e d i n t h e l i t e r a t u r e . The e l e c t r o n i c s p e c t r a o f a l i p h a t i c compounds l i e m o s t l y i n t h e vacuum UV and c o n s e q u e n t l y have r e c e i v e d r e l a t i v e l y l i t t l e a t t e n t i o n because o f t h e i n s t r u m e n t a l d i f f i c u l t i e s o f w o r k i n g i n t h i s o p t i c a l r e g i o n . S a t u r a t e d a l i p h a t i c compounds, p a r t i c u l a r l y t h o s e c o n t a i n i n g non-bonding e l e c t r o n p a i r s l i k e a l c o h o l s , e t h e r s , a mines, ketones and h a l i d e s show c h a r a c t e r i s t i c a b s o r p t i o n bands i n t h e UV r e g i o n o beyond t h e q u a r t z l i m i t ( -v 2000 A) and t h e s e bands may be v a l u a b l e f o r a t h e o r e t i c a l u n d e r s t a n d i n g o f e l e c t r o n i c s t r u c t u r e as w e l l as f o r c h e m i c a l a n a l y s i s o f t h e s e compounds. The s p e c t r a o b t a i n e d i n t h i s work a r e a n a l y s e d and e x c i t e d s t a t e s a s s i g n e d a c c o r d i n g t o t h e scheme d e v e l o p e d by R o b i n and K u e b l e r [ 6 4 ] and H a r s h b a r g e r e t a l [6 5 ] u s i n g t h e measured term v a l u e s w i t h r e s p e c t t o v a r i o u s i o n i z a t i o n p o t e n t i a l s o b t a i n e d by PES. The s p e c t r a can t h e n be i n t e r p r e t e d i n terms o f Rydberg e x c i t a t i o n s . Comparison w i t h a v a i l a b l e UV s p e c t r a i s a l s o h e l p f u l i n t h e a n a l y s i s o f t h e s p e c t r a . A main beam w i t h a FWHM o f a p p r o x i m a t e l y 0.050 eV was used and r e s u l t e d i n energy l o s s s p e c t r a o f w a t e r comparable w i t h e a r l i e r work [77-81 ] . E l e c t r o n impact s p e c t r a were o b t a i n e d a t an impact energy o f 100 eV o r 50 eV w i t h s c a t t e r i n g a n g l e s o f 2° and 10 ° . The s p e c t r a a t 10° d i d not show any g r e a t d i f f e r e n c e from t h o s e a t 2° f o r a l l t h e compounds s t u d i e d e x c e p t f o r t h e e x p e c t e d much s m a l l e r i n t e n s i t y . The samples used were o b t a i n e d c o m m e r c i a l l y and were used, w i t h o u t f u r t h e r p u r i f i c a t i o n . No s i g n i f i c a n t i m p u r i t i e s were i n d i c a t e d by t h e s p e c t r a . The en e r g y s c a l e , f i x e d w i t h r e s p e c t t o t h e e l a s t i c a l l y s c a t t e r e d s i g n a l , compares w e l l w i t h o p t i c a l a b s o r p t i o n work. 7.2.Water, Methanol and D i m e t h y l E t h e r . The ground s t a t e c o n f i g u r a t i o n and o u t e r o r b i t a l e n e r g i e s o f t h e water m o l e c u l e ( C 2 v ) a r e w e l l known t o be ( l a ^ 2 ( 2 a ] ) 2 ( l b 2 ) 2 ( 3 a ] ) 2 ( l ^ ) 2 1 A 1 -18.54 -14.76 -12.62 eV The o r b i t a l e n e r g i e s a r e quoted from r e f e r e n c e [64] . The l b ^ o r b i t a l i s c o n s i d e r e d t o c o n t a i n t h e oxygen l o n e p a i r (2px) p e r p e n d i c u l a r t o t h e m o l e c u l a r p l a n e . The o r b i t a l 3a^ may be d e s c r i b e d as i n v o l v i n g H-H bonding c h a r a c t e r and l b 2 i n v o l v i n g H-H a n t i - b o n d i n g c h a r a c t e r [82] . • Methanol has a l o w e r symmetry, C s < The m o l e c u l a r o r b i t a l o r d e r i n g and e n e r g i e s a r e [64]: ( l a 1 ) 2 ( 2 a ' ) 2 ( 3 a 1 ) 2 ( 4 a 1 ) 2 ( 5 a ' ) 2 ( l a 1 1 ) 2 ( 6 a ' ) 2 ( 7 a ' ) 2 (2a"') 2 -32.2 -22 .65 -17.62 -15.64 -15.21 -12.62 -10.96 eV The m o l e c u l a r o r b i t a l s 2a" and 7a' a r e d e r i v e d f r o m 2pir o r b i t a l s l a r g e l y on t h e oxygen, w h i l e l a " and 5a' a r e 2pir o r b i t a l s l a r g e l y on 100. the m e t h y l group. D i m e t h y l e t h e r a l s o has C 2 y symmetry. Cradock and W h i t e f o r d [ 8 3 ] have g i v e n a m o l e c u l a r o r b i t a l d e s c r i p t i o n o f CH 3-0-CH 3. From PES d a t a , t h e en e r g y o r d e r i n g o f t h e M.O.'s i s a s s i g n e d t o be ( l a i ) 2 ( 2 a n ) 4 ( 1 b 2 ) 2 (CH b o n d i n g ) 1 2 ( 2 b 2 ) 2 ( 3 a ] ) 2 ( l ^ ) 2 (-16.5,-14.2) -13.43 -11.91 -10.04 eV The e f f e c t i v e d e g e n e racy o f t h e CH bonding l e v e l s i s removed by i n t e r a c t i o n w i t h one o f t h e CO bonding l e v e l s . F i g u r e 21 shows t h e e l e c t r o n i m p a ct s p e c t r a o f w a t ^ r , methanol and d i m e t h y l e t h e r a t 100 eV impact e n e r g y and 2° s c a t t e r i n g a n g l e . T a b l e 3 g i v e s a summary o f t h e t r a n s i t i o n s o c c u r r i n g i n t h e s e compounds and a t e n t a t i v e a s s i g n m e n t based on t h e term v a l u e scheme. The a s s i g n m e n t s f o r H 20 and CH 30H a r e , w i t h a few e x c e p t i o n s , e s s e n t i a l l y t h o s e s u g g e s t e d i n r e f . 64. We have e x t e n d e d t h e d i s c u s s i o n t o i n c l u d e t h e l e v e l s o f CH 30CH 3 and w i t h t h e a i d o f r e f . 77-81, a l s o made some a d d i t i o n a l a s s i g n m e n t s f o r t h e h i g h e r s t a t e s o f H 20. A c o m p a r i s o n o f t h e t h r e e s p e c t r a i s g i v e n below. The f i r s t p r o m i n e n t f e a t u r e i n t h e H 20 sp e c t r u m i s a d i f f u s e broad band e x t e n d i n g from 6.5 eV t o 8.5 eV w i t h a maximum (A) a t % 7.4 eV. T h i s has been a s s i g n e d as a lb-j -+ 3s Rydberg t r a n s i t i o n [ 6 4 ] . I t i s broad because t h e upper s t a t e i s OH a n t i b o n d i n g . The second band i s a l s o broad w i t h a t h r e s h o l d a t ^ 8.8 eV and a maximum (B) a t 9.66 eV, a f t e r w h i c h i t i s o v e r l a p p e d by a s e r i e s o f s h a r p p e a k s . The t e r m v a l u e f o r t h i s second t r a n s i t i o n w i t h r e s p e c t t o t h e 3a^ I.P. (14.76 eV) i s 5.10 eV. Comparing t h i s w i t h t h e 5.2 eV te r m v a l u e o f t h e f i r s t b r oad band w i t h r e s p e c t t o t h e lb-| I.P. (12.62 e V ) , i t i s e v i d e n t t h a t t h i s band p r o b a b l y 100 eV, 2* 6.00 8.00 10.00 12.00 14.00 ENERGY LOSS(eV) F i g u r e 21. E l e c t r o n impact s p e c t r a o f H 20, CH 30H and CH 3OCH 3 a t 100 eV, 2° H20 ( l a 1 ) 2 ( 2 a 1 ) 2 ( l b 2 ) 2 ( 3 a 1 ) 2 ( 1b 1 ) : C H 3 O H . . . (5a 1 ) 2 ( l a " ) 2 ( 6 a , ) 2 ( 7 a , ) 2 ( 2 a " ) 2 C H 3OCH3 . . . ( C H I ) M ( C H I I ) n ( 2 f c 2 ) 2 ( 3 a 1 ) 2 ( 1 b energy(eV) t rans i t ion term value(eV) Peak energy(eV) t rans i t ion term value(eV) Peak energy(eV) t rans i t ion A 6.67 l b j—>3s B C 7.34 \ 7.63 ] Ib j—*3p D 8.46 Ib i—-» 3d 3ai —>3s E 9.20 3a i—}3p F 9.95 2b 2 —>3s G 10.48 3a i—>3d H 10.84 2b 2 —}3p I 11.58 C H T —>3p J 12.92 . CH11—>3s 7.4 9.66 10.00 10.38 10.76 10.16 10.58 10.76) 11.01 11.12 11.38 11.53 11.75 11.91 12.07 12.24 I b j—>3sa 1 3aj—> 3saj Ibi —>3pai lb , 3pbx Ibi—> 4sax Ibx—^ 3d lbx—> 4pai I b i—>4pb x Ibj—> 5sai lbx—> 5p l b r l b r I b i— > 7 s d L \ Ibi—> 6d 6sai •5d 5.2 5.10 2.62 2.46 1.61 1.50 1.24 1.09 0.87 0.71 0.55 0.38 E G F H I 6.69 9.22 9.44' 9.83, 9.63 11.90 13.43 2a" —->3s 2 a " - ^ 3 p 2a"—>3p 2a"—}3d 7 a ' — » 3 p 2a"—>4p l a "—>3s 5a' —>3s 4.27 3.25 2.66 1.74 3.18 2.79 1.33 3.74 4.19 3.37 2.70 2.41 1.58 3.45 2.71 3.48 1.43 2.59 2.6 3.6 espective I.P. can be obtained by adding the term value to the t rans i t ion energy. Table 3 Electronic Transit ions in water, methanol and dimethyl ether. o ro 103. c o r r e s p o n d s t o a 3a-j -+ 3s Rydberg t r a n s i t i o n . The broadness i s a l s o due t o t h e upper s t a t e b e i n g OH a n t i - b o n d i n g . The f i r s t band i n t h e methanol s p e c t r u m i s a l s o d i f f u s e and broad e x t e n d i n g f r o m 6.0 - 7.4 eV. The upper s t a t e i s s t i l l OH a n t i - b o n d i n g . I t peaks (A) a t 6.7 eV and g i v e s a t e r m v a l u e o f 4.3 eV with, r e s p e c t t o the 2a" I.P. (10.96 e V ) . S i n c e i t has been o b s e r v e d [64] t h a t 3s term v a l u e s d e c r e a s e on a l k y l a t i o n , t h e t r a n s i t i o n i s a s s i g n e d t o t h e 2a" •> 3s Rydberg t r a n s i t i o n . The Rydberg c h a r a c t e r has been c o n f i r m e d by Robin and K u e b l e r [ 6 4 ] . The t r a n s i t i o n from t h e s e c o n d ' h i g h e s t o c c u p i e d M.O., 7a' t o 3 s , e x p e c t e d a t about 12.62 - 4.3 = 8.3 eV, i s p r o b a b l y b u r i e d under o t h e r s t r o n g f e a t u r e s i n t h e s p ectrum. In t h e c a s e o f d i m e t h y l e t h e r t h e f i r s t band becomes s h a r p e r and f i n e s t r u c t u r e s have been o b s e r v e d i n h i g h r e s o l u t i o n o p t i c a l a b s o r p t i o n s p e c t r a [ 8 4 ] . The peak (A) a t 6.67 eV g i v e s a t e r m v a l u e o f 3.37 eV w i t h r e s p e c t t o t h e l b ] I.P. (10.04 eV) and t h i s t r a n s i t i o n i s a s s i g n e d as t h e Ib-j 3s Rydberg t r a n s i t i o n . The d e c r e a s e o f 3s term v a l u e s on a l k y l a t i o n i s w e l l i l l u s t r a t e d , i f t h i s a s s i g n m e n t i s c o r r e c t , by t h e 3s term v a l u e s o f 5.2, 4.3 and 3.4 eV i n H^O, CH 30H and CH-jOCH^ r e s p e c t i v e l y . The 6.67 eV band i n d i m e t h y l e t h e r i s s h a r p e r than t h e c o r r e s p o n d i n g band i n w a t e r . A l s o , i t s i n t e n s i t y i s r e l a t i v e l y much l a r g e r than the c o r r e s p o n d i n g peak i n m e t h a n o l . The o t h e r t r a n s i t i o n t o 3s f r o m the second h i g h e s t o c c u p i e d M.O., 3a-j, o c c u r s as t h e f o u r t h peak (D) i n the spectrum a t 8.46 eV. T h i s i s a s s i g n e d on t h e b a s i s o f i t s term v a l u e o f 3.45 eV w i t h r e s p e c t t o t h e 3 a ] I.P. (11.91 e V ) . A s e r i e s o f s h a r p peaks appear i n t h e s p e c t r u m o f H 20 i n t h e e n e r g y l o s s r e g i o n above 10 eV. The f i r s t f i v e p e a k s , (C, F, D, G, E) b e l o n g t o two d i s t i n c t e x c i t e d s t a t e s where t h e v i b r a t i o n a l l e v e l s o f one s t a t e 104. a r e l o c a t e d h a l f way between t h o s e o f t h e o t h e r . These c o r r e s p o n d t o th e Rydberg t r a n s i t i o n from t h e l b ^ s t a t e (oxygen l o n e p a i r ) t o t h e two components o f 3p. Johns [85] , u s i n g an argument based on r o t a t i o n a l f i n e s t r u c t u r e i n UV s p e c t r o s c o p y , i d e n t i f i e d t h e symmetry o f t h e s t a t e s a t 10.00 (C) and 10.38 (D) t o be ^B^, w h i l e t h e peaks a t 10.16 ( F ) and 10.58 (G) a r e o f ^ symmetry. Based on i n t e n s i t y v a r i a t i o n s w i t h s c a t t e r i n g a n g l e i n EIS S k e r b e l e and L a s s e t t r e [79] c o n s i d e r e d t h e s m a l l peak a t 10.76 eV (E) t o have c o n t r i b u t i o n s f r o m both c o m b i n a t i o n s , 2v-| o f t h e A s t a t e and v-j + v 2 o f t h e B s t a t e . The second members o f t h e A and B s t a t e s (lb-, + 4p) o c c u r a t 11.38 ( J ) and 11.53 eV (K) w h i l e t h e s m a l l peak a t 11.91 eV (M) c o r r e s p o n d s t o t h e t h i r d member (lb-j 5p) . The d o u b l e t a t 11.01 (H) and 11.12 eV ( I ) c o r r e s p o n d s t o t h e t r a n s i t i o n s (lb-j 4 s ) and (lb-j -*• 3d) r e s p e c t i v e l y . The h i g h e r members o f t h e s e two s e r i e s o v e r l a p s t r o n g l y and appear as s i n g l e peaks a t 11.75 ( L ) , 12.07 (N) and 12.24 eV (0). A f u r t h e r f e a t u r e t o be mentioned i n t h e spectrum o f w a t e r i s a v e r y s m a l l peak a t 6.18 eV. T h i s peak has p r e v i o u s l y been o b s e r v e d by S k e r b e l e e t a l [80] and may c o r r e s p o n d t o an o p t i c a l l y f o r b i d d e n t r a n s i t i o n t o a low l y i n g t r i p l e t s t a t e . In t h e methanol s p e c t r u m , t h e two bands (B and C) a t 7.82 and 8.33 eV r e p r e s e n t t r a n s i t i o n s f r o m 2a" t o t h e two components o f 3p. On a more d e t a i l e d scan (see i n s e r t ) o f t h e s e two bands, v i b r a t i o n a l s t r u c t u r e s a r e r e v e a l e d . The f i r s t band has an aver a g e v i b r a t i o n a l s p a c i n g o f ^ 0.096 eV w h i l e t h e second one has a s p a c i n g o f 0.110 eV. The 3pu s p l i t t i n g i n methanol ( F i g u r e 21) , 0.59 eV, i s much l a r g e r t h a n t h a t i n w a t e r (0.16 eV) and so the v i b r a t i o n a l s t a t e s o f t h e s e bands i n CHgOH do n o t i n t e r m i n g l e . The term v a l u e f o r t h e 7.82 eV band (B) 105, (3.25 eV) r e p r e s e n t s an extreme v a l u e f o r - 3 p - t e r m v a l u e s [64].>-The n e x t f e a t u r e s i n t h e methanol s p e c t r u m a r e f o u r s m a l l . . p a r t i a l l y ..resolved.-, peaks (D, E, F, 6) superimposed on a broad band. The s h o u l d e r (D) a t 9.22 eV has a term v a l u e o f 1.74 eV w i t h r e s p e c t t o t h e 2a" I.P. and i s a s s i g n e d t o be a 2a" 3d t r a n s i t i o n . A l s o on t h e b a s i s o f i t s t e r m v a l u e , t h e peak, (F) a„t^9.63 eV .is a s s i g n e d 2a". + 4p w h i l e t h o s e a t 9.44 (E) and. 9.83 eV (G) a r e a s s i g n e d t o t h e two components Of 7 a 1 3p. Term v a l u e s a r e g i v e n i n Ta.ble 3. The n e x t two broad bands (H and I ) o c c u r above t h e f i r s t I.P. The f i r s t one a t 11.90 eV has a t e r m v a l u e o f 3.74 eV w i t h r e s p e c t t o t h e l a " I.P. a t 15.64 eV and so can be a s s i g n e d as la".-> 3s w h i l e , t h e n e x t peak a t 13.43 eV. i s - c o n s i s t e n t w i t h a 5a' -»• 3s t r a n s i t i o n on t h e grounds o f i t s term v a l u e w i t h r e s p e c t t o the 5a' I.P. a t . 17.62 eV. , . . In t h e x a s e o f d i m e t h y l , e t h e r , t h e l b ^ 3p Rydberg, t r a n s i t i o n : o c c u r s as a s t e p (B) a t 7.34 eV and a peak (C) a t 7.63 eV. <The term v a l u e s o f 2.70 and 2.4.1 eV w i t h r e s p e c t t o t h e lb-| I.P. a r e comparable w i t h t h e v a l u e s f o r w a t e r , showing t h a t the. change o f 3p term v a l u e s on. a l k y l a t i o n i s much l e s s d r a s t i c t h a n 3s term v a l u e s . The lb-j 3d t r a n s i t i o n s p r o b a b l y o v e r l a p w i t h t h e 3a-j -»• 3s t r a n s i t i o n mentioned b e f o r e a t 8.46 eV (D). On. the b a s i s o f term v a l u e s (see T a b l e 3 ) , t h e peaks. (E.,..F,,G, H) a t 9.20, 9,95.,.10.48 and 10.84-eV, a r e a s s i g n e d 3 a ] •+ 3p,. 2 b 2 3 s , , 3a-j -> 3d and 2 b 2 -»• 3p r e s p e c t i v e l y . Cradock and W h i t e f o r d [83],.have a s s i g n e d two peaks, i n t h e i r PES s p e c t r u m - t o be due t o i o n i z a t i o n o f t h e CH bonding o r b i t a l s I and I I a t 14.2 and 16.5 e.V. Our EIS s p e c t r u m shows a s h o u l d e r ( I ) at. 11.58.eV and t h i s ,is a s s i g n a b l e t o t h e - t r a n s i t i o n CH (I.) -> 3p., .leading,-to a-, term, v a l u e .of. 2t 6 eV. . The next.maximum^is a t -v 106. 12.9 eV ( J ) and so has a term v a l u e o f 3.6 eV w i t h r e s p e c t t o t h e C H ( I I ) I.P. a t 16.5 eV. So t h i s s h o u l d c o r r e s p o n d t o a t r a n s i t i o n f r o m C H ( I I ) + 3s 7 . 3 . E t h y l e n e O x i d e . E t h y l e n e o x i d e ha? C 2 v symmetry. I t s ground s t a t e e l e c t r o n i c c o n f i g u r a t i o n [ 6 7 ] i s ( l a i ) 2 ( 2 a i ) 2 ( l D l ) 2 ( 3 a i ) 2 ( 4 9 l ) 2 ( 2 b 1 ) 2 ( l b 2 ) 2 ( 5 a T ) 2 ( l a 2 ) 2 (3b^)2 ( e a ^ 2 ( 2 b 2 ) 2 - 1 7-4-16.6 -14.2 -13.7 -11.7 -10.57 eV The l b 2 , l a 2 and 2 b 2 a r e TT o r b i t a l s . The e l e c t r o n i m p a c t s p e c t r u m a t 50 eV and 2° s c a t t e r i n g a n g l e i s shown i n F i g u r e 22. The two bands o c c u r r i n g i n t h e 7-8 eV e n e r g y - l o s s r e g i o n show some v i b r a t i o n a l s t r u c t u r e . I t a p p e ars t h a t t h e s e two bands l i e on t o p o f a b r o a d e r a b s o r p t i o n w h i c h s t a r t s a t about 6.5 eV. The v i b r a t i o n a l s p a c i n g o f t h e f i r s t and second band a r e about 0.095 and 0.130 eV r e s p e c t i v e l y . F e a t u r e s above 8.6 eV have been a r r a n g e d by UV s p e c t r o s c o p i s t s i n t o Rydberg s e r i e s . The f i r s t a s s i g n m e n t by L i u and Duncan [ 8 6 ] gave an i o n i z a t i o n p o t e n t i a l o f 10.81 eV w h i c h does not a g r e e w i t h a v a l u e o f 10-565 eV o b t a i n e d i n a l a t e r p h o t o i o n i z a t i o n d e t e r m i n a t i o n by Watanabe [ 8 7 ] . A f t e r r e i n v e s t -i g a t i n g and r e a s s i g n i n g t h e Rydberg s e r i e s , Lowrey and Watanabe [ 8 8 ] o b t a i n e d a p r e c i s e agreement between t h e Rydberg l i m i t and t h e p h o t o -i o n i z a t i o n v a l u e o f t h e I.P. Basch e t a l . [67] have s t u d i e d t h e o p t i c a l and p h o t o e l e c t r o n s p e c t r a o f e t h y l e n e o x i d e . F o l l o w i n g t h e s u g g e s t i o n o f La P a g l i a [ 8 9 ] , t h e y i n c l u d e d t h e l o w e r bands a t 7.24 and 7.89 eV as Rydberg s e r i e s , b e i n g t h e f i r s t members (n = 3) p f t h e s e r i e s (2b 2 i r -»• ns) C O cn < cn CO cn < >-CO z : UJ z : 50eV,2e 2 2b 2—^nd/nd+1/3 n 7.33 eV 2 b 2 — • n p / n p + V j 6.00 700 8.00 9.00 10.00 11.00 12.00 1300 1400 ENERGY LOSS (eV) F i g u r e 22. E l e c t r o n impact s p e c t r a o f e t h y l e n e o x i d e a t 50 eV, 2° o 108. and ( 2b 2iT -* np) r e s p e c t i v e l y . They have s u b s t a n t i a t e d t h e Rydberg c h a r a c t e r s o f t h e s e t r a n s i t i o n s by r u n n i n g t h e condensed phase s p e c t r u m and by comparing w i t h t h e i s o m e r i c m o l e c u l e a c e t a l d e h y d e . We have a r r a n g e d t h e f e a t u r e s i n our e l e c t r o n i m p a c t s p e c t r u m i n t o Rydberg s e r i e s (based on t h e a s s i g n m e n t s o f Basch e t a l . [67]) 2 b 2 r r -* n s , np, nd (see T a b l e 4 ) . The term v a l u e f o r t h e 2b2-rr ->• 3s t r a n s i t i o n i s 3.33 eV w h i l e t h a t f o r t h e 2b 2TT •> 3p t r a n s i t i o n i s 2.68 eV. T h i s i s c o n s i s t e n t w i t h t he v a l u e s o f 3.37 and 2.69 eV r e s p e c t i v e l y i n t h e open c h a i n a n a l o g u e CrtgOCHg, a l t h o u g h t h e agreement between t h e 3d term v a l u e s (1.92 eV i n e t h y l e n e o x i d e and 1.58 eV i n d i m e t h y l e t h e r ) i s not as good. Most members o f t h e Rydberg s e r i e s a r e accompanied by v i b r a t i o n a l t r a n s i t i o n s a s s o c i a t e d w i t h v i b r a t i o n f r e q u e n c y v 3 (0.140 eV) as l i s t e d i n T a b l e 4. The s p l i t t i n g o f the f i r s t band, 0.090 eV, can be e x p l a i n e d by a s s o c i a t i n g i t w i t h a vg v i b r a t i o n . The Rydberg t r a n s i t i o n s seem t o be superimposed on b r o a d e r bands w h i c h a r e p r o b a b l y due t o i n t e r - v a l e n c e - s h e l l t r a n s i t i o n s . A d i s c u s s i o n o f i n t e r - v a l e n c e - s h e l l t r a n s i t i o n i s g i v e n by Basch e t a l [67]. 7 . 4 . E t h y l , I s o p r o p y l and t - B u t y l A l c o h o l s . The e l e c t r o n i m p a ct s p e c t r a o f e t h y l a l c o h o l , i s o p r o p y l a l c o h o l and t - b u t y l a l c o h o l a r e p r e s e n t e d i n F i g u r e 23. A summary o f t h e t r a n s i t i o n s i s g i v e n i n T a b l e 5. The im p a c t energy i s 100 eV and t h e s c a t t e r i n g a n g l e i s 2 ° . As was t h e c a s e w i t h methyl a l c o h o l , a l l t h e s e compounds show a r a t h e r weak s t r u c t u r e l e s s band (A) i n t h e 6.5 eV t o 7.5 eV en e r g y l o s s r e g i o n w h i c h s h o u l d c o r r e s p o n d t o t h e t r a n s i t i o n s f r o m t h e h i g h e s t f i l l e d M .0. (symmetry a") t o t h e 3s Rydberg o r b i t a l . The 3s te r m v a l u e s f o r CH 3CH 20H, (CH^CHOH and (CH 3)' 3C0H a r e 3.80, 3.62 and 3.46 eV 2b,7T 1 ns 2b,TT 1 ns+vj 2b„TT I ns+v5 2b„TT J np 2b,TT 1 np+vg 2b,7T I nd 2b ?7T i nd+v3 7.24 (3) + 7.33 (3) + 7.89 (3 ) f 8.02 (3) + 8.64 (3 ) f 8.78 (3) + 8.97 (4) [9.10] (4 ) f 9.32 (4) 9.45 (4) [9.53] (4) 9.69 (5) 9.83 (5) 9.81 (5) [9.93] (5) TO. 00 (6) 10.14 (6) ! [10.19] (7) [10.33] (7) [10.29] (8) 10.43 (8) 10.57* H 10.70* H + values of n are given in the brackets; energies are expressed in eV. * photoionization I.P. re f . 20. [ ] value quoted from opt ica l absorption ref . 21 Table 4 Rydberg series in ethylene oxide no. CO h-01 < m rr < CO z: UJ A B: D . - „*,*-. • •• cy.-.... • B * . 1 0 0 eV, 2 ° • CHoCHoOH F n ° ^ P B ••••"V'-^.V." 1 0 0 eV, 2 ° (CH 3) 2CHOH A D E B A A-1 0 0 eV, 2 ° (CH 3) 3COH 6.00 8.00 10.00 12.00 14.00 ENERGY LOSS (eV) F i g u r e 23. E l e c t r o n impact s p e c t r a o f e t h y l , i s o p r o p y l and t - b u t y l a l c o h o l s a t 100 eV, 2°. CH3CH20H . . . (^) m (*3 ) n (a') 2 (a ' ' )2* (CH3)2CH0H . (CH3)3C0H . . . (* J m (*3 ) n (a ' ) 2 ( a " ) 2 k energy(eV) t rans i t ion term value(eV) Peak energy(eV) t rans i t ion term value(eV) Peak energy(eV) t rans i t ion term value.( 6.82 a "—>3s 3.80 A 6.80 a"—-»3s 3.62 A 6.79 a " — » 3 s 3.46 7.80 a" —>3p 2.82 B 7.92 a"—>3p 2.50 B 8.17 a"—>3p 2.08 8.13 2.49 C 8.89 a"—>3d 1.53 C 8.64 a" —?>3d 1.61 8.93 a "—>3d 1.69 9.32 a '—>3p 2.39 9.5 D D a ' — » 3 p 2.0 9.45 a " — » 4 p .1.17 : E 10.07 * 5 — » 3 s 3.68 E 10.18 *3—>3p 2.17 a '—>3p 2.75 F 10.85 i>k—»3p 2.23 F 11.30 <K—>3d 1.48 0.69 <|>3—^ 3p 2.62 G 11.51 *s—>3p 2.24 1.37 ipi,—»3p 2.45 Jhen the symmetry of the M.O.s are not known, tf^ designatesthe £ t n highest f i l l e d M.0. Respective L P . can be obtained by adding the term value to the trans i t ion energy. Table 5 . E lectronic Transit ions in e thy l , isopropyl and t-butyl a lcohols. 112. r e s p e c t i v e l y w i t h r e s p e c t t o t h e i r f i r s t I.P.'s ( a " ) . T h i s i s c o n s i s t e n t w i t h t h e o b s e r v a t i o n t h a t 3s term v a l u e s a r e d e c r e a s i n g w i t h a l k y l a t i o n . However, comparing w i t h t h e 3s term v a l u e s i n the s e r i e s . H 20, CH 30H and CH 30CH 3 ( 5 . 2 , 4.25 and 3.37 eV r e s p e c t i v e l y ) , i t i s o b v i o u s t h a t r e p l a c i n g a hydrogen atom a d j a c e n t t o a C atom by a m e t hyl group causes a s m a l l e r d e c r e a s e i n t h e 3s term v a l u e t h a n r e p l a c i n g a hydrogen atom a d j a c e n t t o an 0 atom. The second f e a t u r e i n t h e s p e c t r a o f t h q a l c o h o l s shows some d i f f e r e n c e s . W h i l e methanol shows two bands w i t h v i b r a t i o n a l s t r u c t u r e a t 7.71 and 8.30 eV, t h e s p e c t r a o f t h e h e a v i e r m o l e c u l e s become p r o g r e s s -i v e l y more d i f f u s e and no v i b r a t i o n a l s p l i t t i n g can be r e s o l v e d . The e t h y l a l c o h o l s p e c t r u m shows a s h o u l d e r (B) a t 7.80 eV and a peak (C) a t 8.13 eV. Term v a l u e s o f 2.82 and 2.49 eV w i t h r e s p e c t t o t h e f i r s t I.P. ( a " ) a t 10.62 eV s u g g e s t t h e s e a r e t r a n s i t i o n s f r o m t h e a" M.O. to t h e s p l i t 3p m a n i f o l d . The s p l i t t i n g o f 0.33 eV i s o n l y about h a l f t h a t o f CH 30H (0.59 eV) and comparable t o t h a t o f CH 30CH 3 (0.27 e V ) . For (CH 3) 2CH0H th e 3p s p l i t t i n g i s a p p a r e n t l y even s m a l l e r and o n l y one peak (B) a s s i g n e d a" -»• 3p i s o b s e r v e d a t 7.92 eV. I t s t e r m v a l u e w i t h r e s p e c t t o t h e a" I.P. (10.42 eV) i s 2.50 eV. Coming t o ( C H 3 ) 3 C 0 H t h e second f e a t u r e i n t h e s p e c t r u m i s a s t e p (B) a t 8.17 eV. T h i s has a term v a l u e o f o n l y 2.08 eV w i t h r e s p e c t t o the a" I.P. (10.25 e V ) . Because o f t h i s low v a l u e , i t i s d o u b t f u l whether t h i s t r a n s i t i o n can be a s s i g n e d as a" -»• 3p. One p o s s i b l e e x p l a n a t i o n i s t h a t t h e a" 3p t r a n s i t i o n i s r i d i n g on t o p o f a s t e e p l y r i s i n g v a l e n c e t r a n s i t i o n and so t h e peak maxima i s s h i f t e d t o h i g h e r e n e r g i e s , g i v i n g an a p p a r e n t l y s m a l l e r term v a l u e . The n e x t peak (C) i n the ( C H 3 ) 3 C 0 H s p e c t r u m o c c u r s a t 8.64 eV 113. which g i v e s a term v a l u e o f 1.61 eV w i t h r e s p e c t t o t h e a" I.P. and so c o r r e s p o n d s t o a a" -»• 3d t r a n s i t i o n . The c o r r e s p o n d i n g t r a n s i t i o n s i n (CH 3) 2CH0H and CH 3CH 20H a r e l e s s d i s t i n c t . The (CH 3) 2CH0H s p e c t r u m shows a s h o u l d e r (C) a t 8.89 eV (term v a l u e 1.53 e V ) . The CH 3CH 20H spectr u m has a s t e e p s l o p e w i t h a change i n g r a d i e n t (D) o c c u r r i n g a t about 8.93 eV. I t i s d i f f i c u l t t o t e l l w i t h any c e r t a i n t y as t o whether t h i s i s due t o t h e t r a n s i t i o n a" ->• 3d. The s e c o n d , t h i r d and f o u r t h i o n i z a t i o n p o t e n t i a l s o f e t h a n o l have been d e t e r m i n e d by PES [90] t o be 12.20, 13.31 and 13.82 eV r e s p e c t i v e l y . Peaks ( E , F, G) a t 9.45, 10.69 and 11.37 eV i n the sp e c t r u m o f e t h y l a l c o h o l have term v a l u e s o f 2.75, 2.62 and 2.45 eV w i t h r e s p e c t t o t h e '. above I.P.'s and so p r o b a b l y r e p r e s e n t t r a n s i t i o n s from the c o r r e s p o n d i n g M.O.'s t o t h e 3p Rydberg s t a t e . The l a s t peak a t 12.8 eV c a n n o t be a s s i g n e d on t h e term v a l u e scheme and i s p r o b a b l y an i n t e r - v a l e n c e - s h e l l t r a n s i t i o n . The peak (E) a t 9.45 eV i s r a t h e r b r o a d and t h e a" ->- 4p t r a n s i t i o n , w i t h a term v a l u e o f about 1.0 eV, may be c o n t r i b u t i n g t o t h i s band. F e a t u r e s i n t h e spect r u m o f (CH 3) 2CH0H above 9.0 eV a r e l e s s d i s t i n c t . The h i g h e r I.P.'s o b s e r v e d by PES [ 9 0 ] a r e 11.71, 12.68, 13.08, 13.75, 15.14 and 15-80 eV. The s t e p (D) a t 9.32 eV has a term v a l u e o f 2.39 eV w i t h r e s p e c t t o t h e second I.P. and so can be a s s i g n e d to a t r a n s i t i o n f r o m ^ 2 ( f o r c o n v e n i e n c e , ^ i s used t o denote t h e nth h i g h e s t f i l l e d M.0.) t o t h e 3p Rydberg s t a t e . Humps ( E , G) a t 10.07 and 11.51 eV have term v a l u e s o f 3.68 and 2.24 eV w i t h r e s p e c t t o t h e 5 t h I.P. (13.75 eV) and t h e r e f o r e a r e a s s i g n e d t o t r a n s i t i o n s f r o m t o t h e 3s and 3p Rydberg s t a t e s r e s p e c t i v e l y . One f u r t h e r peak (F) a t 10.85 eV can be a s s i g n e d t o a t r a n s i t i o n from ^ A t o 3p on a c c o u n t o f i t s term 114. v a l u e o f 2.23 eV w i t h r e s p e c t t o t h e 4 t h I.P. The s p e c t r u m o f ( C H ^ C O H r i s e s s t e e p l y above 9.0 eV and comes t o a p l a t e a u between 9.6 and 10.5 eV A f t e r t h i s i t f a l l s g e n t l y and becomes f l a t a g a i n i n t h e r e g i o n 13-14 eV. A s m a l l hump (F) p e a k i n g a t 11.3 eV i s superimposed on t h i s . H i g h e r I.P. have been o b s e r v e d by PES [ 9 0 ] a t 11.48, 12.35, 12.78, 15.42 and 16.50 eV I f t h e t r a n s i t i o n (B) a t 8.17 eV i s r e g a r d e d as a" -> 3p, d e s p i t e i t s low term v a l u e o f 2.08 eV w i t h r e s p e c t t o t h e 1 s t I . P . , t h e c o r r e s p o n d i n g t r a n s i t i o n f rom ^ t o 3p i s e x p e c t e d a t about 11.48-2.08 = 9.4 eV. T h i s t r a n s i t i o n may c o r r e s p o n d t o t h e o n s e t o f t h e p l a t e a u a t ^ 9.5 eV, t h e peak maximum b e i n g s h i f t e d t o h i g h e r energy a g a i n by r i d i n g on t o p o f a s t e e p l y r i s i n g v a l e n c e t r a n s i t i o n . The p l a t e a u between 9.6 and 10.5 eV i n t h e 100 eV s p e c t r u m i s t h e r e s u l t o f s e v e r a l o v e r l a p p i n g t r a n s i t i o n s . These may be the Rydberg t r a n s i t i o n s from ^ and tj^ t o t h e 3p s t a t e superimposed on a s t r o n g i n t e r - v a l e n c e - s h e l l t r a n s i t i o n . The peak (F) a t 11.30 eV has a term v a l u e o f 1.47 eV w i t h r e s p e c t t o t h e 4 t h I.P. and may be a s s i g n e d t o have a 3d upper s t a t e . 5 . D i e t h y l E t h e r and T e t r a h y d r o f u r a n . The e l e c t r o n impact s p e c t r a ( E I S ) o f d i e t h y l e t h e r and i t s a l i c y c l i c a n a l o g u e , t e t r a h y d r o f u r a n ( F i g u r e 24) l o o k v e r y s i m i l a r , p a r t i c u l a r l y i n t h e e nergy l o s s r e g i o n o f 6.0-8.5 eV. Three peaks a r e e x h i b i t e d on t o p o f a r i s i n g u n d e r l y i n g continuum. F i n e s t r u c t u r e s i n t h e r e g i o n 6-8 eV, o b s e r v e d i n t h e o p t i c a l s p e c t r a [84,91,92] a r e not r e s o l v e d h e r e . In o r d e r t o a s s i g n t h e peaks i n t h e E I S , the p h o t o e l e c t r o n s p e c t r a (PES) o f t h e s e compounds have been measured i n t h i s l a b o r a t o r y [ 9 3 ] . The f i r s t v e r t i c a l I.P. o f d i e t h y l e t h e r i s d e t e r m i n e d t o be 9.63 eV w h i l e t h a t o f 115. 100 eV, 2 CO z: >-< tt: DO < >-CO U J B A A B ;-s * * i r V ' " .V ff • * D «.»-r >•<«' C2H5OC2H5 H u ..-V'->-.v CH2~CH 2 C H 2 CH. (THF) 6.00 8.00 10.00 12.00 14.00 ENERGY LOSS (eV) F i g u r e 24. E l e c t r o n impact s p e c t r a o f d i e t h y l e t h e r and t e t r a h y d r o f u r a n a t 100 eV, 2° 116. t e t r a h y d r o f u r a n i s 9.73 eV. The f i r s t t h r e e peaks (A, B, C) i n t h e EIS a r e t r a n s i t i o n s from t h e h i g h e s t f i l l e d M.O. (b-j assuming C 2 v symmetry) t o t h e 3 s , 3p, and 3d Rydberg s t a t e s r e s p e c t i v e l y . T r a n s i t i o n e n e r g i e s and term v a l u e s a r e summarised i n T a b l e 6. The t h i r d peak (C) i n d i e t h y l e t h e r i s broad and t h e r e may be some c o n t r i b u t i o n f r o m a t r a n s i t i o n between the second h i g h e s t f i l l e d M.O. t o t h e 3s Rydberg s t a t e because t h i s peak has a term v a l u e o f about 3 eV w i t h r e s p e c t t o t h e 2nd I.P. (11.09 e V ) . H i g h e r I.P.'s o f d i e t h y l e t h e r a r e o b t a i n e d a t 11.09, 11.35, 11.62, 12.13, 13.17, 14.04, 14.78 and 16.55 eV. Peaks above 8.5 eV i n t h e EIS may be a s s i g n e d t o t r a n s i t i o n s f r o m t h e v a r i o u s f i l l e d M.O.'s t o t h e 3s o r 3p Rydberg s t a t e a c c o r d i n g t o t h e term v a l u e scheme. S i m i l a r t r e a t m e n t i s p o s s i b l e f o r t e t r a h y d r o f u r a n f o r w h i c h h i g h e r I.P.'s a r e o b s e r v e d a t 11.51, 12.02, 12.51, 12.97, 13.91, 14.19, 14.54, 15.35, 15.79, and 16.84 eV. A l i s t o f t r a n s i t i o n e n e r g i e s and term v a l u e s i s g i v e n i n T a b l e 6. In g e n e r a l , term v a l u e s i n t e t r a h y d r o f u r a n a r e a t l e a s t 0.15 eV l a r g e r than t h o s e i n d i e t h y l e t h e r . T h i s i s d i f f e r e n t from t h e c a s e o f d i m e t h y l e t h e r and i t s c y c l i c a n a l o g u e , e t h y l e n e o x i d e , where the 3s and 3p term v a l u e s o f each do not d i f f e r by more tha n 0.04 eV from t h e o t h e r . I t s h o u l d a l s o be noted t h a t w h i l e the s p e c t r a o f t e t r a h y d r o f u r a n and d i e t h y l e t h e r l o o k v e r y s i m i l a r , t h e s p e c t r u m o f e t h y l e n e o x i d e i s d r a s t i c a l l y d i f f e r e n t from t h a t o f d i m e t h y l e t h e r . T h i s d i f f e r e n c e must mean t h a t t h e bonding i n e t h y l e n e o x i d e i s not as s i m p l e as s u g g e s t e d by the s i n g l e - b o n d e d f o r m u l a . The h i g h e s t f i l l e d M.O. i n e t h y l e n e o x i d e may not s i m p l y be t h e non-bonding e l e c t r o n o f t h e 0 atom as i n w a t e r , a l c o h o l s and e t h e r s . Walsh [ 9 4 ] has s u g g e s t e d t h a t e t h y l e n e o x i d e has a d o u b l e bond c h a r a c t e r s i m i l a r t o e t h y l e n e . I n d e e d , L i u and Duncan [ 8 6 ] have C J L O C J L • • • ('1'if )m( <i>s)n(<*i ) 7 ( b 1 ) 2 * C H 2 C H 2 O C H 2 i n 2 ...MnU'3)n Peak e n o r g y ( c V ) t r a n s i t i o n t e r m value(e~V) Peak e n e r g y ( e V ) t r a n s i t i o n t e r m v a l u e ( e V ) A 6.58 b : — > 3 s 3.05 A 6.57 b 1 ~ > 3 s 3.16 B 7.24 b ! — > 3 p 2.39 B 7.19 b i — > 3 p . 2.54 C 8.09 b 2 >3d/ 1.54 C 8.03 b i ~ > 3 d 1.70 3 i — > 3 s 3.00 D D 8.80 ^ 3 — ^ 3 5 3.22 8.98 * 3 — > 3 p 2.37 9.54 E ^3 " '3D 2.48 E 10.18 <!'G — ^ 3 s 2.99 F 11.03 12.39 i>7 —>3s 3.16 F </>o — ? 3 p 2.39 11.40 G <l>8 —>3s 3.14 H 13.61 * n — > 3 s 3.23 ScnJtf Syfr-ry o f t h e M.O.s a r e n o t known, * d e s i g n a t e s t h e * t h h i q h e s t f n i d „ Q R e s p e c t i v e I.P. c a n b e . o b t a i n e d by a d d i n g t h e t l r m v a l u e t o t h e t r a n s i t i o n e n e r g y . 6 E l e c t r o n i c t r a n s i t i o n s i n d i e t h y l e t h e r and t e t r a h y d r o f u r a n . 118. i n t e r p r e t e d t h e i r s p e c t r u m o f e t h y l e n e o x i d e based on e x c i t a t i o n s f r o m a m o l e c u l a r bonding o r b i t a l i n v o l v i n g two c a r b o n s and one oxygen r a t h e r t h a n a non-bonding o r b i t a l i n oxygen. 7 . 6 . E f f e c t o f A l k y l S u b s t i t u t i o n on EIS P h y s i c a l o r g a n i c c h e m i s t s have d e v i s e d v a r i o u s means t o measure q u a n t i t a t i v e l y p o l a r e f f e c t s and t o s e p a r a t e them from s t e r i c and r e s o n a n c e e f f e c t s . T a f t [95] gave t h e f o l l o w i n g e q u a t i o n f o r e v a l u a t i n g t h e p o l a r e f f e c t o f s u b s t i t u e n t s R on the r a t e o f normal h y d r o l y s i s o f e s t e r s , RCOOR' a* 5 [ l o g ( k / k o ) B - l o g ( k / k o ) A ] / 2 . 4 8 (7.1) a * i s a s u b s t i t u e n t c o n s t a n t dependent o n l y upon th e n e t p o l a r e f f e c t o f t h e s u b s t i t u e n t ( c o r r e s p o n d i n g t o the r a t e c o n s t a n t k) r e l a t i v e t o t h a t f o r t h e s t a n d a r d o f c o m p a r i s o n ( k Q , R=CH.j). B and A ( s u b s c r i p t s ) r e f e r t o o t h e r w i s e i d e n t i c a l a l k a l i n e and a c i d i c r e a c t i o n s r e s p e c t i v e l y . F o l l o w i n g t h e example o f Baker and B e t t e r i d g e [ 9 6 ] , who g i v e p l o t s o f T a f t a* v a l u e s o f t h e a l k y l s u b s t i t u e n t s v s . oxygen l o n e p a i r I.P.'s o f ROH, F i g u r e 25 shows a p l o t o f t h e 3s term v a l u e and t h e f i r s t v e r t i c a l I.P. [64,83,93] o f t h e compound a g a i n s t t h e sum o f t h e a* v a l u e f o r both s u b s t i t u e n t s a t t a c h e d t o t h e oxygen atom. The p o i n t s f o r t h e 3s t e r m v a l u e l i e a p p r o x i m a t e l y on a s t r a i g h t l i n e showing t h a t t h e r e i s a r o u g h l y c o n s t a n t r a t e o f d e c r e a s e i n t h e 3s term v a l u e w i t h i n c r e a s i n g p o l a r e f f e c t o f t h e s u b s t i t u e n t . With the e x c e p t i o n o f w a t e r , t h e p o i n t s f o r t h e f i r s t v e r t i c a l I.P. o f t h e s e compounds when p l o t t e d a g a i n s t za*, a l s o l i e on a s t r a i g h t l i n e p a r a l l e l t o t h e l i n e f o r 3s t e r m v a l u e s . T h i s means t h a t t h e b i n d i n g e n e r g y o f t h e h i g h e s t f i l l e d M.O. d e c r e a s e s 119. > CD 13 12-II-10-9 8^ 7 4-3-2-V • ,<cr -a -a' ro o CM x o ro o nr 0 0 U X O o ro ro X X O U -r O cvi. ^ X X 31 O o X o ro V V X o Ist vertical LP. o^-3s term -—3p term -17—3d term 0 -0.4-0.2 0.0 0.2-04 0.6 0.8 1.0 1.2 cr F i g u r e 25. E f f e c t ' o f a l k y l s u b s t i t u t i o n on' Rydberg' t e r m v a l u e s ' a n d f i r s t i o n i z a t i o n p o t e n t i a l s i n a l k y l d e r i v a t i v e s o f w a t e r . 120. a t t h e same r a t e as t h e b i d n i n g e nergy o f t h e 3s Rydberg o r b i t a l . We a l s o p l o t t h e 3p term v a l u e s and 3d term v a l u e s w i t h r e s p e c t t o t h e f i r s t I.P. i n t h e same g r a p h . ( F o r s p l i t 3p l e v e l s , we choose t h e a r i t h m e t i c mean o f t h e two s p l i t t e r m s . ) . I t can be seen t h a t t h e r a t e o f d e c r e a s e o f t h e 3p term v a l u e ( i . e . b i n d i n g e n e r g y o f t h e 3p Rydberg o r b i t a l ) i s l o w e r w h i l e t h e 3d t e r m v a l u e s ( b i n d i n g e n e r g y o f t h e 3d Rydberg o r b i t a l ) a r e a l m o s t c o n s t a n t . The d e c r e a s e i n t h e f i r s t I.P. ( b i n d i n g e n e r g y o f t h e h i g h e s t f i l l e d M.O. i . e . t h e non-bonding e l e c t r o n i n oxygen) w i t h i n c r e a s i n g p o l a r e f f e c t i s e x p e c t e d because an i n c r e a s e i n n e g a t i v e c h a r g e on t h e oxygen atom due t o char g e d o n a t i o n by a d j a c e n t a l k y l groups w i ' l l l o w e r t h e l o n e p a i r b i n d i n g e n e r g y . An e l e c t r o n i n t h e 3s Rydberg s t a t e i s more p e n e t r a t i n g than theft i n t h e 3p o r 3d Rydberg s t a t e s . T h e r e f o r e the 3s b i n d i n g energy may s t i l l be a f f e c t e d t o t h e same e x t e n t by p o l a r e f f e c t s o f t h e s u b s t i t u e n t s as i n t h e c a s e o f t h e h i g h e s t f i l l e d M.O. The r e s u l t i s t h a t f o r compounds c o n t a i n i n g CO bonds ( e x c e p t e t h y l e n e o x i d e ) , the p o s i t i o n o f t h e f i r s t t r a n s i t i o n i s q u i t e i n s e n s i t i v e t o a l k y l s u b s t i t u t i o n . These a l l o c c u r a t about 6.6 - 6.8 eV. T h i s f a c t may be u s e f u l f o r i d e n t i f i c a t i o n o f CO bands i n s a t u r a t e d a l i p h a t i c compound. E l e c t r o n s i n the 3p and 3d Rydberg s t a t e become more and more d i f f u s e and the d i s t a n c e from t h e c o r e i s l a r g e r . As a r e s u l t b i n d i n g e nergy i s l e s s s u b j e c t e d t o t h e i n f l u e n c e o f changes i n t h e c o r e n e g a t i v e c h a r g e s due t o p o l a r e f f e c t s o f t h e a l k y l s u b s t i t u e n t s . The r a t e o f d e c r e a s e o f 3p b i n d i n g e n e r g i e s i s o n l y about 1/6 t h a t o f t h e 3s b i n d i n g e nergy w h i l e t h e b i n d i n g e n e r g y o f t h e more d i f f u s e 3d e l e c t r o n show no o b v i o u s dependence on t h e p o l a r e f f e c t o f a l k y l s u b s t i t u e n t s . When a hydrogen atom a d j a c e n t t o an oxygen atom i s r e p l a c e d by a methyl g r o u p , t h e d e c r e a s e i n 3s term v a l u e i s much l a r g e r than i n t h e case when the hydrogen atom a d j a c e n t t o 121. a c a r b o n atom i s r e p l a c e d by a methyl group. T h i s i s s i m p l y because t h e p o l a r e f f e c t o f a methyl group on t h e c h a r g e o f t h e oxygen atom i s s m a l l e r where i t i s i n t h e $ p o s i t i o n . With a t a b l e o f T a f t a* v a l u e s [95] and t h e graph i n F i g u r e 25, the e nergy p o s i t i o n o f t h e f i r s t few t r a n s i t i o n s i n t h e e l e c t r o n i c s p e c t r u m o f common a l k y l d e r i v a t i v e s o f w a t e r can be p r e d i c t e d i n most c a s e s t o w i t h i n ± 0.2 eV u s i n g t h e term v a l u e scheme. C o n v e r s e l y , t h i s may be o f v a l u e i n r e c o g n i z i n g t h e a l k y l s u b s t i t u e n t s . A l c o h o l s have a p o s i t i v e Ea* v a l u e and a l s o can p r o b a b l y be d i s t i n g u i s h e d from e t h e r s by t h e h i g h e r r e l a t i v e i n t e n s i t y o f t h e f i r s t band i n e t h e r s . A l s o , t h e p r o f i l e o f t h e f i r s t band i n a l c o h o l i s much b r o a d e r and d i f f u s e . R o b i n has t a k e n a s l i g h t l y d i f f e r e n t a p p r o a c h i n c o n s i d e r i n g t h e e f f e c t o f a l k y l s u b s t i t u t i o n i n t h e e l e c t r o n i c s p e c t r a o f o r g a n i c m o l e c u l e s . Some d i s c u s s i o n o f t h i s i s i n s e c t i o n 6.1. D e t a i l s a r e a v a i l a b l e i n r e f . 66. 122. CHAPTER V I I I ELECTRONIC SPECTRA OF SOME CARBONYL COMPOUNDS BY  ELECTRON IMPACT SPECTROSCOPY 8.1. I n t r o d u c t i o n . O n ly a few c a r b o n y l compounds have e n e r g y l o s s e l e c t r o n impact s p e c t r a r e p o r t e d i n t h e l i t e r a t u r e . S i l v e r m a n and L a s s e t t r e [ 9 7 ] p r e s e n t e d low r e s o l u t i o n s p e c t r a o f a c e t o n e and 2-butanone a t impact e n e r g i e s o f 220 and 500 eV and s c a t t e r i n g a n g l e s o f 2° and 7°. No a t t e m p t was made t o l o c a t e t h e e l e c t r o n i c s t a t e s i n t h e s e compounds. The o n l y r e p o r t e d h i g h r e s o l u t i o n e l e c t r o n impact s p e c t r u m o f a c a r b o n y l compound i s t h a t o f f o r m a l d e h y d e , s t u d i e d by Weiss e t a l . [ 9 8 ] . A l t h o u g h no h i g h r e s o l u t i o n e l e c t r o n impact work has been done on h i g h e r a l d e h y d e s and k e t o n e s , t h e vacuum u l t r a v i o l e t a b s o r p t i o n s p e c t r a have been r e p o r t e d some y e a r s ago f o r f o r m a l d e h y d e [ 9 9 , 1 0 0 ] , a c e t a l d e h y d e [ 1 0 1 ] , a c e t o n e [102,103] and a c r o l e i n ( p r o p e n a l ) [ 1 0 4 ] . More r e c e n t l y , Lucazeau and S a n d o r f y [105] have measured t h e fa r - U V s p e c t r a o f some s i m p l e a l d e h y d e s . Some o f t h e t r a n s i t i o n s have been a s s i g n e d t o v a r i o u s Rydberg s e r i e s . One of t h e main d i f f i c u l t i e s i n a s s i g n i n g Rydberg s e r i e s a t t h e ti m e was t h e l a c k o f an a c c u r a t e , i n d e p e n d e n t method t o d e t e r m i n e i o n i z a t i o n p o t e n t i a l s . T h i s can sometimes l e a d t o i n c o r r e c t o r c o n t r o v e r s i a l a s s i g n m e n t s i f t h e s e r i e s l i m i t chosen i s wrong. A l s o , h i g h e r i o n i z a t i o n p o t e n t i a l s c a n n o t be d e t e r m i n e d e a s i l y from o p t i c a l a b s o r p t i o n s p e c t r a . P r e s e n t l y , p h o t o -e l e c t r o n s p e c t r o s c o p y s t a n d s as a c o n v e n i e n t and a c c u r a t e method t o d e t e r m i n e t h e v a r i o u s i o n i z a t i o n p o t e n t i a l s o f compounds. U s i n g t h e 123. measured term v a l u e w i t h r e s p e c t t o v a r i o u s i o n i z a t i o n p o t e n t i a l s and t h e c a l c u l a t e d quantum d e f e c t , many e x c i t e d s t a t e s can be a s s i g n e d on t h e b a s i s o f Rydberg t r a n s i t i o n s . . Energy l o s s s p e c t r a o f t h e compounds s t u d i e d were d e t e r m i n e d a t an i mpact energy o f 100 eV and a s c a t t e r i n g a n g l e o f 2°. The samples used were o b t a i n e d c o m m e r c i a l l y and were used w i t h o u t f u r t h e r p u r i f i c a t i o n . The energy l o s s s c a l e was f i x e d w i t h r e s p e c t t o t h e e l a s t i c a l l y s c a t t e r e d peak. P h o t o e l e c t r o n s p e c t r a o f t h e compounds s t u d i e d ( i f n o t r e p o r t e d i n l i t e r a t u r e ) were measured i n t h i s l a b o r a t o r y . The p h o t o e l e c t r o n s p e c t r a a r e shown i n t h e a p p e n d i x . 8 . 2 . S a t u r a t e d A l d e h y d e s 8.2.1. Formaldehyde and a c e t a l d e h y d e . The ground s t a t e e l e c t r o n c o n f i g u r a t i o n and o u t e r o r b i t a l e n e r g i e s ( v e r t i c a l ) o f t h e f o r m a l d e h y d e m o l e c u l e ( C 2 v ) a r e g i v e n by T u r n e r e t a l . [82] as ( l s 0 ) 2 ( l s c ) 2 ( l a ] ) 2 ( 2 9 ] ) 2 ( 3 3 l ) 2 ( l b 2 ) 2 ( l b , ) 2 ( 2 b 2 ) 2 .... 1A ] -16.60 -16.01 -14.39 -10.88 eV The 2 b 2 o r b i t a l c o n t a i n s e s s e n t i a l l y t h e oxygen non-bonding e l e c t r o n s and t h e l b , o r b i t a l t h e s t r o n g l y bonding e l e c t r o n s i n t h e CO T r-bond. When one o f t h e hydrogen atoms i s r e p l a c e d by a m e t h y l group t o fo r m a c e t a l d e h y d e , t h e symmetry i s l o w e r e d t o C g. The a, and b 2 o r b i t a l s i n C 2 v symmetry a r e c o r r e l a t e d w i t h t h e a' o r b i t a l i n C g symmetry w h i l e t h e b, o r b i t a l c o r r e l a t e s w i t h t h e a" o r b i t a l s . A t t h e same ti m e two a 1 and one a" o r b i t a l s (CH b o n d i n g ) a r e i n t r o d u c e d . So t h e e l e c t r o n c o n f i g u r a t i o n o f t h e a c e t a l d e h y d e m o l e c u l e can be r e p r e s e n t e d as 124. ( l s Q ) 2 ( l s ^ ) 2 ( l s ^ ) 2 ( l a 1 ) 2 (2a«) 2 ( 3 a 1 ) 2 (4a«) 2 ( 5 a 1 ) 2 ( l a " ) 2 ( 6 a 1 ) 2 ( 2 a " ) 2 ( 7 a 1 ) 2 By a n a l o g y , 7 a 1 r e p r e s e n t s t h e oxygen non-bonding e l e c t r o n s w h i l e 2a" c o n t a i n s t h e CO T r-bonding e l e c t r o n s . The en e r g y p o s i t i o n o f t h e l a " o r b i t a l i s d e f i n i t e l y l o wer ( h i g h e r IP) t h a n t h e 2a" and t h e 7a' o r b i t a l s , but i t s p o s i t i o n r e l a t i v e t o o t h e r o r b i t a l s i s not known. Weiss e t a l . [ 9 8] have r e p o r t e d t h e e l e c t r o n impact spectrum o f fo r m a l d e h y d e i n t h e energy l o s s range between 0 and 16 eV. In t h e r e g i o n 7 - 1 1 eV, s t r o n g Rydberg s e r i e s a r e o b s e r v e d and can be i d e n t i f i e d w i t h t h e s, p and d s e r i e s r e p o r t e d i n l i t e r a t u r e from u l t r a v i o l e t a b s o r p t i o n s t u d i e s [ 9 9 , 1 0 0 ] . A c c o r d i n g t o Weiss e t a l . [ 9 8 ] t h e f i r s t s e r i e s has i t s f i r s t member a t 7.10 eV and a term v a l u e o f 3.78 eV w i t h r e s p e c t t o t h e f i r s t v e r t i c a l I.P. o f 10.88 eV d e t e r m i n e d by PES [ 8 2 ] . T h i s g i v e s a l a r g e quantum d e f e c t o f 1.11 and so c o r r e s p o n d s t o a t r a n s f e r o f an e l e c t r o n from t h e h i g h e s t f i l l e d o r b i t a l o f t h e ground s t a t e 2 b 2 t o t h e nsa-j o r b i t a l s . The next two s t r o n g peaks a t 7.98 and 8.14 eV c o r r e s p o n d t o t h e f i r s t member o f t h e Rydberg s e r i e s t o two o f t h e o r b i t a l s : a , , b, and b 2 but t h e t r a n s i t i o n s 2 b 2 •+ npb, a r e f o r b i d d e n i n m o l e c u l e s o f C 2 v symmetry. The quantum d e f e c t s f o r t h e s e n p b 2 and npa-j Rydberg s e r i e s a r e 0-83 and 0.74 r e s p e c t i v e l y . The f o u r t h Rydberg s e r i e s , w i t h t h e f i r s t member a t 8.88 eV, p r o b a b l y c o r r e s p o n d s t o a t r a n s f e r o f an e l e c t r o n f r o m 2 b 2 t o nd a l t h o u g h t h e quantum d e f e c t (0.39) i s r a t h e r l a r g e f o r t h i s a s s i g n m e n t . One more s h a r p peak a t 9.03 eV may c o r r e s p o n d t o a n o t h e r component o f t h e s p l i t 3d Rydberg o r b i t a l s . We have d e t e r m i n e d t h e h i g h r e s o l u t i o n e l e c t r o n impact energy l o s s 125. s pectrum o f a c e t a l d e h y d e i n t h e e nergy l o s s r e g i o n o f 6.4 - 10.0 eV ( F i g u r e 2 6 ) . The vacuum u l t r a v i o l e t a b s o r p t i o n s p e c t r a i n t h e 6.8 -10.0 eV r e g i o n and t h e 6.8 - 8.4 eV r e g i o n have been i n v e s t i g a t e d by Walsh [101 ] and Lake and H a r r i s o n [ 1 0 6 ] r e s p e c t i v e l y . The p h o t o e l e c t r o n s p e c t r u m d e t e r m i n e d i n t h i s l a b o r a t o r y shows th e f i r s t band t o c o n s i s t o f t h r e e v i b r a t i o n a l components a t 10.21, 10.37 and 10.56 eV r e s p e c t i v e l y c o r r e s p o n d i n g t o t h e removal o f t h e non-bonding e l e c t r o n i n oxygen ( 7 a 1 ) . The f i r s t band i n t h e e l e c t r o n impact spectrum o f a c e t a l d e h y d e a l s o e x h i b i t s t h r e e components, A, B and C a t 6.82, 6.97 and 7.14 eV r e s p e c t i v e l y (see F i g u r e 2 6 ) T h e term v a l u e o f t h e f i r s t component w i t h r e s p e c t t o t h e f i r s t v e r t i c a l I.P. o f 10.21 eV i s 3.39 eV. In agreement w i t h Walsh [ 1 0 1 ] , t h i s i s a s s i g n e d t o a 3s Rydberg upper s t a t e w i t h o u t any v i b r a t i o n a l e x c i t a t i o n . The s e p a r a t i o n between A and B i s 0.148 ± 0.005 eV w h i l e t h a t between B and C i s 0.172 ± 0.005 eV. The d i f f e r e n c e i n t h e s e s p a c i n g s i s t o o l a r g e t o be a c c o u n t e d f o r by e x c i t a t i o n o f t h e same v i b r a t i o n a l mode. So B i s t e n t a t i v e l y a s s i g n e d 3s + v^, p r o b a b l y c o r r e s p o n d i n g t o t h e C = 0 s t r e t c h i n g i n t h e e x c i t e d s t a t e , w i t h a v i b r a t i o n a l e nergy o f 0.148 eV w h i l e C i s a s s i g n e d 3s + v-| (C-H s t r e t c h ) w i t h a v i b r a t i o n a l energy o f 0.320 eV. The c a l c u l a t e d quantum d e f e c t f o r peak A i s 1.00 and from t h i s t h e o t h e r members o f t h e 7a' -> ns s e r i e s a r e p r e d i c t e d a t 8.70, 9.36, 9.67 and 9.88 eV f o r n = 4, 5, 6, 7 r e s p e c t i v e l y . Peaks a r e o b s e r v e d i n our s p e c t r u m w i t h e n e r g i e s o f 8.82, 9.43, ^.71 and 9.88 eV r e s p e c t i v e l y (peaks K, P, S, U) and have been a s s i g n e d t o t h e s e t r a n s i t i o n s . The 4s + upper s t a t e may have c o n t r i b -u t i o n s t o t h e peak L a t 8.96 eV. The most i n t e n s e peak i n t h e s p e c t r u m , D, o c c u r s a t 7.47 eV. 8.0 9.0 Energy Loss(eV) 10.0 F i g u r e 26. E l e c t r o n impact s p e c t r u m o f a c e t a l d e h y d e a t 100 eV, 2°. 127. T h i s g i v e s a term v a l u e o f 2.74 eV w i t h r e s p e c t t o t h e f i r s t v e r t i c a l I.P. (10.21 eV) and t h e r e f o r e a quantum d e f e c t o f 0.77. T h i s seems t o i n d i c a t e t h a t t h e upper s t a t e i s one o f t h e s p l i t 3p Rydberg o r b i t a l s a n a l o g o u s t o t h e c a s e o f f o r m a l d e h y d e . Three such o r b i t a l s i n f o r m a l d e h y d e , a,, b-j and b^ become t h e a 1 , a" and a' o r b i t a l s r e s p e c t i v e l y i n t h e l o w e r symmetry o f a c e t a l d e h y d e . A l l t h r e e a r e now a l l o w e d i n C s symmetry. The broad peak F a t 7.78 eV p r o b a b l y c o n s i s t s o f two o f t h e o v e r l a p p i n g 3p Rydberg s t a t e s ( 3 p 1 ) w h i l e t h e r e l a t i v e l y s h a r p e r peak D i s p r o b a b l y due t o a s i n g l e component ( 3 p ) . Peaks E and G can t h e n be s i m p l y e x p l a i n e d by h a v i n g 3p + v 4 and 3p'•+ v 4 upper s t a t e s . So t h e two peaks F and G, w h i c h a r e l e f t u n a s s i g n e d by Walsh [ 1 0 1 ] , can now be i n t e r p r e t e d as Rydberg t r a n s i t i o n s 7a' -> 3 p 1 ( + v 4 ) . The c a l c u l a t e d p o s i t i o n s f o r t h e h i g h e r members o f t h e np Rydberg s e r i e s a r e 8.91, 9.45 and 9.72 eV w h i l e t h o s e f o r t h e np' Rydberg s e r i e s a r e 9.01, 9.50 and 9.74 eV r e s p e c t i v e l y . The r e s o l u t i o n o f t h e p r e s e n t s p e c t r o m e t e r i s not enough t o s e p a r a t e them and so t h e y appear as s i n g l e peaks L, Q and T a t 8.96, 9.51 and 9.73 eV r e s p e c t i v e l y . Peak M can be r e g a r d e d as a v i b r a t i o n a l component ( v ^ ) o f peak L. Peak H a t 8.43 eV has a term v a l u e o f 1.78 eV w i t h r e s p e c t t o t h e f i r s t v e r t i c a l I.P. (10.21 eV) and t h u s a quantum d e f e c t o f 0.24. T h i s i s a s s i g n e d t o t h e t r a n s i t i o n t o one o f t h e 3d Rydberg o r b i t a l s . T h i s peak H i s v e r y a symmetric and shows a broad s h o u l d e r on t h e low e n e r g y s i d e . T h i s may be caused by o t h e r 3d components o v e r l a p p i n g one a n o t h e r . Small peaks I and J h a v i n g e n e r g y s e p a r a t i o n s o f 0.13 and 0.27 eV w i t h r e s p e c t t o H may c o r r e s p o n d t o one o r two v i b r a t i o n a l quanta r e s p e c t i v e l y . The peaks N a t 9.24 eV and t h e s m a l l s t e p R a t 9.64 eV can be a s s i g n e d 128. 4d and 5d upper s t a t e s r e s p e c t i v e l y . A summary o f t h e Rydberg t r a n s i t i o n s i d e n t i f i e d i n a c e t a l d e h y d e i s p r e s e n t e d i n T a b l e 7 and t h e o b s e r v e d energy o f t h e peaks a g r e e w i t h t h o s e g i v e n by Walsh [101] t o b e t t e r t h a n 0.02 eV. The 7 a 1 ns s e r i e s i s one o f t h e l o n g e s t Rydberg s e r i e s o b s e r v e d i n o p t i c a l s p e c t r o s c o p y . The I.P. f o r t h e 7a' o r b i t a l was d e t e r m i n e d a c c u r a t e by Walsh [101] from h i s spectrum t o be 10.229 eV and t h i s v a l u e i s c o n s i s t e n t w i t h our d e t e r m i n a t i o n o f 10.211 ± 0.010 eV by PES. 8.2.2. P r o p i o n a l d e h y d e and i s o b u t y r a l d e h y d e . F i g u r e 27 shows the e l e c t r o n impact s p e c t r a o f a c e t a l d e h y d e , p r o p i o n a l d e h y d e and i s o b u t y r a l d e h y d e a t an impact energy o f 100 eV and 2° s c a t t e r i n g a n g l e o v e r t h e energy l o s s range 3 - 1 3 eV. The s p e c t r a o f a l l t h r e e compounds between 3 t o 9 eV a r e v e r y s i m i l a r . A l s o t h e e l e c t r o n impact spectrum o f p r o p i o n a l d e h y d e ( F i g u r e 27, m i d d l e ) o b s e r v e d by us i s i n good agreement w i t h t h e vacuum u l t r a v i o l e t s p e c t r a s t u d i e d by Barnes and Simpson [ 1 0 7 ] , In t h e energy l o s s r e g i o n o f about 4 eV, t h e r e i s a v e r y broad and weak t r a n s i t i o n . M u l l i k e n [ 1 0 8 ] has e x p l i c i t l y g i v e n t h e e l e c t r o n c o n f i g u r a t i o n f o r t h e normal s t a t e s o f f o r m a l d e h y d e and a c e t a l d e h y d e . T h e i r s t r u c t u r e s , i o n i z a t i o n p o t e n t i a l s and t h e l o w e s t energy band s p e c t r a were i n t e r p r e t e d i n r e l a t i o n t o t h e s e c o n f i g u r a t i o n s . The l o w e s t energy band system c o r r e s p o n d s [108] t o t h e e x c i t a t i o n o f a non-bonding e l e c t r o n i n oxygen t o an o r b i t a l w h i c h i s l a r g e l y l o c a l i s e d i n t h e C = 0 bond, and w h i c h has a n t i - b o n d i n g c h a r a c t e r . McMurray [109] has used i n t e n s i t y c a l c u l a t i o n s t o h e l p i n d e c i d i n g w h i c h o f t h e two t h e o r e t i c a l l y p r e d i c t e d t r a n s i t i o n s s h o u l d be i d e n t i f i e d w i t h t h e weak, l o w e s t energy t r a n s i t i o n c h a r a c t e r i s t i c o f t h e u n c o n j u g a t e d " ^ C = 0 PEAK OBSERVED ENERGY (eV) TERM3 VALUE ( e V ) ASSIGNMENT CALCULATED ENERGY (eV) CALCULATED QUANTUM DEFECT A B C 6 . 8 2 6 . 9 7 7 . 1 4 3 .39 3 .24 3.07 7 a ' 3s -> 3s + -> 3s + v i 1 . 0 0 D E F G 7 . 4 7 7 .59 7 . 7 8 7 . 90 2.74 2.62 2.43 2.31 7a' ->• 3p + 3p + vk -> 3 p ' * 3 p ' + V t f 0.77 0.64 H I J 8.43 8 .56 8 . 70 1.78 1.65 1.51 7a' + 3d ->• 3d + vi» + 3d + 2V!, 0.24 K L 8.82 8 .96 1.39 1.25 7a' -> 4s -»• 4s + vk 8.70 L M 8 .96 9 .06 1.25 1.15 7a' •»• 4p 4p + v^ 8.91, 9.01 N 0 9 .24 • 9.38 0.97 0.83 7a' -» 4d + 4d + v 4 9.25 P 9.43 0.78 7a' 5s 9.36 Q 9.51 0.70 7a' -> 5p, 5p' 9.45, 9.50 R 9.64 0.57 7a' •*• 5d 9.61 S 9.71 0.50 7a'' + 6s 9.67 T 9.73 0.48 7a' 6p, 6p' 9.72, 9.74 . U 9.88 0.33 3.39 7a T -t- 7s l a " + 3p 9.83 V 10.39 2.88 l a " + 3p TABLE 7 Rydberg transitions in acetaldehyde a is Assigned with respect to PES ionization potentials for acetaldehyde; 10.21, 13.3 14.2 IOOeV,2 c D 130. H Q CH3CHO x4 M I CO h->-CH <• r r \-m r r < >-H CO 100 eV, 2' x4 A D E F G CH3CH2CHO " i i-i 0_'t H t CM f LL) h-50eV,2 c 100 eV, 2° - ' A B £ C G J(CH3)2CHCHO E F D * "SI CM - ] 1 1 1 r 6 8 10 ENERGY LOSS (eV) 12 F i g u r e 27. E l e c t r o n impact s p e c t r a o f a c e t a l d e h y d e , p r o p i o n a l d e h y d e and i s o b u t y r a l d e h y d e a t 100 eV, 2°. 131. group. In terms o f t h e l o c a l i s e d LCAO MO and t h e AO a p p r o x i m a t i o n s used,, one o f t h e s e t r a n s i t i o n s i s f o r b i d d e n w h i l e t h e c a l c u l a t e d i n t e n s i t y f o r t h e o t h e r a l l o w e d t r a n s i t i o n i s much t o o l a r g e t o be c o m p a t i b l e w i t h t h e low i n t e n s i t i e s o b s e r v e d f o r t h e t r a n s i t i o n . T h i s t r a n s i t i o n s h o u l d , t h e r e f o r e , be a s c r i b e d t o t h e f o r b i d d e n t r a n s i t i o n n -> IT*. In t h i s n o t a t i o n , n r e p r e s e n t s t h e non-bonding l o n e p a i r o f e l e c t r o n s on t h e oxygen atom; a t h e e l e c t r o n s i n t h e C-0 a-bond and TT t h e e l e c t r o n i n t h e C-0 T r-bond. The s u p e r s c r i p t * i n d i c a t e s an a n t i -bonding m o l e c u l a r o r b i t a l . That t h e 4 eV t r a n s i t i o n i n a l d e h y d e s i s a c t u a l l y o p t i c a l l y f o r b i d d e n can be c o r r o b o r a t e d by t h e e l e c t r o n i m p act spectrum o f i s o b u t y r a l d e h y d e run a t two d i f f e r e n t impact e n e r g i e s , 100 eV and 50 eV ( F i g u r e 27, b o t t o m ) . I t i s o b v i o u s t h a t i n t h e 50 eV s p e c t r a , t h e i n t e n s i t y o f t h e 4 eV t r a n s i t i o n r e l a t i v e t o t h e o p t i c a l l y a l l o w e d peak A a t 6.7 eV i s much l a r g e r than i n t h e c a s e o f 100 eV impact energy. So t h e a s s i g n m e n t o f t h i s t r a n s i t i o n t o n -> TT* by o p t i c a l s p e c t r o s c o p i s t s seems t o be w e l l e s t a b l i s h e d . T h i s t r a n s i t i o n s t a r t s below. 3. eV and e x t e n d s up t o about 5 eV.. E x t e n s i v e o p t i c a l s t u d i e s have been made o f t h i s r e g i o n o f t h e s p e c t r a o f a l d e h y d e s (see r e f . 6 2 ) . At the low energy s i d e o f t h i s t r a n s i t i o n , a l a r g e number o f bands w i t h a c o m p l i c a t e d f i n e s t r u c t u r e a r e o b s e r v e d ; , a t h i g h e r energy t h e bands become d i f f u s e and merge i n t o a c o n t i n u o u s a b s o r p t i o n . The v i b r a t i o n a l s t r u c t u r e i s e x t r e m e l y c o m p l i c a t e d and c o n t r a d i c t o r y v a l u e s f o r t h e v i b r a t i o n a l f r e q u e n c i e s and even t h e p o s i t i o n o f t h e 0-0 band may be found i n t h e l i t e r a t u r e . The r e s o l u t i o n o f our s p e c t r o m e t e r i s not , s u f f i c i e n t t o see any o f t h e s e f i n e s t r u c t u r e s . The o t h e r peaks i n t h e s p e c t r a o f p r o p i o n a l d e h y d e and i s o b u t y r -132. a l d e h y d e can a l s o be i n t e r p r e t e d i n terms o f Rydberg t r a n s i t i o n s f o l l o w i n g t h e example o f a c e t a l d e h y d e . I t seems t h a t t h e peaks become b r o a d e r i n t h e s e more complex m o l e c u l e s and l i t t l e v i b r a t i o n a l s t r u c t u r e i s o b s e r v e d . The a s s i g n m e n t s a r e summarised i n T a b l e 8, where iji r e p r e s e n t s t h e n t h h i g h e s t f i l l e d m o l e c u l a r o r b i t a l . In p r o p i o n a l d e h y d e , the peak A a t 6.78 eV i s a s s i g n e d 3s and some v i b r a t i o n a l s t r u c t u r e , a l t h o u g h not w e l l r e s o l v e d , i s s t i l l e v i d e n t . The -> 3p t r a n s i t i o n s o n l y appear as a broad peak B a t 7.42 eV and t h e d i f f e r e n t components a r e not d i s t i n g u i s h e d . The •-»• 3d t r a n s i t i o n a p p e ars as a s h o u l d e r C a t 8.21 eV w h i l e i ^ ' -> 4s and 4p appears as s e p a r a t e peaks D and E a t 8.44 and 8.79 eV. The s m a l l b u l g e F a t 9.13 eV on t h e i n c r e a s i n g ramp may c o r r e s p o n d t o e i t h e r if^ -> 5s o r ^ 3s. The broad peak G w i t h a maximum a t 9.67 eV i s l i k e l y t o be t h e e n v e l o p e o f many Rydberg t r a n s i t i o n s l e a d i n g t o t h e second and t h i r d I.P. a t 12.4 and 13,2 eV r e s p e c t i v e l y . A s i m i l a r broad peak V i n t h e spectrum o f a c e t a l d e h y d e m a x i m i s i n g a t about 10.4 eV may be t h e e n v e l o p e o f t h e t r a n s i t i o n from t h e l a " (n o r b i t a l ) t o d i f f e r e n t components o f t h e 3p Rydberg o r b i t a l . The r e a s o n i n g b e h i n d t h i s a s s i g n m e n t i s t h a t t h e term v a l u e s f o r Rydberg t r a n s i t i o n s a r e q u i t e i n d e p e n d e n t o f t h e o r i g i n a l o r b i t a l [ 6 4 , 6 5 ] . F o r i s o b u t y r a l d e h y d e , t h e ^-j -»• 3s t r a n s i t i o n A a t 6.69 eV shows no v i b r a t i o n a l s t r u c t u r e a t a l l but two s m a l l peaks C and D do appear on t h e h i g h energy s i d e o f peak B a t 7.40 eV. So B i s a s s i g n e d 3p w h i l e C and D a r e a s s i g n e d t h e two v i b r a t i o n a l components o f ty-^ -»• 3p*. T h i s i s a r e a s o n a b l e assignment i f t h e d e c r e a s e (compare T a b l e s 7 and 8) i n 3p t e r m v a l u e s i n g o i n g f r o m CH^CHO t o (CH^CHCHO i s assumed t o be t h e same (0.3 eV) f o r each 3p component (see T a b l e s 7 and 8 ) . The CH3CH2CHO Propionaldehyde (CH^CHCHO isobutyraldehyde PEAK ENERGY (eV) TRANSITION TERM3 VALUE (eV) PEAK ENERGY (eV) TRANSITION TERM 3 VALUE (eV) A 6.78 *1 -y 3s 1 3.21 A 6.69 *1 3s 3.13 B 7.42 • l 3p 2.57 i B 7.40 -> 3p 2.42 C 8.21 , *1 3d 1.78 C D 7.69 7.83 1 3 p ' 2.13 1.99 D 8.44 *1 4s 1.55 E 8.79 . ' *1 4p 1.20 E 8.11 *1 *1 3d 4s 1.70 F 9.13 *1 -V 5s 3s 0.86 3.24 \ F 8.63 *1 4p 1.19 G 9,7 ^2 ^ 3 -V -> 3p . 3s 2.7 3.5 G H ' 9.4 10.0 •*3 If; 3 n -> -»• 3p 3s 3p 3s 2.6 3.2 2.6 3.4 TABLE 8 E l e c t r o n i c T r a n s i t i o n i n propionaldehyde r.nd isobutyraldehyde a) assigned with respect to PES i o n i z a t i o n p o t e n t i a l s (for propionaldehyde; 9.99, 12.4, 13.2, 13.7, and 14.1 eV and for isobutyraldehyde; 9.82, 12.0, 12.6, 13.4 and 14.1 e V ) . 134. -*• 3d and 4s a r e p r o b a b l y t o o c l o s e i n energy t o be r e s o l v e d and t h e y appear as t h e asymmetric peak E a t 8.11 eV. The •> 4p t r a n s i t i o n p r o b a b l y appears as peak F a t 8.63 eV. Broad peaks G and H s h o u l d be the e n v e l o p e o f Rydberg s t a t e s l e a d i n g t o h i g h e r I.P.'s l i s t e d i n T a b l e 8. 8.2.3. Rydberg and v a l e n c e a s s i g n m e n t s . The Rydberg a s s i g n m e n t i s by no means t h e o n l y i n t e r p r e t a t i o n o f t h e s p e c t r a o f a l d e h y d e s . F o r example, t h e t h r e e h i g h e s t f i l l e d m o l e c u l a r 2 2 2 o r b i t a l s i n a c e t a l d e h y d e , ( 6 a 1 ) (2a") ( 7 a 1 ) c o r r e s p o n d t o t h e a , TT and n e l e c t r o n s r e s p e c t i v e l y mentioned i n t h e l a s t p a r a g r a p h . So t h e t h r e e t r a n s i t i o n s o f l o w e s t energy c o u l d be n -> TT*, n -»• a* and v •> TT* on t h e v a l e n c e t r a n s i t i o n p i c t u r e . Walsh [ 1 0 1 ] has a l s o i d e n t i f i e d t h e t r a n s i t i o n s i n t h e 6.8 eV r e g i o n i n a c e t a l d e h y d e , as b e i n g due t o t h e 7 a 1 •> 3s t r a n s i t i o n , and/or t h e n -> a * t r a n s i t i o n . A t t h e same t i m e , t h e t r a n s i t i o n a t 7.5 eV was c l a s s i f i e d as a Rydberg t r a n s i t i o n , 7a' -> 3p and/or the i n t e r - v l a e n c e - s h e l l t r a n s i t i o n TT -> IT*. So i t a p p e a r s p o s s i b l e t o c l a s s i f y t h e upper s t a t e s o f t h e s e two t r a n s i t i o n s e i t h e r as a p e r t u r b e d Rydberg s t a t e o r as an i n t e r - v a l e n c e - s h e l l s t a t e , e.g., t h e 3s Rydberg o r b i t a l can a l s o be c o n s i d e r e d as t h e a* o r b i t a l . The p h o t o e l e c t r o n s p e c t r u m o f a c e t a l d e h y d e shows f i r s t a s h a r p band accompanied by v i b r a t i o n a l s t r u c t u r e w i t h t h e v e r t i c a l I.P. a t 10.21 eV. The second band i s broad and peaks a t about 13.3 eV. I f t h e ir IT* t r a n s i t i o n o c c u r s a t about 7,5 eV, t h e b i n d i n g e n e r g y o f t h e TT* o r b i t a l i s 13.3 - 7.5 = 5.8 eV and we e x p e c t t h e n •> TT* t r a n s i t i o n t o be broad and o c c u r a t about 10.2 - 5.8 = 4.4 eV. T h i s i n d i c a t e s t h a t t h e i n t e r - v a l e n c e - s h e l l t r a n s i t i o n p i c t u r e i s a l s o c o n s i s t e n t w i t h t h e o b s e r v e d e l e c t r o n i m p a ct 135. spectrum and p h o t o e l e c t r o n spectrum but t h e r e i s some d i f f i c u l t y i n e x p l a i n i n g t h e o c c u r r e n c e o f peaks F and G ( F i g u r e 26) l e f t u n a s s i g n e d by Walsh [ 1 0 1 ] . We a r e i n f a v o u r o f t h e Rydberg a s s i g n m e n t because o f t h e good m a t h e m a t i c a l f i t f o r a c e t a l d e h y d e and t h e f a c t t h a t t h e o v e r a l l s p e c t r a o f a l d e h y d e s can be i n t e r p r e t e d e a s i l y and s y s t e m a t i c a l l y . S i m i l a r a s s i g n m e n t s a r e s u g g e s t e d by Lucazeau and S a n d o r f y [ 1 0 5 ] . Basch e t a l . [67] have c l a i m e d t h a t Rydberg s t a t e s can be d i s t i n g u i s h e d from non-Rydberg s t a t e s by r u n n i n g t h e o p t i c a l s p e c t r a a t h i g h p r e s s u r e s o r i n a condensed phase ( i . e . , as a s o l u t i o n o r as a p o l y c r y s t a l l i n e f i l m ) where t h e Rydberg t r a n s i t i o n s s h o u l d be s u p p r e s s e d and t h e s p e c t r a t h e n u s u a l l y o n l y show broad f e a t u r e l e s s c o n t i n u o u s a b s o r p t i o n bands w h i c h can be a s s i g n e d t o v a l e n c e s h e l l e x c i t a t i o n s . T h i s e f f e c t can be c l e a r l y seen i n t h e work o f Lucazeau and S a n d o r f y [ 1 0 5 ] . 8.2.4. E f f e c t o f a l k y l s u b s t i t u e n t s . In t h e p r e v i o u s c h a p t e r on t h e e l e c t r o n impact s p e c t r a o f t h e a l k y l d e r i v a t i v e s o f w a t e r t h e e f f e c t o f a l k y l s u b s t i t u e n t s on Rydberg o r b i t a l e n e r g i e s has been d i s c u s s e d u s i n g T a f t a* v a l u e s , w h i c h a r e a q u a n t i t -a t i v e measure o f t h e net p o l a r e f f e c t o f t h e s u b s t i t u e n t . As shown i n F i g u r e 28, t h e p l o t o f t h e f i r s t I . P . , the 3 s , 3p and 3d term v a l u e s a g a i n s t t h e sum o f t h e T a f t a* v a l u e s o f t h e s u b s t i t u e n t s on both s i d e s o f t h e c a r b o n y l group (£a*) a r e a p p r o x i m a t e l y s t r a i g h t l i n e s . As i n t h e c a s e f o r t h e a l k y l d e r i v a t i v e s o f w a t e r , t h e s l o p e o f t h e s t r a i g h t l i n e f o r t h e 3s term v a l u e s i s g r e a t e r t h a n t h a t f o r t h e 3p term v a l u e s . 1 3 6 . 3d term U ~ T — — i 1 1 1 1 n — ~ n r~ 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 F i g u r e 28. E f f e c t o f a l k y l s u b s t i t u t i o n on Rydberg term v a l u e s and f i r s t i o n i z a t i o n p o t e n t i a l s - i n a l d e h y d e s . 137. F i n a l l y , t h e s t r a i g h t l i n e f o r t h e 3d term v a l u e has t h e s m a l l e s t s l o p e . The e f f e c t o f r e p l a c i n g one hydrogen i n f o r m a l d e h y d e by an a l k y l s u b s t i t -u e n t i s t o l o w e r t h e I.P. and t h e 3s term v a l u e more t h a n t h e 3p t e r m v a l u e . The change i n t h e 3d term v a l u e i s u s u a l l y s m a l l . T h i s e f f e c t has been e x p l a i n e d by t h e d i f f e r e n t d e g r e e s o f p e n e t r a t i o n o f t h e d i f f e r e n t Rydberg o r b i t a l s . There i s a s h i f t o f about 0.2 eV o f t h e p o s i t i o n o f t h e band A towards l o w e r energy when t h e hydrogen o f f o r m a l d e h y d e i s r e p l a c e d by methyl and a s m a l l e r s h i f t towards l o w e r energy i s o b s e r v e d when t h e a-hydrogen i n a c e t a l d e h y d e i s r e p l a c e d by m e t h y l . T h i s i s r e f l e c t e d i n t h e s l o p e o f t h e s t r a i g h t l i n e f o r t h e 3s t e r m v a l u e b e i n g somewhat s m a l l e r t h a n t h a t f o r t h e f i r s t I.P. S i n c e t h e e l e c t r o n impact s p e c t r a o f t h e s e a l d e h y d e s l o o k v e r y s i m i l a r , a p o t e n t i a l method f o r q u a l i t a t i v e a n a l y s i s o f a l i p h a t i c a l d e h y d e s i s t o r e c o g n i s e t h e a l d e h y d i c group from t h e e l e c t r o n impact s p e c t r u m and t o d e t e r m i n e t h e a l k y l s u b s t i t u e n t s from t h e p l o t o f t h e f i r s t I.P. ( o b t a i n e d by p h o t o e l e c t r o n s p e c t r o s c o p y ) a g a i n s t Ea*. 8 . 3 . S a t u r a t e d Ketones. 8.3.1. A c e t o n e and 2-butanone. The e l e c t r o n c o n f i g u r a t i o n s o f f o r m a l d e h y d e and a c e t a l d e h y d e have been d i s c u s s e d i n s e c t i o n 8.2.1. Based on t h e p h o t o e l e c t r o n work o f T u r n e r e t a l . [ 8 2 ] on f o r m a l d e h y d e and i t s symmetry c o r r e l a t i o n t o a c e t a l d e h y d e , i t i s s u g g e s t e d t h a t t h e h i g h e s t f i l l e d m o l e c u l a r o r b i t a l i n t h e s e two compounds c o n t a i n s t h e non-bonding e l e c t r o n s on t h e oxygen atom and t h e second h i g h e s t f i l l e d m o l e c u l a r o r b i t a l c o n t a i n s t h e 138. e l e c t r o n s i n t h e C-0 Tr-bond. We have o b s e r v e d t h e p h o t o e l e c t r o n s p e c t r a o f a c e t a l d e h y d e and a c e t o n e t o be v e r y s i m i l a r , ( s ee a p p e n d i x ) a t l e a s t f o r t h e f i r s t two bands, e x c e p t f o r a s h i f t o f about 0.7 eV t o l o w e r energy when one more methyl group r e p l a c e s t h e a l d e h y d i c hydrogen i n a c e t a l d e h y d e t o g i v e a c e t o n e . Of c o u r s e , more bands a r e o b s e r v e d f o r a c e t o n e t h a n a c e t a l d e h y d e because more C-H bonding o r b i t a l s a r e a v a i l a b l e f o r i o n i z a t i o n . C o n s e q u e n t l y , i t i s not u n r e a s o n a b l e t o b e l i e v e t h a t t h e o r d e r i n g o f t h e two h i g h e s t o r b i t a l s i s t h e same f o r a c e t o n e and a c e t a l d e -hyde so t h a t t h e h i g h e s t f i l l e d M.O. ( i ^ ) c o n t a i n s t h e non-bonding e l e c t r o n s on t h e oxygen atom. As i n t h e c a s e o f a l d e h y d e s , t h e s p e c t r a o f ketones c o n t a i n a broad r e g i o n o f weak t r a n s i t i o n m a x i m i s i n g a t about 4.3 eV. T h i s i s t h e n -> IT* t r a n s i t i o n and has been d i s c u s s e d f o r a l d e h y d e s i n s e c t i o n 8.2.2. F o l l o w i n g t h e example o f a l d e h y d e s , i t i s p o s s i b l e t o a s s i g n t h e s p e c t r a a t h i g h e r energy l o s s t o Rydberg t r a n s i t i o n s . F i g u r e 29 shows t h e e l e c t r o n impact s p e c t r a o f a c e t o n e * and 2-butanone o v e r t h e energy l o s s r e g i o n 6.0 - 9.7 eV a t an i m p a c t e n e r g y o f 100 eV and 2° s c a t t e r i n g a n g l e . The p h o t o e l e c t r o n s p e c t r a o f t h e s e compounds have been s t u d i e d and t h e f i r s t f i v e I.P.'s a r e l i s t e d a t t h e bottom o f T a b l e s 9 and 10. The vacuum u l t r a v i o l e t s pectrum o f a c e t o n e was s t u d i e d by Noyes e t a l . [ 1 1 0 ] and Duncan [ 1 0 2 ] . On the b a s i s o f i n t e n s i t y , Duncan [102 ] s e l e c t e d , from t h e numerous e l e c t r o n i c s t a t e s , t h r e e t h a t f i t i n t o a Rydberg s e r i e s c o n v e r g i n g t o a l i m i t o f 10.26 eV. T h i s v a l u e i s h i g h e r t h a n an I.P. o f 9.705 eV f o u n d l a t e r by Watanabe [ 1 0 3 ] f r o m p h o t o i o n i z a t i o n s t u d i e s . S u b s e q u e n t l y Watanabe [103 ] r e a n a l y s e d t h e V e r y r e c e n t l y a paper appeared (Huebner e t a l . , J . Chem. Phys. 59_, 5434 ( 1 9 7 3 ) ) r e p o r t i n g t h e h i g h r e s o l u t i o n e l e c t r o n i m p a ct spectrum o f a c e t o n e . A s i m i l a r i n t e r p r e t a t i o n ( i . e . i n terms o f Rydberg t r a n s i t i o n s ) t o t h a t o f t h e p r e s e n t work has been g i v e n . CH3COCH3-100eV,2° '39-cy j r— i 1 1 1 1 1 1 1 1 1—~i—• i 1 r 1 6 . 0 7.0 8.0 9.0 CD § CH3COC2H5-100eV2° j 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 r 6.0 7.0 8.0 9.0 ENERGY LOSS (eV) F i g u r e 29. E l e c t r o n impact s p e c t r a o f CHgCOCHg and CH 3C0C 2H • a t 100 eV, 2° 140. o p t i c a l s pectrum [ 1 0 2 ] and f o u n d a d i f f e r e n t s e r i e s o f e l e v e n members c o n v e r g i n g t o t h e I.P. a t 9.705 eV. The f i r s t member o f t h i s s e r i e s o c c u r s a t 8.09 eV. Based on t h i s we c o r r e l a t e t h e s t r o n g e s t peak i n t h e e l e c t r o n impact s p e c t r u m a t 8.09 eV (G) w i t h t h i s t r a n s i t i o n . I t s term v a l u e i s 1.62 eV w i t h r e s p e c t t o our PES measurement o f 9.71 eV f o r t h e f i r s t I.P. o f a c e t o n e . T h i s seems t o f i t a 4s Rydberg upper s t a t e w i t h a c a l c u l a t e d quantum d e f e c t o f 1.09. H i g h e r members o f t h i s ^ -j ns s e r i e s a r e p r e d i c t e d a t 8.81, 9.14 and 9.32 eV r e s p e c t i v e l y f o r n = 5, 6, 7. So t h e peaks K, L and M a t 8.82, 9.12 and 9.30 eV a r e a s s i g n e d as s u c h . The Rydberg f o r m u l a t h e n p r e d i c t s t h e Tp.-j -v 3s t r a n s i t i o n t o o c c u r a t 5.96 eV, w h i c h d i f f e r s f rom t h e e n e r g y o f t h e f i r s t component o f t h e f i r s t s h a r p band by 0.4 eV. The a v e r a g e v i b r a t i o n a l s p a c i n g o f t h i s band i s 0.135 ± 0.005 eV. T h i s i s comparable w i t h t h e s p a c i n g between t h e peaks G and H. So i f we a s s i g n t h e f i r s t band a t ^ 6 . 5 eV t o ^ 3s p l u s v i b r a t i o n a l components, H can be a s s i g n e d as t h e v i b r a t i o n a l component o f t h e 4s Rydberg s t a t e . The v i b r a t i o n a l mode e x c i t e d i s p r o b a b l y t h e methyl d e f o r m a t i o n as s u g g e s t e d by Lawson and Duncan [111] from t h e v i b r a t i o n a l a n a l y s i s o f t h i s band i n a c e t o n e . As i n t h e c a s e o f t h e spectrum o f a c e t a l d e h y d e , i t i s not u n r e a s o n a b l e t o r e g a r d t h e f i r s t band A i n t h e a c e t o n e s p e c t r u m as t h e 3s Rydberg t r a n s i t i o n d e s p i t e t h e 0.4 eV d i f f e r e n c e between t h e o b s e r v e d and t h e c a l c u l a t e d e n e r g i e s . L a r g e d e v i a t i o n s o f o b s e r v e d energy o f t h e 3s Rydberg s t a t e from t h e c a l c u l a t e d v a l u e have a l s o been o b s e r v e d i n o t h e r m o l e c u l e s c o n f o r m i n g t o C 2 v symmetry ( e . g . w a t e r [ 6 4 ] , e t h y l e n e o x i d e [ 6 7 ] ) . The h i g h e r symmetry may be t h e cause o f some p e r t u r b a t i o n s w h i c h a f f e c t t h e energy o f Rydberg s t a t e s . Weiss [ 1 2 1 ] has s u g g e s t e d t h e 141. p e r t u r b a t i o n o f a t o m i c Rydberg o r b i t a l s by v a l e n c e t y p e t r a n s i t i o n s s u c h as T  -> TT*. T h i s p e r t u r b a t i o n may not n e c e s s a r i l y be l o c a l i s e d i n t h e immediate v i c i n i t y o f t h e T  -* TT* but can be e x t e n s i v e . I t i s a w e l l - e s t a b l i s h e d f a c t t h a t t h e term v a l u e s o f 3d Rydberg s t a t e s o f compounds c o n t a i n i n g l o n e p a i r e l e c t r o n s r e m a i n e s s e n t i a l l y c o n s t a n t on a l k y l a t i o n [ 6 4 ] . Based on t h e 3d term v a l u e (1.78 eV) i n a c e t a l d e h y d e , we a s s i g n e d t h e peak F a t 7.87 eV i n t h e spectrum t o be \\>1 3d. The term v a l u e i s 1.84 eV and t h e c a l c u l a t e d quantum d e f e c t i s 0.28. The Rydberg f o r m u l a p r e d i c t s h i g h e r members a t 8.73, 9.10 and 9.26 eV. So t h e s t e p J a t 8.69 eV i s a s s i g n e d a 4d Rydberg upper s t a t e and t h e 5d and 6d Rydberg t r a n s i t i o n s s h o u l d have c o n t r i b u t i o n s t o t h e peaks L and M a t 9.12 and 9.30 eV r e s p e c t i v e l y which have p r e v i o u s l y been a s s i g n e d t o 6s and 7s Rydberg upper s t a t e s . The o n l y f e a t u r e s t h a t a r e l e f t u naccounted f o r up t o now a r e t h e peaks D, E and I . They may b e l o n g t o t h e \\>i -»• np s e r i e s . I f we assume th e s h o u l d e r I between t h e 4s and 4d t r a n s i t i o n s t o be 4p, t h e term v a l u e and quantum d e f e c t (1.30 eV and 0.76) a r e c omparable t o t h o s e o f a c e t a l d e h y d e (1.25 eV and 0.77). The Rydberg f o r m u l a t h e n p r e d i c t s t h e 3p s t a t e a t 6.99 eV and t h e 5p and 6p a t 8.95 and 9.21 eV r e s p e c t i v e l y . The peak D a t 7.42 d i f f e r s f r o m t h e p r e d i c t e d v a l u e o f 3p a l s o by 0.4 eV ( c f . t h e c a s e f o r 3 s ) . A p e r t u r b -a t i o n s i m i l a r t o t h a t f o r t h e c a s e o f t h e 3s Rydberg s t a t e may a l s o be r e s p o n s i b l e f o r t h e d e v i a t i o n o f t h e p o s i t i o n o f t h e 3p s t a t e from t h e c a l c u l a t e d v a l u e . I f t h e Rydberg a s s i g n m e n t i s assumed f o r peak D, t h e s h o u l d e r E can be i n t e r p r e t e d as a n o t h e r component o f t h e 3p m a n i f o l d . T a b l e 9 g i v e s a summary o f o u r a s s i g n m e n t s . The spectrum o f 2-butanone l o o k s v e r y s i m i l a r t o t h a t o f a c e t o n e , OBSERVED TERM ENERGY (eV) . VALUE (eV) a ASSIGNMENT CALCULATED CALCULATED ENERGY (eV) QUANTUM DEFECT A B C 6.36 6.50 6.63 3.35 3.21 3.08 i ' l 3S? ->• 3s + V2 3s + 2v2 5.96 D E 7.42 7.55 2.29 2.16 <h -> 3p? - 3p» 6.99 F 7.87 1.84 3d 0.28 G H 8.09 i U.22 1.62 1.49 4»i -»- 4s -> 4s + V2 1.09 I 8.41 1.30 $1 •*• 4p 0.76 J 8.69 1.02 •*• 4d 8.73 K 8.82 0.89 i>\ -»- 5s *1 -;- 5p 8.81 8.95 L 9.12 0.59 *1 -> 5d * 6s 9.10 9.14 M 9.30 0.41 -•- 6p *1 -> 6d 7s 9.21 9.29 9.32 TABLE 9 Rydberg transitions in acetone (a) Assigned with respect to PES ionization potentials of 9.71, 12.6, 13.5, 14.1, 143. p a r t i c u l a r l y i n t h e 6.0 - 8.5 eV energy l o s s r e g i o n . The f i r s t band e x h i b i t s f o u r v i b r a t i o n a l components w i t h an a v e r a g e s p a c i n g o f 0.135 ± 0. 005 eV, which i s t h e same as t h a t i n a c e t o n e . The term v a l u e o f t h e f i r s t v i b r a t i o n a l component w i t h r e s p e c t t o t h e f i r s t I.P. o f 9.52 eV i s d e c r e a s e d t o 3.19 eV on r e p l a c i n g one o f t h e a-hydrogens i n a c e t o n e by a m e t h y l group as i n 2-butanone. In c o n t r a s t t o t h e c a s e o f a c e t o n e , the f e a t u r e s i n t h e spectrum o f 2-butanone can e a s i l y be f i t t e d i n t o t h r e e Rydberg s e r i e s ^-j -*• n s , np and nd. A summary and a c o m p a r i s o n between t h e c a l c u l a t e d and o b s e r v e d e n e r g i e s i s g i v e n i n F i g u r e 29 (bottom) and T a b l e 10. The o n l y u n c e r t a i n t y i s t h e e x i s t e n c e o f t h e peaks K and 0. The i n t e r p r e t a t i o n o f t h e 2-butanone spectrum i n terms of Rydberg s e r i e s seems t o a f f i r m o u r Rydberg a s s i g n m e n t o f t h e a c e t o n e s p e c t r u m . The h i g h e r and r i s i n g c ontinuum i n 2-butanone above 9 eV i s p r o b a b l y due t o Rydberg t r a n s i t i o n s l e a d i n g t o t h e second and h i g h e r 1. P.'s w h i c h a r e more c l o s e l y spaced i n 2-butanone ( 1 2 . 3 , 12.6 and 13.0 eV) t h a n i n a c e t o n e (12.6, 13.5 and 14.1 e V ) . I t seems t h a t t h e peaks i n t h e b i g g e r m o l e c u l e 2-butanone a r e i n t r i n s i c a l l y b r o a d e r t h a n t h o s e i n a c e t o n e s i n c e t h e v i b r a t i o n a l s t r u c t u r e i n t h e f i r s t band i s l e s s w e l l r e s o l v e d f o r t h e same v i b r a t i o n a l s p a c i n g . Three peaks E, F and F' a r e seen i n t h e -j 3p r e g i o n i n s t e a d o f two as i n a c e t o n e . The s h o u l d e r F' i s . l e s s i n t e n s e t h a n t h e o t h e r two. I f we assume 2-butanone t o conform t o C s symmetry, t h e t h r e e components o f the 3p m a n i f o l d a r e o f a ' , a 1 and a" symmetry. The a s s i g n m e n t o f t h e t h r e e components t o t h e d i f f e r e n t symmetries can be a c h i e v e d by s t u d y i n g t h e e l e c t r o n i m p a c t s p e c t r a a t d i f f e r e n t i m p a c t e n e r g i e s , 100 eV, 70 eV and 30 eV. (See F i g u r e 3 0 ) . A t t h e s e impact e n e r g i e s , t h e i n t e n s i t y o f pF..v OBSERVED TERM CALCULATED CALCULATED ENERGY (eV) VALUE (eV) a A ^ i u v xm ENERGY (eV) QUANTUM DEFECT A 6.33 3.19 *1 -> 3s 0.94 B 6.46 3.06 3s + v 2 C 6.59 2.93 3s + 2v2 D 6.72 2.80 -y 3s + E 7.26 2.26 fl y 3pa' 0.55 F 7.41 2.11 *1 ->- 5pa" 0.46 F» 7.57 1.95 • *1 y 3pa' G 7.71, 1.81 •*1 y 3d 0.26 H 7.90' 1.62 -y 3d» 0.10 I 8.06 1.46 *1 -y 4s 8.07 J 8.19 1.33 y 4s + K? *1 -y 4p 8.38 L 8.53 0.99 y 4p' 8.43 *1 -y 4d 8.55 M 8.68 0.84 •y 4d' 8.63 5s 8.70 . N 8.85 0.67 fi -y 5p 8.83 -y 5p* 8.S6 0? fi y 5d 8.92 P 9.00 0.52 fi -y 6s 8.99 Q 9.11 0.41 fi y 6p 9.07 fi •y 7s 9.15 TABLE 10 Rydberg transitions in 2-butanone (a) Assigned with respect to PES ionization potentials of 9.52, 12.3, 12.6, 13.0, 14.3 cV F i g u r e 30. E l e c t r o n impact s p e c t r a o f t h e f i r s t two bands o f C H 3C0C 2H 5 a t 30, 70 and 100 eV. 146. t h e peak E and peak F' r e l a t i v e t o peak A r e m a i n q u i t e c o n s t a n t ( 0 . 5 3 , 0.51 and 0.51 f o r E and 0.35, 0.37 and 0.39 f o r F ' ) . On t h e o t h e r hand, t h e r e l a t i v e i n t e n s i t y o f peak F t o peak A i n c r e a s e s as t h e impact energy i s l o w e r e d ( 0 . 5 1 , 0.53 and 0.68 r e s p e c t i v e l y a t 100 eV, 70 ev and 30 ev impact e n e r g y ) . T h i s seems t o i n d i c a t e t h a t peak E and F' may b e l o n g t o t h e same symmetry and so a r e a s s i g n e d a'. The d i f f e r e n t b e h a v i o u r o f peak F on d e c r e a s i n g t h e impact energy s u g g e s t s t h a t i t s h o u l d be a s s i g n e d a d i f f e r e n t symmetry ( a " ) . 8.3.2. H i g h e r k e t o n e s . F i g u r e 31a, b, c shows t h e e l e c t r o n impact s p e c t r a o f methyl i s o b u t y l k e t o n e , methyl i s o p r o p y l ketone and methyl t - b u t y l ketone r e s p e c t i v e l y o v e r t h e e n e r g y l o s s r e g i o n o f 6 - 10 eV a t an i m p a c t e n e r g y o f 100 eV and 2° s c a t t e r i n g a n g l e . Duncan [112 ] has s t u d i e d t h e vacuum u l t r a v i o l e t s p e c t r a o f methyl n - p r o p y l k e t o n e , m e t h y l i s o p r o p y l k e t o n e and d i e t h y l k e t o n e i n t h e energy r e g i o n 6.2 - 8.3 eV. The e l e c t r o n i c t r a n s i t i o n s and t h e i r v i b r a t i o n a l s t r u c t u r e were d i s c u s s e d i n c o m p a r i s o n w i t h a c e t o n e and 2-butanone. I t i s c o n c l u d e d t h a t most t r a n s i t i o n s a r e p r o b a b l y o f a Rydberg t y p e , l e a d i n g t o I.P.'s i n t h e neighbourhood o f 10 eV. H o l d s w o r t h and Duncan [113] d i s c u s s e d t h e e f f e c t o f c o n s e c u t i v e s u b s t i t u t i o n o f t h e a-hydrogens i n a c e t o n e by methyl groups on t h e i n t e n s i t y o f t h e i r e l e c t r o n i c t r a n s i t i o n s i n t h e vacuum u l t r a - v i o l e t . In T a b l e 11, we have a s s i g n e d most s t r u c t u r e s i n t h e s p e c t r a t o Rydberg t r a n s i t i o n s based on term v a l u e s and t h e c a l c u l a t e d quantum d e f e c t s . The broad peaks a t h i g h energy l o s s a r e p r o b a b l y t h e e n v e l o p e o f more t h a n one t r a n s i t i o n . I t i s n o t e d t h a t i n t h e s e h i g h e r k e t o n e s , t h e s p e c t r a o n l y show broad f e a t u r e s 147. |100eV,2° CO >-tr < er CD c r < CO LU h-A B (a) ( b ) (c) B E p P lCH 3 ) 2 CHCH o C0CH a; H 0 E (CH 3) 2CHCOCH : H V B D (CH 3) 3CCOCH 3 T 8 9 ENERGY LOSS(eV) 10 F i g u r e 31. E l e c t r o n impact s p e c t r a o f ( C H ^ C H C f ^ C O C H ^ (CH 3) 2CHC0CH 3 and ( C H 3 ) 3 C C 0 C H 3 a t 100 eV, 2°. PEAK (CH 3) 2CH 2COCH 3 ENERGY (eV) TRANSITION TERM VALUE (eV) f A 6.45 *1 -+ 3s 2.97 B 6.53 3s + V2 2.89 C 7.34 *1 + 3p 2.08 D 7.73 *1 3d 1.69 E 7.97 *1 •+ 4s 1.45 F 8.27 *1 •> 4p 1.15 G 8.48 *1 •> 4d 0.94 *1 + 5s *2 -»• 3s 2.9 H 9.0 *3 3s 2.9 I 9.7 <"+ 3s 3.2 TABLE 11 E l e c t r o n i c t r a n s i t i o n s (CH3)2CHOCH3 PEAK ENERGY (eV) TRANSITION TERM VALUE (eV)' A 6.41 *1 -y 3s 2.95 B 7.19 *1 - 3p 2.17 C 7.84 *1 •* 3d? 1.52 D 7.97 *1 •+ 4s 1.39 E 8.22 *1 -> 4p 1.14 F 9.2 ^3 ->- 3s 3.1 G 9.9 *3 - 3p •*• 4s 2.4 2.7 (CH 3) 3CC0CH 3 PEAK ENERGY (eV) TRANSITION A B C? D E F G H 6.40 7.12 7.6 7.79 8.05 8.33 8.55 9.7 ih •* 3s *1 -> 3p i-i + 3d i>i 4s ij>l •*• 4p *1 4d 5s $2 ~* j S <l<3 •* 3s TERM VALUE (eV) 2.81 2.09 1.6 1.42 1.16 0.88 2.83 2.8 TABLE 11 E l e c t r o n i c t r a n s i t i o n s i n methyl isobutyl ketone, methyl isopropyl ketone and methyl t-butyl ketone 149. p r o b a b l y because t h e r e a r e so many v i b r a t i o n a l modes. I n p a r t i c u l a r , t h e shape o f t h e n ->• 3s band 6.4 eV) i s v e r y s e n s i t i v e t o t h e a l k y l g r o u p . Sharp v i b r a t i o n a l s t r u c t u r e o b s e r v e d i n a c e t o n e and 2-butanone seems t o d i s a p p e a r f o r t h e h i g h e r k e t o n e s s t u d i e d . The f i r s t band i n t h e s p e c t r a of m e t h y l i s o p r o p y l ketone (b) and methyl t - b u t y l ketone ( c ) a p p e a r s as a c o n t i n u o u s d i f f u s e band w h i l e t h a t o f m e t h y l i s o b u t y l ketone (a) s t i l l shows some i n d i c a t i o n o f v i b r a t i o n a l s t r u c t u r e i n t h e f i r s t band. A d e t a i l e d s t u d y o f t h e shape o f t h i s band u s i n g o p t i c a l s p e c t r o s c o p y has been p r e s e n t e d by I t o e t a l . [ 1 1 4 ] . The second band i n methyl i s o p r o p y l ketone and methyl t - b u t y l ketone i s more i n t e n s e than t h e f i r s t band w h i l e t h e r e v e r s e i s t r u e f o r o t h e r k e t o n e s s t u d i e d i n wh i c h t h e a l k y l groups a r e not branched a t t h e a-carbon. T h i s may be a u s e f u l f e a t u r e t o d i s t i n g u i s h between t h e s e two k i n d s o f k e t o n e s . H o l d s w o r t h and Duncan [113] have a l s o o b s e r v e d t h a t t h e i n t e n s i t y o f t h e 6.4 eV band d e c r e a s e s when t h e a-hydrogens i n a c e t o n e a r e r e p l a c e d by methyl groups w h i l e t h e i n t e n s i t y o f t h e t r a n s i t i o n i n t h e r e g i o n a t about 7.4 eV i n c r e a s e s . No s a t i s f a c t o r y e x p l a n a t i o n has y e t been g i v e n f o r t h i s phenomenon. 8.3.3. E f f e c t o f a l k y l s u b s t i t u e n t s . As i n t h e c a s e o f a l d e h y d e s , a p p r o x i m a t e l y s t r a i g h t - l i n e p l o t s a r e o b t a i n e d when t h e f i r s t I .P., t h e 3 s , 3p and 3d term v a l u e s a r e p l o t t e d a g a i n s t t h e sum o f T a f t a* v a l u e s (Ea*) o f t h e two a l k y l groups a t t a c h e d t o t h e c a r b o n y l group ( F i g u r e 3 2 ) . The b e h a v i o u r o f t h e 3 s , 3p and 3d terms i s t h e same as i n a l d e h y d e s ( s e c t i o n 8.2.4.) and t h e a l k y l d e r i v a t -i v e s o f w a t e r ( s e c t i o n 7 . 6 ) . The s h i f t o f t h e 3s peak maxima t o l o w e r e n e r g i e s on a l k y l a t i o n i s s m a l l e r t h a n i n t h e c a s e o f a l d e h y d e s and so the 150. F i g u r e 32. E f f e c t o f a l k y l s u b s t i t u t i o n on Rydberg term v a l u e s and f i r s t i o n i z a t i o n p o t e n t i a l s i n k e t o n e s . 151. s t r a i g h t l i n e s f o r t h e f i r s t I.P. and t h e 3s term v a l u e d e p e n d e n c i e s a r e a p p r o x i m a t e l y p a r a l l e l . In o p t i c a l s p e c t r o s c o p y [112,113] a b i g g e r s h i f t o f t h e peak maxima o f t h e 7.4 eV band t o l o w e r e n e r g i e s has been o b s e r v e d as more a-hydrogens i n a c e t o n e a r e r e p l a c e d by m e t h y l g r o u p s . I n o u r Rydberg model t h i s can be e a s i l y e x p l a i n e d by t h e f a c t t h a t t h e 3p Rydberg e l e c t r o n i s l e s s p e n e t r a t i n g t h a n t h e e l e c t r o n s i n t h e h i g h e s t f i l l e d m o l e c u l a r o r b i t a l and t h e r e f o r e t h e b i n d i n g e n e r g i e s o f t h e 3p Rydberg o r b i t a l d e c r e a s e l e s s r a p i d l y than t h e b i n d i n g e n e r g y o f t h e h i g h e s t f i l l e d m o l e c u l a r o r b i t a l . As a r e s u l t , the t r a n s i t i o n e n ergy t o t h e 3p Rydberg s t a t e , w h i c h i s t h e d i f f e r e n c e between t h e two b i n d i n g e n e r g i e s , i s a l s o d e c r e a s i n g w i t h i n c r e a s i n g a l k y l a t i o n . 8 . 4 . U n s a t u r a t e d Compounds 8.4.1. P r o p e n a l ( a c r o l e i n ) . F i g u r e 33 shows t h e e l e c t r o n impact s p e c t r a o f p r o p e n a l and methyl v i n y l ketone o v e r t h e energy l o s s r e g i o n o f 2 - 13 eV a t an impact energy of 100 eV and 2° s c a t t e r i n g a n g l e . The p h o t o e l e c t r o n s p e c t r u m o f p r o p e n a l has been s t u d i e d by T u r n e r e t a l . [ 8 2 ] . The f i r s t two bands p o s s e s s v i b r a t i o n a l f i n e s t r u c t u r e , t h e f i r s t peak b e i n g t h e most i n t e n s e . The f i r s t two v e r t i c a l I.P.'s a r e 10.11 and 10.93 eV r e s p e c t i v e l y . We have o b t a i n e d t h e p h o t o e l e c t r o n s p e c t r u m o f methyl v i n y l ketone i n t h i s l a b o r a t o r y ( s e e A p p e n d i x ) . The f i r s t band i s s h a r p and shows v i b r a t i o n a l s t r u c t u r e . The f i r s t peak i s most i n t e n s e and g i v e s a v e r t i c a l I.P. o f 9.61 eV. The second band has f i v e v i b r a t i o n a l components, w i t h t h e second one b e i n g t h e most i n t e n s e , g i v i n g a v e r t i c a l second I.P. o f 152. 00 CH2=CH-CHO 10OeV,2° 3.8 eV B i 6 ! x 8 • • •• • .' ' i • v c ' M I K Ml N D' 33 3 G J IL | CC < 2 cr GO < 6 8 IO >-CO UJ ns CH 2 =CHCOCH 3 ^ 100eV, 2° f 3.6 eV x 4 -np V 6,7 g IT • ' -33 G rl J 12 N ''•"'•v.-.V..1 1 1 1 6 8 ENERGY LOSS (eV) IO 12 F i g u r e 33. E l e c t r o n impact s p e c t r a o f p r o p e n a l and methyl v i n y l ketone a t 100 eV, 2°. 153. 10.62 eV. The second s h a r p band i n t h e p h o t o e l e c t r o n s p e c t r u m seems t o be a c h a r a c t e r i s t i c o f u n s a t u r a t e d c o n j u g a t e d c a r b o n y l compounds, f o r i t does n o t o c c u r i n t h e p h o t o e l e c t r o n s p e c t r a o f s a t u r a t e d a l d e h y d e s and k e t o n e s . T u r n e r e t a l . [ 8 2 ] have a s s i g n e d t h e f i r s t band i n t h e p h o t o -e l e c t r o n spectrum o f p r o p e n a l t o t h e l o s s o f an e l e c t r o n from t h e non-bonding o r b i t a l ( i ^ ) and t h e second band t o t h e l o s s o f an e l e c t r o n from th e h i g h e r o f t h e two o c c u p i e d TT o r b i t a l s (ij^). We assume t h a t t h e p h o t o e l e c t r o n s p e c t r u m o f m e t h y l v i n y l k e t o n e , whose EIS i s t o be d i s c u s s e d l a t e r , can be i n t e r p r e t e d i n a s i m i l a r f a s h i o n . The vacuum u l t r a v i o l e t s pectrum o f p r o p e n a l has been s t u d i e d by Walsh [104] and t h e f e a t u r e s above 7.5 eV a r r a n g e d i n t o t h r e e Rydberg s e r i e s . In our spectrum we o b s e r v e s e r i e s I I I [104] w i t h members C, G, J , L a t 7.58, 8.89, % 9.4 and 9.65 eV r e s p e c t i v e l y w h i c h have been a s s i g n e d as t h e np Rydberg s e r i e s (n = 3, 4, 5, 6 ) . The quantum d e f e c t i s 0.68. The s h o u l d e r D a t 7.74 eV i s s e p a r a t e d from t h e peak C by l e s s than 0.16 eV and t h i s may be a s s o c i a t e d w i t h a v i b r a t i o n a l quantum. The s m a l l s h o u l d e r D 1 a t ^ 7.9 eV may c o r r e s p o n d t o a n o t h e r component o f the 3p m a n i f o l d ( p r o b a b l y 3p' as i n a c e t a l d e h y d e - see s e c t i o n 8.2.1.) A summary o f t h e Rydberg t r a n s i t i o n s i s p r e s e n t e d i n T a b l e 12. The f i r s t p r o m i n e n t f e a t u r e i n t h e e l e c t r o n impact spectrum o f p r o p e n a l i s a s t r o n g d i f f u s e peak w i t h a maximum a t about 6.35 eV. I t s term v a l u e o f 3.76 eV, w i t h r e s p e c t t o t h e f i r s t I .P., i s c o n s i s t e n t w i t h a 3s upper s t a t e ( c f . f o r m a l d e h y d e 3.78 eV, a c e t a l d e h y d e 3.39 e V ) . The c a l c u l a t e d quantum d e f e c t (1.10) i s a l s o c o n s i s t e n t w i t h t h i s a s s i g n m e n t ( c f . f o r m a l d e h y d e , 1.11 and a c e t a l d e h y d e , 1.00). The h i g h e r members o f t h i s s e r i e s -+ ns a r e t h e n p r e d i c t e d t o o c c u r a t 8.49, 9.22 and 9.54 eV r e s p e c t i v e l y . So PEAK OBSERVED ENERGY (eV) TERM VALUE (eV)' ASSIGNMENT CALCULATED ENERGY (eV) CALCULATED QUANTUM DEFECT A 6.35 3.76 -* 3s 1.10 B 7.09 3.84 2^ -» 3s 1.12 C D D' 7.58 7.74 7.9 2.53 2.37 2.2 3p 4»i 3p + v *1 3p» 0.68 E 8.49 1.62 $1 4s 8.49 F 8.63 2.30 fl •*• 3p 0.57 G 8.89 1.22 *1 * 4p 8.88 H 9.22 0.89 tyl •*• 5s 9.22 I 9.29 1.64 $2 4 s 9.29 J ^ 9.4 0.71 fl •* 5p 9.39 K 9.55 0.56 1^ 6s 9.54 L 9.65 0.46 fl 6p 9.63 M 10.03 0.90 i|>2 •+ 5s 10.03 N 10.53 0.40 2^ + 7s 10.54 0 12.10 3.7 3 s TABLE 12 Rydberg transitions in propenal (a) Assigned with respect to TES ionization potentials of 10.11, 10.93, 13.5, 14.8, 15.3, 16. 155. t h e f e a t u r e s o c c u r r i n g a t 8.49, 9.22 and 9.55 eV i n our s p e c t r a (peaks E, H and K) can be a s s i g n e d 4 s , 5s and 6s Rydberg upper s t a t e s . The sharp peak B a t 7.09 eV has a term v a l u e o f 3.84 w i t h r e s p e c t t o t h e second I.P. a t 10.93 eV. The c a l c u l a t e d quantum d e f e c t i s 1.12 and so i t i s a s s i g n e d as a ^ 3s Rydberg t r a n s i t i o n . The n = 4 and 5 members o f t h e ^ 2 "*" n s s e r i e s appear a t 9.29 ( I ) and 10.03 (M) as p r e d i c t e d , w h i l e h i g h e r s t a t e s a r e p r o b a b l y c o n t r i b u t i n g t o t h e broad e n v e l o p e N. The term v a l u e o f peak F a t 8.63 eV w i t h r e s p e c t t o t h e second I.P. a t 10.93 eV i s 2.30 eV and so can be a s s i g n e d t o t h e Rydberg t r a n s i t i o n from 2^ t 0 o n e °f t n e components o f 3p. The o t h e r components may have c o n t r i b u t i o n s t o peak E. The broad peak N around 10.5 eV may have c o n t r i b u t i o n s from Rydberg t r a n s i t i o n s l e a d i n g t o t h e second and t h i r d I.P.'s w h i l e t h e broad f e a t u r e m a x i m i s i n g a t about 12.1 eV may be t h e e n v e l o p e o f Rydberg t r a n s i t i o n s from T r a n s i t i o n s t o t h e nd Rydberg s e r i e s a r e p r o b a b l y b u r i e d under o t h e r f e a t u r e s i n t h e sp e c t r u m . A weak t r a n s i t i o n i s o b s e r v e d i n our spectrum as t h e broad band w i t h a maximum a t 3.8 eV ( c f . 4.30 eV i n a c e t a l d e h y d e ) . That t h i s low energy t r a n s i t i o n i s n IT* was e s t a b l i s h e d by I n u z u k a , who d i d t h e o r e t i c a l c a l c u l a t i o n s [ 115] and s t u d i e d t h e e f f e c t o f s o l v e n t s o n . t h i s t r a n s i t i o n [ 1 1 6 ] . T h i s r e g i o n has a l s o been t h e i n t e r e s t o f o t h e r o p t i c a l s p e c t r o s c o p -i s t s [ 117,118,119]. V i b r a t i o n a l s t r u c t u r e o f t h i s band, which i s not r e s o l v e d i n our s p e c t r u m , has been a n a l y s e d by Eastwood and Snow [119] and Inuzuka [ 1 2 0 ] . With t h e e x c e p t i o n o f t h e ^  np s e r i e s , o ur i n t e r p r e t a t i o n o f t h e e l e c t r o n impact spectrum o f p r o p e n a l does not a g r e e w i t h t h a t f o r t h e o p t i c a l s pectrum g i v e n by Walsh [ 1 0 4 ] , who a s s i g n e d t h e peaks A (6.35 eV) 156. and B (7.09 eV) t o i n t e r v a l e n c e t r a n s i t i o n s * TT -»• TT* and n -> a* r e s p e c t i v e l y . From t h e above p a r a g r a p h , t h e b i n d i n g e n e r g y o f t h e TT* o r b i t a l i s t h e d i f f e r e n c e between t h e b i n d i n g energy o f t h e n o r b i t a l (10.1 eV from PES) and t h e n •+ TT* t r a n s i t i o n e n ergy (3.8 e V ) . T h i s g i v e s a v a l u e o f 6.3 eV f o r t h e b i n d i n g e n e r g y o f t h e TT* o r b i t a l (see F i g u r e 3 4 ) . The b i n d i n g e nergy o f t h e TT e l e c t r o n i s g i v e n by t h e second I.P. (10.9 eV) f r o m t h e p h o t o e l e c t r o n s p e c t r u m . T h e r e f o r e t h e t r a n s i t i o n TT -»• TT* s h o u l d maximise a t 10.9 - 6.3 = 4.6 eV i n s t e a d o f Walsh's v a l u e o f 6.35 eV. T h e r e f o r e , we s u g g e s t t h a t Walsh's a s s i g n m e n t o f peak A as TT •> TT* i s i n c o r r e c t . A l s o , i t i s o b v i o u s t h a t any t r a n s i t i o n i n t h e 4.6 eV r e g i o n ( F i g u r e 33) i s e x t r e m e l y weak. U n l e s s f o r some p e c u l i a r r e a s o n t h e TT -> TT* t r a n s i t i o n i n a c e t a l d e h y d e s h o u l d be much s t r o n g e r t h a n t h a t o b s e r v e d i n p r o p e n a l , we e x p e c t t h e TT ^ TT* t r a n s i t i o n i n a c e t a l d e h y d e t o be weak as w e l l , i n w h i c h c a s e t h e a s s i g n m e n t o f t h e p r o m i n e n t f e a t u r e s i n t h e s p e c t r a o f c a r b o n y l compounds (see s e c t i o n s 8.2. and 8.3.) t o Rydberg t r a n s i t i o n s r a t h e r t h a n v a l e n c e t r a n s i t i o n s has a f i r m e r f o u n d a t i o n . In the c a s e o f a c e t a l d e h y d e , t h e p a r t i c u l a r v a l u e (13.3 eV) o f t h e b i n d i n g energy o f t h e T r-bonding o r b i t a l l e a d s t o a s i m i l a r e x p e c t e d energy f o r the v a l e n c e t r a n s i t i o n TT TT and t h e Rydberg t r a n s i t i o n n -> 3p. T h i s chance c o i n c i d e n c e does n o t o c c u r i n t h e s p e c t r u m o f p r o p e n a l . However, the e v i d e n c e i n our spectrum does not p r e c l u d e Walsh's a s s i g n m e n t o f peak B a t 7.09 eV as n -»• a* s i n c e the s m a l l s h o u l d e r D' a t 7.9 eV happens t o l i e a t t h e e x p e c t e d p o s i t i o n f o r t h e TT -*• a* t r a n s i t i o n . (The d i f f e r e n c e between t h e n -> a* and t h e TT ,-»- a* t r a n s i t i o n e n e r g i e s i s e x p e c t e d t o be + T h i s a s s i g n m e n t was made i n 1945 b e f o r e t h e a d v e n t o f PES. Hence t h e b i n d i n g energy o f t h e TT o r b i t a l was unknown. orbital energy ion 0.0 eV 3p' 3s TT -T > a> 00 ro n W,) >\ CD > CD L O ro CD > CD K > CD CD > CD CD > cu L O ro CD ' V -2.2eV •3.0 eV •3.8eV T -6.3eV •10. leV p E S •10.9 eV r " •l2.7eV F i g u r e 34. Energy l e v e l s and e l e c t r o n i c t r a n s i t i o n s i Rydberg orbitals valence orbitals filled orbitals A our assignment expected transitions on the basis of Walshs assignment. 8 „ predicted position of 7T~orbital 'TT if Walsh's assignment is correct. p r o p e n a l . Ul 158. o f s i m i l a r magnitude t o t h e d i f f e r e n c e between t h e n and t h e IT b i n d i n g e n e r g i e s . ) A l t h o u g h B has a l r e a d y been a s s i g n e d as ^ •+ 3s and D' as ^1 -> 3p' the p o s s i b i l i t y s t i l l e x i s t s t h a t t h e y can a l s o be a s s i g n e d as v a l e n c e t r a n s i t i o n s n a* and TT ->• a* r e s p e c t i v e l y . A t t h e p r e s e n t t i m e , we c a n n o t t e l l t o what e x t e n t e i t h e r o r both a r e c o n t r i b u t i n g . However, e v i d e n c e from o p t i c a l s p e c t r o s c o p y and p h o t o e l e c t r o n s p e c t r o s c o p y seems t o i n d i c a t e t h a t t h e 6.35 eV band (A) i s t h e Rydberg t r a n s i t i o n -> 3s and not TT -> TT* as s u g g e s t e d by Walsh (Walsh's a s s i g n m e n t would r e q u i r e t h e TT o r b i t a l t o have an o r b i t a l e nergy o f -12.7 eV whereas t h e PES s p e c t r u m i n d i c a t e s a v a l u e o f -10.9 e V ) . 8.4.2. M e t h y l v i n y l k e t o n e . The e l e c t r o n i m p act s p e c t r u m o f m e t h y l v i n y l ketone ( F i g u r e 33) i n w h i c h t h e a l d e h y d i c hydrogen i n p r o p e n a l i s r e p l a c e d by a methyl g r o u p , l o o k s v e r y s i m i l a r t o t h a t o f p r o p e n a l . The d i f f e r e n c e between t h e f i r s t and second I.P. i s about 1 eV. The term v a l u e o f t h e peak A w i t h r e s p e c t t o t h e f i r s t I.P. i s 3.36 eV, as compared t o 3.76 eV i n p r o p e n a l . S i n c e t h e l o w e r i n g o f t h e 3s term v a l u e on a l k y l a t i o n has been o b s e r v e d b e f o r e ( s e c t i o n s 8.2.and 8 . 3 . ) , we a s s i g n peak A t o t h e ->- 3s Rydberg t r a n s i t i o n and t h e c a l c u l a t e d quantum d e f e c t , 0.99, i s c o n s i s t e n t w i t h an s Rydberg o r b i t a l . U s i n g t h e Rydberg f o r m u l a , peaks F, I and K a t 8.02, 8.70 and 9.12 eV a r e a s s i g n e d t r a n s i t i o n s ^ ->- ns (n = 4, 5, 6 ) . A c o m p a r i s o n o f the o b s e r v e d and c a l c u l a t e d energy f o r a l l Rydberg t r a n s i t i o n s o b s e r v e d i s shown i n T a b l e 13. The t r a n s i t i o n ^ 3s i s e x p e c t e d t o o c c u r around 3.4 eV below t h e second v e r t i c a l I.P. o f 10.6. So t h e peak D a t 7.34 eV i s a s s i g n e d t o t h i s t r a n s i t i o n and t h e h i g h e r members o f t h i s ty0 -* ns OBSERVED TERM CALCULATED CALCULATED * " ENERGY (eV) VALUE (eV) a AbblolSMLM ENERGY (eV) QUANTUM DEFECT 0.99 0.85 0.96 0.42 A 6.25 3.36 *1 > 3s B 6.66 2.95 *1 -»• 3p C 6.85 2.76 D 7.34 3.28 2^ •*• 3s E 7.56 2.05 *1 3d F 8.08 1.53 • *1 -> 4s 8.11 G 8.25 1.36 _*1 •* 4p 8.24 H 8.50 • 1.11 fl -* 4d 8.55 I 8.70 0.91 fl + 5s 8.76 J 8.81 0.80 *1 - 5p 8.82 K 9.12 0.49 fl •*• 6s 9.07 fl 6p 9.09 1.50 fl + 4s 9.14 L 9.82 0.80 fl + 5s 9.78 M 10.18 0.44 fl * 6s 10.08 fl + 7s 10.25 TABLE 13 Rydberg transitions in methyl vinyl ketone (a) Assigned with respect to PES ionization potentials of 9.61, 10.62,13.1, 13.9, 14.4, 15.1. 160. s e r i e s a r e e x p e c t e d a t 9.14, 9.78, 10.08 and 10.25 eV f o r n = 4, 5, 6, 7 r e s p e c t i v e l y . A c t u a l l y , a peak K and a s t e p L a r e o b s e r v e d a t 9.12 and 9.83 eV. The broad peak a t 10.18 eV may be t h e c o n v o l u t i o n o f t h e -*• 6s and -> 7s t r a n s i t i o n s . The o n l y f e a t u r e t h a t can be a s s i g n e d t h e 3p Rydberg t r a n s i t i o n i s t h e s h o u l d e r B a t 6.66 eV. The term v a l u e o f 2.95 eV w i t h r e s p e c t t o t h e f i r s t I.P., and t h e c a l c u l a t e d quantum d e f e c t (0.85 eV) a r e h i g h e r t h a n t h o s e i n p r o p e n a l but a r e s t i l l c omparable t o t h o s e [ 9 8] o f f o r m a l d e h y d e (2.81 eV and 0.83 r e s p e c t i v e l y ) . The d i f f e r e n c e i n quantum d e f e c t between p r o p e n a l and methyl v i n y l ketone i n d i c a t e s t h e d i f f e r e n t d e g rees o f p e n e t r a t i o n o f t h e np Rydberg e l e c t r o n i n t o t h e m o l e c u l a r c o r e . The Rydberg f o r m u l a g i v e s t h e h i g h e r members as peaks G, J , K a t 8.25, 8.81 and 9.12 eV r e s p e c t i v e l y . The s h o u l d e r E a t 7.56 eV and t h e s m a l l peak A a t 8.50 eV a r e a s s i g n e d -»• 3d and 4d t r a n s i t i o n s . The c a l c u l a t e d quantum d e f e c t o f 0.42 i s a l s o comparable t o t h a t o f fo r m a l d e h y d e . The broad peak N m a x i m i s i n g a t about 11.8 eV p r o b a b l y e n v e l o p e s Rydberg t r a n s i t i o n s from ^ and ( f i f t h and s i x t h I.P. a t 13.9 and 14.4 eV r e s p e c t i v e l y ) . The maximum o f t h e n -* IT* t r a n s i t i o n i n methyl v i n y l ketone (3.6 eV) i s s h i f t e d t o l o w e r energy compared t o t h a t o f p r o p e n a l (3.8 e V ) . t 161. CHAPTER IX  CONCLUSION E l e c t r o n i m p act s p e c t r o s c o p y s e r v e s as an a l t e r n a t i v e method t o p h o t o a b s o r p t i o n f o r o b s e r v i n g e l e c t r o n i c t r a n s i t i o n s . In t h e s h o r t w a v e l e n g t h r e g i o n ( e . g . vacuum u l t r a v i o l e t o r s o f t X - r a y r e g i o n ) , i t i s a s t r o n g c o m p e t i t o r w i t h o p t i c a l s p e c t r o s c o p y s i n c e i t by-passes many d i f f i c u l t i e s e n c o u n t e r e d i n o p t i c a l work such as a v a i l a b i l i t y o f c o n t i n u o u s s o u r c e s , i n monochromation and i n a b s o l u t e c a l i b r a t i o n o f photon i n t e n s i t i e s . A l t h o u g h t h e r e s o l v i n g power a v a i l a b l e i n o p t i c a l s p e c t r o s c o p y a t l o n g e r w a v e l e n g t h s i s s u p e r i o r t o t h a t o f E I S , t h e c o n d i t i o n s become more f a v o u r a b l e f o r EIS a t s h o r t e r w a v e l e n g t h s , p a r t i c -u l a r l y w i t h r e c e n t a c h i e v e m e n t s i n a n a l y s e r and e l e c t r o n o p t i c a l d e s i g n , where a r e s o l u t i o n o f 0.005 - 0.010 eV w i t h u s a b l e i n t e n s i t y i s t o be e x p e c t e d i n t h e near f u t u r e . I n t h i s work, two o f t h e many c a p a b i l i t i e s o f EIS have been e x p l o r e d , namely o p t i c a l l y f o r b i d d e n t r a n s i t i o n s and m o l e c u l a r Rydberg s t a t e s . Thus EIS i s c a p a b l e i n p r i n c i p l e o f g i v i n g a t o t a l l i s t i n g o f t h e energy l e v e l s o f a m o l e c u l e . O p t i c a l l y f o r b i d d e n t r a n s i t i o n s a r e i n a c c e s s i b l e t o o p t i c a l s p e c t r o s c o p y w h i l e i n t h e c a s e o f m o l e c u l a r Rydberg t r a n s i t i o n s , t h e broad band s t r u c t u r e o f t h e s p e c t r a o f l a r g e m o l e c u l e s do n o t make t h e l o w e r r e s o l v i n g power o f EIS t o o much o f a d i s a d v a n t a g e and t h e r e a r e some p o s s i b i l i t i e s f o r development o f t h i s t e c h n i q u e as a means f o r c h e m i c a l a n a l y s i s . There a r e o t h e r a p p l i c a t i o n s o f EIS o r i t s v a r i a t i o n s w h i c h w i l l p r o v i d e i n f o r m a t i o n about e x c i t a t i o n 162. c r o s s s e c t i o n s , a u t o i o n i z i n g s t a t e s , n e g a t i v e i o n f o r m a t i o n and t h e energy p o s i t i o n s o f u n f i l l e d M.O.'s, some o f w h i c h c a n n o t be s t u d i e d by o t h e r methods. 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APPENDIX PHOTOELECTRON SPECTRA OF SOME ALDEHYDES & KETONES In t h e c o u r s e o f our work t o i n t e r p r e t t h e e l e c t r o n impact s p e c t r a o f c a r b o n y l compounds ( c h a p t e r 8 ) , we r e q u i r e d t h e v e r t i c a l i o n i z a t i o n p o t e n t i a l s o f t h e o u t e r m o s t and some i n n e r f i l l e d m o l e c u l a r o r b i t a l s i n al d e h y d e s and k e t o n e s . A s e a r c h o f t h e l i t e r a t u r e i n d i c a t e s t h a t h i g h r e s o l u t i o n p h o t o e l e c t r o n s p e c t r a o f many o f t h e s e compounds have n o t been r e p o r t e d . The o n l y h i g h r e s o l u t i o n s p e c t r a r e c o r d e d a r e t h o s e o f f o r m -a l d e h y d e and p r o p e n a l ( a c r o l e i n ) by T u r n e r e t a l [ 8 2 ] . Dewar and Worley [122] measured t h e p h o t o e l e c t r o n s p e c t r a o f a c e t a l d e h y d e , p r o p i o n -a l d e h y d e , a c e t o n e and 2-butanone ( t o g e t h e r w i t h -63 o t h e r o r g a n i c compounds) a t low r e s o l u t i o n u s i n g a s i m p l e r e t a r d i n g - p o t e n t i a l g r i d - t y p e s p e c t r o -meter and r e p o r t e d t h e f i r s t and some h i g h e r a d i a b a t i c I . P . ' s . Cocksey e t a l . [123] have used a p a r a l l e l p l a t e p h o t o e l e c t r o n s p e c t r o m e t e r o p e r a t i n g a t medium r e s o l u t i o n t o measure t h e f i r s t i o n i z a t i o n p o t e n t i a l s o f a s e r i e s o f a l i p h a t i c a l d e h y d e s , k e t o n e s , a l c o h o l s , e t h e r s and i o d i d e s . EXPERIMENTAL o We have measured t h e 584 A p h o t o e l e c t r o n s p e c t r a o f s i x ke t o n e s and t h r e e a l d e h y d e s u s i n g a h i g h - r e s o l u t i o n p h o t o e l e c t r o n s p e c t r o m e t e r employ-i n g a 127 degree c y l i n d r i c a l a n a l y s e r . The a p p a r a t u s has been d e s c r i b e d - e l s e w h e r e [ 1 2 4 ] . N i t r o g e n was used f o r energy c a l i b r a t i o n . RESULTS AND DISCUSSION F i g u r e 35 shows t h e p h o t o e l e c t r o n s p e c t r a , from ^9 eV t o 18 eV, o f 170. I 1 1 1 1 1 1 H 1 1 1 9 10 II 12 13 14-15 16 17 18 19 IONIZATION POTENTIAL (eV) o F i g u r e 35. 584 A p h o t o e l e c t r o n s p e c t r a o f CH 3CH0, CH 3CH 2CH0 and (CH 3) 2CHCH0. / • 171. a c e t a l d e h y d e , p r o p i o n a l d e h y d e and i s o b u t y r a l d e h y d e . As i n t h e c a s e o f fo r m a l d e h y d e [ 8 2 ] v i b r a t i o n a l s t r u c t u r e i s o b s e r v e d i n t h e f i r s t band o f a c e t a l d e h y d e and p r o p i o n a l d e h y d e . The band p o s i t i o n s s h i f t t o l o w e r e n e r g y w i t h i n c r e a s e d a l k y l a t i o n . The v i b r a t i o n a l s p a c i n g i n b o t h t h e s e compounds i s a p p r o x i m a t e l y 0.16 eV. The f a c t t h a t t h e f i r s t v i b r a t i o n a l peak i s most i n t e n s e and a l s o t h e s i m i l a r i t y t o t h e sp e c t r u m o f f o r m a l d e -hyde s u g g e s t t h a t t h i s band i n b o t h a c e t a l d e h y d e and p r o p i o n a l d e h y d e i s due t o t h e i o n i z a t i o n o f an e l e c t r o n i n t h e e s s e n t i a l l y non-bonding o r b i t a l on t h e oxygen atom. When t h e a l k y l c h a i n s t a r t s t o branch a t t h e a-carbon as i n i s o b u t y r a l d e h y d e , v i b r a t i o n a l s t r u c t u r e i n t h e f i r s t band i s o b l i t e r a t e d , p r o b a b l y due t o t h e o c c u r r e n c e o f f u r t h e r v i b r a t i o n a l components. There a r e f o u r broad peaks i n t h e p h o t o e l e c t r o n s p e c t r u m o f a c e t a l d e h y d e i n t h e 12 eV t o 18 eV r e g i o n c o r r e s p o n d i n g t o i o n i z a t i o n s o f t h e i n n e r M.O.'s. As a l k y l a t i o n i n c r e a s e s , more peaks appear a t t h i s r e g i o n . F o l l o w i n g t h e example o f f o r m a l d e h y d e [ 8 2 ] , t h e second I.P. p r o b a b l y c o r r e s p o n d s t o t h e i o n i z a t i o n o f t h e -rr-electrons i n t h e C=0 do u b l e bond. The energy p o s i t i o n t e n d s t o d e c r e a s e as a l k y l a t i o n i n c r e a s e s . No a t t e m p t has been made t o i n t e r p r e t t h e i n d i v i d u a l h i g h e r I . P . ' s , w h i c h are p r o b a b l y due t o i o n i z a t i o n s o f t h e v a r i o u s C-H bonding o r b i t a l s . Chadwick and K a t r i b [ 1 2 5 ] have r e c e n t l y p r e s e n t e d an i n t e r p r e t a t i o n o f the PES o f a c e t a l d e h y d e i n terms o f M.O. s t r u c t u r e . F i g u r e 36 shows t h e p h o t o e l e c t r o n s p e c t r a o f a c e t o n e , 2-butanone, methyl i s o b u t y l k e t o n e , m e t h y l i s o p r o p y l k e t o n e , methyl t - b u t y l k e t o n e and methyl v i n y l k e t o n e i n t h e energy range o f ^  9 - 19 eV. The g e n e r a l f e a t u r e s o f t h e p h o t o e l e c t r o n s p e c t r a o f t h e s a t u r a t e d k e t o n e s ( w i t h t h e e x c e p t i o n o f methyl v i n y l k e t o n e ) a r e v e r y s i m i l a r t o t h o s e o f a l d e h y d e s . 172. CH 3C0CH 3 CH 3CH 2C0CH 3 (CHJIpHCKPOCH, ( (CH3)2CHC0CH3 (CH3)3CC0CH3 CH2=CHC0CH3 I I 1 2 1 3 1 4 1 5 1 6 17 1 8 1 9 2 0 IONIZATION POTENTIAL (eV) F i g u r e 36. 584 A p h o t o e l e c t r o n s p e c t r a o f CH 3COCH 3, . CH 3CH 2COCH 3, (CH 3) 2CIICH 2C0CH 3, ( C H ^ C C O C H g and C H 2 = CHC0CH 3. 173. The f i r s t band i s r e l a t i v e l y s h a r p but t h e second and h i g h e r bands a r e broad and o v e r l a p w i t h one a n o t h e r . These h i g h e r bands o c c u r a t l o w e r e n e r g i e s t h a n t h o s e i n t h e a l d e h y d e s . T h e r e i s a l s o a s h i f t o f t h e f i r s t band t o l o w e r e n e r g i e s as a l k y l a t i o n i n c r e a s e s . As i n t h e c a s e o f a l d e h y d e s , v i b r a t i o n a l s t r u c t u r e can be r e s o l v e d i n t h e f i r s t band o f t h o s e k e t o n e s i n w h i c h no b r a n c h i n g o f t h e a l k y l c h a i n o c c u r s a t t h e a - c a r b o n ( i . e . a c e t o n e , 2-butanone and methyl i s o b u t y l k e t o n e ) . The s i m i l a r i t y between t h e p h o t o e l e c t r o n s p e c t r a o f k e t o n e s and a l d e h y d e s seems t o s u g g e s t t h a t t h e y can be i n t e r p r e t e d i n t h e same way. The f i r s t band i s most l i k e l y due t o t h e i o n i z a t i o n o f t h e non-bonding e l e c t r o n on oxygen and t h e second I.P. due t o i o n i z a t i o n o f t h e i r - o r b i t a l i n t h e C=0 bond. Most o f t h e h i g h e r I.P.'s a r e p r o b a b l y due t o C-H bonding M.O.'s and t h e i r number i n c r e a s e s as a l k y l a t i o n i n c r e a s e s . T a b l e 14 shows the i o n i z a t i o n p o t e n t i a l s w h i c h have been o b s e r v e d i n t h e p h o t o e l e c t r o n s p e c t r a o f a l d e h y d e s and k e t o n e s . The p h o t o e l e c t r o n spectrum o f t h e u n s a t u r a t e d c o n j u g a t e d k e t o n e , methyl v i n y l ketone d i f f e r s from t h o s e o f s a t u r a t e d c a r b o n y l compounds i n t h a t i t e x h i b i t s a second s h a r p band w i t h r e s o l v e d v i b r a t i o n a l s t r u c t u r e . In the c a s e o f p r o p e n a l ( a c r o l e i n ) s i m i l a r b e h a v i o u r has been r e p o r t e d by T u r n e r e t a l . [ 8 2 ] who a t t r i b u t e d t h e second band t o t h e l o s s o f an e l e c t r o n f r o m t h e h i g h e r o f t h e two o c c u p i e d T r - o r b i t a l s . T h i s i s p r o b a b l y a d i s t i n g u i s h i n g f e a t u r e f o r an u n s a t u r a t e d c o n j u g a t e d c a r b o n y l compound and i t s s i g n i f i c a n c e i n t h e i n t e r p r e t a t i o n o f t h e vacuum u l t r a v i o l e t o r e l e c t r o n impact s p e c t r a has been d i s c u s s e d ( s e c t i o n 8.4.1.). The e f f e c t o f a l k y l s u b s t i t u t i o n o f t h e I.P.'s o f a l d e h y d e s and k e t o n e s , has been d i s c u s s e d i n C h a p t e r 8. The p l o t s o f t h e f i r s t I.P. and COMPOUND 1st BAND BANDS A l 3 V ] b 2nd 3rd 4th 5th 6th 7th 8th 9th 10th HCHOC 10.88 14 .39 10 .01 16.60 CH3CH0 10.22 10.21 13, ,2 14 .1 15.3 16.4 CH3CH2CHO 9.97 . 9.99 12, .4 13 .2 13.7 14.1 15.4- 16-3 (CH3)2CHCHO 9.69 9.82 12. .0 12 .6 13.4 14.1 15.6 16, .5 CH3C0CH3 9.71 9.71 12, .6 13 .5 14.1 15.6 18.0 18, ,9 CH 3CH 2C0CH 3 9.54 9.52 12. ,2 12 .6 13.0 14.3 14.8 15, .3 15, .9 17.6 (CH 3) 2CHCH 2C0CH 3 9.34 9.42 11. ,4 11 .9 13.0 13.6 14.3 15. ,5 17, .6 18.6 (CH3)2CHCOCH3 9.30 9.36 11. ,8 12 .6 13.9 14.2 14.6 15. ,8 17, .4 13.6 (CH 3) 3CCOCH 3 9.14 9.21 11. .4 12 .5 13.6 14.6 15.4 16. ,1 16, .9 18.4 CH2=CH-CH0c 10.11 10. 93 13, .5 14.8 15.3 16.1 16. .4 17, .0 18.0 CH2=CH-COCH3 9.61 10. 62 13, .1 13.9 •14.4 15.1 16. 0 17. ,5 18.7 Table Ik Ionization potentials (eV) for some carbonyl compounds a Al indicates adibatic ionizat ion po ten t i a l , from Cocksey et al [6] bVI indicates ver t ica l ionizat ion potent i a l , this work (except for HCHO and CH2=CH-CH0) from photoelectron spectra reported by Turner et a l , ref . 4. 18.0 -pa 175. Rydberg term v a l u e s a g a i n s t t h e sum o f t h e T a f t a * v a l u e s o f t h e s u b s t i t u e n t s on both s i d e s o f t h e f u n c t i o n a l groups have a l s o been d i s c u s s e d . PUBLICATIONS 1. Wing-cheung Tarn § C. E. Brion, Excitation of optically forbidden transitions in argon and neon by electron impact, J. Electron Spectrosc. 2_, 111 (1973). 2. Wing-cheung Tarn § C. E. Brion, A rotatable gas-tight c o l l i s i o n chamber for electron spectrometers. J . Electron Spectrosc. 3, 82 (1974). 3. Wing-cheung Tarn $ C. E. Brion, Electron impact spectra of some alkyl deri-vatives of water and related compounds, J. Electron Spectrosc, 3, 263 (1974). 4. Wing-cheung Tam fT C. E. Brion, Rydberg series of HCN observed by electron impact spectroscopy, J. Electron Spectrosc., 3_ 281 (1974). 5. Wing-cheung Tam $ C. E. Brion, Electronic spectra of some carbonyl compounds by electron impact spectroscopy I. saturated aldehydes J. Electron Spectrosc, 4_143 (1974). 6 . Wing-cheung Tam § C. E. Brion, Electronic spectra of some carbonyl compounds by electron impact spectroscopy II. saturated ketones J . Electron Spectrosc, in press 7. Wing-cheung Tam 5 C. E. Brion, Electronic spectra of some carbonyl compounds by electron impact spectroscopy III. unsaturated compounds J. Electron Spectrosc, i n press 8. Wing-cheung Tam, D. Yee $ C. E. Brion, Photoelectron spectra of some alde-hydes and ketones, J . Electron Spectrosc, in press 

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