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LARGE FINITE SYSTEMS

P R O C E E D I N G S O F T H E T W E N T I E T H J E R U S A L E M S Y M P O S I U M O N

Q U A N T U M C H E M I S T R Y A N D B I O C H E M I S T R Y H E L D I N

J E R U S A L E M , I S R A E L , M A Y 1 1 - 1 4 , 1 987

Edited by

J O S H U A J O R T N E R

Department of Chemistry, University of Tel-Aviv, Israel

A L B E R T E P U L L M A N

and B E R N A R D P U L L M A N

Institut de Biologie Physico-Chimique (Fondation Edmond de Rothschild), Paris, France

D. R E I D E L P U B L I S H I N G C O M P A N Y

A M E M B E R O F T H E K L U W E R ^ · " A C A D E M I C P U B L I S H E R S G R O U P

D O R D R E C H T / B O S T O N / L A N C A S T E R / T O K Y O

T A B L E O F C O N T E N T S

P R E F A C E IX

P . J . D E L A N G E and J . KOMMANDEUR / T h e Quantum Yield of N o n -R e s o n a n t Light Scat te r ing 1

E . C . LIM / Exci ted S ta tes of Molecular D imers 11

A. AMIRAV / Rotational Ef fects on Intramolecular Rad ia t ion less T rans i t ions - "The Story of Pyraz ine" 19

R. M A R Q U A R D T and M. Q U A C K / T h e D y n a m i c s of Polyatomic Mo lecu les During and After Coheren t Excitation 31

R. D. L E V I N E / S p e c t r a l F luctuat ions in Finite S y s t e m s 45

R. K O S L O F F , A. HAMMERICH a n d M. A . R A T N E R / T i m e Dependent Quantum M e c h a n i c a l Ca lcu la t ions of the D issoc ia t ion D y n a m i c s of the C lus te r H e n - l 2 53

W. W. D U L E Y / Proper t ies of L a r g e Finite S y s t e m s : Const ra in ts from Ast rophys ica l Observa t ions 67

H. L E V A N O N / Porphyrin D imers : T h e Photoexcited Triplet State a s a Probe for St ructure and D y n a m i c s 75

M. C A S T E L L A , P. C L A V E R I E . J . L A N G L E T . P h . MILL IE , F . PIUZZI and A. T R A M E R / Coupl ing Between Local ly Exci ted and C h a r g e T r a n s f e r S ta tes of Je t C o o l e d Molecular C o m p l e x e s 83

R. VAN Z E E , W. B . B O S M A , T, Z W I E R , M . C . DUVAL a n d B . S O E P / In termolecular Potential a n d Dissoc ia t ion of Exci ted State Mercury A m m o n i a C o m p l e x e s 101

J . F A R G E S , M . F , D E F E R A U D Y , 8 . R A O U L T a n d G , T O R C H E T / F rom F i v e - F o l d to Crysta l l ine Symmetry in L a r g e C l u s t e r s 113

T. P. MARTIN. T. B E R G M A N N and B. W A S S E R M A N N / C l u s t e r E n e r g y S u r f a c e s 121

vi T A B L E O F

R . S . B E R R Y / P h a s e C h a n g e s : T h e Interplay of D y n a m i c s a n d Equi l ibr ium in Fini te S y s t e m s

U . LANDMAN. R . N . B A R N E T T . C . L. C L E V E L A N D a n d J . J O R T N E R / E lec t ron Local izat ion in Water C l u s t e r s

S . L E U T W Y L E R a n d J U R G B O S I G E R / R a r e - G a s Solvent C l u s t e r s : O r d e r - D i s o r d e r T rans i t ions and Solvent S h e l l E f fec ts

R . J . L E R O Y . J . C . S H E L L E Y a n d D. E I C H E N A U E R / S p e c t r a . S t ruc ture a n d D y n a m i c s of S F 6 - ( A r ) n C l u s t e r s

G . KURISKI a n d A . NITZAN / L a s i n g a n d St imulated R a m a n P r o c e s s e s in S p h e r i c a l a n d Sphero ida l Droplets

O . E C H T . Μ . K N A P P . C . S C H W A R Z a n d Ε. R E C K N A G E L / E l e c t r o n At tachment to C l u s t e r s

H. H A B E R L A N D . C . L U D E W I G T . H - G . S C H I N D L E R a n d D. R. W O R S N O P / B e a m s of E l e c t r o n s Solvated in C l u s t e r s

N . R . K E S T N E R a n d S . DHAR / T h e o r e t i c a l S t u d i e s of S o d i u m Water C l u s t e r s : The i r Ionization a n d Excitat ion E n e r g i e s

D. S C H A R F . U. LANDMAN a n d J . J O R T N E R / Isomerizat ion in A l k a l i -Hal lde C l u s t e r s Induced by E lec t ron At tachment

D. THIRUMALA) / E lec t ron Local izat ion by Atomic a n d Molecular C l u s t e r s

E . B L A I S T E N - B A R O J A S . I. L. G A R Z O N a n d M. A V A L O S / St ructura l a n d Dynamica l Proper t ies of C l u s t e r s on a Subst ra te

D. J . D O N A L D S O N . S . S A P E R S . V. VAIDA a n d R. NAAMAN / Photodissoc la t lon of Methyl Iodide C l u s t e r s

U . E V E N . P . J . D E L A N G E . P . J . R E N K E M A a n d J . KOMMANDEUR / T h e Yield of E x o - E l e c t r o n s from C lus te r Bombardment of Metall ic S u r f a c e s

J . M. A N D R E / T h e Role of L a r g e O l igomers in Des ign ing Mater ia ls of Interest for their E l e c t r i c a l a n d Optoe lec t ron ic Proper t ies

E . S C H U M A C H E R a n d M. K A P P E S / i so la ted . B a r e Metal C l u s t e r s : A b u n d a n c e s and Ionization

J . K O U T E C K Y . V. B O N A C I C - K O U T E C K Y . I. B O U S T A N I . P. F A N T U C C I a n d W. P E W E S T O R F / E l e c t r o n i c S t ructure a n d B a s i c Proper t ies of S m a l l Alkali Metal C l u s t e r s

T A B L E O F C O N T E N T S V I I

K . D . B I E R . T . L . H A S L E T T . A . D . KIRKWOOD and M. MOSKOVITS / L a s e r S p e c t r o s c o p y of Matr ix- Isolated C l u s t e r s : Diatomic and Tr la tomlc M a n g a n e s e 319

A. NITZAN / Sma l l D ie lect r ic C l u s t e r s : S i ze and S h a p e D e p e n d e n c e of

Photophysica l and P h o t o c h e m i c a l Proper t ies 333

F . H E N S E L / F lu ids That Exhibit C h a n g e s in E l e c t r o n i c Structure 3 4 5

M. S H A P I R O and T . S E I D E M A N / C o h e r e n t Control and L a s e r C a t a l y s i s of C h e m i c a l R e a c t i o n s 361

J . M. D R A K E . J . K L A F T E R and P. LEVITZ / S tud ies on the Structure of Porous S i l i c a s : T h e F r a c t a l D i l emma 379

E . R I E D L E / D o p p l e r - F r e e S p e c t r o s c o p y , an Opportunity for State S p e c i f i c Investigat ions in L a r g e Mo lecu les 387

INDEX O F S U B J E C T 3 9 9

DO Ρ PLER-F REE SPECTROSCOPY, AN OPPORTUNITY FOR STATE SPECIFIC INVESTIGATIONS IN LARGE MOLECULES

Ε. R i e d l e I n s t i t u t für P h y s i k a l i s c h e und T h e o r e t i s c h e Chemie T e c h n i s c h e Universität München L i c h t e n b e r g s t r . *J D-8046 G a r c h i n g , West Germany

ABSTRACT. C o n v e n t i o n a l h i g h r e s o l u t i o n s p e c t r o s c o p y i n t h e gas phase a l l o w s t h e s e l e c t i o n o f s i n g l e v i b r o n i c s t a t e s o f l a r g e m o l e c u l e s . The e x t r e m e r o t a t i o n a l c o o l i n g i n a s u p e r s o n i c j e t can be o f g r e a t h e l p f o r t h i s s e l e c t i o n . H o w e v e r , many i n v e s t i g a t i o n s p o i n t t o t h e i m p o r t a n t r o l e o f r o t a t i o n - v i b r a t i o n c o u p l i n g f o r t h e dynamic b e h a v i o u r o f l a r g e m o l e c u l e s . S u b - D o p p l e r e x p e r i m e n t s l i k e D o p p l e r -f r e e t w o - p h o t o n s p e c t r o s c o p y p e r m i t t h e n e c e s s a r y r e s o l u t i o n o f s i n g l e r o v i b r o n i c t r a n s i t i o n s . I t i s d e m o n s t r a t e d f o r t h e e x a mple o f benzene, t h a t e x p e r i m e n t s can now be p e r f o r m e d , w h i c h c o m p l e t e l y r e s o l v e t h e r o t a t i o n a l s t r u c t u r e o f t h e v i b r o n i c bands and p e r m i t t h e measurement o f t h e l i n e w i d t h and t h e decay b e h a v i o u r o f s i n g l e r o v i b r o n i c s t a t e s . These i n v e s t i g a t i o n s l e a d t o a d e t a i l e d u n d e r s t a n d i n g o f t h e i n f l u e n c e o f r o t a t i o n on t h e s p e c t r o s c o p y and t h e dynamic s o f t h e benzene m o l e c u l e .

1. INTRODUCTION

S p e c t r o s c o p y i s t h e p r i m e s o u r c e o f i n f o r m a t i o n on t h e e n e r g y l e v e l s , t h e s t r u c t u r e and t h e dynamic b e h a v i o u r o f m o l e c u l e s . E s p e c i a l l y h i g h r e s o l u t i o n o p t i c a l s p e c t r o s c o p y has c o n t r i b u t e d a l a r g e d e a l t o t h e p r e s e n t u n d e r s t a n d i n g o f m o l e c u l a r s y s t e m s . For l a r g e m o l e c u l e s t h e o b t a i n a b l e r e s o l u t i o n i n c o n v e n t i o n a l s t u d i e s i s p r i n c i p a l l y l i m i t e d by t h e D o p p l e r - b r o a d e n i n g i n t h e gas phase. T h i s p r e v a i l s i n most cases t h e o b s e r v a t i o n o f s i n g l e r o v i b r o n i c t r a n s i t i o n s . The a d d i t i o n a l p r o b l e m o f h o t band c o n g e s t i o n and e x t e n s i v e r o t a t i o n a l iη homo geneous b r o a d e n i n g was p a r t i a l l y o v ercome by t h e use o f s u p e r s o n i c j e t s and t h e i r l ow r o t a t i o n a l and v i b r a t i o n a l t e m p e r a t u r e s . H o w e v e r , s t i l l t h e v a s t m a j o r i t y o f a l l dynamic i n v e s t i g a t i o n s o f l a r g e m o l e c u l e s i s o n l y a b l e t o s t u d y s i n g l e v i b r o n i c l e v e l s (SVL) i n s t e a d o f s i n g l e r o v i b r o n i c l e v e l s (SRVL).

387 J. Jortner et al. (eds.), Large Finite Systems, 387-398. © 1987 by D. Reidel Publishing Company.

388 Ε. R I E D L E

I n r e c e n t y e a r s d i f f e r e n t D o p p l e r - f r e e t e c h n i q u e s were d e v e l o p e d t o i n c r e a s e t h e r e s o l u t i o n beyond t h e l i m i t s e t by t h e D o p p l e r - b r o a d e n i n g and s u c c e s s f u l l y t e s t e d f o r a t o m i c s y s t e m s and s m a l l m o l e c u l e s / 1 / . The a p p l i c a t i o n o f t h e s e t e c h n i q u e s t o t h e s t u d y o f l a r g e m o l e c u l e s i s n o n t r i v i a l due t o t h e l a r g e number o f t h e r m a l l y p o p u l a t e d l e v e l s and t h e c o m p l e x i t y o f t h e i r s p e c t r a . However, r e c e n t l y a number o f i n v e s t i g a t i o n s have shown, t h a t t e c h n i q u e s l i k e D o p p l e r -f r e e t w o - p h o t o n s p e c t r o s c o p y / 2 / , s p e c t r o s c o p y i n h i g h l y c o l l i m a t e d m o l e c u l a r beams / 3 / , iηtermodulated f l u o r e s cence / 4 / and s a t u r a t i o n s p e c t r o s c o p y / 5 / r e n d e r r o t a t i o -n a l l y r e s o l v e d s p e c t r a even f o r t h e s e m o l e c u l e s . I n a d d i t i o n t o t h e r o t a t i o n a l l y r e s o l v e d s p e c t r a a l s o l i n e w i d t h measur e m e n t s / 6 / and decay t i m e m easurements / 7 , 8 / o f s i n g l e r o v i b r o n i c s t a t e s were o b t a i n e d and even t h e measurement o f e m i s s i o n s p e c t r a o f t h e s e s t a t e s seems now p o s s i b l e . The e x p e r i m e n t a l a r r a n g e m e n t s needed f o r t h e s e i n v e s t i g a t i o n s and t y p i c a l r e s u l t s , t h a t show t h e i m p o r t a n c e o f such u l t r a h i g h r e s o l u t i o n e x p e r i m e n t s , w i l l be d i s c u s s e d f o r t h e example o f D o p p l e r - f r e e t w o - p h o t o n s p e c t r o s c o p y o f benzene .

2 . CW DOPPLER-FREE TWO-PHOTON SPECTROSCOPY

2 . 1 . The e x p e r i m e n t a l s e t up

The r e c o r d i n g o f D o p p l e r - f r e e t w o - p h o t o n s p e c t r a i s based on t h e s i m u l t a n e o u s a b s o r p t i o n o f two p h o t o n s f r o m c o n t e r -p r o p a g a t i n g l i g h t beams o f an e x t r e m e l y n a r r o w band t u n a b l e l a s e r / 9 / . C o n t r a r y t o t h e D o p p l e r - b r o a d e n e d a b s o r p t i o n o f two p h o t o n s f r o m one l a s e r beam, t h e D o p p l e r - s h i f t o f t h e tw o p h o t o n s b a l a n c e s i t s e l f e x c a c t l y f o r t h i s s i t u a t i o n and a D o p p l e r - f r e e s p e c t r u m c an be o b s e r v e d . S i n c e t h e a b s o r p t i o n p r o b a b i l i t y i n t h e t w o - p h o t o n p r o c e s s i s v e r y weak and depends q u a d r a t i c a l 1 y on t h e l a s e r i n t e n s i t y , a d r a m a t i c i n c r e a s e i n s i g n a l i s o b s e r v e d i f t h e e x p e r i m e n t i s n o t p e r f o r m e d by s i m p l e ba c k r e f 1 e c t i ο η o f t h e l a s e r beam b u t r a t h e r w i t h i n t h e s t a n d i n g wave f i e l d o f an e x t e r n a l r e s o n a t o r / 6 , 1 0 , 1 1 / . The e x p e r i m e n t a l s e t up d e r i v e d f r o m t h i s c o n s i d e r a t i o n a nd used i n o u r e x p e r i m e n t s i s shown i n f i g . 1 and has been d e s c r i b e d i n d e t a i l / 6 , 1 2 / ·

The h i g h s p e c t r a l r e s o l u t i o n ( 1 MHz) i s p r o v i d e d by a cw r i n g l a s e r sytem ( C o h e r e n t CR 6 9 9 / 2 1 ) pumped by t h e v i o l e t l i n e s o f a K r + l a s e r (CR 3 0 0 0 K UV) and p r o v i d i n g t y p i c a l l y 3 0 0 mW l a s e r power a r o u n d 5000 A w i t h C o u m a r i n 1 0 2 d y e . The benzene c e l l i s p l a c e d w i t h i n t h e c o n c e n t r i c e x t e r n a l r e s o n a t o r ( m i r r o r s o f 7 0 % and 9 9 % r e f l e c t i v i t y ) , whose l e n g t h i s l o c k e d t o t h e l a s e r f r e q u e n c y . E x p e r i m e n t s a r e

D O P P L E R - F R E E S P E C T R O S C O P Y 389

' ι ι DYE LASER Η Kr» LASER

REFERENCE CAVITY

x.t

DC S DC S VAX 102

\ 1 —I 11/780

: EXT. CAVITY

F i g u r e 1. E x p e r i m e n t a l s e t up used f o r t h e r e c o r d i n g o f D o p p l e r - f r e e t w o - p h o t o n s p e c t r a o f benzene /6,12/.

t y p i c a l l y p e r f o r m e d w i t h benzene p r e s s u r e s below 1 t o r r t o a c h i e v e n e a r l y c o l l i s i o n l e s s c o n d i t i o n s . The f l u o r e s c e n c e e m i t t e d by t h e e x c i t e d m o l e c u l e s i s m o n i t o r e d w i t h a s i n g l e -p h o t o n - c o u n t i n g s y s t e m , i . e . f l u o r e s c e n c e e x c i t a t i o n s p e c t r a a r e r e c o r d e d . For t h e c a l i b r a t i o n o f t h e s p e c t r a t h e t r a n s m i s s i o n o f a h i g h l y s t a b l e 150 MHz Fabry-Perοt-Etalon i s r e c o r d e d s i m u l t a n e o u s l y w i t h t h e m o l e c u l a r s p e c t r u m . The f r e e s . p e c t r a l r a n g e o f t h i s e t a l o n has been measured t o 1 p a r t i n 10^.

2.2. The r o t a t i o n a l l y r e s o l v e d s p e c t r u m

As a t y p i c a l r e s u l t t h e f i r s t 6 cm**1 o f t h e D o p p l e r - f r e e s p e c t r u m o f t h e Q - b r a n c h o f t h e l 4 1 Q - b a n d o f C6H6 a t 396 5 6 . 90 cm" 1 i s shown i n f i g . 2 /1 3 , 1 ^ / . The s p e c t r u m c o n s i s t s o f 6 i n d i v i d u a l l a s e r s c a n s a n d t h e f r e q u e n c y s c a l e has been l i n e a r i z e d a c c o r d i n g t o t h e t r a n s m i s s i o n p a t t e r n o f t h e 150 MHz FPI /15/. The o b s e r v e d l i n e s c o r r e s pond t o w e l l r e s o l v e d s i n g l e r o t a t i o n a l l i n e s . The D o p p l e r -w i d t h o f 1.7 GHz w o u l d n o t a l l o w t h e r e s o l u t i o n o f t h e i n d i v i d u a l r o v i b r o n i c t r a n s i t i o n s s i n c e t y p i c a l l y 10 l i n e s a r e l o c a t e d w i t h i n t h e D o p p l e r - w i d t h . A l l t h e l i n e s can be a s s i g n e d w i t h i n t h e model o f a s e m i r i g i d s y m m e t r i c t o p . A f i t t o t h e o b s e r v e d l i n e p o s i t i o n s r e n d e r s t h e r o t a t i o n a l c o n s t a n t s o f t h e e x c i t e d s t a t e w i t h an a c c u r a c y o f 10""7 cm" 1 and t h e q u a r t i c c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s w i t h an a c c u r a c y o f 1 0 " 1 0 cm" 1 /15/. A s i m i l a r a c c u r a c y has even been r e a c h e d f o r t h e a s y m m e t r i c t o p m o l e c u l e benzene-d! /16/.

390 Ε. R I E D L E

IGHz] -220 -200 -180

F i g u r e 2. P a r t o f t h e D o p p l e r - f r e e room t e m p e r a t u r e s p e c t r u m o f t h e Q - b r a n c h o f t h e 1 4 1

0 - b a n d o f C6H6 / 1 3 . 1 1 * / . E v e r y l i n e c o r r e s p o n d s t o an i n d i v i d u a l r o v i b r o n i c t r a n s i t i o n . A l l t h e l i n e s have been a s s i g n e d .

The r e m a i n i n g d e v i a t i o n s ( r e s i d u a l s ) between t h e c a l c u l a t e d l i n e p o s i t i o n s a nd t h e o b s e r v e d ones a r e a b o u t 10 MHz. T h i s e x t r e m e a g r e e m e n t i s d e m o n s t r a t e d i n f i g . 3 f o r t h e l 4 1

0 - b a n d o f 1 , 3 » 5 - C 6 H 3 D 3 /15/. I t i s a g a i n s e e n , t h a t D o p p l e r - f r e e t w o - p h o t o n s p e c t r o s c o p y a l l o w s t h e c o m p l e t e r e s o l u t i o n o f t h e e l e c t r o n i c s p e c t r u m and t h e s p e c t r u m i s e x t r e m e l y w e l l r e p r o d u c e d w i t h t h e s i m p l e model o f a s e m i r i g i d s y m m e t r i c t o p .


F i g u r e 3. P a r t o f t h e D o p p l e r - f r e e s p e c t r u m o f t h e Q-branch o f t h e I 4 1 0 - b a n d o f 1,3,5-CßH3D3. The e x p e r i m e n t a l s p e c t r u m ( l o w e r t r a c e ) i s compared t o t h e c a l c u l a t e d s p e c t r u m ( u p p e r t r a c e ) o f a s e m i r i g i d s y m m e t r i c t o p /15/.

2.3. P e r t u r b a t i o n s i n t h e s p e c t r u m

I n some p a r t s o f t h e s p e c t r u m , a t h i g h e r r o t a t i o n a l e n e r g y , d i f f e r e n c e s between t h e e x p e r i m e n t a l s p e c t r u m and t h e c a l c u l a t e d one a r e o b s e r v e d . S i n g l e l i n e s o f t h e c a l c u l a t e d s p e c t r u m a r e n o t o b s e r v e d i n t h e e x p e r i m e n t a l one, i n s t e a d t w o weaker l i n e s a r e o b s e r v e d a t s l i g h t l y s h i f t e d p o s i t i o n s /17/. I f t h e s e p a i r s o f l i n e s a r e l a b e l e d w i t h t h e r o t a t i o n a l quantum numbers o f t h e m i s s i n g l i n e , t h e dependence o f t h e d e v i a t i o n s on t h e quantum number J o f t o t a l a n g u l a r momentum can be p l o t t e d f o r each v a l u e o f K, t h e quantum number o f t h e p r o j e c t i o n o f 3 on t h e f i g u r e a x i s o f t h e m o l e c u l e . The r e s u l t i s shown i n f i g . 4 f o r t h e Q-branch o f t h e I 4 l 0 - B a n d o f C6H6 /1 3 . 1 1 * / .

The t y p i c a l J-dependence o f t h e d e v i a t i o n s f o u n d i s t h a t o f an a v o i d e d c r o s s i n g . A c a r e f u l a n a l y s i s shows / 1 7 / , t h a t t h e o b s e r v e d p e r t u r b a t i o n s a r e caused by t h e c o u p l i n g o f l i g h t r o t a t i o n a l s t a t e s o f t h e 14 1 v i b r o n i c s t a t e t o

392 Ε. R I E D L E

ι ι ι I I I I I j I I I I ] ι ι ι ι ι Κ = 6

I ι ι ι ι ι I I I I J ι ι ι ι ι ι ι ι I I ι ι ι I 1 ι ι ι 1 I I I ]

-οοοοοο©οοοοοοβΟΟΟΟΟΟΟΟΟΟΟΟΟΟΟΟΟΟΟΟΟΟ0—

Κ=7 Κ=12 -οοοοοοοοοοοοοοοοοοοοοοοοοοοοοοο ο— - ο ο ο ο ο ο ο ο ο ο ο ο 6 ο 0 θ ο °0°oe^

Κ=8 οοοοο οοοοοοοοοοοοοοοοοοοοοοοοοο— \ Κ=16

- o o o o o o o o " ^ Ο ο ° ° ο ο ο * > ο ο ο

Κ=9 ° β ο » ο ο β ο

- o o o o o . o o o * ö ^ ^ Μ β -Κ=13

~ ° ο ο 0 · ο ί ^ - ? 0 0 » 0 0 < > ο ο ο β ο ^ 7 β

"ο Κ = 1 7 ο

°0OOOOOooOoOOOCOOOOO

- 2 GHz 0 0

Κ=10 Κ=14 0 """"»«»»«'«X'Oooooooooooo oooooooooooooooooöö^

Κ=18 β ο °ο οοοοο οοοοοοοοοοοοοοοοοΟ—_

— 2 GHz

Κ=19 — Ο Ο ΟΟΟ ΟΟ ΟΟΟΟΟ ΟΟΟΟΟΟΟΟΟΟ

• Κ=15 ° 0 ° ο 0 θ ο

οοοοοοοοοο ooööoT ; ί£££οροοβ

Κ=11 °ο Κ=20 οοοοοοοοοοοοοοοόοοοοοοο ""ο •

οοοοοοο οοοοοοοοοοοοοοο —

10 20 30 40 ι ι ι I ι ι ι ι I ι ι ι ι 1 ι ι ι ι I

J=10 20 30 40 I ι ι ι ι I ι ι ι ι I ι ι ι ι I ι ι ι ι

20 30 40 I I I I I I I I I I I I I I

F i g u r e 4. R e s i d u a l s ( c a l c u l a t e d - o b s e r v e d ) o f t h e f r e q u e n c i e s o f r o t a t i o n a l l i n e s i n t h e s p e c t r u m o f t h e 1 ̂ 1 ο band o f C5H5 as a f u n c t i o n o f t h e f i n a l s t a t e quantum number J* f o r s e v e r a l v a l u e s o f Κ 1 / 1 3 . 1 1 * / .

d a r k r o v i b r o n i c s t a t e s i n t h e e l e c t r o n i c S-j s t a t e . As a r e s u l t two e i g e n s t a t e s w i t h m i x e d v i b r o n i c c h a r a c t e r r e s u l t and b o t h can be seen i n t h e s p e c t r u m . These a r e t h e t w o l i n e s o b s e r v e d i n t h e e x p e r i m e n t a l s p e c t r u m . From t h e p o s i t i o n s o f t h e two l i n e s t h e c o u p l i n g m a t r i x e l e m e n t can be c a l c u l a t e d f o r each p a i r /18/. The c o u p l i n g shows a s t r o n g dependence on J and K. T h i s l e a d s t o t h e c o n c l u s i o n t h a t t h e o b s e r v e d c o u p l i n g must be caused by p e r p e n d i c u l a r C o r i -o l i s c o u p l i n g r a t h e r t h a n by a n h a r m o n i c o r p a r a l l e l C o r i o l i s c o u p l i n g /18/. T h i s r o t a t i o n a l dependence o f t h e v i b r o n i c n a t u r e o f t h e e i g e n s t a t e s can o n l y be d e t e r m i n e d f r o m r o t a -t i o n a l l y r e s o l v e d s p e c t r a .

2.4. Homogeneous l i n e w i d t h measurements

The b r o a d e n i n g o f t h e t r a n s i t i o n s o f l a r g e m o l e c u l e s due t o f a s t n o n r a d i a t i v e decay can n o r m a l l y o n l y be i n f e r r e d f r o m t h e d i f f u s e n e s s o f t h e v i b r o n i c bands /Ί9/. O n l y f o r e x t r e m e l y s t r o n g b r o a d e n i n g beyond t h e r e s i d u a l r o t a t i o n a l


c o n t o u r i n a s u p e r s o n i c j e t and t h e f a v o u r a b l e c o n d i t i o n o f w i d e l y spaced v i b r o n i c bands i s a measurement o f l i n e b r o a d e n i n g even f o r t h e GHz r e s o l u t i o n o f Doppl er - 1 i m i t e d s p e c t r o s c o p y p o s s i b l e /20/. However, s u c h an e x p e r i m e n t w i l l n o t r e v e a l t h e r o t a t i o n a l dependence o f t h e b r o a d e n i n g . On t h e o t h e r h and, t h e e x t r e m e l y h i g h r e s o l u t i o n (Δν below 10 MHz) o f our cw s e t up a l l o w s t h e measurement o f homogeneous l i n e w i d t h s o f s i n g l e r o v i b r o n i c t r a n s i t i o n s . T h i s has been shown f o r t h e 1 4 1

0 1 20 ~ f e a n d o f ^6^6 a t 3412 cm-1 v i b r a

t i o n a l e x c e s s e n e r g y /6/. I n t h i s band o n l y t h e Κ = 0 l i n e s a r e o b s e r v e d i n o u r r o t a t i o n a l l y r e s o l v e d f l u o r e s c e n c e e x c i t a t i o n s p e c t r a / 2 1 / , s i n c e a l l Κ Φ 0 s t a t e s decay v e r y r a p i d l y and no f l u o r e s c e n c e i s o b s e r v e d f r o m t h e s e s t a t e s . The r e m a i n i n g Κ = 0 l i n e s a r e a l s o b r o a d e n e d and t h e b r o a d e n i n g i s f o u n d t o i n c r e a s e f r o m 1.3 MHz f o r t h e J =» 0 s t a t e t o 46.1 MHz f o r t h e J = 14 s t a t e /6/. T h i s s t r o n g r o t a t i o n a l dependence o f t h e homogeneous l i n e w i d t h shows t h e i m p o r t a n c e o f r o t a t i o n a l l y r e s o l v e d o b s e r v a t i o n s f o r t h e d e t e r m i n a t i o n o f t h e decay b e h a v i o u r o f e x c i t e d s t a t e s of l a r g e m o l e c u l e s .

2.5. E m i s s i o n s p e c t r a

The v i b r o n i c c h a r a c t e r o f e x c i t e d m o l e c u l a r s t a t e s can be d e t e r m i n e d f r o m SVL e m i s s i o n s p e c t r a . However, t h e a n a l y s i s o f l i n e p o s i t i o n s shows, t h a t t h e v i b r o n i c c h a r a c t e r depends s t r o n g l y on t h e r o t a t i o n a l s t a t e o f t h e m o l e c u l e ( s e e a b o v e ) . T h e r e f o r e t h e SRVL e m i s s i o n s p e c t r u m i s needed f o r t h e i d e n t i f i c a t i o n o f t h e c o u p l e d b a c k g r o u n d s t a t e s . To o b t a i n such an e m i s s i o n s p e c t r u m , a s i n g l e r o v i b r o n i c s t a t e has t o be pumped i n a D o p p l e r - f r e e e x p e r i m e n t and t h e e miss i o n has t o be s p e c t r a l l y r e s o l v e d . T h i s r e q u i r e s , t h a t t h e dye l a s e r f r e q u e n c y r e m a i n s i n r e s o n a n c e w i t h t h e m o l e c u l a r t r a n s i t i o n f r e q u e n c y f o r a l o n g t i m e , t y p i c a l l y t o a p r e c i s i o n o f 1 MHz/h. I n a d d i t i o n enough f l u o r e s c e n c e i n t e n s i t y has t o be p r o d u c e d t o a l l o w s p e c t r a l r e s o l u t i o n . These p r o b l e m s have r e c e n t l y been s o l v e d i n o u r l a b o r a t o r y . F i r s t e m i s s i o n s p e c t r a o f s i n g l e r o v i b r o n i c s t a t e s w i l l be p r e s e n t e d i n a f o r t h c o m i n g p u b l i c a t i o n /22/.

394 Ε. R I E D L E

3. PULSED DOPPLER-FREE TWO-PHOTON SPECTROSCOPY

3 . 1 . The e x p e r i m e n t a l s e t up

For t h e i n v e s t i g a t i o n o f t h e decay o f i n d i v i d u a l l e v e l s p u l s e d e x c i t a t i o n o f t h e m o l e c u l e s has t o be used. The e x p e r i m e n t a l s e t up i s shown i n F i g . 5 /7,13/ - E x t r e m e l y n a r r o w band p u l s e d l a s e r l i g h t i s p r o d u c e d by p u l s e d a m p l i f i c a t i o n o f t h e cw l i g h t . W i t h t h r e e s t a g e s o f e x c i m e r l a s e r pumped a m p l i f i e r s we can g e n e r a t e l i g h t p u l s e s o f 500 KW peak power and n e a r l y F o u r i e r t r a n s f o r m l i m i t e d b a n d w i d t h . W i t h an a d d i t i o n a l p a r a s i t i c c a v i t y a r o u n d t h e se c o n d a m p l i f i e r t h e p u l s e l e n g t h can be v a r i e d b e t w e e n 2.5 ns and 10 ns and t h e f r e q u e n c y w i d t h a c c o r d i n g l y between 50 MHz and 180 MHz. A f t e r p a s s i n g t h r o u g h t h e sample c e l l t h e l a s e r beam i s r e f l e c t e d back i n t o i t s e l f t o a l l o w t h e D o p p l e r - f r e e a b s o r p t i o n . The two beams a r e c o u n t e r c l o c k w i s e c i r c u l a r l y p o l a r i z e d t o s u p p r e s s t h e D o p p l er-broadeηed b a c k g r o u n d / 2 3 / . The r e s u l t i n g U V - f 1 u o r e s c e n c e s i g n a l i s e i t h e r i n t e g r a t e d f o r t h e r e c o r d i n g o f s p e c t r a o r i t s t i m e b e h a v i o u r i s r e c o r d e d w i t h a t r a n s i e n t d i g i t i z e r . I t i s w o r t h m e n t i o n i n g t h a t i n D o p p l e r - f r e e t w o - p h o t o n a b s o r p t i o n a l l m o l e c u l e s r e g a r d l e s s o f t h e i r v e l o c i t y c o n t r i b u t e t o t h e o b s e r v e d s i g n a l . M o l e c u l e s a r e o n l y e x c i t e d t o one s i n g l e l e v e l i f t h e l a s e r f r e q u e n c y i s s e t t o a r e s o l v e d r o t a t i o n a l l i n e i n t h e s p e c t r u m r e g a r d l e s s o f t h e number o f l i n e s w i t h i n t h e D o p p l e r - w i d t h . T h i s a l l o w s t h e o b s e r v a t i o n o f t h e decay o f an i n d i v i d u a l l e v e l /7,8/.

opt.

Amplifier JlrTA Amplifier I inn *. I I I

Excimer Laser V Laser

\ -Plate

F i g u r e 5. E x p e r i m e n t a l s e t up f o r decay t i m e measurements o f i n d i v i d u a l r o t a t i o n a l l e v e l s o f S] b e n z e n e . F l u o r e s c e n c e decay i s o b s e r v e d a f t e r p u l s e d D o p p l e r - f r e e t w o - p h o t o n e x c i t a t i o n w i t h t h e a m p l i f i e d l i g h t o f t h e cw l a s e r ( t a k e n f r om r e f . 7 , 1 3 ) .


3.2. The r e s o l u t i o n a c h i e v e d w i t h p u l s e d e x c i t a t i o n

The r e s o l u t i o n a c h i e v e d w i t h t h e p u l s e d s e t up i s l i m i t e d by t h e l e n g t h o f t h e l i g h t p u l s e t o a b o u t 100 MHz. T h i s i s by one o r d e r o f m a g n i t u d e l o w e r t h a n t h e r e s o l u t i o n a c h i e v e d w i t h t h e cw s e t up. However, s t i l l most o f t h e r o t a t i o n a l l i n e s i n t h e t w o - p h o t o n s p e c t r a o f t h e Q - b r a n c h can be r e s o l v e d /23/> as can be seen f r o m t h e upper p a r t o f f i g . 6 / 7 / . The t o p s p e c t r u m shows p a r t o f t h e D o p p l e r - f r e e s p e c t r u m o f t h e l 4 1Q-band o f C6H6 as r e c o r d e d w i t h t h e cw s e t up and t h e löwer s p e c t r u m t h e same s p e c t r a l r a n g e as r e c o r d e d w i t h t h e p u l s e d s e t up. C l e a r l y t h e r e s o l u t i o n o f s i n g l e r o v i b r o n i c l i n e s can be s e e n .

Ί 1 I 1 I I ι I 1 I 1

0 200 400 0 200 400 tins]

F i g u r e 6. P a r t o f t h e Q-branch o f t h e I 4 10 - b a n d o f CßHß

under t h e h i g h r e s o l u t i o n o f t h e cw s e t up ( t o p ) and t h e l o w e r r e s o l u t i o n o f t h e p u l s e d s e t up ( m i d d l e t r a c e ) . At t h e b o t t o m t h e f l u o r e c e n c e decay c u r v e s measured f o r t h e two n e i g h b o u r i n g l i n e s ( J 1 κ f = s 2 1 1 7) a a n d J f K , = : 1 8 8 a r e shown on a h a l f - l o g a r i t h m i c s a c a l e . B o t h l i n e s a r e w e l l r e s o l v e d , even w i t h t h e p u l s e d s e t up. J 1 ^ t = (21 ι γ ) a i s one component o f t h e p e r t u r b e d z e r o o r d e r s t a t e J f K i » 2 1 i 7 , w h e r e a s J f j ( t = l 8 8 i s an u n p e r t u r b e d s t a t e ( t a k e n f r o m r e f . 7 ) .

396 Ε. R I E D L E

3 . 3 . Decay t i m e measurements

The r e s o l u t i o n o f s i n g l e r o v i b r o n i c l i n e s w i t h t h e p u l s e d s e t up a l l o w s t h e measurement o f t h e decay b e h a v i o u r o f s i n g l e r o v i b r o n i c s t a t e s . T h e s e m e a s u r e m e n t s h a v e been p e r f o r m e d f o r a number o f s t a t e s i n t h e 14 1 m a n i f o l d / 7 / . Two examples a r e shown i n t h e l o w e r p a r t o f f i g . 6. A l l d e c a y c u r v e s measured were f o u n d s i n g l e e x p o n e n t i a l . For s t a t e s f o u n d u n p e r t u r b e d i n t h e s p e c t r a l a n a l y s i s a c o n s t a n t d e c a y t i m e was f o u n d i n d e p e n d e n t o f t h e r o t a t i o n o f t h e m o l e c u l e . T h i s i s i n a g r e e m e n t w i t h t h e o r e t i c a l p r e d i c t i o n s f o r a i n t e r - s y s t e m - c r o s s i n g ( I S C ) decay i n t h e s t a t i s t i c a l l i m i t /24/.

The two decay c u r v e s shown i n f i g . 6, h o w e v e r , show a d i f f e r i n g decay b e h a v i o u r o f t h e u n p e r t u r b e d J f K t = 1 Ö 8 a n d t h e

p e r t u r b e d ( J ' κ T = 2 1 1 7 ) a s t a t e . The f a s t e r decay r e s u l t s f r o m t h e c o u p l i n g o f t h e l i g h t 14 1 r o t a t i o n a l s t a t e t o a d a r k s t a t e , t h a t d e c a y s much f a s t e r . T h r o u g h t h e above m e n t i o n e d m i x i n g o f t h e s t a t e s , t h e r e s u l t i n g e i g e n s t a t e has a decay t i m e i n t e r m e d i a t e between t h e d a r k and t h e l i g h t s t a t e . S i n c e t h e s p e c t r a l a n a l y s i s a l l o w s us t o d e t e r m i n e t h e d e g r e e o f m i x i n g o f t h e s t a t e s , we can d e t e r m i n e t h e decay t i m e o f t h e u n p e r t u r b e d d a r k s t a t e f r o m t h e measured decay t i m e o f t h e e i g e n s t a t e . I t i s f o u n d t o be much s h o r t e r t h a n t h e decay t i m e o f t h e 1 4 1 s t a t e . I n t h i s way does t h e measu r e m e n t o f t h e decay o f p e r t u r b e d s t a t e s a l l o w t h e d e t e r m i n a t i o n o f t h e d e c a y b e h a v i o u r o f s t a t e s n o r m a l l y n o t o b s e r v a b l e ( i . e . d a r k s t a t e s ) .

4. SUMMARY AND CONCLUSION

S u b - D o p p l e r t e c h n i q u e s can be used s u c c e s s f u l l y f o r t h e c o m p l e t e r o t a t i o n a l r e s o l u t i o n o f t h e e l e c t r o n i c s p e c t r u m o f l a r g e m o l e c u l e s . I n t h i s a r t i c l e t h i s has been d e m o n s t r a t e d f o r t h e example o f D o p p l e r - f r e e t w o - p h o t o n s p e c t r o s c o p y o f benzene. The r o t a t i o n a l r e s o l u t i o n i s i m p o r t a n t f o r t h e i n v e s t i g a t i o n o f dynamic p r o c e s s e s , as r o t a t i o n - v i b r a t i o n c o u p l i n g (seen as p e r t u r b a t i o n s i n t h e s p e c t r u m ) i n f l u e n c e s t h e decay b e h a v i o u r o f l a r g e m o l e c u l e s s i g n i f i c a n t l y . The e x t r e m e l y h i g h r e s o l u t i o n o f t h e cw s e t up a l l o w s t h e measur e m e n t o f t h e homogeneous l i n e w i d t h o f s i n g l e r o v i b r o n i c l i n e s . D o p p l e r - f r e e e x c i t a t i o n w i t h e x t r e m e l y n a r r o w band p u l s e d l a s e r l i g h t p e r m i t s t h e measurement o f t h e d e c a y t i m e o f s i n g l e r o v i b r o n i c s t a t e s .

The i n c r e a s e d s e l e c t i v i t y i n s u b - D o p p l e r s p e c t r o s c o p y w i l l l e a d t o a more d e t a i l e d u n d e r s t a n d i n g o f t h e d y n a m i c a l p r o c e s s e s i n l a r g e m o l e c u l e s . I n v i e w o f t h e p r e s e n t e d e x a mples o f s t r o n g r o t a t i o n a l e f f e c t s on t h e decay b e h a v i o u r


o f benzene, one s h o u l d be v e r y c a r e f u l i n t h e i n t e r p r e t a t i o n o f e x p e r i m e n t a l r e s u l t s w i t h l i m i t e d s p e c t r a l r e s o l u t i o n . The e x p e r i m e n t a l s e t up needed f o r s u b - D o p p l e r i n v e s t i g a t i o n s i s n o n t r i v i a l , b u t t h e e x i s t i n g p r o b l e m s can be o v e r come by c a r e f u l d e s i g n o f t h e e x p e r i m e n t . The w e a l t h o f a d d i t i o n a l i n f o r m a t i o n a v a i l a b l e f r o m e x p e r i m e n t s w i t h c o m p l e t e l y d e f i n e d m o l e c u l a r s t a t e s w i l l c e r t a i n l y j u s t i f y t h e i n v e s t e d e f f o r t .

5 . ACKNOWLEDGEMENT

The a u t h o r w i s h e s t o t h a n k P r o f . Neusser f o r c a r e f u l r e a d i n g o f t h e m a n u s c r i p t and h e l p f u l comments. F i n a n c i a l s u p p o r t by t h e D e u t s c h e F o r s c h u n g s g e m e i n s c h a f t i s g r a t e f u l l y acknowl e d g e d .

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