chapter 1 - theory of vibrational spectroscopy

7/28/2019 Chapter 1 - Theory of Vibrational Spectroscopy

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C H A P T E R 1Th eory of V ibrational SpectroscopyI . T h e o r yI I. E x a m p l e s o f M o l e c u l a r S t r u c t u r e

A . L i n e a r m o l e c u l e s : IA ~ O, IB - I cB . S p h e r i c a l T o p M o l e c u l e s : IA -- I 8 -- I cC . S y m m e t r i c To p M o l e c u l e s

1. Pro la te : IA < I B -- I c2 . O b l a t e Top: IA ~ I 8 < I c

D . A s y m m e t r i c T op M o l e c u l e s : IA 5~ I B ~ I c (w he re IA < I 8 < I c,a n d t h e r o t a t i o n a l c o n s t a n t s a r e o r d e r e d A > B > C )

I I I . P r e s s u r e Ef f e c tI V. T e m pe r a t u r e Ef f e c tV . V a p o r - P h a s e v s C o n d e n s e d IR S p e c t r aV I . F e r m i R e s o n a n c e ( E R . ) a n d O t h e r F a c t o r sR e f e r e n c e s

F i g u r e sF i g u r e 1 - 1 9 ( 3 ) F i g u r e 1 - 9 17 ( 4 )F i g u r e 1 - 2 1 0 ( 3 ) F i g u r e 1 - 1 0 1 8 ( 4 )F i g u r e 1 - 3 1 1 ( 3 ) F i g u r e 1 - 11 1 9 ( 4 )F i g u r e 1 - 4 1 2 ( 3 ) F i g u r e 1 - 1 2 2 0 ( 4 )F i g u r e 1 - 5 1 3 ( 3 ) F i g u r e 1 - 1 3 2 1 ( 5 )F i g u r e 1 - 6 1 4 ( 3 ) F i g u r e 1 - 1 4 2 2 ( 5 )F i g u r e 1 - 7 1 5 ( 3 ) F i g u r e 1 - 1 5 2 3 ( 5 )F i g u r e 1 - 8 1 6 ( 4 ) F i g u r e 1 - 1 6 2 4 ( 6 )

* N u m b e r s i n p a r e n t h e s e s i n d i c a t e i n - t e x t p a g e r e f e r e n c e .


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2 Theory of Vibrat iona l Spectroscopyspectra have been presented in Reference (5). The infrared and Raman metho ds are based on thefact that within any molecule the atoms vibrate with in a few definite, sharply defined frequenciescharacteristic of the molecule. These vibrational frequencies occur in the region of theelectromagnetic spec trum 13333 cm -1 to 50 c m - 1 and beyond. Only those molecular vibrationsproducing a dipole-moment change are IR active, allowed in the IR, and only those molecularvibrations producing polarization of the electron cloud are Raman active, allowed in the Raman.In the vapor-phase, molecules are free to rotate in three-dimensional (3D) space. The molecularrotational moment s of inertia are governed by molecular geometry, and the atomic mass of eachatom in the molecule together with their relative spatial positions within the molecule.Therefore, in the vapor-phase, molecules undergo transitions between quantized rotationstates as well as quantized vibrational transitions. The result is that a transition between theground state and the first excited state of a normal mode is accompanied by a manifold ofrotational transitions. This leads to a complex rotation-vibration band for every IR activemolecular vibration. Overtones are also IR active for molecules without a center of symmetry,and they result from transitions between the ground state and the second excited state of anormal vibration. Combination tones result from simultaneous transitions from the ground stateto the first excited state of two or more normal vibrations. Both combination tones and overtonesare also accompanied by manifold rotational transitions. In the liquid or sol ution phase, rot ationof the molecule in space is restricted. Therefore, the rotation-vibration bands are "pressurebroadened," and do not exhibit the sharp manifold rotational translational lines.

The number of molecular vibrations allowed in the IR or R for a given molecule is governedby the number of atoms in the molecule together with its molecular geometry. For nonlinearmolecules, the total number of normal vibrations is determine d by the equati on 3N-6, where N isthe number of atoms in the molecule. Because the molecules are free to vibrate, rotate, andtranslate in 3D space, N is multiplied by 3. The number 6 is subtracted because the number ofpossible molecular vibrations is not determined by rotation and translation of the molecule. Forlinear molecules, the total number of normal vibrations is determined by equation 3N-5.

In order to determine the active IR and Raman normal vibrations for any molecule, one has toapply a method known as Group Theory (1-4). Application of Group Theory also allows thedetermination of which overtones and combination tones are active in either the IR or Raman.

Pure molecular rotation transitions are also IR active, and they occur in the IR spectrum in theregion below 600 c m - 1 for small molecules having a permanent dipole, such as H20, NH3, PH3, etc.

In the vapor-phase, interpretation of the rotation-vibration bond contour is helpful in theelucidation of molecular structure. Band contours result from a combination of molecularsymmetry and the moments of inertia IA, IB, and I c about three mutua lly perpe ndic ular axes.

I I. E X A M P L E S O F M O L E C U L A R S T R U C T U R E


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Var iable s in Data Inte r pr e tat ion 3N i t r o g e n o x i d e , N O ;C a r b o n d i o x i d e , O = C = O ;C a r b o n d i s u l f i d e , S = C = S ; a n dA c e t y l e n e , H - C ~ C - H .In t h e ca s e o f l i n ea r m o l ecu l e s , IA i s t h e m o m e n t o f i n e r ti a a l o n g t h e m o l e c u l a r a x i s , a n d IB

a n d I c a r e m u t u a l l y p e r p e n d i c u l a r a x es . T h e i n f r a r e d a c t iv e s t r e t c h i n g v i b r a t i o n s p r o d u c e ad i p o l e - m o m e n t c h a n g e a l o n g t h e m o l e c u l a r s y m m e t r y a x i s , a n d t h e r e s u l t i n g r o t a t i o n - v i b r a t i o nb a n d c o n t o u r i s c a l le d a p a r a ll e l b a n d . I n t h is c a s e, t h e P a n d R b r a n c h e s a r e p r e d o m i n a t e w i t hn o c e n t e r Q b r a n c h .

F i g u r e 1 .1 s h o w s t h e I R v a p o r - p h a s e s p e c t r u m o f h y d r o g e n b r o m i d e . T h e P b r a n c h o f H B ro c c u r s i n t h e r e g i o n 2 3 0 0 - 2 5 5 0 c m - 1 a n d t h e R b r a n c h o c c u r s i n t h e r e g i o n 2 5 0 0 - 2 7 2 5 c m - 1 .F i g u r e 1 . 2 s h o w s t h e I R v a p o r - p h a s e s p e c t r u m o f h y d r o g e n c h l o r id e . T h e P b r a n c h o f H C 1 o c c u r si n t he r e g io n 2 6 0 0 - 2 8 8 0 c m - 1 a n d t he R b r a n c h o c c u r s in t h e r e g io n 2 9 0 0 - 3 0 8 0 c m - 1 T h ero t a t i o n a l s u b b an d s p ac i n g s a r e c l o s e r t o g e t h e r fo r H Br t h an t h o s e fo r H C1 , an d t h i s i s b ecau s et h e i n d i v i d u a l r o t a t i o n s u b b a n d s i n t h e P a n d R b r a n c h e s a r e d e p e n d e n t u p o n t h e m o m e n t s o fi n e rt i a, a n d b e c o m e m o r e c l o se l y s p a c e d a s I B a n d I c b e c o m e l ar g er . N e i t h e r H B r n o r H C 1e x h i b i t s a c e n t r a l Q b r a n c h f o r t h e h y d r o g e n - h a l o g e n s t r e t c h i n g v i b r a t i o n .

F i g u r e 1 .3 s h o w s a n I R v a p o r - p h a s e s p e c t r u m f o r c a r b o n m o n o x i d e i n t h e r e g i o n 1 9 5 0 -2 3 0 0 c m - 1 . I n th i s ca s e th e P b r a n c h o c c u r s i n t h e r e g i o n 2 0 0 0 - 2 1 5 0 c m - 1 , a n d t h e R b r a n c ho c c u r s i n t h e r e g i o n 2 1 5 0 - 2 2 5 0 c m - 1 . B o t h t h e P a n d R b r a n c h e s e x h i b i t c l o se l y s p a c e d r o t a t i o ns u b b a n d s o f th e C O s t r e t c h i n g v i b ra t i o n , p r o d u c i n g e s s e n t i a ll y a s o l id c o n t i n u u m o f a b s o r p t i o nl ines.

F i g u r e 1 . 4 s h o w s a n I R v a p o r - p h a s e s p e c t r u m o f n i t r o g e n o x i d e . T h e N O s t r e t c h i n g v i b r a t i o ni s a s s ig n e d t o t h e p a r a l le l b a n d o c c u r r i n g i n t h e r e g i o n 1 7 6 0 - 1 9 7 0 c m - 1 . H o w e v e r , i t s h o u l d b en o t ed t h a t t h i s i s an ex cep t i o n a l ca s e fo r l i n ea r m o l ecu l e s , b ecau s e a cen t r a l Q b ran ch i s o b s e rv edn e a r 1 8 7 2 c m - 1 . T h i s e x c e p t i o n r e s u lt s f r o m t h e p r e s e n c e o f a n u n p a i r e d e l e c t r o n i n n i tr o g e no x i d e c a u s i n g a r e s u l t a n t e l e c t r o n i c a n g u l a r m o m e n t u m a b o u t t h e m o l e c u l a r a x i s , w h i c h g i v e sr is e t o a Q b r a n c h i n t h e p a ra l le l b a n d ( 1 ). T h e P b r a n c h s u b b a n d s o c c u r b e l o w 1 8 7 2 c m - 1 , a n dt h e R b r a n c h s u b b a n d s o c c u r a b o v e 1 8 7 2 c m - 1 . O t h e r w i s e , a b a n d w i t h t h i s c o n t o u r f o r l i n e a rm o l e c u l e s w o u l d b e c a l l e d a p e r p e n d i c u l a r b a n d .

F i g u r e 1 . 5 i s a v a p o r - p h a s e I R s p e c t r u m o f c a r b o n d i o x id e . T h e p e r p e n d i c u l a r b a n d f o r C O 2e x h ib i ts i ts Q b r a n c h n e a r 6 7 0 c m - 1 w i t h a P b r a n c h n e a r 6 5 6 c m - 1 a n d a n R b r a n c h n e a r6 8 0 c m - 1 T h i s C O 2 b e n d i n g v i b r a t i o n i s d o u b l y d e g e n e r a t e . T h e p a r a ll e l b a n d f o r t h ea n t i s y m m e t r i c C O 2 s t r e t c h i n g v i b r a t i o n o c c u r s i n t h e r e g i o n 2 3 0 0 - 2 4 0 0 c m - 1 . T h e P b r a n c ho c c u r s n e a r 2 3 5 0 c m - 1 a n d t h e R b r a n c h o c c u r s n e a r 2 3 6 0 c m - 1 .

F i g u r e 1 .6 is a n I R v a p o r - p h a s e s p e c t r u m o f c a r b o n d i s u lf id e . T h e P b r a n c h o f th e p a r a l le lb a n d o c c u r s n e a r 1 5 6 0 c m - 1 a n d t h e R b r a n c h o f th e p a r a l le l b a n d o c c u r s n e a r 1 5 4 0 c m - 1 f o rt h i s an t i s y m m et r i c CS2 s t r e t ch i n g v i b ra t i o n .


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4 Theory of V ibrational Spectroscopyfor ace ty lene a re the in -phase ( ~ C -H )2 s t r e tch ing v ib ra t ion , the C=--C s t r e tch ing v ib ra t ion , andt h e o u t - o f- p h a s e ( = C - H ) 2 b e n d i n g v i b r a t io n . A R a m a n a c ti v e fu n d a m e n t a l f o r C O 2 a n d C S2 i st h e s y m m e t r i c C O 2 a n d C S2 s t r e t c h i ~ r g v i b r a t i ~ . ~ C o m p a r i s o n o f t h e f re q u e n c y s e p a ra t i o nbe tw een the subb ands o f the P and R b ranch es sh ows tha t i t i s l e ss fo r CS2 than fo r CO2, and th i sis a resul t of a larger IB = Ic fo r CS2 com pared to CO2.

B . S P H E R I C A L T O P M O L E C U L E S " I A - - I B - - I cMolecu les in th i s c las s have T d sym m et ry , and exam ples a re m ethane and sym m et r ica l lysubs t i tu te d c a rbon te t r aha lides . In th i s case IR act ive fundam enta l s exh ib i t P, Q an d R b ranch esin the vapor -phase com parab le to tha t exh ib i t ed by perpend icu la r v ib ra t ions in l inear m olecu les .

F igure 1 .8 is an IR vapor -phase sp ec t rum fo r m eth ane . T he an t i sym m et r ic C H 4 s t r e tch ingv i b r a t io n i s t ri p l y d e g en e r a te , t h e p e r p e n d i c u l a r b a n d e x h i b it s t h e Q b r a n c h n e a r 3 0 2 0 c m - 1 ,t h e P b r a n c h i n t h e r e g i o n 2 8 5 0 - 3 0 0 0 c m - 1 , a n d t h e R b r a n c h i n t h e r e g i o n 3 0 4 0 - 3 1 8 0 cm - 1 .T he t r ip ly degenera te an t i sym m et r ic C H 4 bend ing v ib ra t ion a l so appear s as a perpend icu la rb a n d . T h e Q b r a n c h o c c u r s n e a r 1 3 0 3 c m - 1 , t h e P b r a n c h i n t h e r e g i o n 1 2 0 0 - 1 2 9 0 c m - 1 ,a n d t h e R b r a n c h i n t h e r e g io n 1 3 1 0 - 1 3 8 0 c m - 1 . N u m e r o u s s u b b a n d s a r e n o t e d i n t h e Pa n d R b r a n c h e s o f b o t h v i b r at i o n s. T h e s y m m e t r i c C H 4 s t r e tch ing v ib ra t ion i s on ly ac t ive in theR a m a n ( 2 9 1 4 c m - 1 ) , a n d t h e s y m m e t r i c C H 4 bend ing v ib ra t ion , t r ip ly degenera te , i s on lyR a m a n a c t i v e ( 1 3 0 6 c m - 1 ) . T h e a n t i s y m m e t r i c C H 4 s t r e tch ing v ib ra t ion , t r ip ly degenera te ,a n d t h e s y m m e t r i c C H 4 b e n d i n g v i b r a t i o n , d o u b l y d e g e n e r a t e , a r e b o t h I R a n d R a m a nactive.

F igure 1 .9 show s an IR vapor -phase sp ec t rum of ca rbon te t r a fluor ide . T he an t i sym m e t r ic C F 4s t r e tch ing v ib ra t ion i s t r ip ly degenera te , and i t s Q b ra nch i s no ted near 12 69 cm -1 . T hea n t i s y m m e t r i c C F 4 bend ing v ib ra t ion i s t r ip ly degenera te . I t s Q b ranch i s no ted near6 3 0 c m - 1 , a n d t h e P a n d R b r a n c h e s a r e n o t e d n e a r 6 1 9 c m - 1 a n d 6 5 0 c m - 1 , r e s pe c ti v el y.Because the m om ents o f ine r t i a a re la rge, the subban ds o f the P and R b ranch es a re so nar row lys p a c e d t h a t t h e P a n d R b r a n c h e s a p p e a r a s a c o n t i n u u m .

C . S Y M M E T R I C T O P M O L E C U L E S1. P ro la te : I A < IB = Ic ( e s s e n t i a l l y r o d s h a p e d )Molecules in th is c lass have C3v sym m et ry . E xam ples inc lude the m ethy l ha l ides , p ropyne , and1-ha lopropynes .


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Variables in Data Interpretation 5

T h e P a n d R b r a n c h e s o f t h e p a ra l le l b a n d s f o r th e s e m e t h y l h a l i d e s a r e g i v e n h e r e :

CH3C1 CH3Br CH3IBranch cm - 1 cm - 1 cm - 1 A s s i g n m en tP 2 95 2 2 98 0 2 9 8 0 s y m m e t r i c H 3R 2981 2985 2958 stretchingP 1346 1293 1 2 6 1 symmetric CH 3R 1366 1319 1235 ben dingP 713 598 518 c - x stretchingR 748 622 540

T h e p a r a l l e l b a n d s a r e n o n d e g e n e r a t e .T h e P , Q , a n d R b r a n c h e s o f t h e p e r p e n d i c u l a r b a n d s f o r t h e s e m e t h y l h a l i d e s a r e g i v e n h er e :

CH3C1 CH3Br CH3IBranch cm - 1 cm- 1 cm - 1 AssignmentP -~ 3000-3150 ~ 3020-3140 ~ 30 20 -3 14 0 antis ym me tr ic H3 stretchingQ --~ 1325-1600 ~ 1300-1600 ~ 13 00 -1 60 0 anti sym me tr ic H3 bendingR -~ 940-1120 "~ 850-1050 ~ 770-1000 CH3 rocking

T h e p e r p e n d i c u l a r m o d e s a r e d o u b l y d e g e n e r a t e .F i g u r e s 1 . 13 a n d 1 . 14 a r e I R v a p o r - p h a s e s p e c t r a o f 1 - b r o m o p r o p y n e a n d 1 - i o d o p r o p y n e ,r e s p e c t i v e l y . D e t a i l e d a s s i g n m e n t s f o r t h e s e t w o c o m p o u n d s a r e g i v e n i n R e f e r e n c e ( 6 ) .

2 . O b l a t e T o p " IA = I B < I c ( e s s e n t i a l l y d i s c s h a p e d )M o l e c u l e s i n t h is c l as s h a v e D 6h s y m m e t r y , a n d m o l e c u l e s w i t h t h is s y m m e t r y i n c l u d e b e n z e n e ,b e n z e n e - d 6 , a n d t h e h e x a h a l o b e n z e n e s , w h i c h c o n t a i n o n l y F 6 , C 1 6, B r6 , o r I6 . O b l a t e s y m m e t r i ct o p m o l e c u l e s e x h i b i t b o t h p a r a l le l a n d p e r p e n d i c u l a r b a n d s . P l a n a r m o l e c u l a r v i b r a t i o n s e x h i b i tp a r a l l e l b a n d s , a n d o u t - o f - p l a n e v i b r a t i o n s e x h i b i t p e r p e n d i c u l a r b a n d s . T h e s e c o m p l e xm o l e c u l e s e x h i b i t r el a ti v e ly s i m p l e I R v a p o r - p h a s e I R sp e c t ra , b e c a u s e t h e s e m o l e c u l e s h a v e ac e n t e r o f s y m m e t r y , a n d o n l y a f e w n o r m a l m o d e s a r e I R a c t iv e .


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6 Theory of V ibrational SpectroscopyD . A S Y M M E T R I C T O P M O L E C U L E S : I A ~ I B ~ I c ( W H E R EI A < I B < Ic , A N D T H E R O T A T I O N A L C O N S T A N T S A R EO R D E R E D A > B > C )Mol e c u l e s i n t h i s c l a s s w i l l e xh i b i t t ype A , B , a nd C ba nds p rov i d i ng t he d i po l e mome nt c ha ngedur i ng t he no rma l v i b ra t i on i s pa ra l l e l t o t he a , b , o r c a x i s , r e spe c t i ve l y . Mi xe d ba nd c on t oursd e s c r ib e d a s t y p e A B a r e e x h i b i t e d b y m o l e c u l e s w h e r e t h e d i p o le m o m e n t c h a n g e d u r i n g t h enor m a l v i b ra t i on i s no t e x a c t l y pa ra l l e l to t he a o r b sym m e t ry a x i s .

F i gu re 1 .16 i s a va po r -pha se IR spe c t ru m o f e t hy l e n e ox i de . Type B ba n ds e xh i b i t no c e n t ra lpe a k , a nd c l a ss i c t ype B ba nd s a re no t e d ne a r 1269 a nd 875 c m - 1 . F or t he 1269 c m - 1 b a n d t h e Pa n d R b r a n c h e s a r e a s s ig n e d n e a r 1 2 4 7 a n d 1 2 9 2 c m - 1 , respec t ive ly , and the Q I a n d Q II b r a n c h e sa r e a s s ig n e d n e a r 1 2 6 3 a n d 1 2 7 4 c m - 1 , r e s p ec t iv e ly . F o r t h e 8 7 5 c m - 1 b a n d , t h e P a n d Rb r a n c h e s a r e a s s i g n e d n e a r 8 4 8 a n d 8 9 4 c m - 1 , respec t ive ly , and the Q I a n d Q II b r a n c h e s a r ea s s i g n ed n e a r 8 6 9 a n d 8 8 1 c m - 1 , respec t ive ly . The 1269 c m - 1 ba nd i s a s s i gne d t o r i ng b re a t h i ng ,t h e 8 7 5 c m - 1 b a n d t o a r i n g d e f o r m a t i o n . T h e w e a k t y p e C b a n d w i t h a Q b r a n c h n e a r 8 2 0 c m - 1i s a s s i gne d t o CH 2 roc k i ng (7 ) .

I I I . P R E S S U R E E F F E C TW i t h i nc re a s i ng p re s su re t he re a re mo re f re q ue n t c o l l is i ons o f l i k e mo l e c u l e s , o r be t w e e n amo l e c u l e a nd a d i l ue n t ga s suc h a s n i t roge n o r he l i um, a n d t h i s ha s t he e f fe c t o f b ro a de n i ng t hev a p o r - p h a s e I R b a n d c o n t o u r s r e s u l t in g f r o m m o l e c u l a r r o t a t i o n - v i b ra t i o n . T h i s e f fe c t i s te r m e dp r e s s u r e b r o a d e n i n g . T h e i n d i v i d u a l s u b b a n d s ( o r li n e s) b e c o m e i n c r e a s i n g ly b r o a d d u e t ore s t r i c t e d ro t a t i on i n t he va por pha se due t o f r e q ue n t mol e c u l a r c o l l i s i ons . Unde r h i gh p re s su re ,t h e s u b b a n d s a r e c o m p l e t e ly b r o a d e n e d s o t h a t t h e m o l e c u l a r v i b r a t i o n s w i t h h i g h l y r e s t r i ct e dm o l e c u l a r r o t a t i o n p r o d u c e I R b a n d s h a p e s w i t h n o a p p a r e n t s u b b a n d s . T h u s , t h e s e p r e s s u r eb r o a d e n e d v a p o r - p h a s e I R b a n d s f o r v a r i o u s m o l e c u l a r s t r u c t u r e s h a v e s h a p e s c o m p a r a b l e t ot he i r IR ba n d sh a pe s ob se rve d i n t he i r ne a t l i q u i d o r so l u t i on pha se s . T h i s i s so be c a use , i n t hene a t l i q u i d o r so l u t i on pha se s , t he re a re f r e q ue n t c o l l i s i ons be t w e e n l i k e mol e c u l e s o r mol e c u l a rc o l li s io n s b e t w e e n s o l u te m o l e c u l e s a n d b e t w e e n s o l u t e a n d s o l v e n t m o l e c u l e s f o r m o l e c u l e s i nso l u t i on , w h i c h re s t r i c t mo l e c u l a r ro t a t i on o f t he se mol e c u l e s .

In o rde r t o me a su re t he i n t e ns i t i e s o f t he IR v i b ra t i ona l ba n ds fo r e t ha n e a nd e t ha ne -d6 i n t hev a p o r - p h a s e , t h e s a m p l e s w e r e p r e s s u r i z e d u p t o 5 0 a t m t o b r o a d e n t h e b a n d s ( 8 ).

IV . T E M P E R A T U R E E F F E C T


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Variables in Data Interpretat ion 7

H o t b a n d s a r e a l so t e m p e r a t u r e d e p e n d e n t , a n d c h a n g e i n t e m p e r a t u r e c a u s e s c h a n g e i n IRb a n d i n t e n s i t y ( 3 ) .

W h e n m o l e c u l e s e x i s t as r o t a ti o n a l c o n f o r m e r s ( r o t a m e r s ) , t h e y a r e a l so a f fe c t e d b y c h a n g e si n t e m p e r a t u r e , b e c a u s e t h e c o n c e n t r a t i o n o f th e d i f fe r e n t r o t a m e r s i s d e p e n d e n t u p o nt e m p e r a t u r e . T h e r e f o r e , i t i s e s s e n t i a l t o re c o r d I R s p e c t r a a t d i f f e r e n t t e m p e r a t u r e s i n c a s e sw h e r e m o l e c u l e s e x i s t a s r o t a m e r s i n o r d e r t o d e t e r m i n e w h i c h b a n d s r e s u l t f r o m t h e s a m er o t a m e r .

V . V A P O R - P H A S E V S C O N D E N S E D I R S P E C T R AT h e I R g r o u p f r e q u e n c ie s o f m o l e c u l e s a r e d e p e n d e n t u p o n p h y s i c a l p h a s e . T h e s e f r e q u e n c yd i f f e r e n c e s r e s u l t f r o m s o l u t e - s o l v e n t i n t e r a c t i o n v i a d i p o l a r i n t e r a c t i o n o r f r o m w e a k i n t e r -m o l e c u l a r h y d r o g e n b o n d i n g . L a r ge f r e q u e n c y d i ff e re n c e s , a s la r g e as 4 0 0 c m - 1 , r e s u l t f r o ms t r o n g i n t e r m o l e c u l a r h y d r o g e n b o n d i n g b e t w e e n m o l e c u l e s o r b e t w e e n s o l u t e a n d s o lv e n t .T h e s e e f f ec t s a r e a b s e n t i n t h e v a p o r p h a s e , e s p e c i a l ly a t t e m p e r a t u r e s a b o v e 1 8 0 ~ a t o r d i n a r yp r e s s u r e . T h e v i b r a t i o n a l f r e q u e n c y c h a n g e s w i l l b e e x t e n s i v e l y d i s c u s s e d i n l a t e r c h a p t e r s .

V l . F E R M I R E S O N A N C E ( E R . ) A N D O T H E R F A C T O R SS o m e m o l e c u l e s e x h i b i t t w o o r m o r e b a n d s i n a r e g i o n w h e r e o n l y o n e f u n d a m e n t a l v i b r a t i o n i se x p e c t e d , e x c l u d i n g t h e p r e s e n c e o f ro t a t i o n a l c o n f o r m e r s . I n t h i s ca s e F e r m i r e s o n a n c e b e t w e e na fu n d a m e n t a l a n d a n o v e r t o n e o r c o m b i n a t i o n t o n e o f t h e s a m e s y m m e t r y s p e c ie s i n te r a c ts . T h ec o m b i n a t i o n o r o v e r t o n e g a in s i n t e n s i ty a t t h e e x p e n s e o f t he i n t e n s i t y o f t h e f u n d a m e n t a l . T h er e s u l t i s t h a t o n e b a n d o c c u r s a t a h i g h e r f r e q u e n c y a n d o n e b a n d o c c u r s a t a l o w e r f r e q u e n c yt h a n e x p e c t e d d u e t o t h i s r e s o n a n c e i n t e r a c t i o n b e t w e e n t h e t w o m o d e s . L a n g s e t h a n d L o r d ( 9 )h a v e d e v e l o p e d a m e t h o d t o c o r r e c t f o r E R . ( 1 0 ) . 1 T h i s e q u a t i o n i s p r e s e n t e d h e r e :

W o - W a + W b 4- w a - - w b 9 Ia -- I--------~b2 2 I a + I b

w h e r e , W a a n d W b a r e t h e o b s e r v e d v i b r a t i o n a l f r e q u e n c i e s , I a a n d I b t h e i r b a n d i n t e n s i t ie s , a n dt h e t w o v a l u e s o f W o c a l c u l a te d b y t h e e q u a t i o n w i ll b e a p p r o x i m a t e l y t h e u n p e r t u r b e df re q u e n c ie s . T h e a m o u n t o f E R . i s d e p e n d e n t u p o n t h e u n p e r t u r b e d f r e q u e n c ie s o f t h ef u n d a m e n t a l a n d t h e c o m b i n a t i o n o r o v e r to n e . I f t w o b a n d s o f e q u a l i n te n s i t y a r e o b s e rv e d ,e a c h b a n d r e s u lt s f r o m a n e q u a l c o n t r i b u t i o n f r o m t h e f u n d a m e n t a l v i b r a t i o n a n d a n e q u a lc o n t r i b u t i o n f r o m t h e c o m b i n a t i o n t o n e o r o v e r t o n e . T h e c o m b i n a t i o n o r o v e r t o n e m a y o c c u ra b o v e o r b e l o w t h e f u n d a m e n t a l f re q u e nc y . I n t h e c a se i n w h i c h t h e b a n d s a r e o f u n e q u a li n te n s i ty , b o t h b a n d s a r e s ti ll a m i x t u r e o f b o t h v i b r a t i o n s b u t t h e s t r o n g e r b a n d h a s m o r e


8/24

8 Th e o r y o f V i b r a t i o n a l Sp e c t r o s c o p y

c a s e s w h e r e o n e n e e d s t o p e r f or m a n o r m a l c o o r d i n a t e a n a l y s is , o r w h e n c o m p a r i n g I R d at a o fc e rt a in c la s s es o f c o m p o u n d s w h e r e n o t a ll o f th e c o m p o u n d s s h o w e v i d e n c e f o r E R .

P ar am e t e r s s u c h as b on d f or c e c on s t an t s , b on d l e n g t h s , b on d an g l e s , f ie l d ef f e c ts , i n d u c t i v ee f f ec t s , an d r e s on an c e e f f ec t s are i n d e p e n d e n t o f p h ys i c a l p h as e an d t h e s e p ar am e t e r s ar e u s e f u li n t h e e l u c i d a t i on o f m o l e c u l a r s t r u c t u r e v i a IR s p e c t r a - s t r u c t u r e i n t e r p r e t a ti on .

R E F E R E N C E S1. Herzberg, G. (1945). Molecular Spectra and M olecular Structure II . Infrared and Ram an Spectra o f Polyatomic M ole-

cules, New Jersey: D. Van Nost rand Company, Inc .2. Wils on, E. B. Jr . , Decius, J . C. , and Cross, P. C. (19 55). Molecular V ibrations, New York: McG raw-Hi l l Book Co mpany,

Inc.3. Pot ts, W. J. Jr. (1 963 ). Chem ical Infrared Spectroscopy, New York: Joh n W iley & Sons , Inc.4. Co lthu p, N. B. , Daly, L. H. , and W iberley, S. E. (1990). Introduction to Infrared and Raman Spectroscopy, 3rd ed . ,

Boston: Academ ic Press.5. Nyquist , R. A. (1984). The Interpretation o f Vapor-Phase Infrared Spectra: Gro up Frequency Da ta, vol. 1, Philadelphia:

Sadher Research Labora tor ies , Divis ion of Bio-Rad L abora tor ies .6. Nyquist , R. A. (1965). Spectrochim Acta, 21, 1245.7. Lord, R. C. and Nolin, B. (1956). J . C hem . Phys ., 24, 656.8. Nyq uist , I . M., Mills, I. M., Person, W. B., and C rawford , B. Jr . (19 57). J . C hem . Phys ., 26, 552.9. Langseth, A. and Lord, R. C. (1948). Kg l. Danske Videnskab Selskab Mat-fys. Med d, 16, 6.

10. Nyquist , R. A. , Fouchea, H. A. , Hoffman, G. A. , and Hasha, D. L. (1991). Appl. S pectrosc., 45, 860.


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Variab les in Da ta In te rpre ta t ion 9

FIGURE 1 .1 In fra red vapor-phase spec trum for hydrogen bromide (5 -cm g lass ce ll wi th KBr windows : 60 0m m HgHBr).


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10 Theory of Vibrational Spectroscopy

FIGURE 1.2 Infrared vapor-phase spectrum for hydrogen chloride (5-cm glass cell with KBr windows: 200 mm Hg HC1,total pressure 600 mm Hg with N2).


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Var iab les in Da ta In te rp re ta t ion 11

FIGURE 1 .3 In f ra red vapor -phase spec t ru m fo r ca rbon mon oxide (5 -cm g lass ce l l w i th KBr windows: 400 mm Hg CO,t o ta l p r e s su r e 6 0 0 m m H g w i t h N 2 ) .


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12 Theory of Vibrational Spectroscopy

FIGURE 1.4 Infrared vapor-phase spectrum for nitrogen oxide, NO.


13/24

VaaenDaaInepao

1

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14/24

1

T

oVboSr

ez2oo~Dt~o~3rooeqoLcc3i.oDo


15/24

VaenDaaInepao

1

ez2oo~Doobt~oLooL!eLEro~oot.4kd


16/24

1

T

oVboSr

i~DbboL~OoLt~~L~~t~ot~0


17/24

VaaenDaaInepao

1

eZ2OO~Dg00ghOL2OOO~L00t~|OOL~00O~t~k


18/24

1

T

oVboSr

i~mr00rom2co00t~L|~z~~0t~~Qk


19/24

VaaenDaaInepao

1

.s=~oo~D~00oLGoo00ooE,ut~r"oo,Q0og


20/24

2

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ezoo~Dt1t~t~oLOorqokt~it~.~.o>.1~t3t~ot~>eL


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VaaenDaaInepao

2

eL)JOOOrt3(0t~.xOe


22/24

2

T

oVboSr

eeLooLrot~P


23/24

VaaenDaaInepao

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,eoco~~DL)~o

oroo~ot~14

,Qr~oogh

do_t~


24/24

2

T

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~o~Do0ooooL~QthoL00tho00t~og

chapter 1 - theory of vibrational spectroscopy

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