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Identification of a ¹Δ [delta] u - ¹Σ [sigma] ⁺g transition of CS₂ in the near ultraviolet 1972

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IDENTIFICATION OF A  L A -  1Z + TRANSITION OF CS 2 u g IN THE NEAR ULTRAVIOLET by DAVID NELSON MALM B . S c , Un i ve r s i t y of B r i t i s h Columbia, 1970 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE In the Department of Chemistry We accept t h i s thes i s as conforming to the requ i red standard THE UNIVERSITY OF BRITISH COLUMBIA October, 1972 In present ing th i s thes i s in p a r t i a l f u l f i lmen t o f the requirements for an advanced degree at the Un i ve r s i t y of B r i t i s h Columbia, I agree that the L ib ra r y sha l l make i t f r ee l y ava i l ab l e for reference and study. I f u r the r agree that permission for extensive copying o f th i s thes i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s representa t i ves . It is understood that copying or p u b l i c a t i o n o f t h i s thes i s f o r f i nanc i a l gain sha l l not be allowed without my wr i t t en permiss ion . Department of CHEMISTRY, The Un i ve r s i t y of B r i t i s h Columbia Vancouver 8, Canada Date 6 1972. ABSTRACT The strongest f e a t u r e s i n the ab s o r p t i o n spectrum of CS 2 i n o o the r e g i o n 2900A to 3500A are i d e n t i f i e d , from temperature s t u d i e s , as a IT -> TT  L A -  I I t r a n s i t i o n , where the Renner-Teller e f f e c t has s p l i t u g the *A s t a t e i n t o *B2 and *A2 component s t a t e s of a bent molecule. A n a l y s i s of some of the l e a s t s e v e r e l y perturbed bands of the  1 B 2 -  1 E + 8 o t r a n s i t i o n s (3300 - 2900A) shows that they form a p a r a l l e l - p o l a r i z e d p r o g r e s s i o n i n the bending v i b r a t i o n , to an upper s t a t e w i t h r(C - S) = I . 5 4 4 A , <SCS = 1 6 3°, and a b a r r i e r to l i n e a r i t y of ~ 1400 cm - 1 . Two h i t h e r t o unrecognized progressions of 'hot' bands, a weak v i b r o n i c II — n o o and a stronger v i b r o n i c A - A p r o g r e s s i o n i n the r e g i o n 3300A to 3500A, are assigned to the  1 A 2 -  1 E +  t r a n s i t o n . This i s a new type of t r a n s i t i o n , which does not appear i n c o l d a b s o r p t i o n , but whose 'hot' bands can o b t a i n an amount of i n t e n s i t y ( p r o p o r t i o n a l to K 2 ) through Renner-Teller m i x i n g . ( i i ) TABLE OF CONTENTS PAGE A b s t r a c t ( i ) L i s t of Tables and Figu r e s ( i i i ) Acknowledgment (v) I . INTRODUCTION 1 I I . EXPERIMENTAL 4 I I I . THEORY A. Symmetry P r o p e r t i e s of CS 2 10 B. V i b r a t i o n a l Energy L e v e l P a t t e r n s 13 C. R o t a t i o n a l Energy L e v e l P a t t e r n s 19 D. R o t a t i o n a l Constants of CS 2 24 E. Nuclear Spin S t a t i s t i c s 25 F. S e l e c t i o n Rules 29 IV. THE V SYSTEM 34 A. Temperature Studies and P o l a r i z a t i o n of the V System 34 B. R o t a t i o n a l A n a l y s i s 38 C. V i b r a t i o n a l P a t t e r n of the V Sta t e 53 D. E l e c t r o n i c Species of the V State 59 E. V i b r o n i c C o r r e l a t i o n In a  1 A U E l e c t r o n i c State 61 V. THE T STATE 67 A. The Renner-Teller E f f e c t i n a 1 A U E l e c t r o n i c State 68 B. General Features of the T System 75 C. N 2 Laser E x c i t e d Fluorescence of CS 2 a t 3371A 76 D. The P o t e n t i a l Energy Curves f o r the *A U S t a t e 77 V I . DISCUSSION 81 References 84 Appendix I 87 Appendix I I 91 Appendix I I I 93 ( i i i ) L i s t of Tables and Figu r e s Table Page I Character Tables of D , and C P o i n t Groups 11 ooh Zy I I C o r r e l a t i o n of Species of D and C 2 v P o i n t Groups 12 I I I V i b r a t i o n a l Frequencies of X 1 Z +  (ground) E l e c t r o n i c States of CS 2  8  19 IV R o t a t i o n a l L i n e Assignments of the 3236A and 3322A Bands 44 o o V R o t a t i o n a l Line Assignments of the 3275A and 3365A Bands 46 VI a . R o t a t i o n a l Term Values of the Upper States of the 3236A and 3322A Bands . 49 b. R o t a t i o n a l Term Values of the Upper States of the 3275A and 3365A Bands 50 V I I V i b r a t i o n a l Term Values of the V State of CS 2 55 V I I I V i b r a t i o n a l Term Values of the R State of CS 2 66 IX V i b r a t i o n a l Term Values of the T St a t e of CS 2 70 (iv) Figure Page 1. 4 Meter White C e l l Experimental Arrangement and Order Separator 6 2. Ground State Vibrational Energy Level Pattern of CS 2 18 3. Principal Inertial Axes of Non-Linear CS 2 24 4. Rotational Energy Level Patterns 28 o 5. CS 2 Absorption Spectrum (3400-2900A) 35 6. The 0 0 0, K* = 0 - 0 0° 0 and 0 0 0, K' = 0 - 0 2° 0 Bands of the V System 42 7. The 0 0 0, K' = 1 - 0 l 1 0 and 0 0 0, K» = 1 - 0 3 1 0 Bands of the V System 4 3 8. Rotational Term Values of the 0 0 0, K' = 0 and 0 0 0, K' = 1 Levels of the V State plotted against J(J + 1) 52 9. Vibrational Term Values of the V State 54 10. Correlation of Vibronic Levels of a A state in Linear and Bent Limits 62 11. Behaviour of Vibronic Levels of a A state with a Barrier to Linearity 64 12. Medium and High Resolution Spectra of CS 2 in the N 2 Laser Wavelength Region (3371A) 69 13. The Potential Energy Curves for the *A state of CS 2 79 (v) ACKNOWLEDGMENT The author wishes to thank h i s research supe rv i so r , Dr . A . J . Merer, as we l l as Dr . C h r i s t i a n Jungen, fo r t he i r adv ice and encouragement i n the research upon which t h i s thes i s i s based. A s p e c i a l word of thanks i s a lso due E.M. who gave much needed support throughout the 'dog days ' of thes i s w r i t i n g and to Rose Chabluk fo r her f i n e job i n the typ ing of t h i s t h e s i s . - 1 - I . INTRODUCTION Carbon d i s u l f i d e has a complex e l e c t r o n i c a b s o r p t i o n spectrum o o i n the v i s i b l e and u l t r a v i o l e t r e g i o n s . In the r e g i o n 4300A to 2900A there are s e v e r a l r e l a t i v e l y weak systems ( 1 - 6 ) , and i n the r e g i o n 2300&. O to 1800A (7-8) there are s e v e r a l systems of much stronger a b s o r p t i o n . A number of in t e n s e bands between 1850A and 1375A (7) (probably b e l o n g - i n g to s e v e r a l e l e c t r o n i c t r a n s i t i o n s ) have not been a n a l y s e d . From 1375& to 600A Rydberg s e r i e s converging to the CS 2 i o n i z a t i o n l i m i t s have been c h a r a c t e r i z e d (9-10). The e l e c t r o n i c c o n f i g u r a t i o n of CS 2 i n i t s e l e c t r o n i c ground s t a t e i s ... « y 2  <*u> 2  'V* l z g CS 2 i s l i n e a r i n the ground e l e c t r o n i c s t a t e w i t h a C-S bond l e n g t h of I . 5 5 4 5 A (11-12). The shape and bonding c h a r a c t e r i s t i c s of the f i l l e d and u n f i l l e d o r b i t a l s a v a i l a b l e to CS 2 are di s c u s s e d by Walsh ( 1 3 ) . The lowest energy e x c i t e d e l e c t r o n c o n f i g u r a t i o n i s ... ( n g) where TT* i s an anti-bonding o r b i t a l . The c o n f i g u r a t i o n g i v e s r i s e to *E*, 1 E ,  1 A ,  3 E + ,  3 E and  3 A s t a t e s . Only one of the p o s s i b l e TT i r * u u u u u t r a n s i t i o n s i s f u l l y allowed by the s p i n and o r b i t a l symmetry s e l e c t i o n r u l e s , and t h i s has been i d e n t i f i e d w i t h the strong 2100A a b s o r p t i o n e bands ( 1 3 ) . A r o t a t i o n a l a n a l y s i s of a few o f the 2100A bands (14) showed the t r a n s i t i o n to be p a r a l l e l - p o l a r i z e d ,  1 B 2 -  1 E + , going to an upper s t a t e i n which CS 2 i s s l i g h t l y bent w i t h an S-C-S bond angle of 153° and a C-S bond l e n g t h of 1.66X. The v i b r a t i o n a l s t r u c t u r e i s not - 2 - w e l l understood, though there i s no doubt that the upper e l e c t r o n i c s t a t e i s the K TT* 1 B 2 C*E+) s t a t e . ^ u o o In the r e g i o n 3800A to 3300A Liebermann (4) found s i x v i b r a - t i o n a l bands to have  1 E -  1 E -type r o t a t i o n a l s t r u c t u r e s . More r e c e n t l y , Kleman (15) showed that the a b s o r p t i o n i n the r e g i o n 4300A to 3300A c o n s i s t s of two e l e c t r o n i c systems. In the lowest e x c i t e d e l e c t r o n i c s t a t e , which he c a l l e d the R s t a t e , the molecule i s bent, w i t h an S-C-S bond angle of 135.8° and a C-S bond l e n g t h of 1.66A. A lo n g p r o g r e s s i o n i n the bending frequency, v ^ 3  311 cm - 1 , and a s h o r t e r p r o g r e s s i o n i n the symmetric s t r e t c h i n g frequency, v j = 691.5 cm - 1 , were a s s i g n e d , as w e l l as numerous 'hot' bands from e x c i t e d v i b r a t i o n a l l e v e l s of the ground e l e c t r o n i c s t a t e . Kleman was unable t o i d e n t i f y the e l e c t r o n i c s t a t e of * the Tr -»• ir e x c i t a t i o n r e s p o n s i b l e f o r the R system except to say that the R system was p a r a l l e l - p o l a r i z e d , w i t h a B 2 upper s t a t e . Although the R bands are s i n g l e t i n appearance, the magnetic r o t a t i o n spectrum (16) and the Zeeman e f f e c t (17) i n d i c a t e t h a t the R s t a t e i s a c t u a l l y a t r i p l e t s t a t e . The lowest t r i p l e t e l e c t r o n i c s t a t e , as p r e d i c t e d by t h e o r e t i c a l c o n s i d e r a t i o n s (13,18), i s the ^A^ (ir -*• IT ) s t a t e . In the bent molecule the o r b i t a l degeneracy of the  3 A^ e l e c t r o n i c s t a t e i s l i f t e d , g i v i n g r i s e t o  3 A 2 and  3 B 2 component s t a t e s . More comprehensive Zeeman e f f e c t s t u d i e s ( 1 9 ) , as w e l l as t h e o r e t i c a l c a l c u - l a t i o n s ( 2 0 ) , assigned the R s t a t e as a Hund's c o u p l i n g case (c) s p i n m u l t i p l e t sub-component (B 2) of a  3 A 2 e l e c t r o n i c s t a t e . The Zeeman - 3 - spectrum of s o l i d CS 2 at 4.2°K (21) showed weak magnetic f i e l d induced a b s o r p t i o n to the other two s p i n m u l t i p l e t sub-components ( A j , B j ) of the  3 A 2 s t a t e , 36 cm - 1  to the red of the B 2 sub-component r e s p o n s i b l e f o r the R system. As p r e d i c t e d by Hougen (20), t h i s o b s e r v a t i o n i s c o n s i s t e n t w i t h the  3 A 2 ( 3 ^ u) component s t a t e l y i n g lower i n energy than the  3 B 2 ( 3 ^ u) component s t a t e . Kleman i d e n t i f i e d a second e l e c t r o n i c system (which he c a l l e d the S system) i n the r e g i o n 3700A to 3350A; t h i s c o n s i s t s of another p a r a l l e l - p o l a r i z e d p r o g r e s s i o n i n the upper s t a t e bending frequency, v£ = 270 cm - 1 . The r o t a t i o n a l s t r u c t u r e of the v i b r a t i o n a l bands i s s i m p l e , l i k e that of the R bands. The s t r o n g e s t CS 2 a b s o r p t i o n i n the n e a r - u l t r a v i o l e t , i n the e e r e g i o n 3400A to 2900A, was c a l l e d the V system by Kleman. The complex- i t y of the V system has so f a r prevented a v i b r a t i o n a l or r o t a t i o n a l a n a l y s i s . R e c e n t l y , however, the a b s o r p t i o n spectrum of the V system was observed i n matrices at 20°K and 77°K by Bajema, Goutermann and Meyer ( 2 2 ) , who found a c o n s i d e r a b l e s i m p l i f i c a t i o n of the v i b r a t i o n a l s t r u c t u r e i n the m a t r i x over the gas phase spectrum. The m a t r i x spec- trum c o n s i s t s e s s e n t i a l l y of a s i n g l e p r o g r e s s i o n of 580 ± 30 cm - 1, which they assigned as the symmetric s t r e t c h i n g v i b r a t i o n of a molecule l i n e a r i n the upper s t a t e . The complexity of the V s t a t e was a t t r i b u t e d t o the e f f e c t s o f Renner-Teller i n t e r a c t i o n i n a  1 A e l e c t r o n i c s t a t e o f u a l i n e a r molecule. However, the c o n c l u s i o n reached i n t h i s t h e s i s i s that the 580 cm - 1  i n t e r v a l corresponds to the bending v i b r a t i o n of a bent molecule w i t h a 1 B 2 ( 1A ) upper s t a t e . - 4 - I I . EXPERIMENTAL Low r e s o l u t i o n survey s p e c t r a of C S 2 were taken on a Cary 14 r e c o r d i n g spectrophotometer. A 10 cm c e l l was f i l l e d w i t h C S 2 vapour t o 4 cm pressure and then opened to the a i r to g i v e a pressure- broadened spectrum.^ Without pressure-broadening, a l l a b s o r p t i o n bands of w i d t h l e s s than the r e s o l u t i o n of the Cary 14 would be recorded w i t h i n c o r r e c t i n t e n s i t i e s . Medium r e s o l u t i o n gas phase s p e c t r a (approximately 150,000 r e s o l v i n g power) were photographed i n the second order of a 21 f t f o c a l l e n g t h Eagle-mounted concave g r a t i n g spectrograph. Quartz gas c e l l s f i t t e d w i t h S u p r a s i l windows were used to g i v e path lengths of 80 cm and 160 cm. I t was necessary i n a l l experiments to use a e Coming 7-54 f i l t e r t o remove wavelengths of l e s s than 2300A from the i n c i d e n t r a d i a t i o n t o prevent p h o t o d i s s o c i a t i o n of CS 2 (23) according to the r e a c t i o n cs2 h v > CS(A1n) + S ( 3 P 2 ) This r e a c t i o n i s e n e r g e t i c a l l y p o s s i b l e at wavelengths l e s s than o 0 2778 ± 10A, but because there i s almost no a b s o r p t i o n from 2800A to o 2300A, decomposition i s troublesome o n l y w i t h i n c i d e n t l i g h t of wave- l e n g t h l e s s than 2300A. With a 20p s l i t and CS 2 pressure ranging from ^ A l l p ressures w i l l be quoted i n u n i t s of cm or mm of Hg. 1 mm Hg = 133.32 N/m 2 . - 5 - 0.2 mm to 5 mm, exposure times were of the order of 10 sec u s i n g Kodak SA-1 p l a t e s . Wavelength c a l i b r a t i o n f o r a l l s p e c t r a photographed was w i t h a 120 ma iron-neon hollow-cathode lamp of the l a b ' s own d e s i g n . The temperature dependence of the n e a r - u l t r a v i o l e t bands was i n v e s t i g a t e d by photographing s p e c t r a of CS 2 at - 7 8 ° , 2 3° , '85°, 100° and 200°C. Elevated temperatures were achieved by wrapping the c e l l w i t h e l e c t r i c h e a t i n g tape over which was wound asbestos c l o t h i n s u l a - t i o n . V arying the a p p l i e d v o l t a g e on the h e a t i n g tape gave the d e s i r e d temperature. As measured w i t h a mercury thermometer next to the c e l l s u r f a c e , a r e g u l a t i o n of ±2°C was a c h i e v e d . To compare r e l a t i v e i n t e n s i t i e s of bands as a f u n c t i o n of temperature, the number of absorbing molecules i n the l i g h t path had to be kept constant at the d i f f e r e n t temperatures. This presented no problem except at -78°C, f o r , even a t room temperature, the vapour pressure of CS 2 i s 300 mm, f a r i n excess of the pressure needed to o b t a i n s u f f i c i e n t a b s o r p t i o n . However, a t -78° the vapour pressure of CS 2 i s only 0.2 mm. Since the n e a r - u l t r a v i o l e t a b s o r p t i o n i s compar- a t i v e l y weak, t h i s n e c e s s i t a t e d the use of very long a b s o r p t i o n path l e n g t h s . Using a 4 m White-type m u l t i p l e r e f l e c t i o n c e l l (24,25) of the l a b ' s own design (as shown i n F i g . 1 ) , path'lengths of up to 128 m co u l d be a t t a i n e d . The c e l l c o n s i s t s of 85 mm pyrex t u b i n g , to the ends of which o r d i n a r y pyrex pipe f l a n g e s are a t t a c h e d . S t e e l end-plates sealed by '0' r i n g s are secured to the f l a n g e s to produce a vacuum s e a l . One XENON LAMP 25 cm LENS D MIRRORS 35 cm CYLINDRICAL L E N S ^ ORDER SEPARATOR SPECTROGRAPH 25 cm SPHERICAL FIELD LENS FIG. (1) 4 Meter White C e l l and Order Separator CONCAVE MIRROR FORE SLIT MAIN SLIT PRISM - 7 - end-plate c a r r i e s the S u p r a s i l entrance and e x i t windows, w h i l e the other end-plate has e x t e r n a l c o n t r o l s f o r the concave 'D'-shaped m i r r o r s . I n s e r t e d i n the c e l l near the quartz windows i s a 'boat' which holds i n p o s i t i o n the shouldered c i r c u l a r concave m i r r o r . The number of t r a v e r s a l s of the c e l l ( m u l t i p l e s of 4) was c o n t r o l l e d by manipulation of one of the D m i r r o r s . For temperature s t u d i e s a t -78°C, dry i c e was packed between the White c e l l and i t s s t y r o f o a m - i n s u l a t e d box. To a t t a i n e l e v a t e d temperatures, the White c e l l was wrapped w i t h h e a t i n g tape and i n s u l a t - i n g asbestos c l o t h . Due t o the l a r g e mass of pyrex t u b i n g , a tempera- tu r e of only 85 ± 5°C was p o s s i b l e . With the White c e l l set f o r 12 t r a v e r s a l s 0v48 m path l e n g t h ) , a CS 2 pressure at -78°C of 0.2 mm and a 30u s l i t w i d t h , exposures on the Eagle spectrograph were about 10 minutes w i t h Kodak SA-1 p l a t e s . High r e s o l u t i o n s p e c t r a (approximately 625,000 r e s o l v i n g power) were photographed i n the 16 t n * - 19 t * 1-  orders of a 7 m f o c a l l e n g t h Ebert-mounted plane g r a t i n g spectrograph. To prevent an o v e r - l a p p i n g of s p e c t r a l o r d e r s , an order separator c o n s i s t i n g e s s e n t i a l l y of a s m a l l quartz prism monochromator was placed between the s p e c t r o - graph (main) s l i t and the e x t e r n a l o p t i c s ( F i g . 1 ) . By r o t a t i n g the S u p r a s i l quartz p r i s m , the wavelength of l i g h t f a l l i n g on the main s l i t c o uld be v a r i e d . By a d j u s t i n g the f o r e - s l i t width between lOOu and o 1500u, the 'bandpass' admitted could be v a r i e d from approximately 40A to 300A. With the White c e l l set f o r 12 t r a v e r s a l s , a f o r e - s l i t w i d t h - 8 - of 400u and a main s l i t w i d t h of 20p, exposures of about 10 minutes were r e q u i r e d w i t h Kodak SA-1 p l a t e s . C a l i b r a t i o n of the h i g h r e s o l u - t i o n s p e c t r a was achieved by i n c r e a s i n g the order separator bandpass so that s e v e r a l orders adjacent to the molecular s p e c t r a l order were photographed. This i s necessary because at the h i g h d i s p e r s i o n of the Ebert spectrograph (0.137A/mm i n 17 t n * order) the d e n s i t y of i r o n c a l i - b r a t i o n l i n e s i n any one order i s not s u f f i c i e n t f o r accurate i n t e r - p o l a t i o n between them. CS 2 ( F i s h e r RG) was used without f u r t h e r p u r i f i c a t i o n except f o r de-gassing under vacuum at l i q u i d n i t r o g e n temperature. The s t a n d - ard a l l g l a s s vacuum l i n e used a d u a l chamber r o t a r y pump and an o i l d i f f u s i o n pump. Gas pressures were measured w i t h a thermocouple gauge and w i t h a manometer f i l l e d w i t h Dow Corning. 707 s i l i c o n e f l u i d (12.8 mm s i l i c o n e o i l = 1 mm Hg). Dow s i l i c o n e h i g h vacuum stopcock grease, used throughout the vacuum l i n e , was the only grease t h a t r e s i s t e d formation of bubbles of d i s s o l v e d CS 2. An u l t i m a t e vacuum of 0.001 mm was r o u t i n e l y achieved w i t h a l l a b s o r p t i o n c e l l s . The gas c e l l s were f i l l e d to the d e s i r e d pressure simply by a l l o w i n g the f r o z e n , de-gassed CS 2 to warm s l o w l y , l i q u e f y and evaporate. The h i g h r e s o l u t i o n p l a t e s were measured on a Grant automatic r e c o r d i n g p h o t o e l e c t r i c comparator i n the P h y s i c s Department, and a l l the measurements were reduced to vacuum wavenumbers by means of a computer programme that performed a l e a s t squares f i t of the i r o n and neon ref e r e n c e l i n e wavelengths (26) to a 4-term p o l y n o m i a l . I t i s estimated that r e l a t i v e p o s i t i o n s of unblended l i n e s are accurate to b e t t e r than ±0.01 cm - 1 . Band head p o s i t i o n s used i n the v i b r a t i o n a l a n a l y s i s were measured from h i g h c o n t r a s t photographic enlargements of the medium r e s o l u t i o n p l a t e s . I n t e r p o l a t i o n between two c l o s e r e f e r e n c e l i n e s p rovided a r e l a t i v e band head accuracy of ±1 cm - 1 . - l O - I H . THEORY A. Symmetry P r o p e r t i e s of C S 2 The p o i n t group of l i n e a r CS 2 i s  a n a  that of bent CS 2 i s C2v> t h e i r c h a r a c t e r t a b l e s are given as Table I . The l a b e l l i n g of the symmetry a x i s i s d i f f e r e n t f o r the two p o i n t groups because, according to M u l l i k e n ' s convention ( 2 7 ) , the z a x i s i s the molecular a x i s f o r the l i n e a r molecule, but the two-fold r o t a t i o n a x i s (C 2) f o r the bent molecule. When l i n e a r CS 2 becomes bent, a l l symmetry operat i o n s of D . not r e t a i n e d i n C„ are no longer d e f i n e d . The c o r r e l a t i o n o f °°h 2v symmetry operations between and i s as f o l l o w s : C 2, the one remaining r o t a t i o n about an a x i s p e r p e n d i c u l a r to the l i n e a r a x i s becomes the C 2 ( z ) r o t a t i o n i n the point group; a ^ , r e f l e c t i o n i n a plane p e r p e n d i c u l a r to the l i n e a r a x i s becomes c r ^ x z ) ; s i m i l a r l y , the one remaining r e f l e c t i o n , o"^, becomes o" v(yz). A l l other D operat i o n s are undefined, i n c l u d i n g the i n v e r s i o n o p e r a t i o n , so that the *g,u' species d e s i g n a t i o n s of the l i n e a r molecule are undefined f o r the bent molecule. The r e s u l t i n g c o r r e l a t i o n of species i s given as Table I I . The a x i s c o r r e l a t i o n f o r D , w i t h C i s as f o l l o w s : x •«-+• x, «°h 2v ' y +-*•' z , z •*-»• y. The l i n e a r molecule non-degenerate p o i n t group species c o r r e l a t e i n a one-to-one manner w i t h the p o i n t group s p e c i e s . However, a l l other s p e c i e s are doubly degenerate and c o r r e l a t e w i t h A + B species of C2v« That i s , the c o r r e l a t i o n of symmetry sp e c i e s i s unique only when the symmetry i s lowered upon bending the l i n e a r mole- c u l e ; the c o r r e l a t i o n i s ambiguous when bent CS 2 becomes l i n e a r . TABLE I D , and C Point Groups c o h 2v I 2C* CO 2C 2 * OO 2C 3 * » 00 V 2S* OO 2S 2 * ••• OO s 2 = i z + g 1 1 1 1 1 1 1 1 1 1 u 1 1 1 1 -1 -1 1 -1 -1 -1 z E~ g 1 1 1 1 -1 1 -1 1. 1 1 R z Z~ u 1 1 1 1 1 -1 -1 -1 -1 -1 n g 2 2cos(j) 2cos2(j) 2cos3<j> 0 -2 0 -2cos<f> -2cos2cf> . . . 2 R ,R x y n u 2 2cos<J> 2cos2<}> 2cos3cj> 0 +2 0 2cos<j> 2cos2<f> ... -2 A g 2 2cos2<}> 2cos4cf> 2cos6<{> 0 +2 0 2cos2<J> 2cos4<J> 2 A u 2 2cos2<}> 2cos4(j) 2cos6<|) 0 -2 0 -2cos2<f> -2cos4<j> -2 g 2 2cos3<{> 2cos6<}> 2cos9<{) 0 -2 0 -2cos3<}> -2cos6(j) 2 u • * • 2 2cos3<}> 2cos6<j> • • • 2cos9(|) • • • • • 0 +2 • • • 0 2cos3<J> • • • 2cos6<j> * • * • • < -2 • • « TABLE I (continued) C 2 V I c 2 CT(x_) V a ( y * ) V Al 1 l 1 1 z A 2 1 1 -1 -1 R X B l 1 -1 1 -1 x,R y B 2 1 - l -1 1 y,R p o i n t group a x i s system p o i n t group a x i s system The x a x i s i s out of the plane of the paper. TABLE I I C o r r e l a t i o n of Species of D , and C Po i n t Groups * °°h 2v + + n D , I i f E n A A • • o °°h S u g u g u g u g u C 2v A i A 2 B l B 2 A2+B2 Al+Bi Al+B! A2+B2 A2+B2 A 2+B 2 • o o - 13 - B. V i b r a t i o n a l Energy L e v e l P a t t e r n s In order to gain f a m i l i a r i t y w i t h the c o n v e n t i o n a l spec- t r o s c o p i c nomenclature used throughout t h i s t h e s i s , a cursor y develop- ment of the theory of v i b r a t i o n and r o t a t i o n of a symmetric t r i a t o m i c molecule w i l l be o u t l i n e d . We begin w i t h a c o n s i d e r a t i o n of the theory of Normal Modes of v i b r a t i o n . The three t r a n s l a t i o n a l degrees of freedom possessed by each of the N c o n s t i t u e n t atoms become the t r a n s l a t i o n a l , v i b r a t i o n a l and r o t a t i o n a l degrees of freedom of the molecule formed from these atoms. The number of v i b r a t i o n a l degrees of freedom i s thus 3N - 6, (or 3N - 5 f o r a l i n e a r molecule which has only two r o t a t i o n a l degrees of freedom). I t i s very d i f f i c u l t to consider the v i b r a t i o n s of a polyatomic mole- c u l e u s i n g C a r t e s i a n displacement coor d i n a t e s because the v i b r a t i o n a l motions are q u i t e c l o s e l y i d e n t i f i a b l e as s t r e t c h i n g s of bonds, bond angle changing motions, or t w i s t i n g s . For t h i s reason i t i s customary to i n t r o d u c e Normal coordinates of v i b r a t i o n , which correspond to the a c t u a l motions of the atoms, w i t h s u i t a b l e mass-weighting. The d e t a i l e d motions of the atoms are governed by the Force F i e l d , a set of p o t e n t i a l energy expressions c o n t a i n i n g the Force Constants and the Normal c o o r d i n a t e s : these are co n v e n i e n t l y w r i t t e n as a Taylor s e r i e s i n the 3N - 5(6) Normal coord i n a t e s - 14 - With the choice of o r g i n as the ' E q u i l i b r i u m C o n f i g u r a t i o n ' the f i r s t two terms may be removed, and the q u a d r a t i c c r o s s terms v a n i s h because the Normal coordinates are d e f i n e d to cause them to be z e r o . The p o t e n t i a l energy i s thus V = f [ f Q2 + h i g h e r terms (2) k  \ a Q k / o I f the h i gher terms are n e g l e c t e d , the P o t e n t i a l Energy i s j u s t a sum of q u a d r a t i c terms, one f o r each v i b r a t i o n , k. This i s analogous t o the s i t u a t i o n of a c l a s s i c a l system undergoing simple harmonic motions, and i s known as the 'Harmonic Approximation'. The v i b r a t i o n a l h a m i l t o n i a n f a c t o r i z e s , i n harmonic a p p r o x i - mation, i n t o a sum of one-dimensional h a m i l t o n i a n s , one f o r each v i b r a - t i o n a l motion k where the * k ' s are the Force Constants, i . e . (3 2 V/9Q 2 ) Q and the P k's are the momentum operators conjugate to the Q^'s. The eigenvalues of t h i s h a m i l - t o n i a n , the 'Harmonic O s c i l l a t o r ' h a m i l t o n i a n , are well-known (28,29) to be E = I (v f c + |) h vfc j o u l e s (4) k where the v^'s are non-negative i n t e g e r s , and the  v k ' s  are r e l a t e d to the Force Constants by X k = 4*2 v 2  (5) I t i s customary to d e f i n e the q u a n t i t y =  v i c / c »  s o t n a t » *- n c m u n i t s , the v i b r a t i o n a l energy l e v e l s are E/hc - I (v + |) cok cm - 1 (6) k The e f f e c t s of the cubic and higher terms omitted from the h a m i l t o n i a n are to add c o r r e c t i o n s to t h i s e x p r e s s i o n , c a l l e d Anharmonicity Terms. A l i n e a r symmetric t r i a t o m i c molecule has 3N-5 = 4 v i b r a t i o n s , but two of these correspond to i d e n t i c a l bending motions executed at r i g h t a n g l e s , and t h e r e f o r e have the same frequency v ; these are s a i d to be 'degenerate' and one speaks l o o s e l y of the molecule as "having three v i b r a t i o n s , one of which i s degenerate". The other two v i b r a t i o n s correspond to symmetric and antisymmetric combinations of the s t r e t c h i n g s of the two bonds. The v i b r a t i o n a l energy l e v e l p a t t e r n i s s t i l l g iven by equation ( 6 ) , w i t h the summation running over both components of the degenerate bending v i b r a t i o n . There i s , however, an a d d i t i o n a l property a s s o c i a t e d w i t h the bending v i b r a t i o n , which i s the v i b r a t i o n a l angular momentum. P h y s i c a l l y i t s o r i g i n may be v i s u a l i s e d as f o l l o w s . I n a normal v i b r a - t i o n a l l the atoms move w i t h the same frequency so that the C a r t e s i a n components of the displacements change according to s i n e c u r v e s . The s u p e r p o s i t i o n of two i d e n t i c a l bending motions of equal amplitude at r i g h t angles and w i t h a 90° phase s h i f t r e s u l t s i n the motions of the i n d i v i d u a l atoms d e s c r i b i n g a c i r c l e about the l i n e a r a x i s as i l l u s t r a t e d below. - 16 - Such an add i t i on of two harmonic motions at r i g h t angles r e s u l t i n g i n r o t a t i on about the l i n e a r ax is i s equiva lent to impart ing an angular momentum to the n u c l e i with the vector of the v i b r a t i o n a l angular momentum along the l i n e a r a x i s . The i n d i v i d u a l atoms execute a f u l l r o t a t i o n about the l i n e a r ax is at the frequency of the degenerate bend- ing v i b r a t i o n . In mathematical terms the v i b r a t i ona l angular momentum a r i s e s because i t i s convenient to transform from Normal coordinates to c y l i n - d r i c a l po la r coord ina tes , when the product of two one-dimensional harmonic o s c i l l a t o r e igenfunct ions becomes an Assoc iated Laguerre func t ion m u l t i p l i e d by an angular f a c t o r , (l//2 ;n r)e 1^^. This angular f a c t o r , as i s we l l known (31), corresponds to an angular momentum i n a system with a x i a l symmetry. The nota t ion used for a bending v i b r a t i o n i s that the e igenfunct ions are descr ibed by quantum numbers v 2 and I, where v 2 i s the sum of one dimensional o s c i l l a t o r quantum numbers, and £ i s the v i b r a t i o n a l angular momentum quantum number, which (from the p roper t i es of the Assoc ia ted Laguerre funct ion) may take the values v 2 » v 2 ~ 2 » « . • , - v 2 . As we show below, i t i s convenient , for r o t a t i o n a l energy l e v e l c a l c u l a t i o n s , to d e f i n e the v i b r a t i o n a l angular momentum op e r a t o r , G. The eigenvalue of i t s z-component i s , of course , £(tl), i . e . Anharmonic terms cause components of a v i b r a t i o n a l l e v e l v 2 w i t h d i f f e r e n t values of to l i e a t s l i g h t l y d i f f e r e n t e n e r g i e s . The v i b r a t i o n a l l e v e l s are c l a s s i f i e d as E, II, A, ... according to whether |£| = 0, 1, 2, ... . In f a c t , any angular momentum s t a t e s are c l a s s i - f i a b l e i n t h i s manner. The lowest v i b r a t i o n a l l e v e l s of the ground s t a t e of CS 2 are given i n Table I I I and i l l u s t r a t e d i n F i g . 2. The symmetric and a n t i - symmetric s t r e t c h i n g Normal v i b r a t i o n s are designated V j and v 3 > w i t h quantum numbers v 1 and v 3 , r e s p e c t i v e l y ; the doubly degenerate bending v i b r a t i o n i s l a b e l l e d by the values of v 2 and £. The species of the v i b r a - t i o n a l wavefunctions i n the p o i n t group are a l s o given i n F i g . 2. The £ n o t a t i o n ( v j V 2 v 3 ) s p e c i f i e s the v i b r a t i o n a l l e v e l of a l i n e a r symmetric t r i a t o m i c molecule. The energy l e v e l s of the 'fundamentals' ( v ^ = 1) and the 'overtones' ( v ^ = 2 , 3, ... ) are shown, but the 'combination l e v e l s ' are not g i v e n . - 18 E / C M " v, 1 6 0 0 4 A g u 1 2 0 0 i n 3 - U u 8 0 0 4 0 0 1 + 0 0 E 2 A 8 1 n. u -Q__+ g FIG. (2) Fundamental and L o w e s t - l y i n g Overtone L e v e l s of the X 1 ^ 8 Ground St a t e of  1 2 C 3 2 S 2 Referred to the v i = v 2 = v 3 = 0 L e v e l (15,31). - 19 - TABLE I I I Fundamental and Low e s t - l y i n g Overtone L e v e l s (cm - 1 ) of the X X E Ground State of }2C32S2 Referred to the v : = v 2 = v 3 = 0 L e v e l (15,31) ( V 1 V 2 V 3 ) L e v e l (1 0° 0) 657.98 (0 0° 1) 1532.35 (0 l 1  0) 395.9 (0 2 2  0) 791.9 (0 2° 0) 802.6 (0 3 3  0) 1187.8 (0 3 1  0) 1207.2 C. R o t a t i o n a l Energy L e v e l P a t t e r n s The general e x p r e s s i o n f o r the r o t a t i o n - v i b r a t i o n Hamiltonian of a polyatomic molecule i n the r i g i d rotator-harmonic o s c i l l a t o r approximation (32) i s . (J - P ) 2 . . . I V X 1 U 2 _. I V i n2 a = x,y,z a k k The l a s t two terms represent the Normal v i b r a t i o n s of the molecule and have been d i s c u s s e d . The f i r s t term r e f e r s to the k i n e t i c energy f o r - 20 - nucl e a r r o t a t i o n about the three p r i n c i p a l i n e r t i a l axes,as w e l l as the i n t e r a c t i o n of r o t a t i o n a l and i n t e r n a l angular momenta. We now consider the n u c l e a r r o t a t i o n a l k i n e t i c energy. The nucl e a r r o t a t i o n a l angular momentum R i s not quantized: the conserved q u a n t i t i e s are J , the t o t a l angular momentum, and P, the i n t e r n a l angular momentum,which c o n s i s t s of the v i b r a t i o n a l , e l e c t r o n s p i n and e l e c t r o n o r b i t a l angular momenta, i . e . P = G + S + L . (2) The n u c l e a r r o t a t i o n a l angular momentum i s thus obtained by v e c t o r s u b t r a c t i o n . R = J - P (3) There i s at once a d i f f e r e n c e between a l i n e a r molecule and a n o n - l i n e a r molecule. Since the mass of the l i n e a r molecule i s con- c e n t r a t e d along the a x i s , 1^ i s undefined, and 1^ = I . For a non- l i n e a r t r i a t o m i c molecule the three moments of i n e r t i a are a l l d i f f e r e n t and non-zero, and the p l a n a r i t y c o n d i t i o n , I = 1 + I , a p p l i e s . x y z We assume that the molecule i s i n an e l e c t r o n i c s i n g l e t o r b i t a l l y non-degenerate s t a t e , so that S and L may be omitted: the only remaining i n t e r n a l angular momentum a r i s e s from v i b r a t i o n . I t can be shown (33,34) that the v i b r a t i o n a l angular momentum only makes important c o n t r i b u t i o n s to the r o t a t i o n a l energy l e v e l s f o r a l i n e a r molecule, so that the two types of molecular geometries may be c o n s i d - ered s e p a r a t e l y . i ) L i n e a r molecules Expanding the squares, the K.E. operator f o r a l i n e a r molecule i s , ( J 2  + J 2 ) J G + J G , (G 2  + G 2 ) T = I X. + ̂ L * v_JL l _ _ x y_ . . 2 1 1 2 1 The l a s t term (34) has the form of c o r r e c t i o n s to the anharmonicity terms, and we n e g l e c t i t . The f i r s t term may be r e - w r i t t e n T = t l <?2-JS> P ) whose eigenvalues are E = | j [ J ( J + 1) - A 2 ] j o u l e s (6) where the component of J along the a x i s of the molecule i s the z-cbmponent of the v i b r a t i o n a l angular momentum, £(ft). I t i s customary to use wave number u n i t s (cm - 1 ) i n s t e a d of tr u e energy u n i t s ( j o u l e s ) , so t h a t we d i v i d e both s i d e s by he: E/hc = — [ J ( J + 1) - £ 2 ] cm- 1  (7) 8TT c l A g a i n , i t i s customary to abbreviate h / 8 i r 2 c l by the symbol 'B' ( c a l l e d the r o t a t i o n a l c o n s t a n t ) , g i v i n g E/hc = B [ J ( J + 1) - £ 2 ] cm - 1  (8) The e f f e c t s of the second term i n (4) are beyond the scope of t h i s t h e s i s , but g i v e r i s e to the e f f e c t c a l l e d £.-type doubling (33) i n degenerate v i b r a t i o n a l s t a t e s where \z\ > 0: the l e v e l s of a given J are s p l i t by an amount p r o p o r t i o n a l to B[^- J ( J + 1 ) ] ^ and s i n c e i n general B << u>, the s p l i t t i n g i s l a r g e s t f o r = 1 and decreases r a p i d l y f o r l a r g e r I v a l u e s . The magnitude of the s p l i t t i n g , expressed by the energy l e v e l term q [ J ( J + 1 ) ] ^ may reach a few cm - 1 u n i t s at the h i g h e s t observable J v a l u e s . In CS 2 the £-type doubling p r o p o r t i o n a l i t y c o n s t a n t , q, i s o n l y 5.27 x 10~ 5  cm - 1  ( 3 5 ) . i i ) N on-linear molecules Energy l e v e l expressions f o r n o n - l i n e a r t r i a t o m i c molecules cannot be obtained i n c l o s e d form except f o r the lowest J values because the molecules belong to the c l a s s known as Asymmetric t o p s , where a l l three moments of i n e r t i a are d i f f e r e n t . However approximate forms are r e a d i l y obtained by o m i t t i n g the o f f - d i a g o n a l m a t r i x elements of the h a m i l t o n i a n that a r i s e when Symmetric top b a s i s f u n c t i o n s are used (the Near-Symmetric top a p p r o x i m a t i o n ) . The i n t e r n a l angular momentum components can be neglected s i n c e t h e i r e f f e c t i s merely to modify the r o t a t i o n a l constants of the molecule i n a p a r t i c u l a r v i b r a t i o n a l l e v e l ( 3 3 ) . The h a m i l t o n i a n f o r n u c l e a r r o t a t i o n i s then . J 2 3 2  5 2 21 21 21  v x y z With the d e f i n i t i o n of the ' l a d d e r ' operators - 23 - t h i s becomes « " I <2T  +  2 1 - +  t I T " \ <2T + 2T> ̂  + x y z x y + 4 ( 2 I ~ - 2I-> ( J i + J 2 ) ( 1 0 ) Converting to cm - 1  u n i t s , and i n t r o d u c i n g the three r o t a t i o n a l constants . h _ h „ h - l A = B = C = cm  1 8 i r 2 c l 8 u 2 c l 8TT2CI z y x such t h a t A > B > C, we have (ti 2 / h c ) H = \ (B + C) J 2  + [A - | ( B + C ) ] J 2  + 1 (C - B) ( J 2 + J*) (11) Using symmetric top b a s i s f u n c t i o n s , |JK>, w r i t t e n i n m o l e c u l e - f i x e d c o o r d i n a t e s , the m a t r i x elements of these operators are (36,37) <JK|J 2 |JK> = J ( J + l ) f t 2 <JK|Jz|JK> = Kfi (12) <J,K + 1|J+|JK> - *\J(J + 1) - K(K + 1) h The f i r s t two terms i n the h a m i l t o n i a n are d i a g o n a l , and provided •̂ •(C - B) i s s m a l l enough to a l l o w the o f f - d i a g o n a l elements to be neg- l e c t e d , g i v e the energy l e v e l s a s E/hc = [A - -|(B + C)]K 2  + | ( B + C) J (J + 1) cm"1 (13) - 24 - The l a s t term i n the h a m i l t o n i a n , which i s o f f - d i a g o n a l i n K, give s r i s e to what i s c a l l e d the 'asymmetry d o u b l i n g ' of l e v e l s w i t h K t 0. The asymmetry doubling has the same form as the £-type d o u b l i n g , being p r o p o r t i o n a l to [ J ( J + 1 ) ] : however, the p r o p o r t i o n a l i t y constant i s very much l a r g e r , so that the asymmetry doubling of an asymmetric top molecule i s an order of magnitude gre a t e r than the A-type doubling of a l i n e a r molecule. D. R o t a t i o n a l Constants symmetrical t r i a t o m i c molecule are c a l c u l a t e d i n terms of the bond l e n g t h and the i n t e r i o r a n g l e . The three r o t a t i o n a l constants w i l l be evaluated f o r  1 2 C 3 2 S 2 . * s s n o w n i n a  n o n - l i n e a r geometry i n F i g . 3, where the C-S bond l e n g t h i s I and the S-C-S bond angle i s 2<}>. The o r i e n t a t i o n of the three p r i n c i p a l axes of i n e r t i a i s d e f i n e d by the C, symmetry and t h e i r o r i g i n by the center of mass c o n d i t i o n . The three d i f f e r e n t moments of i n e r t i a of a n o n - l i n e a r z(b) C y(a) S T I cos <|>-r I s i n <t> FIG. (3) - 25 - The moments of i n e r t i a are I = 2m.g & 2 sin2cj> 2m m„ I a = -^-l I2 cosH a 2m s + mc. 2m„ I = 2 m c £ 2 [1 - •= c o s 2 * ] c S 2irig + m c where m = 12 amu and m c = 31.97207 amu. Wi th the C-S bond l e n g t h ° - 1 expressed i n A u n i t s , the r o t a t i o n a l cons tants i n cm u n i t s are 1.6684 A = .2 2 , Z cos <f> „ . 0.26363 £2 sin2(j) c = 0.26363 I2 [1 - 0.84199 cos2tj)J To c a l c u l a t e the s t r u c t u r e of C S 2 (& and 2<J)) r e q u i r e s knowledge of o n l y two of the three r o t a t i o n a l c o n s t a n t s because I = 1 + I . x y z E . N u c l e a r S p i n S t a t i s t i c s The t o t a l e i g e n f u n c t i o n of a molecule may be w r i t t e n as a product of the e l e c t r o n i c , v i b r a t i o n a l , r o t a t i o n a l and n u c l e a r s p i n e i g e n f u n c t i o n s . t o t a l e v r s - 26 - The t o t a l e i g e n f u n c t i o n can only be symmetric or a n t i - symmetric under the operations of the p o i n t group corresponding to exchanging p a i r s of i d e n t i c a l n u c l e i . I f the sum of the i n d i v i d u a l n u c l e a r angular momenta of the i d e n t i c a l n u c l e i , c a l l e d I ( f i ) , i s i n t e g r a l , the t o t a l e i g e n f u n c t i o n has to be symmetric w i t h respect to exchange of i d e n t i c a l n u c l e i ( B o s e - E i n s t e i n s t a t i s t i c s ) ; and, i f I i s h a l f - i n t e g r a l , the t o t a l e i g e n f u n c t i o n has to be antisymmetric w i t h respect to exchange of i d e n t i c a l n u c l e i (Fermi-Dirac s t a t i s t i c s ) . In 1 2 C 3 2 S 2 , the two i d e n t i c a l s u l f u r n u c l e i each have zero n u c l e a r s p i n so that B o s e - E i n s t e i n s t a t i s t i c s a p p l y . For a l i n e a r molecule (29) one need co n s i d e r o n l y the symmetry p r o p e r t i e s of the e i g e n f u n c t i o n s under i n v e r s i o n of a l l the p a r t i c l e s i n the centre of mass, and r e f l e c t i o n i n any plane passing through the a x i s . Depending on whether the f u n c t i o n does or does not change s i g n under these o p e r a t i o n s i t i s c l a s s i f i e d as u or g (ungerade or gerade), and - or +, r e s p e c t i v e l y . I f the molecule has a centre of symmetry i t s Hamiltonian i s a l s o i n v a r i a n t w i t h respect to an interchange of the c o o r d i n a t e s of the n u c l e i , and a s t a t e i s c l a s s i f i e d as 'symmetric' or 'antisymmetric w i t h respect t o the n u c l e i ' depending on the behaviour of i t s e i g e n f u n c t i o n w i t h respect to t h i s o p e r a t i o n . An interchange of the c o o r d i n a t e s of the n u c l e i i s e q u i v a l e n t to a change i n the s i g n of the c o o r d i n a t e s of a l l the p a r t i c l e s ( e l e c t r o n s and n u c l e i ) f o l l o w e d by a change i n s i g n of the coordinates of the e l e c t r o n s o n l y , i . e . an i n v e r s i o n f ollowed by the r e f l e c t i o n d escribed above. Hence i t f o l l o w s t h a t , i f the s t a t e i s gerade and p o s i t i v e or ungerade and n e g a t i v e , i t i s symmetric w i t h respect to the n u c l e i . - 27 - Since B o s e - E i n s t e i n s t a t i s t i c s apply f o r the ground v i b r a t i o n a l s t a t e of CS 2 (where \\>e, and ^ g are symmetric), the r o t a t i o n a l eigen- f u n c t i o n must a l s o be symmetric. Now a r o t a t i o n a l e i g e n f u n c t i o n |j£> i s r e l a t e d to the Ass o c i a t e d Legendre polynomial c h a r a c t e r i s e d by the t o t a l and component angular momenta J and I r e s p e c t i v e l y , and i t s behaviour under the i n v e r s i o n o p e r a t i o n i s i|J£> = ( - 1 ) J | J , -£> (2) The r e f o r e , s i n c e % = 0, only even J f u n c t i o n s are symmetric, and are permitted as r o t a t i o n a l e i g e n f u n c t i o n s . A more d e t a i l e d c o n s i d e r a t i o n ( i n c l u d i n g the e f f e c t of the r e f l e c t i o n operation) shows that when > 0, o n l y one member of the £-type doublet f o r each J value i s symmetric and i s p e r m i t t e d . The other r o t a t i o n a l l e v e l s are absent. These p a t t e r n s are i l l u s t r a t e d i n F i g . 4. The nuclear s p i n s t a t i s t i c s of the n o n - l i n e a r CS 2 molecule produce s i m i l a r r o t a t i o n a l p a t t e r n s . The d e r i v a t i o n of the symmetry p r o p e r t i e s (28,29,38) i s more d i f f i c u l t , f o r i t turns out that one must c l a s s i f y the r o t a t i o n a l e i g e n f u n c t i o n s under the operations of the r o t a t i o n a l sub-group C 2: according to the P a u l i P r i n c i p l e only those species c o r r e l a t i n g w i t h the t o t a l l y symmetric r e p r e s e n t a t i o n of C 2 ( i . e . Ax and A 2 of C 2 v^ are p e r m i s s i b l e as r o t a t i o n a l s p e c i e s . Thus, as shown i n F i g . 4, a l t e r n a t e J l e v e l s are absent i n the K = 0 r o t a t i o n a l s t a c k s , and one asymmetry doubling component f o r each J value of the K > 0 stacks i s absent. - 28 - J 3 2 u ( A 2 ) Ai(Bi) + _ . - 3 • + + ? U(B 2) Bl(Ai) Ai(Bx)  + - 1 0 •- + + + 2 u ( A 2 > Al(Bi) + _ . " Bl(Ai) u (K=0 of B 2) /IN -+ 2-CBi) K=l of B 2 ( A 2 ) /IN E u ( B 2 ) + E-(A 2) 1 0 •++ ^ c A l ) " + Z 8 C B 1 > E ~ ( A 2 ) £ J ( B 2 ) +— E ; ( B 2 ) E > 2 ) n u (K=0 of A x) (K=l of Ax) FIG. (4) Asymmetric top species (+-) and r o v i b r o n i c ( o v e r - a l l ) species of the lowest r o t a t i o n a l l e v e l s of a l i n e a r molecule E,, and i n E g' u  _ u u I I U v i b r o n i c s t a t e s w i t h the corresponding species of a bent molecule i n b r a c k e t s . A l l r o t a t i o n a l l e v e l s of B species (dotted l i n e s ) are absent i n  1 2 C 3 2 S 2 and f o r K=l of A 2 dotted and s o l i d l i n e s are exchanged. P a r a l l e l and p e r p e n d i c - u l a r l y p o l a r i z e d t r a n s i t i o n s between r o t a t i o n a l stacks are shown by s o l i d and dotted arrows, r e s p e c t i v e l y . For a l l t r a n s - i t i o n s the r o v i b r o n i c s e l e c t i o n r u l e i s E + ( A i )-<-»-E~(A2). 8 - 29 - F. S e l e c t i o n Rules The i n t e n s i t y of an a b s o r p t i o n or emission t r a n s i t i o n f o r a gaseous molecule i s p r o p o r t i o n a l to the square of the t r a n s i t i o n moment i n t e g r a l R , ,, = <eVr' |u_|e"v"r"> (1) evr , e v r "  1 1.F 1 v  ' where: the symbols 'evr' r e f e r to the e l e c t r o n i c , v i b r a t i o n a l , and r o t a t i o n a l e i g e n f u n c t i o n s of the molecule; the prime and double prime s u p e r s c r i p t s r e f e r to the upper and lower s t a t e s ; and, u i s the t r a n - s i t i o n moment operator r e f e r r e d to space f i x e d coordinates (F) which, f o r an e l e c t r o n i c t r a n s i t i o n , i s the e l e c t r i c d i p o l e moment operator of the molecule. The e l e c t r i c d i p o l e moment operator i s a f u n c t i o n o f i n t e r - n u c l e a r d i s t a n c e s , and i s t h e r e f o r e u s u a l l y expanded as a Tay l o r s e r i e s i n the Normal coordinates of the molecule. The t r a n s i t i o n moment i n t e g r a l then becomes R , „ = <e'v , r*|y n + \ ( % \ Q, |e"v"r"> , (2) ev r ' , e v r " '_0 k \ ̂ k/ where the *F* s u b s c r i p t and the higher terms are o m i t t e d . By n e g l e c t i n g the s m a l l i n f l u e n c e of the nu c l e a r k i n e t i c energy upon the e l e c t r o n i c e i g e n f u n c t i o n (Born-Oppenheimer approxima- t i o n ) , and the (small) i n t e r a c t i o n of r o t a t i o n w i t h other i n t e r n a l motions, we have |evr> = |e>|v>|r> (3) - 30 - Thus, equation (2) becomes (4) The second term i s the t r a n s i t i o n moment of a v i b r a t i o n a l - r o t a t i o n a l ( i n f r a r e d ) t r a n s i t i o n and w i l l not be discussed f u r t h e r . The f i r s t term, however, i s the t r a n s i t i o n moment of an e l e c t r o n i c or pure r o t a - t i o n a l (microwave) t r a n s i t i o n . In a pure r o t a t i o n a l t r a n s i t i o n , e' = e", so t h a t the inner i n t e g r a l i s simply the permanent d i p o l e moment of the molecule. In an e l e c t r o n i c t r a n s i t i o n , t h i s i n t e g r a l i s the e l e c t r o n i c t r a n s i t i o n moment oper a t o r ; the other i n t e g r a l i n the f i r s t term, <v'|v">, i s the Franck-Condon v i b r a t i o n a l overlap i n t e g r a l . The components of the e l e c t r o n i c t r a n s i t i o n moment expressed i n a m o l e c u l e - f i x e d coordinate system (g) are r e l a t e d to the components r e f e r r e d to spac e - f i x e d coordinates (F) by the d i r e c t i o n c o s i n e s , X_ ^ F = I C5) g=x,y.z Using symmetric top ei g e n f u n c t i o n s r e f e r r e d to the m o l e c u l e - f i x e d c o o r d i n a t e s , we have evr'evr .II = <v'|v"> I <J'K'|AFg y e, e, ( > |j"K"> = <v'|v"> £ u g <J'K' "K"> (6) - 31 - The determination of r o t a t i o n a l l i n e s trengths and s e l e c t i o n r u l e s i s done by c a l c u l a t i n g the ' d i r e c t i o n cosine m a t r i x element', the i n t e g r a l w i t h i n the sum. The r e l a t i v e i n t e n s i t i e s of r o t a t i o n a l l i n e s i n a v i b r a t i o n a l band of an e l e c t r o n i c t r a n s i t i o n . a r e given by the square of the l i n e s t r e n g t h (equation (6) w i t h the v i b r a t i o n a l o v e r l a p i n t e g r a l omitted) summed over the spac e - f i x e d components, J and m u l t i p l i e d by the B o l t z - maim p o p u l a t i o n f a c t o r o f the lower r o t a t i o n a l s t a t e . The s e l e c t i o n r u l e s on J and K are determined from the non-vanishing d i r e c t i o n c o s i n e m a t r i x elements (40) as summarized below f o r a l i n e a r molecule. Non-zero component of e l e c t r o n i c t r a n s i t i o n moment S e l e c t i o n Rules ^e'e" z P a r a l i e i p o l a r i z a t i o n AK=K'-K"=0 AJ=±1 I f K=0 AJ=0,±1 i f K+0 Ve",x or p e r p e n d i c u l a r p o l a r i z a t i o n Ve",y AK=±1 AJ=0,±1 The a x i s l a b e l l i n g must be changed f o r the n o n - l i n e a r molecule but the s e l e c t i o n r u l e s are u n a f f e c t e d . - 32 - The p r o j e c t i o n of J on the a x i s of a - l i n e a r molecule i s P; the p r o j e c t i o n of J on the p r i n c i p a l a x i s of l e a s t i n e r t i a (a a x i s ) of a non- l i n e a r molecule i s K. A change i n geometry of the molecule does not a f f e c t the s e l e c t i o n r u l e s although the o r i g i n of the angular momenta i s d i f f e r e n t i n the bent and l i n e a r molecules. With p a r a l l e l - p o l a r i - z a t i o n , a K* = 0 - K" = 0 band (E - E) has a P branch (AJ = -1) and an R branch (AJ = +1) w i t h l i n e s trengths that i n c r e a s e w i t h J ; other p a r a l l e l bands, K =f= 0 (II-II, A-A, e t c . ) have Q branches (AJ = 0) that are weak i n comparison to the R and P branches and whose l i n e s t r e n g t h s decrease w i t h J . With p e r p e n d i c u l a r p o l a r i z a t i o n (E-II, n-E, e t c . ) , the P,Q, and R branches are of comparable i n t e n s i t y , w i t h l i n e strengths i n c r e a s i n g w i t h J . The e l e c t r o n i c t r a n s i t i o n v i b r a t i o n a l s e l e c t i o n r u l e s f o r a l i n e a r molecule are a l r e a d y p a r t i a l l y i n c l u d e d i n the r o t a t i o n a l s e l e c t i o n r u l e s s i n c e P i s e q u i v a l e n t to the v i b r a t i o n a l angular momen- tum I of a l i n e a r molecule. The only other v i b r a t i o n a l s e l e c t i o n r u l e a r i s e s from the requirement that the Franck-Condon overlap i n t e g r a l , <v'|v">, be t o t a l l y symmetric. Thus, any antisymmetric v i b r a t i o n , such as v 2 (̂ JJ) ANC* V3 (0^) of a l i n e a r t r i a t o m i c molecule must f o l l o w the s e l e c t i o n r u l e Av = 0, ±2, ±4, e t c . s i n c e e i g e n f u n c t i o n s belonging to k even v i b r a t i o n a l quantum numbers c o n t a i n a t o t a l l y symmetric component. In a n o n - l i n e a r molecule, the doubly degenerate v i b r a t i o n v 2 becomes a t o t a l l y symmetric v i b r a t i o n and one of the r o t a t i o n s so that t h i s r e s t r i c t i o n no longer a p p l i e s and a l l values of Av are a l l o w e d . - 33 - One f u r t h e r p o i n t to note i s that the Franck-Condon overlap i n t e g r a l , which determines the extent and i n t e n s i t y d i s t r i b u t i o n of a v i b r a t i o n a l p r o g r e s s i o n , depends s t r o n g l y on the change i n geometry of the molecule upon e l e c t r o n i c e x c i t a t i o n . The v i b r a t i o n predominantly e x c i t e d i s that one which most n e a r l y d e s c r i b e s the shape change upon e x c i t a t i o n . I f the shape change i s l a r g e enough, the maximum i n t e n s i t y i n the v i b r a t i o n a l p r o g r e s s i o n may l i e w e l l away from the e l e c t r o n i c o r i g i n band. - 34 - IV. ANALYSIS OF THE V AND T SYSTEMS The low r e s o l u t i o n pressure broadened spectrum of CS 2 i n o o the r e g i o n 2900A to 3400A i s shown as F i g . 5 . At l e a s t three e l e c t r o n i c t r a n s i t i o n s are r e s p o n s i b l e f o r a b s o r p t i o n i n t h i s r e g i o n . The h i g h e r o v i b r a t i o n a l members of the R and S systems l i e i n the r e g i o n 3400-3300A but are very weak ( e m a x % 2 l i t e r s / m o l e cm ( 4 1 ) ) . The s t r o n g e s t a b s o r p t i o n of C S o i n the near u l t r a v i o l e t i s due to the V system (e % 40 l i t e r s / z J  max mole cm ( 4 1 ) ) . However, i t i s s t i l l a weak system compared to the 1 B 2 *• system at 2100A, i n d i c a t i n g that i t i s a ' f o r b i d d e n ' t r a n s i - t i o n . U n l i k e the R and S systems, which e x h i b i t r e g u l a r v i b r a t i o n a l p a t t e r n s and simple r o t a t i o n a l s t r u c t u r e , the V system does not have any r e a d i l y apparent v i b r a t i o n a l progressions,nor i s the r o t a t i o n a l s t r u c t u r e s i m p l e . Under h i g h r e s o l u t i o n , the r o t a t i o n a l s t r u c t u r e of the v i b r a t i o n a l bands of the V system i s dense and i r r e g u l a r w i t h no obvious simple b r a n c h - l i k e s t r u c t u r e . Without temperature s t u d i e s , i t i s not even p o s s i b l e to e s t a b l i s h the ground s t a t e v i b r a t i o n a l numbering of the V bands. A. Temperature Studies and P o l a r i z a t i o n of the V System P a r t of the complexity of the V system i s because bands a r i s i n g from v a r i o u s v i b r a t i o n a l l e v e l s of the ground s t a t e are p r e s e n t , o f t e n w i t h very c o n s i d e r a b l e i n t e n s i t y . To i d e n t i f y these 'hot' bands the spectrum of CS 2 between 2900 and 3500A was photographed a t - 7 8 ° , 2 3° , 100° and 200°C: the bands found to be 'hot' are marked w i t h shading on the Cary spectrophotometer t r a c i n g ( F i g . 5 ) . E / c i r r i 3 4 0 0 0 ' 32COO 3 0 0 0 0 I : I I I I | 1 1 « 1 : 1 1 1 1 ' ! 2 9 0 0 3 0 0 0 3200 3 4 0 0 o Wavelength /A FIG. (5) Room temperature pressure-broadened gas phase absorption spectrum of  1 2 C 3 2 S 2 i n the region 2900A to 3A00A recorded by a Cary 14 spectrophotometer. The shaded areas under the absorption curve i n d i c a t e absorption from e x c i t e d v i b r a t i o n a l l e v e l s of the X 1 E +  ground s t a t e of CS 2. - 36 - A 'hot' band may be recognised by the f a c t that i t s i n t e n s i t y i n c r e a s e s on r a i s i n g the temperature of the gas. The i n t e n s i t y of an allowed v i b r a t i o n a l band i n ab s o r p t i o n i s p r o p o r t i o n a l to the square of the Franck-Condon overlap i n t e g r a l times the number of molecules i n the lower v i b r a t i o n a l l e v e l , which i s given by the Boltzmann d i s t r i b u t i o n N - exp (-Evhc/RT) (1) In equation ( 1 ) , N^, the number of molecules i n l e v e l v , a t energy E^ r e l a t i v e to the zero-point l e v e l , and a t temperature T} i s given as a f r a c t i o n of the number, N Q , i n the zero-point l e v e l . Obviously as the temperature T i s increased i n c r e a s e s r e l a t i v e to N Q , and NQ a c t u a l l y decreases because of the number of molecules promoted to the e x c i t e d v i b r a t i o n a l l e v e l s . 'Hot' bands are t h e r e f o r e r e a d i l y i d e n t i f i e d by comparing s p e c t r a taken a t d i f f e r e n t temperatures, and a rough estimate of the energy of the lower l e v e l may be obtained by comparing sp e c t r a " taken at s e v e r a l d i f f e r e n t temperatures. As soon as the l a r g e number of 'hot' bands i n the V system had been r e c o g n i s e d , a systematic search was made f o r ground s t a t e v i b r a t i o n a l combination d i f f e r e n c e s between bands w i t h common upper s t a t e s but d i f f e r e n t lower s t a t e s . Only the i n t e r v a l s 0 2° 0 - 0 0° 0 and 0 3 * 0 - 0 l 1 0 ( r e s p e c t i v e l y 802 and 811 cm ') could be i d e n t i f i e d , and no i n t e r - v a l s corresponding to 1 0° 0 - 0 0° 0 (the ground s t a t e s t r e t c h i n g v i b r a - t i o n , 658 cm - 1 ) were found d e s p i t e c o n s i d e r a b l e e f f o r t . As i s shown l a t e r , the shape change i n the V system i s almost p u r e l y a change i n the bond angle on e x c i t a t i o n , which i s c o n s i s t e n t w i t h the observed ground s t a t e i n t e r v a l s . - 37 - The observed ground s t a t e i n t e r v a l s only occur at the long wavelength end of the spectrum, where the 'hot' bands are very i n t e n s e . However given the i d e n t i f i c a t i o n of the lower s t a t e s of these bands, together w i t h the known lower s t a t e assignments of the R system, i t i s p o s s i b l e to compare the degree of temperature s e n s i t i v i t y of a l l the bands of the V system a g a i n s t the known bands, and hence roughly e s t a b l i s h the energy of t h e i r lower s t a t e s r e l a t i v e to the z e r o - p o i n t l e v e l . I t i s a l s o p o s s i b l e to make a lower s t a t e v i b r a t i o n a l quantum number assignment, because, assuming that only the bending v i b r a t i o n i s i n v o l v e d , the d i f f e r - ences i n t e m p e r a t u r e - s e n s i t i v i t y are s u f f i c i e n t l y l a r g e to d i s t i n g u i s h bands w i t h v'2' = 0, 1 and 2. I t i s probable that 'sequence bands' i n the symmetric s t r e t c h i n g v i b r a t i o n , of the type lvO - l v O , may occur on the higher temperature p l a t e s , but they do not have such favourable Franck- Condon f a c t o r s as the 'hot' bands i n the bending v i b r a t i o n , and none of them have been r e c o g n i s e d . The observed combination d i f f e r e n c e s a l s o determine t h a t the t r a n s i t i o n i s p a r a l l e l - p o l a r i z e d . The ground s t a t e i n t e r v a l 0 2° 0 - 0 0° 0 occurs between two very strong bands, the ' c o l d ' band a t 3236A (10V i n our n o t a t i o n ) and the 'hot' band at 3322A ( I V ) . I f the t r a n s i - t i o n was p e r p e n d i c u l a r l y - p o l a r i z e d (K' - = ± 1 ) , the presence of the ' c o l d ' band would show that tKe upper s t a t e had K' = 1; then the 'hot' - 38 - band would be s p l i t by the c h a r a c t e r i s t i c 10 cm  1  s e p a r a t i o n between the 0 2° 0 and 0 2 2  0 components of the = 2 l e v e l . However no such s p l i t t i n g (which would be r e a d i l y observable) appears, so that the t r a n s i t i o n i s p a r a l l e l - p o l a r i z e d . T his deduction i s confirmed by the absence of the corresponding s p l i t t i n g s i n other i n s t a n c e s where they would be expected on the b a s i s of pe r p e n d i c u l a r p o l a r i z a t i o n , and a l s o (see below) by the r e s u l t s of the r o t a t i o n a l a n a l y s i s . B. R o t a t i o n a l A n a l y s i s The complexity of the V bands makes r o t a t i o n a l a n a l y s i s of most of the bands q u i t e i m p o s s i b l e . However two obvious p a i r s of bands w i t h common upper s t a t e s (as i n d i c a t e d by the lower s t a t e v i b r a t i o n a l combination d i f f e r e n c e s d e s c r i b e d above) were s u f f i c i e n t l y unperturbed to i n v i t e an attempt at a n a l y s i s . These are the K' = 0 p a i r a t 3236& and 3322A, and the K* = 1 p a i r a t 3275A and 3365A. The 3365A band has not p r e v i o u s l y been recognised as belonging to the V system. R o t a t i o n a l analyses of these bands were p o s s i b l e f o r three reasons. F i r s t , the extremely h i g h r e s o l u t i o n a t t a i n e d on our p l a t e s (the measured f u l l w i d t h a t h a l f maximum of an unblended l i n e being <0.05 cm  1 ) reduced the b l e n d i n g of l i n e s to a minimum. The second f a c t o r which helped g r e a t l y was the c o o l i n g of the gas to -78°C: t h i s - 39 - has the e f f e c t of reducing the Doppler w i d t h of the l i n e s and removing the a b s o r p t i o n l i n e s a r i s i n g from higher r o t a t i o n a l l e v e l s of the lower s t a t e s . F i n a l l y , a recent high r e s o l u t i o n i n f r a r e d a n a l y s i s (35) of the bending v i b r a t i o n l e v e l s of the ground s t a t e has g i v e n accurate constants from which i t was p o s s i b l e to c a l c u l a t e the data (Appendix I ) f o r the a n a l y s i s of the e l e c t r o n i c s p e c t r a . In order to check the accuracy of the i n f r a r e d combination o d i f f e r e n c e s , an a n a l y s i s of a simple E - E band at 3326A (Kleman's 17U band) was undertaken. In t h i s band, which was measured from the same p l a t e as the 3322A band ( I V ) , the r o t a t i o n a l combination d i f f e r e n c e s of 18 branch l i n e s d e v i a t e d by no more than ± 0.006 cm - 1  from t h e i r c a l c u l a t e d v a l u e s . Hence, the i n f r a r e d constants g i v e c a l c u l a t e d com- b i n a t i o n d i f f e r e n c e s as l e a s t as accurate as the measured r e l a t i v e l i n e p o s i t i o n s (± 0.01 cm  1 ) . The w e l l known method of combination d i f f e r e n c e s (42) was used to analyse the bands. I f the p o s i t i o n of a r o t a t i o n a l l e v e l above the v i b r a t i o n a l o r i g i n of the l e v e l i s c a l l e d F ( J ) , the r o t a t i o n a l l e v e l e x p r e s s i o n f o r a v i b r a t i o n a l l e v e l of the ground s t a t e (see s e c t i o n I I I . C ( i ) ) becomes F ( J ) = T0 + B [ J ( J + 1) - I2} - D J 2 ( J+ D 2 + | ( - 1 ) V ( J+ D (1) - 40 - where Tg i s the e l e c t r o n i c term v a l u e , B and D are the r o t a t i o n a l and c e n t r i f u g a l d i s t o r t i o n constants r e s p e c t i v e l y , a n d q i s the £-type doubling c o n s t a n t . Therefore, the r o t a t i o n a l l i n e p o s i t i o n s i n a p a r a l l e l band are given by the expressions R(J) = F 1  ( J + 1) - F " ( J ) = v 0 + 2B 1  + (3B 1  - B " ) J + (B* - B " ) J 2  (2) P( J ) = F ' ( J - 1) - F " ( J ) = VQ - (B' + B")J + (B' - B " ) J 2  (3) where v Q i s the band o r i g i n , and the e f f e c t of the D and q terms has been n e g l e c t e d . However complicated the r o t a t i o n a l s t r u c t u r e s of the upper s t a t e may be, an a n a l y s i s i s i n p r i n c i p l e always p o s s i b l e i f the R and P branch l i n e s t e r m i n a t i n g on the same upper l e v e l can be i d e n t i f i e d . T h e i r s e p a r a t i o n , known as the second combination d i f f e r e n c e A 2 F " ( J ) , i s g i v e n by A 2 F " ( J ) = F " ( J + 1) - F " ( J - 1) = R(J - 1) - P ( J + 1) . (4) In view of the f a n t a s t i c complexity of the spectrum, we have only attempted to analyse p a i r s of bands w i t h a common upper l e v e l but d i f f e r e n t lower v i b r a t i o n a l l e v e l s , because a d d i t i o n a l combination d i f f e r e n c e s become a v a i l a b l e : these are the. s e p a r a t i o n of l e v e l s w i t h the same J i n the two lower l e v e l s , which can of course be a c c u r a t e l y c a l c u l a t e d from the high r e s o l u t i o n i n f r a r e d data (35). There i s a s m a l l d i f f e r e n c e of B w i t h v, r e s u l t i n g from anharmonicity and C o r i o l i s e f f e c t s , which i s s u f f i c i e n t to make, a d i f f e r e n c e of ^ 0.5 cm - 1 between the v i b r a t i o n a l separations of l e v e l s w i t h J " = 0 and J " = 40 i n the bands of i n t e r e s t . This turned out to be p a r t i c u l a r l y u s e f u l because the J dependence of the v i b r a t i o i t a l combination d i f f e r e n c e s allowed a J assignment ( f o r J > 20) to w i t h i n ± 2 quanta. The r o t a t i o n a l a n a l y s i s was c a r r i e d out by a t r i a l and e r r o r search f o r v i b r a t i o n a l and r o t a t i o n a l combination d i f f e r e n c e s . To o o help w i t h the a n a l y s i s of the 3275A and 3365A bands we wrote a computer programme that gave a l l the p o s s i b l e s e t s of four l i n e s (an R and a P l i n e from each band) which were i n agreement w i t h the ground s t a t e combination d i f f e r e n c e s . The four c a l c u l a t e d term values were re q u i r e d to agree w i t h i n 0.04 cm - 1. V - e r e were of course l a r g e numbers of p o s s i b l e s e t s of l i n e s picked out by the computer, but, by c a r e f u l l y checking every p o s s i b l e set to ensure that the r e l a t i v e i n t e n s i t i e s of the four l i n e s , were roughly the same, we managed to e l i m i n a t e so many p o s s i b l e sets t h a t , i n v i r t u a l l y a l l cases, only one assignment remained f o r each r o t a t i o n a l l i n e . The r o t a t i o n a l assignments are given as Tables IV and V; the computer programme i s given as Appendix I I . The r o t a t i o n a l analyses show the f o l l o w i n g . No Q branch i s found i n any of the four bands. Hence, the two bands of F i g . 6 are 2 - £ type, and those of F i g . 7 are II - II type. This r e s u l t confirms  2973420 cm-' 29712.45 cm-1 - 44 - TABLE IV Rotational 3322 A (IV) Line Assignments 12 32 Bands of C S 2 of the 3236 A _ l (cm ). (10V) and ooo,K ' = 0 - 00°0 (10V) ooo,K ' = 0 - 02°0 (IV) II J R(J) P(J+2) R(J) PCJ+2) 0 30 902.24 30 901.62 30 100.42* 30 099.77 2 901.23* 901.62 906.48 908.38 899.71 900.09 904.96 906.84 099.38 099.77 104.63 106.54* 097.83 098.24 103.08* 105.03 4 900.93 902.10 911.29 898.53 899.71 908.87* 099.07 100.27 109.40 096.66 097.83 107.01 6 900.78 903.02 903.51 904.19 904.39 906.53* 897.51 899.71 900.26 900.93 901.12 903.29* 098.93 101.14 101.63 102.37 102.56 104.66 095.63 097.83 098.36 099.07 099.25 101.40 8 903.84 904.96 907.26 908.12 899.71 900.78 903.14 903.96 102.01 103.03 105.41 106.26 097.83 098.93 101.28 102.10 10 898.12 905.01* 906.15 908.08 893.10 899.96* 901.12 903.02 096.24 103.10* 104.27* 106.19 091.21 098.09 099.25 101.14 12 908.60 908.88* 911.13 911.36* 902.71 902.97 905.22* 905.46 106.70 106.93 109.19 109.45* 100.79 101.04 103.30 103.57 14 900.26 • 9.05.72 905.97 909.30 893.49 898.95 899.20 902.57 098.36 103.77 104.02 107.37 091.57 097.00* 097.25 100.61 - 45 - TABLE IV (Continued) 16 30 905.24 30 897.58 30 103.30 30 095.63 905.88 ' 898.24 103.92 096.24 906.33 898.69 104.39 096.70* 909.30 901.67* 107.34 099.68 910.23 902.57 108.28 100.61 910.48 902.82 108.53* 100.87* 18 907.63 899.08 105.64* 097.10 907.76* 899.25 105.81 097.25 908.21 899.71 106.24* 097.68 909.52 900.93 107.50 098.93 20 907.26 897.88 105.25 095.86* 911.01 901.62 109.03 099.62 911.87 902.53* 109.87 100.45 22 908.93 898.69 106.93 096.60* 909.62 899.40 107.60 097.33 910.91 900.65 108.90 098.61 911.59 901.32 109.50 099.25 24 909.88 898.79 107.85 096.66 910.07 898.95 108.02* 096.88 913.07 901.93 111.00 099.85 26 910.70 898.69 108.58* 096.53 910.80 898.79 108.72 096.66* 911.76 899.81 109.64 097.60 913.91 901.93 111.80 099.77 915.00 903.02 112.93 100.89* 28 910.53* 897.58* 108.38* 095.46 914.26 901.40* 112.14 099.25 914.66 901.77 112.54 099.62 30 913.66 899.92 111.46* 097.68 916.11 902.37 113.94 100.10 32 912.73* 898.12 110.50 095.86* 914.94* 900.28* 112.68 098.01 34 914.23* 898.75* 111.92 096.40 36 916.31 899.95* 113.97* 097.59* 38 916.31 899.08 113.94 096.60* 917.04 899.80 114.66 097.35* * measured from high r e s o l u t i o n p r i n t - 4 6 - T A B L E V R o t a t i o n a l Line Assignments o f the 3 2 7 5 A ( 6 V ) and 0 12 32 -1 3 3 6 5 A Bands of C S 2(cm ) . 0 0 0 , K ' = 1 - 0 1 * 0 ( 6 V ) 0 0 0 , K ' = 1 - 0 3 * 0 ( 3 3 6 5 A band) R(J) P(J+2) R(J) P ( J + 2) 1 3 0 5 2 9 . 9 6 3 0 5 2 8 . 9 0 2 9 7 1 9 . 1 0 2 9 7 1 7 . 9 8 2 3 0 . 8 0 2 9 . 3 0 1 9 . 9 3 1 8 . 4 0 3 3 0 . 5 6 2 8 . 6 3 1 9 . 6 6 1 7 . 7 4 2 9 . 9 6 2 8 . 0 2 1 9 . 1 0 1 7 . 0 9 4 3 0 . 9 6 2 8 . 5 5 2 0 . 0 6 1 7 . 6 3 5 6 3 2 . 2 4 2 9 . 0 0 2 1 . 3 4 1 8 . 0 7 7 3 2 . 6 4 2 8 . 9 0 2 1 . 7 4 1 7 . 9 8 3 3 . 0 7 2 8 . 9 3 ' 2 2 . 1 6 1 7 . 9 8 3 3 . 6 9 2 9 . 5 0 2 2 . 7 5 1 8 . 5 8 3 3 . 5 8 2 9 . 0 0 2 2 . 6 7 1 8 . 0 7 3 3 . 7 9 2 9 . 1 9 2 2 . 8 7 1 8 . 2 6 1 0 3 4 . 1 2 2 9 . 0 9 2 3 . 1 7 1 8 . 1 2 3 4 . 4 9 2 9 . 4 3 2 3 . 5 6 1 8 . 4 8 1 1 3 4 . 4 9 2 9 . 0 0 2 3 . 5 6 1 8 . 0 7 3 4 . 8 9 2 9 . 4 3 2 3 . 9 7 1 8 . 4 8 3 5 . 5 5 3 0 . 0 9 2 4 . 6 0 1 9 . 1 0 1 2 3 3 . 8 5 2 7 . 9 6 2 2 . 8 7 1 6 . 9 7 3 4 . 8 1 2 8 . 9 3 2 3 . 8 8 1 7 . 9 8 3 5 . 4 1 2 9 . 5 0 2 4 . 4 8 1 8 . 5 8 1 3 3 5 . 7 9 2 9 . 4 3 2 4 . 8 5 1 8 . 4 8 1 4 3 5 . 7 2 2 8 . 9 3 2 4 . 7 6 1 7 . 9 8 3 6 . 4 3 2 9 . 6 7 2 5 . 4 7 1 8 . 6 7 3 6 . 9 9 3 0 . 2 2 2 6 . 0 0 1 9 . 2 1 1 5 3 5 . 5 5 2 8 . 3 5 2 4 . 6 0 1 7 . 3 6 3 5 . 9 5 2 8 . 7 2 2 5 . 0 0 1 7 . 7 4 - 47 - TABLE V (Continued) 16 17 30 536.81 38.16 35.23 36.75 38.90 39.48 30 529.14 30.47 27.16 28.63 30.80 31.40 29 725.82 27.14 24.24 25.76 27.88 28.46 29 718.12 19.49 16.12 17.63 19.77 20.35 18 34.55 34.66 36.54 37.11 34.66 36.00 38.16 37.44 34.00 35.26 35.41 36.43 37.78 38.22 38.50 39.36 36.43 39.89 41.73 42.19 42.67 37.69 38.16 38.50 39.89 39.29 39.48 41.78 42.70 42.33 42.94 41.55 26.02 26.13 28.02 28.55 25.71 27.07 29.19 28.02 24.17 25.43 25.54 26.58 27.51 27.96 28.23 29.09 25.71 28.72 30.56 31.04 31.52 26.11 26.58 26.91 28.27 27.27 27.43 29.74 30.68 29.84 30.47 28.63 23.51 23.65 25.51 26.09 23.65 25.00 27.14 26.40 22.99 24.24 24.36 25.39 26.70 27.14 27.39 28.27 25.39 28.78 30.64 31.08 31.56 26.56 27.09 27.39 28.78 28.16 28.34 30.64 31.56 31.18 31.80 30.38 14.97 15.11 16.97 17.51 14.64 16.02 18.19 16.97 13.13 14.34 14.51 15.52 16.42 16.85 17.09 17.98 14.64 17.60 19.43 19.93 20.35 14.97 15.48 15.79 17.14 16.12 16.29 18.58 19.49 18.67 19.31 17.43 - 48 - TABLE V (Continued) 29 30 541.14 30 527.82 29 529.98 29 516.62 30 40.59 26.79 29.35 15.52 43.49 29.74 32.27 18.48 31 41.85 27.64 30.64 16.42 44.28 30.09 33.08 18.82 32 40.75 26.11 29.48 14.80 45.48 30.80 34.20 19.49 33 43.44 28.40 32.22 17.09 44.91 29.84 33.66 18.58 - 49 - TABLE VI(a) Assigned R o t a t i o n a l Term Values of the (000),K 1  = 0 1 1 12 32 -1 * Level o f the B 2 ( A u) V St a t e o f C S 2 (cm ) . J * Term Values 1 30 902.27 3 901.88 30 902.28 30 907.13 30 909.04 5 903.11 904.29 913.46 7 905.37 907.58 908.09 908.79 9 911.72 912.80 915.14 916.98 11 910.13 917.00 918.16 920.07 13 925.62 925.88 928.13 928.38 15 923.18 928.62 928.87 932.22 17 934.91 935.55 936.00 938.97 19 944.92 945.07 945.52 946.79 21 953.08 956.84 957.70 23 964.14 964.83 966.12 966.77 25 975.36 975.54 978.52 27 987.27 988.33 988.39 990.50 29 999.10 31 002.86 31 003.24 31 31 015.11 017.56 33 027.93 030.11 35 044.03 37 061.61 39 077.97 078.70 30 908.99 30 911.12 939.89 940.15 991.60 *Term values are averages from 4 r o t a t i o n a l l i n e s w i t h a common upper l e v e l . - 50 - TABLE VI (b) Assigned R o t a t i o n a l Term Values o f the (000), K f  = 1 1 1 12 32 -1 J. L e v e l o f the B 2 ( A ) V State o f C S 2 (cm j . Term Values 1 30 926.18 2 927.46 3 927.87 4 929.12 5 930.64 6 932.83 7 934.73 8 936.93 30 937.52 9 939.41 939.60 10 942.12 942.48 11 944 .89 945.30 30 945.95 12 946.88 947.87 948.46 13 951.66 14 955.38 955.93 15 957.77 958.16 959.00 16 962.52 963.87 17 964.65 966.16 968.30 30 968.89 18 967.91 968.04 969.92 970.47 19 972.17 973.53 975.67 20 979.34 21 980.49 981.73 981.87 982.90 22 989.09 989.53 989.79 990.66 23 992.74 24 31 001.47 31 003.31 31 003.78 31 004.24 25 004.70 005.20 005.51 006.89 26 012.04 012.21 014.51 015.44 27 020.91 021.53 28 026.31 29 032.20 30 038.23 041.16 31 046.24 048.67 32 052.19 056.89 33 062.05 063.51 i* 9 ° Term values (averaged) from the 3275 A (6V) and 3365 A bands - 51 - beyond doubt the p a r a l l e l p o l a r i z a t i o n of the V system. The upper s t a t e term values are given as Table V I ; these term v a l u e s , s u i t a b l y s c a l e d by s u b t r a c t i o n of B" J ( J + 1), are shown p l o t t e d a g a i n s t 000 J ( J + 1) i n F i g . 8. The two E - E bands have only even J " branch l i n e s , as explained i n s e c t i o n I I I . E . The II - II bands, however, have a l l v alues of J " p r e s e n t . The ob s e r v a t i o n of s e v e r a l (up to 6) a s s i g n - ments f o r a s i n g l e branch l i n e i s evidence of the p e r t u r b a t i o n s of the upper s t a t e which plagued any previous attempts a t r o t a t i o n a l a n a l y s i s of the V bands. The s i z e of the p e r t u r b a t i o n s i s i l l u s t r a t e d i n F i g . 8 by the spread of p o i n t s f o r each J ' v a l u e which i s on the order of 5 cm - 1 . Despite these p e r t u r b a t i o n s there i s a d e f i n i t e p o s i t i v e slope of the l i n e s which represents the course of the 'mean' upper s t a t e energy l e v e l s , i n d i c a t i n g t h a t B' > B". The v i o l e t degradation of these bands supports such a r e s u l t . From the slopes and i n t e r c e p t s of the l i n e s are obtained the v i b r a t i o n a l band o r i g i n s and r o t a t i o n a l c o n s t a n t s : Bands To B' (E) 3236A, 3322A" 30902.8 + 0.5 cm - 1  0.1129 ± 0.0010 (n) 3275A, 3365A 30926.5 ± 0.5 0.1144 ± 0.0010 I n the II v i b r o n i c bands, one might expect to f i n d a 'stagger- i n g ' of even and odd J valu e branch l i n e s , caused by the A or £- doubling of a l i n e a r molecule, o r , the asymmetry e f f e c t s i n a n o n - l i n e a r molecule as i l l u s t r a t e d i n F i g . 4. The 'st a g g e r i n g ' w i l l appear as a s l i g h t 3 0 9 1 1 0 'E + 9 0 9 0 - 9 0 7 0 - 9 0 5 0 - "3 9 0 3 . 0 - J > 3 0 9 0 I . O l i J 3 0 8 9 9 . 0 - | 97.0-1 3 0 8 9 5 . 0 _ 3 0 9 3 8 . 0 3 0 0 6 0 0 9 0 0 1 2 0 0 2 0 0 4 0 0 6 0 0 8 0 0 [a] I 5 0 0 1 8 0 0 I O O O 1 2 0 0 FIG. (8) R o t a t i o n a l Term Values of the 000,K' = 0 Lev e l (a) and the 000,K' = 1 L e v e l (b) of the V State of  1 2 C 3 2S2 p l o t t e d against J(J+1). The slope of the l i n e - l e a s t squares f i t t e d to the average term values - i s reduced by s u b t r a c t i n g BQQOJP+I) where BQOO ° 0.1090917 cm - 1 . J[j + l] - 53 - d i f f e r e n c e i n the r o t a t i o n a l constant f o r even and odd J. When the upper s t a t e term values are p l o t t e d s e p a r a t e l y f o r even and odd J , however, the B' values were w i t h i n one standard d e v i a t i o n of each o t h e r . The r o t a t i o n a l p e r t u r b a t i o n s i n the upper s t a t e of the 3275A and 3365A bands make the obs e r v a t i o n of such a 's t a g g e r i n g ' i m p o s s i b l e . Thus, the r o t a t i o n a l a n a l y s i s i n d i c a t e s that C S 2 i n the V s t a t e i s e i t h e r l i n e a r or not s i g n i f i c a n t l y bent. As shown i n s e c t i o n s D and F, CS 2 i s s l i g h t l y bent (163°) i n the V s t a t e so that the c a l c u l a t e d asymmetry 's t a g g e r i n g ' i s much sm a l l e r than the standard d e v i a t i o n , ± 0.0010 cm  1 , i n the r o t a t i o n a l constant of the K' = 1 upper s t a t e . A few spurious r o t a t i o n a l assignments are i n e v i t a b l e i n such a complicated a n a l y s i s . N e v e r t h e l e s s , at l e a s t 90% of the assignments are beyond doubt, which i s c e r t a i n l y s u f f i c i e n t to draw c o n c l u s i o n s r e g a r d i n g the nature of the upper s t a t e s i n v o l v e d . C. V i b r a t i o n a l P a t t e r n of the V Sta t e With the ground s t a t e v i b r a t i o n a l assignments of the V bands e s t a b l i s h e d , the upper s t a t e term values were c a l c u l a t e d by adding the ground s t a t e v i b r a t i o n a l energy to the band head p o s i t i o n s : these are shown i n F i g . 9 and i n Table V I I . Having determined the p a r a l l e l p o l a r i z a t i o n , the V l e v e l s were grouped according to t h e i r v alues of the p r o j e c t i o n of the t o t a l angular momentum on the molecular a a x i s , which i s c a l l e d £ or K (depending on whether the molecule i s l i n e a r or b e n t ) . The V l e v e l s are l a b e l l e d as £, II, A, ... corresponding to K' or £.' = 0 , 1, 2, ... . - 54 - 34000i E / c m - i 33000 - 32000 - 31000- )5 12 r10 3, 8 } ° 3 13 11 )3c } o 3 n }3,o } Q. A FIG. (9) The V State v i b r a t i o n a l term values c l a s s i f i e d by the val u e of £" = 0,1,2 (E,II,A) of the corresponding V bands. Shaded regions i n d i c a t e bands w i t h no h e a d - l i k e o r i g i n ; term values of o v e r - lapped bands are shown as dotted l i n e s . - 55 - TABLE VII Assigned Term Values of the B 1 B 2 ( 1 A u ) - X*E* (V) System of 1 2 C 3 2 S 2 ( c m - 1 ) , Term Values and v i ( l i nea r ) (bent) E n A 30 756 30 757 (2) 0 30 904 (3) 30 928 ( O 31 066 (31 057) 31 339 (31 372) 31 529 (6) ( O 31 519 31 496 31 703 1 (5) 31 625 31 594 (31 712) 31 787 32 140 32 373 (8) 2 (6) 31 974 (7) 32 253 32 499 32 074 32 338 32 240 32 610 32 906 (10) 32 322 (9) 32 772 33 058 32 445 32 974 3 (8) 32 529 32 703 32 747 (5) 30 965 31 178 - 56 - TABLE V I I (continued) Term Values and v 2 ( l i n e a r ) (bent) 32 907 32 945 ( 1 0 ) 33 010 33 133 32 218 ( 1 2 ) 33 389 33 481 33 605 33 703 33 780 33 865 ( l l ) 33 269 33 455 ( 1 3 ) 33 952 The v 2 ( l i n e a r ) quantum number i s the bracketed number to the l e f t of each group of term v a l u e s . - 57 - The p a t t e r n of the E l e v e l s (corresponding to the ' c o l d ' bands) i s very i r r e g u l a r , but can be i n t e r p r e t e d as a very perturbed p r o g r e s s i o n of ^ 580 ± 30 cm" 1 , the same i n t e r v a l as seen i n the m a t r i x spectrum at 77°K (22). Since t h e i r energies are roughly quad- r a t i c i n the p r o j e c t i o n quantum number, the lowest group, w i t h K' or £' = 0 , 1 and 2 can be assigned as the asymmetric top r o t a t i o n a l s t r u c t u r e of a n o n - l i n e a r molecule (see equation (13) of s e c t i o n I I I . C ) w i t h A - -|- (B + C) Z. 33 + 5 cm"1, and, from r o t a t i o n a l a n a l y s i s of £ and II l e v e l s w i t h i n these groups ( s e c t i o n B ) , B - C — 0.11 cm - 1. To be s t r i c t , we should use the bent molecule quantum number K' f o r the p r o j e c t i o n of the angular momentum along the near-symmetric top a a x i s , r a t h e r than the l i n e a r molecule analogue, i . e . K' - l" = 0. T his K-type r o t a t i o n a l s t r u c t u r e i s a l s o seen i n the v 2 = 1 l e v e l s , l a b e l l e d as l i t , I5  a n < * i 6 ( a s  e x p l a i n e d i n s e c t i o n E ) . The p a t t e r n of the V l e v e l s above 32,000 cm - 1  i s q u i t e d i f f e r e n t , however. The E and A l e v e l s i n t h i s r e g i o n c o i n c i d e and the II l e v e l s l i e halfway between the E and A l e v e l s . Such a p a t t e r n (see F i g . 2) i s the v i b r a t i o n a l energy l e v e l p a t t e r n of a l i n e a r molecule. In other words, the energy l e v e l p a t t e r n below 32,000 cm - 1  i s c h a r a c t e r - i s t i c of the K r o t a t i o n a l s t r u c t u r e of a s l i g h t l y bent molecule, which, above 32,000 cm - 1 , becomes the v i b r a t i o n a l p a t t e r n of a l i n e a r molecule w i t h s u c c e s s i v e e x c i t a t i o n s of the degenerate bending v i b r a t i o n . The v i b r a t i o n a l energy of the n o n - l i n e a r molecule t h e r e f o r e exceeds a p o t e n t i a l b a r r i e r to l i n e a r i t y a t ^ 31,900 ± 100 cm - 1 . The b a r r i e r t o - 58 - l i n e a r i t y , H, r e f e r r e d to the zero poi n t energy i s given by H= (31,900 ± 100) - E ( v 2 = 0) + -| v 2 cm - 1 where the l o w e s t - l y i n g V l e v e l i s taken as the 'mean' p o s i t i o n of the v 2 = 0 (K' = 0) group at 30,830 cm - 1 . The b a r r i e r to l i n e a r i t y i s c a l c u l a t e d as 1350 ± 150 cm - 1 . The assignment of the upper s t a t e p r o - g r e s s i o n to the bending v i b r a t i o n r a t h e r than the symmetric s t r e t c h i n g frequency (22) i s confirmed by the v i b r a t i o n a l p a t t e r n of the V s t a t e . The manifolds of v i b r a t i o n a l l e v e l s , as grouped i n F i g . 9, show the bending v i b r a t i o n and K-type r o t a t i o n a l s t r u c t u r e expected f o r a non- l i n e a r molecule that overcomes a b a r r i e r to l i n e a r i t y on e x c i t a t i o n of s e v e r a l quanta of v 2 ( 4 3 ) . The geometry of CS 2 i n the lowest v i b r a t i o n a l l e v e l of the V s t a t e can be determined. Knowing the A and B r o t a t i o n a l c o n s t a n t s , one s o l v e s equations (8) and (9) of s e c t i o n I I I . D f o r £ , the C - S bond l e n g t h , and 2<[>, the S - C - S bond a n g l e . The B values obtained from a n a l y s i s of the 10V and 6V bands are averaged t o g i v e B' = 0.1130 ± 0.0005 cm" 1  so that the geometry of CS 2 can be c a l c u l a t e d : r 0 ( C - S ) = 1.544 ± 0.006A, < S C S = 163 ± 2 ° . The shape change upon e x c i t a t i o n of CS 2 from X 1 E +  to the V s t a t e i s mainly a bond angle change and not a bond l e n g t h change. T h i s i s reasonable i n l i g h t of the o b s e r v a t i o n of e x t e n s i v e 'hot' band s t r u c t u r e - 59 - i n the bending v i b r a t i o n and the absence of the a b s o r p t i o n from the ground s t a t e symmetric s t r e t c h i n g v i b r a t i o n a l l e v e l . According to the Franck-Condon p r i n c i p l e , the c a l c u l a t e d geometry of the V s t a t e lends f u r t h e r support to the assignment of the V s t a t e v i b r a t i o n a l p r o g r e s s i o n to the bending v i b r a t i o n , v 2 ,because t h i s i s the on l y v i b r a t i o n one expects to see given t h i s shape change. D. E l e c t r o n i c Species of the V State The lowest e x c i t e d e l e c t r o n c o n f i g u r a t i o n of CS 2 i n v o l v e s promotion of an e l e c t r o n from the highest occupied o r b i t a l , of symmetry Tr , to an antibonding o r b i t a l of T T ^ symmetry. The e l e c t r o n i c s t a t e s of a (TT ) 3 ( 7 r u ) 1 c o n f i g u r a t i o n are the s i n g l e t and t r i p l e t s t a t e s obtained * by group t h e o r e t i c a l m u l t i p l i c a t i o n , T T ^ X TT . The -rr -»• IT e l e c t r o n i c s t a t e s of CS 2 are t h e r e f o r e ^ ( ^ z ) , ^ ( ^ z ) , 1 \ ( 1 A 2 + 1B 2) 3 I + ( 3 B 2 ) ,  3 Z " ( 3 A 2 ) ,  3 * U ( 3 A 2  + 3fi 2> where the e l e c t r o n i c s p e c i e s of the n o n - l i n e a r molecule are brac k e t e d . As i n d i c a t e d i n s e c t i o n I I I . D , an e l e c t r o n i c t r a n s i t i o n i s allowed i f the integrand of <e'| u |e">, where g = x, y or z , i s t o t a l l y symmetric. 8 A p a r a l l e l - p o l a r i z e d t r a n s i t i o n i n v o l v e s an o s c i l l a t i n g d i p o l e moment p a r a l l e l to the S-S d i r e c t i o n , i . e . of species (or B 2 ) . Hence, the V s t a t e , where the molecule i s n o n - l i n e a r , i s a B 2 s t a t e . - 60 - To decide whether the V s t a t e i s s i n g l e t or t r i p l e t (S = 0 or 1) we must consider the r e s u l t s obtained from the magnetic r o t a t i o n spectrum (16,44). As shown i n Appendix I I I , a magnetic r o t a t i o n spectrum (m.r.s.) a r i s e s from the presence of e i t h e r an e l e c t r o n o r b i t a l or s p i n angular momentum i n one of the two s t a t e s . Now, the  1 E +  ground e l e c t r o n i c s t a t e has no i n t r i n s i c angular momentum 8 so that any observed m.r.s. comes from the upper e l e c t r o n i c s t a t e . The R and S systems of CS 2 e x h i b i t a strong m.r.s. (16); the V system, which i s c o n s i d e r a b l y stronger i n a b s o r p t i o n than the R and S systems, has a much weaker, though o b s e r v a b l e , m.r.s. Since CS 2 i n the V s t a t e i s n o n - l i n e a r so that the o r b i t a l angular momentum i s e s s e n t i a l l y quenched, only the s p i n m u l t i p l i c i t y of the V s t a t e i s i n q u e s t i o n . Since the R system, known to have a t r i p l e t upper s t a t e (21), shows a much stronger m.r.s. than the V s t a t e , the m.r.s. t h e r e f o r e i n d i c a t e s that the V s t a t e i s e s s e n t i a l l y s i n g l e t but that p e r t u r b a t i o n s by t r i p l e t l e v e l s (see s e c t i o n VI) lend some t r i p l e t c h a r a c t e r t o the V s t a t e , and hence, a weak m.r.s. Only two *B2 s t a t e s can a r i s e from the ( U g ) 3  ('"'u) 1  c o n f i g u r a t i o n , which are the  1 E ^ ( 1 B 2 ) and  1 A u ( 1 B 2 component) s t a t e s . The  1 E ^ ( 1 B 2 ) s t a t e o i s the upper s t a t e of the in t e n s e 2100A system, so that the V s t a t e has to be the  1 B 2 component of the  1 A s t a t e . Thus, the e l e c t r o n i c assignment of the V system of CS 2 i s TT -* I T * 1 B 2 ( 1 A ) - X 1 E + . - 61 - E. V i b r o n i c C o r r e l a t i o n s i n a *A E l e c t r o n i c State Figure 10 shows how the v i b r a t i o n a l l e v e l s of a ' i s t a t e of u a l i n e a r molecule c o r r e l a t e w i t h the v i b r a t i o n - r o t a t i o n l e v e l s of the two e l e c t r o n i c s t a t e s which i t becomes when the molecule i s bent. The l e f t - h a n d set of v i b r a t i o n a l energy l e v e l s i s that f o r a  1 E +  s t a t e ; and, g the next set i s that f o r a 1 A s t a t e of a l i n e a r molecule w i t h s m a l l u Renner-Teller i n t e r a c t i o n . Where the Renner-Teller e f f e c t i s important ( s e c . V.A.) the only good quantum number i s the v i b r o n i c angular momentum quantum number K = |A + z\t which becomes the r o t a t i o n a l quantum number K of the s t a t e s of a bent molecule. Obeying the 'non-crossing r u l e ' one can t h e r e f o r e draw the c o r r e l a t i o n s between the l e v e l s of the l i n e a r and bent s t a t e s d i r e c t l y . These,are shown as the t i e l i n e s between the second and t h i r d s e t s of l e v e l s . The column headed ' v i b r o n i c c o r r e l a t i o n ' gives the valu e (v, } f o r each K - r o t a t i o n a l l e v e l . ° bent v,. l i n To i l l u s t r a t e the e f f e c t of a p o t e n t i a l b a r r i e r to l i n e a r i t y upon the energy l e v e l s of a molecule i n a *A ( 1 A 2 +  1 B 2) e l e c t r o n i c s t a t e i t i s u s e f u l to represent the c o r r e l a t i o n s i n a d i f f e r e n t manner. F i g u r e 11 i l l u s t r a t e s s c h e m a t i c a l l y the course of the K-type r o t a t i o n a l l e v e l s of the v i b r a t i o n a l l e v e l s of both the upper and lower component s t a t e s of the n o n - l i n e a r molecule; the b a r r i e r to l i n e a r i t y i s a r b i t - r a r i l y assumed to l i e at about the = 7 l e v e l . The r e a l l y i n t e r e s t i n g r e s u l t of F i g . 11 i s the behaviour of the K-type r o t a t i o n a l l e v e l s of the upper and lower components near the b a r r i e r to l i n e a r i t y . I f there i s no o r b i t a l angular momentum, - 62 - V i b r o n i c C o r r e l a t i o n 1 FIG. (10) C o r r e l a t i o n of v i b r o n i c l e v e l s (shown as t i e l i n e s ) between l i n e a r and bent geometries. The bending v i b r a t i o n quantum numbers of a CS 2-type molecule i n the l i n e a r and bent l i m i t s a r e v l i n  a n d v b e n t ' r e s p e c t i v e l y . The l e v e l s w i t h the same value of K - the Renner-Teller quantum number of a *AU s t a t e of a l i n e a r molecule and the r o t a t i o n a l quantum numbers of a bent molecule - obey a 'non-crossing r u l e ' . - 63 - i . e . i f A = 0, the symmetric top energy l e v e l formula a p p l i e s (equation (13) of s e c t i o n I I I . C ) and the p o s i t i o n s of the K-type r o t a - t i o n a l l e v e l s are q u a d r a t i c i n K. This 'normal' p a t t e r n changes near the b a r r i e r to l i n e a r i t y to the energy l e v e l p a t t e r n of a l i n e a r m o lecule. W i t h i n the upper component, the val u e of the A r o t a t i o n a l constant (defined here as the energy s e p a r a t i o n of the K = 1 l e v e l above the K = 0 l e v e l w i t h i n a v i b r a t i o n a l l e v e l ) s t e a d i l y i n c r e a s e s as v. i n c r e a s e s , u n t i l , near the b a r r i e r to l i n e a r i t y , the val u e of A bent becomes the l i n e a r molecule bending frequency. W i t h i n the lower component, however, the behaviour of the value of A i s unexpected. W e l l below the b a r r i e r to l i n e a r i t y , the values of A i n both components are s i m i l a r though not equal s i n c e the geometries of the molecule i n the upper and lower component s t a t e s are not i d e n t i c a l . However, i n the h i g h e r v i b r a t i o n a l members of the lower component s t a t e the val u e of A decreases and a c t u a l l y becomes negative near the b a r r i e r to l i n e a r i t y , r a p i d l y approaching the l i m i t i n g value of the negative of the l i n e a r molecule bending frequency. A 'negative r o t a t i o n a l c o n s t a n t ' i s an a r t i f a c t of the necessary c o r r e l a t i o n of energy l e v e l s w i t h i n a degenerate e l e c t r o n i c s t a t e , s i n c e a symmetric top A r o t a t i o n a l c o n - s t a n t cannot be d e f i n e d f o r a l i n e a r m olecule. T h i s behaviour of the A r o t a t i o n a l constant i n a A s t a t e has not been recognized b e f o r e . As can be seen i n Table V I I I , i n the R s t a t e the v a l u e of A decreases and becomes negative near the v 2 = 10 l e v e l ( 1 5 ) . Since t h i s e f f e c t was not understood by Kleman, he was unable to a s s i g n higher v i b r a t i o n a l members of the p r o g r e s s i o n . However, we can - 64 - u p p e r u p p e r u p p e r u p p e r l o w e r lower l o w e r l o w e r FIG. (11) Behaviour of v i b r o n i c l e v e l s of the two components of a A s t a t e w i t h a b a r r i e r to l i n e a r i t y at about v l i n = 7. 'Upper' and 'lower' r e f e r to the two components of a A s t a t e i n the bent molecule l i m i t . - 65 - now say that the R s t a t e i s d e r i v e d from the lower component of what would be an o r b i t a l l y degenerate s t a t e of the l i n e a r molecule. The only p o s s i b l e degenerate IT -*• if t r i p l e t s t a t e i s the s t a t e : Hochstrasser and Wiersma (21), and a l s o Douglas and M i l t o n (19) and Hougen (20), had p r e v i o u s l y suggested t h i s assignment from Zeeman e f f e c t s t u d i e s , but we can now confirm t h i s from the v i b r a t i o n a l s t r u c t u r e . On the other hand, the v a l u e of A i n the V s t a t e i n c r e a s e s r a p i d l y near 32,000 cm - 1 , the b a r r i e r to l i n e a r i t y . The V s t a t e must be the upper component s t a t e . The s u b s c r i p t e d c o r r e l a t i o n l a b e l s of the upper component s t a t e , as given i n F i g . 10, can then be a p p l i e d to the V s t a t e term values i n F i g . 9. I t should be noted t h a t , above the b a r r i e r to l i n e a r i t y , those l e v e l s w i t h the same value of the s u b s c r i p t e d c o r r e l a t i o n number (v . ) now c o i n c i d e , as expected. TABLE VIII Term Values of the R 3A 2 ( 3^ u) State of CS 2 1 2CS 2 1 3 CS 2 V2 K = 0 K = 1 K = 2 K = 0 K = 1 K = 2 3 27101.1 7.3 27108.4 14.8 27123.2 27100.3 7.1 27107.4 14.0 27121.4 4 27401.9 7.7 27409.6 16.9 27426.5 27395.9 7.3 27403.2 15.3 27418.5 5 27697.3 8.5 27705.8 18.8 27724.6 27685.6 8.6 27694.2 16.9 27711.1 6 27986.4 9.0 27995.4 21.2 28016.6 27970.0 8.2 27978.2 19.5 27997.7 7 28269.8 6.5 28276.3 23.2 28299.6 28249.4 8.1 28257.5 20.7 28278.2 8 28542.8 7.3 28550.1 16.8 28566.9 28523.0 4.2 28527.2 1.6.3 28543.5 9 28810.0 -2.7 28807.4 28786.4 -7.0 28779.4 10 29081.0 -37.1 29043.9 29044.0 -38.2 29005.8 "Values (in cm"1) from B. Kleman, Can. J . Phys. 41, 2034 (1963). - 67 - V. THE T STATE I t has been shown that the V s t a t e i s the upper Renner-Teller component of a *A s t a t e . One might t h e r e f o r e expect a weak t r a n s i t i o n to the lower component,  1 A 2 ( 1 A u ) l y i n g to longer wavelengths. We have found such an a b s o r p t i o n (which we c a l l the T system, i n keeping w i t h Kleman's nomenclature), l y i n g among the higher bands of the R and S systems. Although a t r a n s i t i o n from a t o t a l l y symmetric lower s t a t e to a *A2 e l e c t r o n i c s t a t e i s e l e c t r i c d i p o l e f o r b i d d e n , a v a r i e t y of mech- anisms can give a non-zero t r a n s i t i o n moment. Thus, a *A2 -  1 Z + t r a n s i t i o n i s allowed by e l e c t r i c quadrupole and magnetic d i p o l e s e l e c - t i o n r u l e s . These types of t r a n s i t i o n s are g e n e r a l l y l e s s i n t e n s e than an e l e c t r i c d i p o l e t r a n s i t i o n by f a c t o r s of ^ 10 5  and ^ 1 0 8 , r e s p e c - t i v e l y ( 4 5). Moreover, i n any polyatomic molecule, most t r a n s i t i o n s (except the e l e c t r o n i c o r i g i n band) allowed i n these ways can appear more s t r o n g l y as v i b r o n i c a l l y allowed 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 v i a H e r z b e r g - T e l l e r m i x i n g . However, another type of v i b r o n i c i n t e r a c t i o n , the Renner- T e l l e r e f f e c t , can cause a t r a n s i t i o n of the type  1 A 2 - to appear, 8 when the  1 A 2 s t a t e i s one component of a degenerate s t a t e whose other component does appear i n a b s o r p t i o n . Such a t r a n s i t i o n i s p a r a l l e l - p o l a r i z e d , K' - £" = 0, and w i t h i n t e n s i t y p r o p o r t i o n a l w i t h K 2 , so that only a b s o r p t i o n from I" = 1 , 2, 3, ... l e v e l s occurs (as discussed i n s e c t i o n A ) . That i s , one expects a t r a n s i t i o n c o n s i s t i n g of 'hot' bands. - 68 - o o In the r e g i o n 3300A to 3400A there are a number of unassigned bands. Only those bands that show no (strong) magnetic r o t a t i o n spec- trum or Zeeman e f f e c t can be considered candidates f o r a s i n g l e t e l e c t r o n i c system. Numerous 'hot' bands of s i n g l e t nature are present i n t h i s r e g i o n and, i n f a c t , two v i b r a t i o n a l progressions were found. The T s t a t e term values are given i n Table IX and a medium r e s o l u t i o n photograph of a few of the T bands i s presented i n F i g . 12. Since the T system i s 'hot' o n l y , the Renner-Teller e f f e c t i s probably causing the t r a n s i t i o n to appear, as des c r i b e d i n the f o l l o w i n g s e c t i o n . A. The Renner-Teller E f f e c t i n a  ! A E l e c t r o n i c State u In o r b i t a l l y degenerate e l e c t r o n i c s t a t e s ( I I , A, $, ...) of l i n e a r molecules the v i b r a t i o n a l and e l e c t r o n o r b i t a l angular momenta are coupled, as f i r s t shown by Renner (46) w h i l e working w i t h E. T e l l e r . Because of the Renner-Teller e f f e c t , the u s u a l Born-Oppenheimer se p a r a - t i o n of molecular motion i n t o e l e c t r o n i c , v i b r a t i o n a l , and r o t a t i o n a l p a r t s breaks down. The Renner-Teller e f f e c t causes the e l e c t r o n i c and v i b r a t i o n a l wavefunctions to be mixed so that one considers v i b r o n i c and r o t a t i o n a l motions. The c o u p l i n g between v i b r a t i o n a l and e l e c t r o n o r b i t a l angular momenta i s des c r i b e d by an e f f e c t i v e h a m i l t o n i a n , d e r i v e d by Renner IL = j 6 2 A  cos2A(x-<t>) (1) Renner  J where x i s the angle between the r a d i u s v e c t o r to a 'valence' e l e c t r o n and an a r b i t r a r y r eference p l a n e , <J> i s the angle between the plane of 3 3 4 9 A 3 3 9 0 A 12U11U 10U s + 4 9 U 8 U 7 U 6 U s+3 I H S H H I B B S V system 0 0 0 - 0 3 0 ( n ) If ft! \ : ' 1 lis m l 1 : ; 0 :; 7ffl i 1 I f •: n fMS n f u, N 2 laser line positions 8 U X a j r = 3 3 7 0 . 0 7 5 5 A 3 3 7 1 . 4 2 8 9 A FIG. (12) CS 2 a b s o r p t i o n at medium r e s o l u t i o n : -78°C ( a ) , 23°C (b) and 100°C ( c ) ; and, the 9U reg i o n at high r e s o l u t i o n : -78°C ( d ) , 23°C (e) and 100°C ( f ) . The (t+2)A and t i l 'hot' bands of the T system are i n the re g i o n of N 2 l a s e r emission. The r o t a t i o n a l a n a l y s i s of the ' c o l d ' 9U band i s shown as a F o r t r a t - l i k e diagram. - 70 - TABLE IX Assigned Term Values of the T * A 2 ( X A ^ State of 1 2 C 3 2 S 2 (cm - 1) t+1 t+2 t+3 t+4 K' = 1 30 024 (30 246) 30 438 30 444 K* = 2 30 031 30 035 30 252 30 259 30 454 30 465 30 662 30 670 30 844 30 851 K' = 3 30 055 - 71 - the bent molecule and the same refe r e n c e p l a n e , 6 i s the supplement to the instantaneous angle of bend and j i s a parameter d e s c r i b i n g the Renner-Teller i n t e r a c t i o n . The Renner-Teller p e r t u r b a t i o n i s best w r i t t e n i n e x p o n e n t i a l form making use of the d e f i n i t i o n I - e.*1**-*) (2) g i v i n g L - 1 j e2A ( e21A( X-#) + ^ K x - ^ j Renner 2  J = 2" J ( q + + q_ ) (3) In the case of a *A s t a t e (A=2), the Renner-Teller h a m i l t o n i a n i s u \ e n n e r = 1 * K  + & > <4> the Renner-Teller h a m i l t o n i a n c o n s i s t s of ' l a d d e r ' operators mixing e l e c t r o n i c and v i b r a t i o n a l s t a t e s according to the r u l e AA = ±2, A£, = + 2. The Renner-Teller term couples the p u r e l y e l e c t r o n i c wave- f u n c t i o n |A> = (l//2T)e 1 A x  (5) w i t h the doubly degenerate o s c i l l a t o r wavefunction, |v£>, which con t a i n s a v i b r a t i o n a l angular momentum term, (l//2y)e*~!l'^. The unper- turbed ' v i b r o n i c ' b a s i s f u n c t i o n i s simply the product of these wave- f u n c t i o n s \hvl> = |A>|v£> . (6) - 72 - Only the t o t a l ( v i b r o n i c ) angular momentum, A + £,is conserved by the Renner-Teller i n t e r a c t i o n . Because of the ' l a d d e r i n g ' property of the o p e r a t o r , the ma t r i x elements of the Renner-Teller h a m i l t o n i a n evaluated i n the |Av£> b a s i s f u n c t i o n s are e n t i r e l y o f f - d i a g o n a l . T h i s suggests that symmetrized l i n e a r combinations of b a s i s f u n c t i o n s , as generated by a Wang t r a n s f o r m a t i o n , w i l l t r a n s f e r the i n t e r a c t i o n mostly to the di a g o n a l m a t r i x elements, and a l s o reduce the s i z e of the o f f - d i a g o n a l elements. Then, second order p e r t u r b a t i o n t h e o r y , r a t h e r than exact d i a g o n a l i z a t i o n , can be a p p l i e d . With the d e f i n i t i o n K = |A + where A and I are signed q u a n t i t i e s , the 'sum' and ' d i f f e r e n c e ' b a s i s f u n c t i o n s are |A*> = (l//2){|2,v,K-2> ± |-2,v,K+2>} (7) The form of the Renner m a t r i x i s i l l u s t r a t e d s c h e m a t i c a l l y below. |A + > |A"> <A + | <A"| The d i a g o n a l sub-matrices c o n t a i n the 'reor d e r i n g m a t r i x elements', so designated because these p a r t s of the i n t e r a c t i o n couple b a s i s f u n c t i o n s of the same symmetry. At t h i s s t a g e , one can a s s o c i a t e the 'sum' ma t r i x w i t h the upper Renner-Teller component and the ' d i f f e r e n c e ' m a t r i x w i t h the lower component. The r e o r d e r i n g m a t r i x elements scramble a l l the v i b r a t i o n a l l e v e l s w i t h i n a component but do not connect the upper and lower component s t a t e s . reord ^ R ^ R H reord - 73 - The m a t r i x elements connecting the upper and lower components take the form \ j <A 4  | ^ + q>_ | A + > (8) which we c a l l the 'Fermi resonance m a t r i x elements'. Expressing these m a t r i x elements i n the |Av£> b a s i s f u n c t i o n s , we have | j (1//2~){<2,V,K-2|±<-2,V,K+2|} | ( l / / 2 ) { | 2,v' ,K-2>+| -2,v' ,K+2>} = \ 3 {<-2,v,K+2|q^|2,v ',K-2> - <2,v,K-2|q^|-2,v',K+2>} . (9) I t can be shown that f o r K = 0 the Fermi resonance m a t r i x elements v a n i s h i d e n t i c a l l y . I n other words, the E +  and E v i b r o n i c s t a t e s can be i d e n t i f i e d w i t h the B 2 (upper) and A 2 (lower) component s t a t e s , r e s p e c t i v e l y , w i t h no i n t e r a c t i o n between them. The K ={= 0 m a t r i x elements can be c a l c u l a t e d e a s i l y i n harmonic approximation w i t h the d e f i n i t i o n ^ ± = e**X ( 1 0) because m a t r i x elements of the r e c t i l i n e a r displacement operators x + have been evaluated ( 4 7 ) . M a t r i x m u l t i p l i c a t i o n g i v e s the m a t r i x .A. elements of the operator x^, and n o t i c i n g that 2TT :±2|e :pti X|+2> = ^ } e ±2± * e** 1 * e ± 2 i * d X 0 = 1 , (11) we have - 74 - <+2,v,K±2|q^_|±2,v,K+2> = Jtt /(V+K)(V-K)(V+K+2)(V-K+2) <+2,v+4,K±2|q^|±2,v,K+2> = -|N /(V±K)(V±K+2)(V±K+4)(V±K+6) <+2,v+2,K±2|q^_|±2,v,K+2> = N /(v+K+2)(v±K)(v±K+2)(v±K+4) (12) <+2,v-2,K±2|q^|±2,v,K+2> = N /(v+K+2)(v+K)(v±K)(v+K-2) <+2,v-4,K±2|q'j|±2,v,K+2> = -|w /(v+K+2) (v+K) (v+K-2) (v+K-4) where N i s a n o r m a l i z a t i o n f a c t o r . The non-vanishing Fermi resonance m a t r i x elements obey the s e l e c t i o n r u l e Av = ±2 , ± 4 . Av = ±2; *0? 2 ' V  = N[/(v-K+2) (v+K) (v+K+2) (v+K+4) - /(v+K+2) (v-K) (v-K+2) (v-K+4)] ————— r K = N /(v+2) 2 -K 2  [/(v+K+2) 2 -2 2  - /(v-K+2) 2 -2 2  ] (13) For v f a i r l y l a r g e , so th a t (v+2) 2  » K 2  and (v±K+2) 2  >>4 H J ^ 2 ' V y N(v+2) [(v+K+2) - (v-K+2)] = 2N(v+2)K (14) Even f o r v = 3, K = 1, t h i s approximation i s accurate w i t h i n 7%. S i m i l a r l y , the Av = ±4 Fermi resonance m a t r i x elements are a l s o p ropor- t i o n a l to K, which i s a 'good' quantum number. Applying these r e s u l t s to C S 2 , the 1 B 2 and *A2 component * 1 s t a t e s of the TT ->- TT AA s t a t e i n t e r a c t w i t h a matrix element p r o p o r t i o n a l to K. The f i r s t order wavefunction of the 1 A 2 s t a t e i s - 75 - ( 0 ) < 1A 2 ( 0 ),vK|^'hBf>,v.K> l ^ . v I O - M°\v*>+1 \l4°\v>K> ^ . ( 1 5) V ' E lA 2,vK" E lB 2,v'K The v i b r o n i c mixing produces a non-zero e l e c t r i c d i p o l e t r a n s i t i o n moment < 1 A| 1) ,vK|y IX1!^ 8 p r o p o r t i o n a l to K such that the t r a n s i t i o n takes the p a r a l l e l p o l a r i z a t i o n o f the ( X A ) -  L Z t r a n s i t i o n . Since the i n t e n s i t y of a t r a n s i t i o n i s p r o p o r t i o n a l to the square of the t r a n s i t i o n moment, the  1 A 2 ( 1 A ^ ) - Xll+ t r a n s i t i o n has a Renner-Teller induced i n t e n s i t y p r o p o r t i o n a l to K 2. g B. General Features of the T System I t i s i n t e r e s t i n g to note how, at 100°C, the A - A bands of the T system are stronger than the II - II bands. The K 2 i n t e n s i t y term i s r e s p o n s i b l e , s i n c e the a d d i t i o n a l f a c t o r of 4 f o r the A - A bands (K" = 2) over the IT — II bands (K" = 1) outweighs the l e s s favourable Boltzmann f a c t o r . Only the Renner-Teller e f f e c t , as explai n e d above, accounts f o r the v i b r o n i c i n t e n s i t i e s . The v i b r o n i c II - II and A - A progressions show a v i b r a t i o n a l i n t e r v a l of ~ 220 cm" 1  which must be assigned as the T s t a t e bending frequency. Because the T s t a t e bending frequency i s about h a l f the ground s t a t e frequency of 396 cm - 1 , II and A bands d i f f e r i n g by two upper s t a t e quanta n e a r l y c o i n c i d e . The T bands are o f t e n doubled and i n a l l cases e x h i b i t r o t a t i o n a l s t r u c t u r e at l e a s t as s e v e r e l y perturbed as that of the V bands so that no r o t a t i o n a l a n a l y s i s has been p o s s i b l e . As i n the V . s t a t e , the term v a l u e s of the T s t a t e show the r o t a t i o n a l s t r u c t u r e - 76 - of a (near) symmetric top molecule. By p l o t t i n g the average p o s i t i o n s of the perturbed l e v e l s of the lowest v i b r a t i o n a l l e v e l a g a i n s t K 2 , an A r o t a t i o n a l constant of 14.7 ± 1.7 cm" 1  i s o b t a i n e d . Using the average of the B r o t a t i o n a l constants found f o r the V s t a t e , the geometry of CS 2 i n the T s t a t e was c a l c u l a t e d : r(C-S) = 1.54it ± 0.006A (assumed) <SCS = 155 ± 2 ° . In p r i n c i p l e , a d e t a i l e d r o t a t i o n a l a n a l y s i s of a II - II band of the T system would a l l o w the magnitude and s i g n of the asymmetry doubling constant to be determined. The sense of the asymmetry doubling i s opposite i n the  1 B 2 and ^ 2 component s t a t e s so that a c o n f i r m a t i o n of the assignment of the T s t a t e as  1 A 2 ( 1 A ) would be p r o v i d e d . F u r t h e r - more, without i s o t o p i c s t u d i e s , the a b s o l u t e v i b r a t i o n a l numbering of the T bands cannot be o b t a i n e d . As y e t , the assignment of the T system must not be considered c o n c l u s i v e . C. N 2 Laser E x c i t e d Fluorescence of C S 2 a t 3 3 7 l l Brus (49) has reported that CS 2 f l u o r e s c e n c e , e x c i t e d by a pulsed N 2 l a s e r , decays e x p o n e n t i a l l y i n the manner expected when the l a s e r i n i t i a l l y populates two f l u o r e s c i n g s t a t e . F i g . 12 shows the o a b s o r p t i o n spectrum near the N 2 l a s e r wavelength (3371A) w i t h the l a s e r * l i n e s marked below the h i g h r e s o l u t i o n s p e c t r a . The l a s e r l i n e s o v erlap & In comparing the CS 2 spectrum w i t h the N 2 l a s e r l i n e s , Brus omitted the vacuum c o r r e c t i o n to the a i r wavelengths of the N 2 e m i s s i o n , as given by Park, Rao and Javan (50); the l a s e r l i n e s do n o t , t h e r e f o r e , f a l l i n the 9U band, as Brus mistakenly thought. - 77 - a II - II and a A - A band of the ( s i n g l e t ) T system, and a weak ' c o l d ' band (8U), which i s known to be a t r i p l e t from i t s comparatively strong m.r.s. (16). Thus i t i s p o s s i b l e that Brus' o b s e r v a t i o n of two expo- n e n t i a l decays of the l a s e r e x c i t e d f l u o r e s c e n c e of CS 2 may be e x p l a i n e d by the f a c t that the l a s e r l i n e s overlap bands belonging to two e l e c - t r o n i c t r a n s i t i o n s , which have s i n g l e t and t r i p l e t upper s t a t e s , r e s p e c - t i v e l y . D. The P o t e n t i a l Energy Diagram of the *A State In a *A s t a t e the p o t e n t i a l energy can be w r i t t e n as v ± (e) = v0 + i ke 2 + -a—. + (I ± I) ne1* (D b+8 2 where + and - r e f e r to the upper ( 1 B 2) and the lower ( 1 A 2) component s t a t e s , r e s p e c t i v e l y . The f i r s t term, V Q , i s a constant; the second and t h i r d terms represent the p o t e n t i a l energy of a bent molecule w r i t t e n as a q u a d r a t i c term perturbed by a L o r e n t z i a n ; and the f o u r t h term d e s c r i b e s the s p l i t t i n g of the  1 A s t a t e as the l i n e a r molecule u bends. A l l the Renner-Teller q u a r t i c s p l i t t i n g i s i n c l u d e d i n the upper s t a t e p o t e n t i a l curve f o r convenience i n c a l c u l a t i o n . The four p o t e n t i a l energy parameters, k, a , b and n can be c a l c u l a t e d from the bond a n g l e s , v i b r a t i o n a l f r e q u e n c i e s and b a r r i e r s to l i n e a r i t y of the component s t a t e s . The p o t e n t i a l curves must have minima at the upper and lower s t a t e e q u i l i b r i u m a n g l e s , 9 + and 6 , and . the second d e r i v a t i v e s of equation (1) evaluated at 6 and 6 are - 78 - r e q u i r e d to reproduce the bending f r e q u e n c i e s , co , i . e . 3V ±(G) 3 2 V ± ( 6 ) 302 = 0 (2) G . = A± . (3) The two f o r c e constants, A , must be c a l c u l a t e d f o r the geometries of CS2 i n the two s t a t e s . A = ( 4 T r 2c/h) {m (m + 2m s i n 2 ^ 0)/2M) r2np u 2 (4) s c s I Lb Aforementioned u n c e r t a i n t i e s i n the a n a l y s i s of the T system make the value of 6 so determined l e s s u s e f u l i n the determination of the parameters than the b a r r i e r to l i n e a r i t y f o r the upper s t a t e , H = V +(0) - V +(0 ) = I - \ k 6 2 - - J L _ - n e j . (5) b+07 Four simultaneous equations (obtained by e v a l u a t i n g equations (3), (5) and the '+' component of (2)) were solved n u m e r i c a l l y w i t h the a i d of a computer programme. The p o t e n t i a l constants give the p o t e n t i a l diagram shown as F i g . 13. The bond angle i n the T s t a t e i s w e l l p r e d i c t e d by equation (1), as i s the b a r r i e r to l i n e a r i t y . I f the lowest energy T band (see Table IX) belongs to the v^ = 0 l e v e l , the T s t a t e b a r r i e r to l i n e a r i t y i s 2000 ± 100 cm - 1, b r a c k e t i n g the c a l c u l a t e d value of 1960 cm - 1. - 79 - FIG. (13) The p o t e n t i a l energy curves of the V and T s t a t e s (upper and lower c u r v e s , r e s p e c t i v e l y ) . V ± ( 8 ) = 29,000 + 1730 6 2 + 0>Q524+e2  + <| ± I> 3 3 9 0 0 B* Using the data 6 + = 1 8° , u + = 560 cm - 1, u)_ = 220 cm - 1 and H = 1350 cm - 1  gave the above s o l u t i o n w i t h 9 _ = 2 8° , H = 1960 cm - 1 . C f . the observed values of 6~ = 25 ± 2° and t e n t a t i v e l y , H = 2000 ± 100 cm - 1 . - 80 - Although the p o t e n t i a l energy ex p r e s s i o n can reproduce the approximate f e a t u r e s of the spectrum, i t should not be regarded as a c o n f i r m a t i o n of the v i b r a t i o n a l a n a l y s i s of the V and T systems. - 81 - V I . DISCUSSION A n a l y s i s of the e l e c t r o n i c a b s o r p t i o n spectrum of CS 2 i n the o. r e g i o n 2900 - 3500A has shown that the strongest a b s o r p t i o n i n t h i s r e g i o n goes to an upper s t a t e of  1 B 2 symmetry where the molecule i s bent at e q u i l i b r i u m . A weaker t r a n s i t i o n at longer wavelengths, which had not been recognized p r e v i o u s l y , i s assigned as going to a *A2 s t a t e , where the  1 B 2 and  1 A 2 s t a t e s are Renner-Teller components of the degen- . * e r a t e A s t a t e (n -»• IT ) of the l i n e a r molecule. The molecular s t r u c - u t u r e i n the ^B2 s t a t e has been determined, and the approximate form of the p o t e n t i a l energy curves f o r the two s t a t e s has been d e s c r i b e d . The o b s e r v a t i o n that the  1 B 2 component of the ^ s t a t e l i e s above the  1 A 2 component when the molecule i s bent giv e s i n f o r m a t i o n about the p o s i t i o n of the so-far unobserved TT -> TT AA 2 ( E ) s t a t e . The TT -> i r * 1 B 2 s t a t e i s known to l i e 15000 cm"1 above the XA z  u u s t a t e (19): by e l e c t r o s t a t i c i n t e r a c t i o n i t must lower the energy of the  1 B 2 component. However the  1 A 2 s t a t e i n t e r a c t s s i m i l a r l y w i t h the 1 A 2 C1^ ) s t a t e , and to account f o r the energy order of the components one can conclude that the  1 Ao ( 1 Z ) s t a t e l i e s above the  1 A s t a t e , i n ^ u u c o n t r a d i c t i o n to the c o n s i d e r a t i o n s of McGlynn et a l . ( 4 1 ) . The v i b r a t i o n a l and r o t a t i o n a l s t r u c t u r e s of the components of the  1 A^ s t a t e are very s e v e r e l y p e r t u r b e d . This i s e s p e c i a l l y so i n the V 1 B 2 component, where only two upper s t a t e l e v e l s could be analysed r o t a t i o n a l l y , and the v i b r a t i o n a l s t r u c t u r e at the short wavelength end - 82 - i s c h a o t i c . Evidence from the magnetic r o t a t i o n spectrum (16) shows that the p e r t u r b i n g s t a t e s are probably t r i p l e t , because the ^ 2 component l e v e l s below the b a r r i e r to l i n e a r i t y (where the o r b i t a l angular momentum i s quenched) are s e n s i t i v e to a magnetic f i e l d . By c l a s s i f y i n g the p o s s i b l e TT -> TT s t a t e s according to the case (c) n o t a t i o n one can show that the ( s t r o n g l y ) p e r t u r b i n g s t a t e s are l i k e l y to be Kleman's R s t a t e , and the ft = 0 component of the  3 E u s t a t e (which i s presumably Kleman'sS s t a t e ) : - n = 0 1l+ B 2 (2100A bands) u 1 Z A 2 u 1 A u A 2(T) + B 2(V) 3 Z ^ B 2(S) A i + B i 3 A u Ai + Bj A 2 + B 2(R) Ai + Bj 3 ^ A 2 Ai + BX The s i n g l e t and t r i p l e t s t a t e s i n t e r a c t by s p i n - o r b i t c o u p l i n g . In the l i n e a r molecule l i m i t t h i s i s d i a g o n a l i n the quantum number ft, and w i l l a l l o w strong c o u p l i n g between the ^ s t a t e and the  3 A„ s t a t e . 2u 2u In the bent molecule the case (c) s p i n - e l e c t r o n i c s t a t e s belonging to the same r e p r e s e n t a t i o n are coupled. Thus the V 1 B 2(^A u) s t a t e w i l l be coupled s t r o n g l y to the R ( 3 A 2 y ) s t a t e at a l l values of the SCS bond a n g l e , but more weakly to the S( 3 Z Q+ u) s t a t e . The observed p e r t u r b a t i o n s i n the T(*A u) s t a t e are t h e r e f o r e not unexpected, s i n c e s i m i l a r s p i n - o r b i t i n t e r - a c t i o n s w i t h l o w e r - l y i n g s t a t e s are p o s s i b l e . - 83 - The d e n s i t y of p e r t u r b a t i o n s i n the V system i s i n t e r e s t i n g because one i s seeing the onset of the sp e c t r o s c o p i c m a n i f e s t a t i o n of the process that permits i n t e r s y s t e m c r o s s i n g from the s i n g l e t to the t r i p l e t manifold of a molecule. The l e v e l s we have analysed r o t a t i o n a l l y belong to the lowest v i b r a t i o n a l l e v e l of the V s t a t e ; even so , there are o f t e n s e v e r a l assigned upper s t a t e l e v e l s w i t h the same J valu e showing that the d e n s i t y of p e r t u r b i n g t r i p l e t l e v e l s i s alr e a d y c o n s i d - e r a b l e . At higher energies the d e n s i t y of l i n e s i s much gr e a t e r and a c c o r d i n g l y the d e n s i t y of p e r t u r b i n g t r i p l e t l e v e l s i s o b v i o u s l y a l s o g r e a t e r . Thus, the spectrum appears to be continuous at low d i s p e r s i o n , although at high r e s o l u t i o n i t appears as a m u l t i t u d e of o v e r l a p p i n g l i n e s so densely packed that t h e i r average separations are l e s s than the l i n e w i d t h . The d i f f u s e a b s o r p t i o n i s not a t r u e continuum spectrum because the l e v e l s s t i l l l i e below the ground s t a t e d i s s o c i a t i o n l i m i t (23). A s i n g l e t r o t a t i o n a l l e v e l i s perturbed by so many t r i p l e t l e v e l s i n the r e g i o n of d i f f u s e a b s o r p t i o n that the molecule could have a greater proba- b i l i t y of being i n the t r i p l e t manifold than i n the s i n g l e t m a n i f o l d . References 1. E.D. W i l s o n , Astrophys. J . 69, 34 (1929). 2. F.A. J e n k i n s , A strophys. J . 70, 191 (1929). 3. W.W. Watson and A.E. P a r k e r , Phys. Rev. 37, 1013 (1931). 4. L.N. Liebermann, Phys. Rev. 60, 496 (1941). 5. C. Ramasastry, P r o c . N a t l . I n s t . S c i . I n d i a A18, 177 (1952). 6. C. Ramasastry, P r o c . N a t l . I n s t . S c i . I n d i a A18, 621 (1952). 7. W.C. P r i c e and D.M. Simpson, P r o c . Roy. Soc. 165A, 272 (1938). 8. C. Ramasastry and K.R. Rao, Indian J . Phys. 21, 313 (1947). 9. Y. Tanaka, A.S. J u r s a , and F . J . LeBlanc, J . Chem. Phys. _32, 1199 (1960). 10. M. Ogawa and H.C. Chang, Can. J . Phys. 48, 2455 (1970). 11. B.P. S t o i c h e f f , Can. J . Phys. 36, 218 (1958). 12. A.H. Guenther, T.A. Wiggins, and D.H. Rank, J . Chem. Phys. 28, 682 (1958). 13. A.D. Walsh, J . Chem. S o c , p. 2266 (1953). 14. A.E. Douglas and I . Zanon, Can. J . Phys. 42, 627 (1964). 15. B. Kleman, Can. J . Phys. 41, 2034 (1963). 16. P. Kusch and F.W. Loomis, Phys. Rev. 55, 850 (1939). 17. A.E. Douglas, Can. J . Phys. 3_6, 147 (1958). 18. R.S. M u l l i k e n , Can. J . Phys. 36, 10 (1958). 19. A.E. Douglas and E.R.V. M i l t o n , J . Chem. Phys. 41, 357 (1964). 20. J.T. Hougen, J . Chem. Phys. 41, 363 (1964). 21. R.M. Hochstrasser and D.A. Wiersma, J . Chem. Phys. 54, 4165 (1971). 22. L. Bajema, M. Gouterman, and B. Meyer, J . Phys. Chem. 75_, 2204 (1971). 23. H. Okabe, J . Chem. Phys. 56, 4381 (1972). 24. J.U. White, J . Opt. Soc. Am. 32, 285 (1942). 25. H.J. B e r n s t e i n and G. Herzberg, J . Chem. Phys. 16_, 30 (1947). - 85 - 26. H.M. Crosswhite, Fe-Ne Hollow Cathode T a b l e s , John Hopkins U n i v e r - s i t y (1965). 27. R.S. M u l l i k e n , J . Chem. Phys. 23, 1997 (1955). 28. G. Herzberg, I n f r a r e d and Raman Spectra of Polyatomic M o l e c u l e s , Van Nostrand, P r i n c e t o n , New J e r s e y , U.S.A. Ch. I I 2. (1945). 29. L.D. Landau and E.M. L i f s h i t z , Quantum Mechanics, 2 n d  E d i t i o n , Pergamon Press and Addison-Wesley P u b l i s h i n g Company, I n c . , Reading, Massachusetts, U.S.A. § 101, 5 104, § 105, (1965). 30. D. Agar, E.K. P l y l e r , and E.D. T i d w e l l , J . Res. N a t l . Bur. Stand. 66A, 259 (1962). 31. H.C. A l l e n , J r . and P.C. Cr o s s , M o l e c u l a r V i b - R o t o r s , John Wiley and Sons, I n c . , New York and London, 7 (1963). 32. H. N i e l s e n , Rev. Mod. Phys. 23, 90 (1951). 33. I.M. M i l l s , M o l . Phys. ]_, 549 (1964). 34. J.T. Hougen, J . Chem. Phys. 36, 519 (1962). 35. D.F. Smith, J r . and J . Overend, J . Chem. Phys. 54, 3632 (1971). 36. E.U. Condon and G.H. S h o r t e l y , The Theory of Atomic S p e c t r a , The U n i v e r s i t y P r e s s , Cambridge, Ch. I l l (1963). 37. J.H. Van V l e c k , Rev. Mod. Phys. 23, 213 (1951). 38. G. Herzberg, E l e c t r o n i c Spectra- of Polyatomic M o l e c u l e s , Van Nostrand, P r i n c e t o n , New J e r s e y , U.S.A. 109-114, 223 (1966). 39. J.T. Hougen, Nat. Bur. Stand. (U.S.) Monogr. 115, Ch. 3 (1970). 40. H.C. A l l e n , J r . and P.C. Cross, M o l e c u l a r V i b - R o t o r s , John Wiley and Sons, I n c . , New York and London, 102 (1963). 41. J.W. R a b e l a i s , J.M. McDonald, V. Scher and S.P. McGlynn, Chem. Rev. 71, 73 (1971). 42. G. Herzberg, I n f r a r e d and Raman Spectra of Polyatomic M o l e c u l e s , Van Nostrand, P r i n c e t o n , New J e r s e y , U.S.A. 390 (1945). 43. R.N. Dixon, Trans. Faraday Soc. 60, 1363 (1964). 44. W.H. Eberhardt, p r i v a t e communication. 45. G. Herzberg, E l e c t r o n i c Spectra of Polyatomic M o l e c u l e s , Van Nostrand, P r i n c e t o n , New J e r s e y , U.S.A. 134-136, 222, 265-271 (1966). - 86 - 46. E. Renner, Z. Phys. 92, 172 (1934). 47. W. M o f f i t and A.D. L i e h r , Phys. Rev. 106, 1195 (1957). 48. A . J . Merer and D.N. T r a v i s , Canad. J . Phys. 44, 353 (1966). 49. L.E. Brus, Chem. Phys. L e t t e r s 12, 116 (1971). 50. J.H. P a r k s , D.R. Rao and A. Javan, A p p l . Phys. 13_, 142 (1968). 51. T. C a r r o l l , Phys. Rev. 52, 822 (1937). 52. W.H. Eberhardt and H. Renner, J . M o l . Spec. 6_, 483 (1961). APPENDIX I V i b r a t i o n a l and R o t a t i o n a l Combination D i f f e r e n c e s of the X*E* Ground E l e c t r o n i c State of  1 2 C 3 2 S 2 The r o t a t i o n a l energy formulae of CS 2 i n i t s ground e l e c - t r o n i c s t a t e used were F ( J ) = v 0 + B v [ J ( J + 1) - £ 2 ] - D y J 2 ( J + l ) 2 + | ( - l ) J q J ( J + D (1) A 2 F v ( J ) = F v ( J + l ) - F v ( J - l ) (2) A 2G(J) = F v , ( J ) - F v „ ( J ) (3) The constants used (35) are summarized below i n cm  1  u n i t s . L e v e l v 0 B D *10 8  q*10 5 u  v v 0 0° 0 0 0.1090917 0.993 0 0 2° 0 801.849 0.1094604 0.810 0 0 l 1 0 396.092 0.1093146 0.953 5.27 0 3 1  0 1206.980 0.1096572 1.49 8.62 The values of equations (1 - 3) were c a l c u l a t e d w i t h the a i d of a computer programme and are given h e r e . - 88 - (0 0° 0) Level (0 2° 0) Level A 2G(J) = J Ffj(J) A 2 F 0 ( J - l ) F 2(J) A 2F 2(J-1) F 2(J) -Fo(J) 0 0 - 801.849 - 801.849 2 0.655 0.655 802.506 0.657 1.851 4 2.182 1.527 804.038 1.532 1.856 6 4.582 2.400 806.446 2.408 1.864 8 7.855 3.273 809.730 3.284 1.876 10 12.000 4.145 813.890 4.159 1.890 12 17.018 5.018 818.925 5.035 1.907 14 22.909 5.891 824.835 5.911 1.927 16 29.672 6.763 831.622 6.786 1.949 18 37.308 7.636 839.284 7.662 1.975 20 45.817 8.509 847.821 8.537 2.004 22 55.198 9.381 857.234 9.413 2.036 24 65.451 10.254 867.522 10.288 2.071 26 76.577 11.126 878.686 11.164 2.109 28 88.576 11.998 890.726 12*. 039 2.150 30 101.447 12.871 903.640 12.915 2.193 32 115.190 13.743 917.430 13.790 2.240 34 129.805 14.615 932.095 14.665 2.290 36 145.293 15.487 947.636 15.540 2.343 38 161.652 16.360 964.052 16.416 2.399 40 178.884 17.232 981.342 17.291 2.459 - 89 - J (0 l 1 0) L e v e l (0 3 1 0) L e v e l A 2 G ( J ) F i ( J ) A 2 F i ( J ) F 3 ( J ) A 2 F 3 ( J ) 1 396.201 - 1207.090 - 810.888 2 96.639 1.093 07.529 1.096 0.890 3 97.294 1.531 08.186 1.536 0.892 4 98.170 1.967 09.064 1.973 0.895 5 99.261 2.405 10.159 2.413 0.897 6 400.575 2.841 11.478 2.850 0.903 7 02.103 3.280 13.009 3.291 0.906 8 03.855 3.716 14.769 3.727 0.914 9 05.819 4.155 16.735 4.169 0.917 10 08.010 4.590 18.937 4.604 0.927 11 10.409 5.030 21.339 5.046 0.931 12 13.040 5.464 23.983 5.480 0.944 13 15.873 5.904 26.820 5.924 0.947 14 18.944 6.338 29.907 6.357 0.963 15 22.211 6.779 33.177 6.801 0.966 16 25.723 7.213 36.708 7.234 0.985 17 29.424 7.653 40.411 7.678 10.987 18 33.376 8.087 44.386 8.111 811.010 19 37.511 8.528 48.522 8.556 1.011 20 41.904 8.961 52.942 8.987 1.038 21 46.472 9.403 57.509 9.433 1.037 22 51.307 9.835 62.375 9.864 1.068 - 90 - J F i ( J ) A 2 F i ( J ) F 3 ( J ) A 2 F 3 ( J ) A 2G(J) 23 456.307 10.277 1267.373 10.310 811.066 24 61.584 10.709 72.685 10.740 1.101 25 67.016 11.152 78.113 11.187 1.097 26 72.735 11.583 83.873 11.617 1.137 27 78.599 12.026 89.730 12.065 1.131 28 84.761 12.457 95.937 12.493 1.176 29 91.056 12.900 1302.223 12.942 1.167 30 97.662 13.331 08.879 13.370 1.217 31 504.387 13.775 15.593 13.819 1.206 32 11.436 14.205 22.697 14.246 1.261 33 18.592 14.649 29.839 14.695 1.247 34 26.085 15.079 37.393 15.122 1.308 35 33.671 15.523 44.960 15.572 1.290 36 41.608 15.952 52.965 15.998 1.357 37 49.623 16.397 60.958 16.449 1.335 38 58.005 16.826 69.413 16.874 1.408 39 66.449 17.271 77.832 17.235 1.383 40 75.276 17.700 86.739 17.750 1.463 - 91 - APPENDIX II CS2 COMBINATION DIFFERENCE PRCGRAMME LINES OF TWO EANDS WITH COMMON UEPER STATES ARE STORED IN 'V(NI) 1 AND •HV(NJ) 1. •PREC IS THE REQUIRED PRECISION (CM-1) OF THE FOUR CALCULATED TERM VALUES GENERATED BY THE R AND P ERANCH ASSIGNMENTS FROM EACH BAND. COMEINATION DIFFERENCES OF CS2 LOWER LEVELS ARE STORED IN ARRAY THE CONSTANTS SHOWN ARE FOR THE V2=1fL=1 AND V2=3,L=1 LEVELS. DIMENSION P (3 7,5),V (250) ,HV (250) ,SH (10),WR (4,6) CO 1 J=1,37 X^FLOAT (J * J + J) P ( j , 1) =-14.017+ (0. 10928 83-0. OC COO 000953 *X) *X P (J,2)=6.870+ (0. 1096141-0.0000000119*X)*X IF (MOD (J,2) .NE.O) GO TO 22 P(J,1)=P ( J , 1)+0.0000527*X P(J,2)=P (J,2) +0.0000862*X 22 P (J,3)=P (J,2)~P (J,1) 1 CONTINUE DO 20 J=2,36 P(J,4)=P (J + 1, 1)-P(J-1, 1) 20 P ( J , 5) =P (J+1 ,2)-P ( J-1, 1) REAE (5,100)NI fNJ rPREC 100 FORMAT (214,F5.3) REAE(5,101) (V (K) , K= 1 ,NI) READ (5,101) (H V (K) , K= 1 , NJ) 101 FORMAT (16F5.3) ZL=F (1,3)-PREC ZU=P (36,3) + PREC LZ= 1 QZ=1.3*PREC DO 2 N=2,NI Z=V(H) WRITE(6,49)Z 49 FORMAT (/ 1 LINE«,F10.3) KK=0 IF ( (Z-HV (LZ) ) .LT.ZL) GO TO 2 4 IF ( (Z-HV (LZ)).LT.ZU) GO TO 5 3 LZ=IZ+1 IF (LZ.GT.NJ) GO TO 2 GO 10 1 5 I=LZ 7 KK=KK+1 SM (KK)=HV (I) 1=1 + 1 IF (I.GT.NJ) GO TO 6 IF ( (Z-fiV (I) ) .GT.ZL) GO TO 7 6 KN=N-1 LN-LZ- 1 DO 8 J=1,35 10 ZA=P(J,3) KL=0 KR=0 - 92 - KS=0 DO 9 1=1,KK IF (ABS (Z-SM (I)-ZA). GT. PR EC) GO TO 9 KL=KL•1 WR (KL.1)=SM (I) 9 CCNTINUE IF(KL.EQ.O) GO TO 8 I=KM ZA=P(J*1,4) 11 IF(I.EQ.0) GO TO 13 IF ( (Z-V (I)+PREC) .LT.ZA) GOTO 12 IF (ABS (Z-V (I) -ZA) .GT.PREC) GO TO 13 KN=I KR=KR +1 WR (KR,2) = V (I) 12 1=1-1 GO TO 11 13 IF (KR.FQ.O) GO TO 8 I=LN ZA=P (J + 1 ,5) 14 IF (I.EQ.O) GO TO 16 IF ( (Z-HV (I) +PREC) .LT.ZA) GO TO 15 IF (ABS (Z-HV (I)-ZA) . GT. PREC) GO TO 16 LN=I KS=KS+1 WR (KS,3)-HV (I) 15 1=1-1 GO TO 14 16 IF (KS.EQ.O) GO TO 8 T=Z*P(J,1) DO 17 1=1,KL 17 HR (I,4)=WR (I, 1) +P(J f 2) DO 18 1=1,KR 18 WR (I,5)=WR (1,2) + P(J + 2,1) DO 19 1=1,KS 19 WR (I,6)=WR (1,3) *P(J + 2,2) IF ( (KL+KR + KS).NE.3) GO TO 21 IF( (ABAX1 (WR (1,4) , WR (1,5) , WR (1,6) )-ABINl (WR (1,4) ,WR (1,5) ,WR (1,6) ) ) 1.GT.QZ) GO TO 8 2 1 WRITE (6, 50) J,T, (WR(I,1) , WR (1,4) ,I=1,KL) 50 FORMAT (' R (',12,•)•,F10.3,45X4(F7.3,F8„3)) WRITE(6,51) (WR (1,2) ,WR (1,5) ,1=1 ,KR) 51 FORMAT (1X4 (F7.3,F8.3)) WRITE(6,52) (WR (1,3) ,WR (1,6) ,1=1 ,KS) 52 FORMAT (•+ •,60X4 (F7.3,F8.3)) 8 CONTINUE 2 CONTINUE STOP END - 93 - APPENDIX I I I * The m a g n e t i c r o t a t i o n s p e c t r u m ( m . r . s . ) o f a gas i s a s p e c - t rum o f t h e l i g h t t r a n s m i t t e d by a gas p l a c e d between c r o s s e d p o l a r i z e r s and w i t h a m a g n e t i c f i e l d a c t i n g upon the gas i n a d i r e c t i o n p a r a l l e l to t he p r o p a g a t i o n o f the l i g h t . The r o t a t i o n o f the p l a n e o f p o l a r i z a t i o n i s p r o p o r t i o n a l to the p r o d u c t o f the magne t i c f i e l d s t r e n g t h t imes the p a t h l e n g t h t i m e s the d e n s i t y o f t he g a s . The m a g n e t i c f i e l d removes the s p a t i a l d e g e n e r a c y o f the t o t a l a n g u l a r momentum, J o f t he m o l e c u l e . Hence , J and the a s s o c i a t e d mag - n e t i c moment, u a r e q u a n t i z e d a l o n g the m a g n e t i c f i e l d d i r e c t i o n i n t o 2J+1 componen t s , i . e . Mj. = J , J - 1 , - J . T h i s i s m a n i f e s t e d as a Zeeman b r o a d e n i n g o f t he r o t a t i o n a l l i n e s i n an e l e c t r o n i c s p e c t r u m . Because r i g h t and l e f t c i r c u l a r l y p o l a r i z e d l i g h t i s s c a t t e r e d by p o s i t i v e and n e g a t i v e Mj. componen t s , r e s p e c t i v e l y , the w ings o f a Zeeman b roadened l i n e show p o s i t i v e o r n e g a t i v e r o t a t i o n o f t he p l a n e o f p o l a r i z a t i o n o f t r a n s m i t t e d l i g h t , as o b s e r v e d t h r o u g h c r o s s e d p o l a r i z e r s . The s t r e n g t h o f t he m . r . s . e f f e c t i s d e t e r m i n e d by t h e magn i tude o f the m a g n e t i c moment, u , a n d , s i n c e o n l y e l e c t r o n o r b i t a l and e l e c t r o n s p i n a n g u l a r momenta g e n e r a t e s i g n i f i c a n t m a g n e t i c moments, o n l y o r b i t a l l y d e g e n e r a t e o r s p i n m u l t i p l e t e l e c t r o n i c s t a t e s g i v e an o b s e r v a b l e m a g n e t i c r o t a t i o n s p e c t r u m . R e f e r e n c e s (51,52).

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