CHAPTER 1

PRINCIPLES OF VIBRATIONAL SPECTROSCOPY

1.1 INTRODUCTION

V l b r a t l o n a l s p e c t r o s c o p y h a s b e e n u s e d t o make

significant c o n t r l b u t l o n s i n many a r e a s of p h y s l c s and

c h e m i s t r y a s w e l l a s I n o t h e r a r e a s of s c l e n c e . I t s main

a p p l i c a t i o n s a r e : t o s t u d y t h e l n t r a r n o l e c u l a r f o r c e s ,

i n t e r m o l e c u l a r i o r c e s o r d e g ~ e e of a s s o c i a t i o n ~ n c o n d e n s e d

p h a a e s rind i n t h e d e t e r m l n a t l o n of m o l e c u l a r s y m n e t r l e s .

O t h e r applications l n c l u d e , t h e r d e n t l f i c a t i o n of f u n c t r o n a l

g r o u p s o r compound ~ d e n t l f l c a t l o n , d e t e r m l n a t l o n of t h e

s t r e n g t h of c h e r n l c a l bond a n d t h e calculation of

the r rnodyna rn lca l p r o p e r t i e s .

Modern m e t h o d s of s p e c t r o s c o p y . ~ n t h e c l t f e r e n t

r e g i o n s 01 r l e c t r o r n n g n e t ~ c s p e c t r u m h a v e p r o v l d e d

indispensable t o o l s f o r t h e i n v e s t l g a t l o n of m o l e c h ~ l a r

s t r u c t u r e . Among w h l c h , v l b r a t l o n a l s p e c t r o s c o p y i s

u n d o u b t e d l y t h c p o s t p o w e r i u l p h y s l c a l t e c h n i q u e f o r t h e

c l u c l d a t l o n of r ; o l e c u l a . s t r u c t u r e . ? h e l n t r o d u c t l o n of h i g h

intensity l a s ( * r e x c l t a t l o n s o u r c e s h a s l e a t o r a p i d

d e v e l o p m e n t of s o p h i e t i c a t e d l n s t r u r n e n t a t l o n . A r a p i d

development t o o k p l a c e 1 n l n f r a r e d s p e c t r o s c o p y i n d e s l g n l n g

and m a n u f a c t u r i n g of d o u b l e beam s p e c t r o p h o t o r n e t e r s and f a r -

i n f r a r e d s p e c t r o n l c t c r s . Due t o t h e c o m p l e n r e n t a r ) n a t u r e o f

i n f r a r e d a n d l<,~rnan s p e c t r o s c o p y , ~ t 1 s l n t e r e s t l n g t o

compare t h e two t e c h n r q u e s f o r s t u d y l n g t h e v l b r a t l o n a l a n d

r o t a t l o n a l e n e r g l e a o f m o l e c u l e .

I h e v l b r a t l o ~ ~ a l s p e c t r u m d e p e n d s on t h e l n t e n s l t y o f

r a d l a t l o n a b s o r b e d ( l n t h e c a s e o f l n f r a r e d absorption

s p e c t r a ) o r s c a t t e r e d ( ~ n t h e c a s e o! Raman s p e c t r a ) by a

g i v e n s u b s t a n c e . The q u a n t u m of e n e r g y a b s o r b e d o r

s c a t t e r e d b v t h e s u b s t a n c e 1 s g o v e r n e d by t h e w e l l known

r e l a t l o n E = h 0 . I h u s , t h e q u a n t u m e n e r g y t 1 s

d l r e c t l y proportional t o t h e f r e q u e n c y 3 a n d wave

n u m b e r g ( = 9 / 1 2 , u h e r c c 1 s t h e v e l o c l t y of l i g h t ) a n d

inversely p r o : i o r t l o n a i t o t h e u a v e l e n g t h h (= c / u ) . Kave

numbers a n d a a v c l e n g t h s a r c t r e q u e n t l y e m p l o y e d f o r t h e

d e s c r l p t l o n of l n f r a r e d and Rarcan s p e c t r a . A l t h o u g h t h e u s e

o f e l t h e r o i t h e t u o q u a n t l t l e s 1 s e q u a l l y ~ u s t l f l e d , wave

numbers a r e p r e f e r r e d f o r number of p r a c t i c a l r e a s o n s .

A c c o r d l n c t o q u a n t u m mechanics, t h e v l b r a t l o n a l e n e r g y

o f r n o l e r u l c s , i . e . , t h e e n e r g ) elated t o t h e o s c l l l a t l o n s

of a t o m l c n u c l e i , c a n a t t a l n o n l y c e r t a l n d l s c r e t e l e v e l s .

l h e m o l e c ~ ~ l r i c c c p t s o r r e l e a s e s e n e r g y d r s c o n : ~ n u o u s l ) l n

d l s c r e t c l u a r t a . I f t h e e n e r g y of t h r q u a n t a o f r a d l a t l o n

w h l c h 1 s e x c h a n g e d by a m o l e c u l e 1s determined, t h e n t h e

s e p a r a t !on o f two e n e r g y l e v e l s b e t w e e n w h i c h t h e t r a n s l t i o n

o c c u r s c a n be f o u n d . ?his 1 s t h e b a s l s f o r u n d r r s t a n d l n g t h e

applications of v ~ b r a t l o n a l s p e c t r o s c o p y .

1.2 R M M N SPECTROSCOPY

Kaman s c a t t e r l n g 1s one of t h e p r o c e s s e s result in^ l ~ o n l

t h e ~ n t e r a c t l o n o f r a d l a t l o n w l t h m a t t e r . A c h a r a c t e r i f i l I C

f e a t u r e o f Raman s c a t t e r l n g 1s t h e c h a n g e i n f r e q u e n c y 1 8 t

t h e s c a t t e r e d l l g h t . As d i s t i n c t f roln l u m i n e s c e n c e , wilt 1 I!

t h e f r e q u e n c y of t h e r e - e m l t t e d r a d l a t l o n r s a l s o c h a l , ~ ~ 4 1 ,

t h e s y s t e m i n Kaman s c a t t e r l n g 1 s n o t e x c i t e d f u r , , I I ~

m e a s u r a b l e l e n g t h o f t l m e t o h l g h e r e n e r g y l e v e l .

When i n c l d e n t l l g h t q u a n t u m 'hdO c o l l l d e s w l t l ~ a

m o l e c u l e ~ t c a n e l t h e r be s ~ a t t e r e d elastically I n W I I I ~ h

c a s e ~ t s e n e r g y r e m a l n s u n a l t e r e d ( H a y l e l g h s c a t t e r i n g ) Irr

l t c a n be s c a t t e r e d l n e l a s t l c a l l y I n w h l c h c a s e i t e l t l ~ ~ ~ r

g l v e s a p a r t o f ~ t s e n e r g y t o t h e m o l e c u l e o r t a k e s B I I I ! I Y Y

f r o m l t . I f t h e m o l e c u l e 1 s l n l t l a l l y a t s t a t e / I > w l t h ll le

e n e r g y t a n d a f t e r l n t e r a c t l o n w l t h n l o n o c h r o m a t l c r a d l a t ~ u n

of f r e q u e n c y J0 g o e s t o s t a t e / f > u l t h e n e r g y L f , l l le

c o n s e r v a t r o n of e n e r g y e n a b i e s us t o u r l t e :

w h e r e hd = Lf - E l , and h ( do ;Sf = h d 6 , t h e e n e r g v o f

t h e s c a t t e r e d p h o t o n .

I f E f = E l , ds = do ( H a y l e l g h Scattering) - h i 7 E l 1 a s =3,, - df1 ( S t o k e s )

Haman S c a t t e r l l i g L t ( t l , a s = & + 2

U 1 1

The Haman s h l f t b g l v e d l r e c t l y t h e e n e r g y d l i i e r e n c e s

o f t h e s y s t e m . ?he Haman l l n e s d l s p l a c e d t o w a r d s t h e s h o r t e r

f r e q u e n c l e s a r e c a l l e d s t o k e s l l n e s and t h o s e d l s p l a c e d

t o w a r d s t h e l o n g e r frequencies a r e c a l l e d a n t l - s t o k e s l l n e s .

Such s c a t t e r l n g of radiation w i t h c h a n g e s of f r e q u e n c y

was f l r s t discovered by C . V . Harnan and K.S. K r l s h n a n i n

l i q u i d s ( 1 ) . Very s h o r t l y a f t e r t h e p a p e r of Raman and

K r l s h n a n was p u b l i s h e d , G.S. L a n g s b e r g and L . I . Mande l s tam

( 2 ) i n R u s s l a r e p o r t e d t h e o b s e r v a t i o n of t h e s i m i l a r e f f e c t

i n q u a r t z . I h e e t f e c t had been p r e d i c t e d on t h e o r e t i c a l

g r o u n d s i n 1923 by A . Smekal ( 3 ) .

I n quan tum t h e o r y of s c a t t e r l n g , t h e l n t e n s l t y a r l s l n g

f rom a t r a n s l t l o n be tween s t a t e s I l > and i f > , u n d e r o r d ~ n a r y

c o n d i t i o n s of Raman s c a t t e r l n g e x p e r l m e r ~ t s , d e p e n d s on t h e

p o l a r i z a b l l i t y t e n s o r , whose components a r e g l v e n by ( 4 ) :

where I I > , I r > and I f > a r e i n i t l a l , l n t e r r n e d l a t e and

f i n a l s t a t e s of t h e m o l e c u l e r e s p e c t l v e l y : 1 p y l i r =

4flP'l r J a n d h e r e , $ 1 s t h e v e c t o r component of t h e e l e c t r l c

d l p o l e moment o p e r a t o r : % d o = i n c l d e n t pho ton e n e r g y ,

h a r f and hJr l a r e t h e transition e n e r g l e s be tneer . r--t f

and r 3 1 states; the sumnation 1s over all the states

r of the molecule except i or f.

F o r a particular transrtion t o be Raman actlve at least

oneeftkr 61% tensor components of the type [ a x y l f l must be

non-zero. The general condition for [ e x y I f i to be non-zero

I I that the product $ x l belongs t o a representation

w h i c h contalna the totally synmetric species, here v' and

are the time independent wave functions of final and

initial a t a t e s o t thk molecule, respectrvely. For the

vibrational Raman spectrum, the vibrational elgen functions

vv, and dv,, of the upper and lower states should be

aubatituted for $' and $. Then, a Raman transltlon between 9

two vibrational levels v i a n d v " 1s allowed, lf at least one *

of the rix products of the t y p e p v , xy qv,, 1s totally

rymnetrieal, i.e. remains unchanged for all the symnetry

operationr of the molecule.

F o r a fundamental vibrational transition, where rn the

initial rtate, all vibrational quantum numbers are zero and

in the final state only the j t h vibrational quantum number

har changed t o unlty3 S h e n for Raman actlvlty:

A rimple harmonlc wave function, (Q ) for the ground v3 I

rtate ( V , = O ) , is always totally symnetrlc and a srmple

harmonic wave functlon with v = 1 h a s the same symnetry I

species as the normal coordrnate Q ( 5 ) . Ikus the ~ n t e g r a l 3

in equation 1.3 1s totally s y m e t r l c if the product Q.xy 1s

totally symnetric. For a non-degenerate fundamental

vibration, this condition 18 satisfied if this vlbratlonal

mode has the same s y m n e t r y s p e c i e s as one of the six

product8 of type xx, xy,. .

1.2.1 Depolariration Ratio

The state of polarization of the Raman scattering

yields valuable information concerning the molecular

vibrations. An aspect of the Raman spectrum that dlffers

fundamentally from the lnfrared 1s the abillty to observe

band p o l a r l z a t ~ o n in llqulds and gases where the molecules

are randomly orrented. Slnce in a typlcal Raman experiment

the rcattering molecule 1s rotating, the observed scattering

will be the average of all orlentatlons of the molecule. To

express the scattering intensity in terms of the derived

p o l r r i z a b i l i t y tensor, ~t is necessary to flnd quantltles

which are invariant underrotatlon. It 1s posslble to

exprerr these invariants ~n terms of two quantitiea

arroeiated with the tensor,

Mean v a l u e

, a. a . Anisotropy y ' = d / r - * y y ) + (*ly -*=! ( 1 5 )

where '!. " (hij /6p )o i J

Then for 90' scattering, the d e p o l a r ~ z a t i o n ratlo f

representing the ratio of ~ n t e n s i t l e s scattered

perpendicular and parallel to the direction of the electrlc

vector E ir given by

2 a L

pn = 6 ~ ' / ( 4 5 q 1 +71' ) ( ' ' 6 )

Uring plane polarized lncldent radlatlon, such as Inner

radiation

I f Pp = 0,75, the llne 1s sald to be depolarized; 11

tp < 0.75, the llne 1s polarized and ? = 0, the llne 1s P

completely polarized.

For the symnetrlc vlbratlons, the slze of the elllpsold

changes but Its orlentatlon does not. This means that the

diagonal elements of the polarlzablllty ellipsoid change,

implying that N' changes and hence the llne must be

polarized i.e. p < 0.75. The antlsymnetrlc vlbratlons, on P

the other hand do not lead to a change ~n the slze

and henre N ' . Hence Haman llnes due to

antisynmetric vibrations are depolarlzed. Information of

this type can be of great use In determlnlng the symmetry

of vibrations.

1.3 INFRARED SPECTROSCOPY

The transitron moment for lnfrared absorptlon ~nvolves

the permanent dipole moment operator, lnstead of the lnduced

dipole moment operator as in the case of Raman scattering.

Therefore, the transjtion probablllty 1s proportional to the

where 3 ia the electrlc dipole moment operator. It can be

ehown that the transition moment has the same transformatlon

properties as

< +l*\i z , < j 1 ~ 1 l 7 and/or ( + I Z I ~ > ')

Ti-us, the lnf rared act ivlty of a non-degenerate fundamental

vibration Q requires, product of the type P j x , Q y or I Y Q,z

to be totally symnetrlc. lhat IS, the fundamental

vibratlondl modes whlch are In the same symnetry specles

with x , y or z vectors are lnfrared actlve.

The absorptlon of lnfrared radlatlon by a molecule can

be given in terms of the absorbance A , by

where IO and I are the Incident and transmitted lntensltles

of the abrorbing frequency, M 1s the transltlon moment

vector of the normal mode, M = a~ / d Q , and h is the

electric field vector of the incident beam at the absorbing

frequency. For a glven normal mode of vibration, the

tranrition moment vector has a definlte orlentatlon ln the

molecule. Conrequently, if the angle between M and E 1s 8 ,

2 the abrorbance is proportional to Cos 8 . In the ordered

molid rtate, the molecules are flxed and the d~rection of

the transition moment vector of each molecule has the same

orientation space. lhe absorbance of a given Infrared band

will then change, depending on 1) the dlrectlon of the

tranrltion moment vector of the particular normal mode wrth

reapect to the molecular axis and ir) the polarlzatlon 1 8 1

the electric vector ) f the lncident radlatlon. A maxlmum

absorbance wlll occur when the electrlc vector of the

r101arization llght 1s parallel to the dlrectlon of the

transition moment and no abeorptlon wlll occur when the two

vectors are perpendlcular. When measurements are made with

the electric vector parallel or perpendlcular to the

preferred directlon, a dichrolc ratlo R ,

R = A,, I AL (1.11)

can be m a r u r e d where A,, the absorbance for llnearly

polarized light.

1.4 MUTUAL EXCLUSION PRINCIPLE

F o r molecules with centre of symnetry, transitions that

are allowed In the Raman spectrum are forbidden in infrared

and conversely, transitions that are allowed In the infrared

rpectrurn are forbidden In Raman. That 1s in Raman effect,

only transltlons between states of same symnetry w i t h

respect t o centre of symnetry(i), can take place ( V g ,

uHu). However In the lnfrared, only transltlons between

states of opposlte symnetry wrth respect t o the centre of

symnetry are allowed ( g H u ) .

It is clear that all the components of electrlc dipole

moment p, change sign for a reflection at the centre of

s y m w t r y , whereas, the components of the lnduced drpole

4 moment w h i c h behave as the product of two components of p,

remain unchanged. Thus for a fundamental vlbrational

trrnrition, only the vlbrational modes(g) w h l c h are

eymnetric wlth respect t o the centre of s y m e t r y can be

Raman active and those are a n t i s y m e t r l c ( u ) w i t h respect t o

centre of symnetry can be infrared active if they also hold

the selection rule requirements.

1.5 INFRARED SPECTROMETER

Infrared spectroscopy 1s one o f the most l~~tuerful

analytical t e c h r , q u e s for chemical ~ d e n t l f l c a t l o n . I h l s

technique when coupled wlth intensity measurements may be

used for quantitative analysis. This method can solve many

problems in organic and rnorganlc chemistry. This technique

is based upon the simple fact that a chemlcal substance

shows marked selective absorption In the infrared spectrum.

The limitations imposed by early lnfrared

spectrometers, viz., restricted range, low sensltlvity and

poor sample preparation often gave diffuse and variable

spectra. But after several decades of technical advance and

much pioneering wor k on simple organlc and well

characterized synthetic mlnerals of known composrtlon, 1t

became clear that infrared spectroscopy could provlde a

wealth of information.

Conventional lnfrared spectrometer suffer from several

disadvantages in sensltlvity, speed and wavelength accuracy.

Most of the light from the source does not ln fact pass

through the sample to the detector, that 1s lost In the

narrownerm of the focuslng slits and results ~n poor

sensitivity. Slnce the spectrum takes minutes to record, the

method cannot be applied to fast process. Consequently, the

dispersive infrared spectrometers sufftr from wavelength

inaccuracies associated wlth the backlash In the mechanical

movemento, much as in the rotatlon of mlrrors and gratings.

An entirely different prlnclple 1s lnvolved In kourler

Transform Infrared (FTIR) Spectroscopy, which centers on a

Michelson Interferometer. Despite the developments ~n

inatrumentatron, the basic optlcal design originally used by

Michelson, is st111 prevalent.

FTIR spectrometer has, for the analysts, three major

advantages over conventional dispersive Infrared

spectrometers. Frrstly, as the radiation 1s not constralned

to pass through any sllt mechanrsm, ~t can ~ n t e r a c t with

much larger ramples than wlth a dispersive instrument whlch

i~ advantages In gettlng hrgh qualrty spectra from samples

that are inherently rather opaque.

Secondly, the accuracy of wavelength determlnatlon 1s

so high that computer averaging of spectra 1s easy, l.e., rt

is easy to enhance the slgnal to norse ratio of the spectra

allowing studles to be made of weak spectral features or of

dilute samples. Thirdly, as the scannlng of a spectrum 1s

very rapid, it 1s posrlble to record spectra very qulckly.

Fl'lR spectroscopy wlth l t s energy advantages, has made

it possible now, to obtaln spectra under conditrons

previously consrdercd dlfflcult or ~ m p o s s l b l e . New

accessorier have been developed just to take advantage of

the capabilities of the F'I technique.

1 .5 .1 SAMPLE HANDLING

The i n f r a r e d s p e c t r a may be o b t a r n e d f o r g a s e s , l l q u l d s

o r s o l i d s .

1 . S o l i d s a r e u s u a l l y examlned a s a m u l l , a pressed-disc,

o r a s a deposited g l a s s y f l l m . M u l l s a r e p r e p a r e d by

t h o r o u g h l y g r l n d i n g 2 - 5 rng o f a s o l i d I n a smooth a g a t e

m o r t a r . G r i n d l n g i s c o n t i n u e d a f t e r t h e a d d l t l o n of one o r

two d r o p s of m u l l l n g o i l . ' f h l s s u s p e n d e d p a r t l c l e s must be

l e s s t h a n Zpm t o a v o l d excessive scattering of r a d l a t r o n .

The m u l l 1 s examlned a s a t h l n f l l m be tween f l a t s a l t

p l a t e s . N u j o l 1 s comnonly used a s a m u l l r n g a g e n t .

The p r e s s e d - d l s c technique d e p e n d s on f a c t t h a t d r y ,

powdered KBr c a n be p r e s s e d under p r e s s u r e I n vacuo t o fo rm

t r a n s p a r e n t d l s c s . The sample 10.5-1.0rng) 1 s l n i t l a l l y rnlxed

w r t h a p p r o x i m a t e l y 100 rng of d r y , powdered KBr. I h e m l x t u r e

i s p r e s s e d w l t h s p e c l a l d l e s u n d e r a p r e s s u r e of 1 0 , 0 0 0 -

1 5 , 0 0 0 pounds p e r s q u a r e I n c h i n t o a t r a n s p a r e n t d l s c . l h e

q u a l i t y o f t h e s p e c t r u m d e p e n d s on t h e rn t l rnacy of t h e

m l x l n g and t h - r e d u c t L o n of t h e s u s p e n d e d p a r t l c l e s

t o 2pm o r l e s s .

D e p o s i t e d f i l m s a r e u s e f u l o n l y when t h e r n a t e r l a l can

be d e p o ~ i t e a from s o l u t l o n o r c o o l e d f rom a m e l t a s m l c r o

c r y s t a l s o r a s a g l a s s y f l l m . Good q u a l l t y s p e c t r a c a n be

o b t a i n e d f rom t h l n f i l m s of p o l y m e r s whlcn a r e c a s t e l t h e r

on s p e c t r a l p l a t e s o r on g l a s s o r some o t h e r s u b s t a n c e f rom

which t h e y c a n be p e e l e d and t h e n mounted i n t h e i n f r a r e d

beam. T h i s i s a v e r y s a t i s f a c t o r y method f o r s a m p l e s t h a t

a r e s o l u b l e i n a s o l v e n t t h a t 1 s relatively volatile.

2. L i q u i d r may be examined n e a t o r rn s o l u t i o n . Neat l i q u i d s

a r e examined be tween s a l t p l a t e s w i t h o u t a s p a c e r . P r e s s l n g

a l i q u i d sample be tween f l a t p l a t e s p r o d u c e s a f l l m of

0 .01 mn o r l e s s I n t h i c k n e s s , t h e p l a t e s b e r n g h e l d t o g e t h e r

by capillarity. S o l u t i o n s a r e h a n d l e d I n c e l l s of 0 . 1 t o

l.Omn t h i c k n e s s . A compensating c e l l , containing p u r e

s o l v e n t i s p l a c e d i n t h e r e f e r e n c e beam. The s p e c t r u m t h u s

o b t a i n e d i s t h a t of t h e s o l u t e e x c e p t I n t h o s e r e g l o ~ i r i n

which t h e s o l v e n t a b s o r b s s t r o n g l y . The s o l v e n t s e l e c t e d

must be d r y and r e a s o n a b l y t r a n s p a r e n t rn t h e r e g l o n of

i n t e r e s t .

1.6 RAUAN SPECTROPHOTOMETER

The Raman e f f e c t 1 s an inherently weak e f f e c t ,

t y p i c a l l y lo -* of t h e l n t e n s l t y of t h e l n c l d e n t e x c l t l n g

r a d i a t i o n and f o r many y e a r s s o u r c e stability and l n t e n s l t y

made Raman s p e c t r o s c o p y e x t r e m e l y d i f f i c u l t particularly I n

c o m p a r i r o n w l t h t h e f a s t e r and l e s s expensive ~ n f r a r e d

s p e c t r o m e t e r t h a t were d e v e l o p e d .

It was not until the early slxtles that the modern

Raman renaissance took place wlth the development of

c o m e r c i a 1 continuous wave (CW) vislble lasers. Suddenly a

highly monochromatic, coherent, narrow beam, hlgh intensity

light source was available whlch revolutlonised Raman

spectroscopy.

In recent y e a r s , micro electronics has further lmproved

the technique such that stepper motor drlves, photon

counting, dlgltal data acqulsrtlon and computer processing

have provided chemrsts, physlcsts and analysts wlth a

technique whlch many clalrn 1s more useful and versatile than

infrared rpectroscopy.

Inrtrumentatlon for Raman spectroscopic studles requlre

the following:

1. Sample holder

2. Light Source (Laser)

3 . A collection optlcs to collect the Raman scattered photons.

4 . A monochromator to separate the Raman slgnal.

5 . A detector to detect the photons at varlous wavelengths and to measure the relatlve lntensitles of the signals.

6, A computer system for the optlmlzatlon of photons collected and to dlsplay spectra.

The above sald requirement are belng considered here in

the detail.

1 .6 .1 Sample Handl ing

Due t o t h e a b i l i t y of t h e v i s l b l e l a s e r s t o p e n e t r a t e

e v e n q u i t e t h l c k g l a s s and t h e v e r y weak Raman s c a t t e r of

t h e g l a r r i t s e l f , i t i s p o s s i b l e t o c o n s t r u c t a wide r a n g e

of s p e c i a l i s t c e l l s and a s s o c i a t e d hardware f o r t h e

e x a m i n a t i o n of s y s t e m s not amenable t o s t u d y by o t h e r

a n a l y t l c s l t e c h n i q u e s . One of t h e g r e a t a d v a n t a g e s of t h e

t e c h n i q u e of kaman s p e c t r o s c o p y 1 s ~ t s a b l l l t y t o be

used f o r t h e s p e c t r a l exarn ina t lon of s y s t e m s under a v e r y

wide r a n g e of t e m p e r a t u r e s and p r e s s u r e and l n

p a r t i c u l a r f o r t h e t lmc r e s o l v e d s t u d y of s u c h s y s t e m s .

1.6.2 The L i g h t S o u r c e

The t y p e s of l a s e r s a v a i l a b l e t o o b t a l n Rarnan s p e c t r a

a r e c o n t i n u o u s wave (CW) and p u l s e d l a s e r s .

( a ) A c o n t i n u o u r wave l a r e r s

Ar t h e name i m p l l e s , t h e continuous wave l a s e r s g l v e a

c o n t i n u o u r s u p p l y of p h o t o n s and a r e by f o r t h e most w l d e i y

used l a s e r s f o r Rarnan s p e c t r o s c o p y a t t h e p r e s e n t t l m e . ?he

a r g o n l a s e r 1 s w l d e l y used v a l u e f o r s t u d i e s r e q u l r l n g b l u e

o r g r e e n e x c r t a t l o n and t h e k r y p t o n l a s e r 1 s of g r e a t e s t

v a l u e i n t h e r e d and y e l l o w r e g r o n s of t h e s p e c t r u m . O f t h e

two, t h e a r g o n l a s e r 1 8 more u s e f u l , p r o v i d e d t h a t t h e r e

i r no r p e c i f l c w a v e l e n g t h requirement. l h i s 1 s because i t

can be o b t a l n e d i n h i g h e r power o u t p u t v e r s r o n s t h a n t h e

k r y p t o n l a s e r . I t 1 s l e s s susceptible t o I n s t a b i l i t y doe t o

p r e s s u r e changr.., i n t h e t u b e , and w i l l g l v e a wide r a n g e

o f l i n e s w l t h o u t t h e need f o r c h a n g i n g t h e l a s e r

o p t i c s . These f a c t o r s make t h e a r g o n l a s e r distinctly t h e

e a s i e r of t h e two f o r t h e n o n - e x p e r t t o use and an

g e n e r a l ~ t a l s o t e n d s t o have l e s s downtime t h a n t h e

k r y p t o n .

(b ) Pulsed lasers

The p u l s e d l a s e r f o r Raman s p e c t r o s c o p y h a s been

l a r g e l y ueed I n n o n l i n e a r s t u d l e s and ~ t s u t l l l t y h a s been

r e a l i s e d i n conventional Raman work r e c e n t l y . The two

s y s t e m s comnonly used a r e e l t h e r t h e p u l s e d Y A G o r Exclmer

l a s e r # . The g r e a t a d v a n t a g e s of t h e s e l a s e r s y s t e m s f o r t h e

Raman s p e c t r o s c o p y 1 s t h e v e r y h l g h d e g r e e of t u n a b l l l t y ,

which t h e y o f f e r . Apar t from t h e h i g h d e g r e e of t u n a b l l l t y ,

p u l s e d l a r e r s y s t e m s p r o v i d e v e r y h l g h power o u t p u t s o f t e n

of t h e o r d e r of Megawat t s . But t h e l r maln drawback l l e s I n

t h e i r v e r y low p u l s e r a t e and t h e s h o r t d u r a t l o n of t h e

p u l s e s . The moat s u c c e s s f u l Raman s y s t e m s u s i n g t u n a b l e

u l t r a v i o l e t p u l e e d l a s e r t h a t described by Asher ( 6 ) whlch

u s e s a g a t e d intensified a r r a y d e t e c t o r and an e l l l p s o l d a l

m i r r o r a8 t h e c o l l e c t i o n o p t i c and 1 s b a s e d on a p u l s c ~ l Y A G

l a s e r .

Clorely connected with the choice of laser 1s the

choice of external optlcs assoclated wlth the spectrometer.

There comprise, laser beam helght adjusting system, the

filtering system for CW lasers and the photon

collection Optics. It 1s an unfortunate feature of CW

laser8 that assoclated wlth any of the lndlvldual laser

gives a serles other outputs, the plasma llnes (7). These

are very much weaker than the laser outputs but sllghtly

stronger than Raman b a n d a . T h 1 s can be resolved uslng

filtering devlce. Another useful alternative 1s thv pre-

monochromator. The other feature of the optlcs external to

the spectrometer system 1s the collectlon optlcs. In the

case o f Instruments which wlll be uslng vlslble radlatlon

exclusively the normal collectlon optlcs 1s a camera lens.

Cassegrain mirrors are particularly good for samples

posltionlng at a slgnlflcant distance, but due to thelr

central reflector lt become ~ n e f f ~ c l e n t at short worklng

distance. I f only one Raman spectrometer 1s to be used for a

wide range of wavelengths lncludlng ultraviolet

work then lt 1s worth havlng both cassegrarn and camera lens

optionr. For ultravlolet work ~t 1s better to have quartz

lenrcr throughout and coated optlcal surfaces,

1 .6 .4 SPECTROMETER

a) Conventional Dlsperslve spectrometer and

spectrographs:

Before considering the relatlve advantages of the klnd

of dispersive monochromator lt 1s worth conslderlng the

difference between the spectrograph and spectrometer. The

grating spectrometer drsperses the llght e n t e r i ~ ~ g the

monochromator and than passes ~t through one or more narrow

slits so that the llght passlng through the detector at any

one time has very narrow bandwidth and may be considered as

monochromatic. A spectrograph other hand uses wlder sllts

and grating which produces much less dispersion and so glves

a relatively broad band of lrght on a multichannel detector.

The maln advantage of the spectrograph 1s ~ t s hlgh

throughput and ~ t s maln disadvantage 1s ~ t s relatively large

spectral band wldth reaching the detector at any one tlme,

resulting ~n poor resolution and poor stray light rejection.

The maln advantage of the spectrometer 1s ~ t s hlgh

resolution associated wlth a hlgh degree of dlsperslr.~~. and

throughput 1s not a8 good as that of the spectrograph. It is

the type of Instrument whlch has tradltlonallv been used

almost exclusively for Raman studles.

A good quality and an ideal instrument 1s the

spectrometer wlth a photomultiplier tube as the detector

which can work reasonably close to the existlng llne ~i,,vlng

~ o o d r e s o l u t ~ o n , and sufficient to obtain apectra of even

very w e a k Raman scattered radiation. The advent o f

multichannel detectors and their raprd development and

performance improvement has once agaln focussed a t t e n t ~ o n on

the rpectrograph type of instrument. The spectrograph is

ideally euited to operation with a multichannel detector

whereas the spectrometer, p a r t ~ c u l a r l y a hlghly dispersive

one, cannot take advantage of the ability of such detectors

to obeerve a wide wavelength range.

1.7 VIBRATIONAL ASSICNtdENTS

The spectra obtained uslng infrared and Raman technique

have been analysed on the basls of molecular syrranetry and

group theory. The normal vibrations can be davided into

two principle groups.

1.7.1 STRETCHING VIBRATIONS

In thin type of vibratrons, the atoms move essentially

along the bond axis, so that the bond length Increases or

decreaser periodically. As this type of vlbratlons

correrpond to one dimensional motion, ~t means that there

w i l l be ( n - 1 ) s t 1 , e i c h l n g v l b r a t l o n s f o r n o n c y c l l c s y s t e m s .

S t r e t c h i n g v i b r a t i o n s a r e of two t y p e s :

( i ) S y m n e t r l c v i b r a t i o n s , and

( i i ) A s y m n e t r l c v i b r a t i o n s .

1 . 7 . 2 BENDING VIBRATIONS

I n t h i s t y p e t h e r e o c c u r s a c h a n g e I n bond a n g l e s

be tween bonds w l t h a comnon a tom o r t h e s e o c c u r when t h e

movement of a g r o u p of a toms w l t h r e s p e c t t o t h e remainder

of t h e m o l e c u l e , w ~ t h o u t movement of t h e a toms In t h e g r o u p

with r e a p e c t t o one a n o t h e r .

Bendlng v i b r a t l o n s a r e more I n number a s compared t o

~ t r e t c h i n g v i b r a t l o n s . They a r e of two t y p e s .

( i ) ~ n - p l a n e b e n d i n g v l b r a t l o n s

( i i ) o u t - o f - p l a n e b e n d l n g v l b r a t l o n s

Molt m o l e c u l e c o n t a l n c h a r a c t e r l s t l c g r o u p s s u c h a s

CH3, NO2 e t c . , and t h e s e u s u a l l y p r o d u c e a c h a r a c t e r l s t l c

g r o u p f r e q u e n c y , which c a n be used t o r i d e n t l f l c a t l o n and

a s s i g n m e n t s . l h e s s g r e u p f r e q u e n c l e s must be u s e d w i t h c a r e ,

s i n c e m i x i n g of t h e g r o u p v l b r a t l o n s c a n o c c u r and c a u s e s

s i g n i f i c a n t and u n e x p e c t e d c h a n g e s I n t h e g r o u p f r e q u e n c y .

The assignments of infrared and Raman spectra of small

moleculer is a relatively slmple process. However, the

complexity of the spectrum increases rapidly wlth each added

atom, unequivocal assignments are still sought for some

moleculer with as few as four or five atoms. lhe assrgnments

of a11 the normal modes of vibration of a large polyatomic

molecule ir rtill problematic.

The tcols whlch are used rn vlbrational assignments

include empirical correlations and the group frequency

concept, infrared and Raman selection rules, rotatronal

structure and the shapes of rnfrared and Raman bands,

frequency ahifts in rsotoprc molecules, the

polarization characteristrc of Raman bands, lnfrared

dichroirm, infrared and Raman lntenslties, theoretical

calculation of vlbrational frequencies and band assignments.

However, for polyatomic molecules generally one has to rely

on Raman and infrared vibrational frequencies. Experlnte ~ t a l

approach alone may not be sufficient for the understanding

of the complicated spectra of complex molecules. Ihere are

three rtages ln the utrlization of new spectral data. lhe

observed frequencles dre frrst classified according to the

normal modes of vibration belonging to each rrreducrble

representation of the point group of the molecule. Following

this, the assignment of frequencies may be made by

correlation wlth related molecules. lhese correlations may

I I ~ carried out usually both on the basls of vlbratlonal

jrcquencics arid band intensltles ( 8 ) .

1 .8 MOLECULAR VIBRATIONS

Molecules In general are associated wlth translational,

vibrational and rotational motlons. W e n a molecule

absorbs or emlts electromagnetlc radlatlon, molecular

spectra arises from transltrons between energy states. lhe

spectra lie ln different reglons of electromagnetlc

radiation. The rotational spectra occurs ~n the microwave

reglon. htlcrowave studles provldes important

informations regardrng the structural parameters and

rotational dlstortlon constants of molecules. lhe

vibrational spectra lle rn the infrared region and the Raman

reglon (10-10000crn-~). lhe condltlons under whlch vrbratlons

are either infrared or Raman actlve, are known as selection

rules. Wigner had shown that the number of normal modes

oscillation of a molecule may be obtalned in a srmple manner

by the application of the group theory, whlch was

extensively applled by krlson (9).

The selection rule for infrared absorption 1s glven as:

5 (2 COB bR 1 ) Xi ( R ) = 0 inactlve (1.12)

? 0 active

where Xi ( H ) 1s t h e c h a r a c t e r of t h e l r r e d u c l b l e

r e p r e r e n t r t i o n r i t o which t h e normal c o o r d i n a t e b e l o n g s , P

i n d i c a t e r t h e s u m n a t i o n o v e r a l l t h e operation t h a t

c o n r t i t u t e t h e g roup .

I n a i m i l a r way, t h e s e l e c t i o n r u l e f o r t h e Raman

s p e c t r a may be g i v e n a s f o l l o w s :

I n b o t h t h e c a n e s , t h e s l g n i n d i c a t e w h e t h e r t h e

o p e r a t i o n r i r a r o t a t i o n o r rotat~on-reflection.

1.9 MOLECULAR CONSTANTS

The f u n d a m n t r l v i b r r t l o n r l frequencies of a m o l e c u l e

a r e g o v e r n e d by

I ) t h e a t o m i c m r s s e a and t h e g e o m e t r i c d l s t r i b u t l o n of t h e

v i b r a t i n g n u c l e i .

b ) t h e f o r c e f i e l d which t e n d s t o r e s t o r e t h e m o l e c u l e t o

i t 8 i n t e r n a l e q u l l l b r i u m d u r l n g any d l s t o r t l o n .

The f o r c e f i e l d r r i s e s from t h e c h a n g e s l n t h e energy

of t h e e l e c t r o n # which b ~ n d t h e m o l e c u l e s t o g e t h e r . l h e

b t r e t c h l n g f o r c e c o n s t a n t (restoring f o r c e p e r u n ~ t

d i r p l a e r m e n t o f a bond) i s a measure of t h e s t r e n g t h o t the

c h e m i c a l bond . t h e s t r e t c h i n g , s t r e t c h - b e n d and benolng

i o r c e c o n s t a n t s a r e e x p r e s s e d I n mdym A - l , mdyno Tad- ' and

mdym i * ' r a d - 2 r e s p e c t i v e l y . I n g e n e r a l , t h e number o f

v i b r a t i o n a l f r e q u e n c i e s associated w ~ t h a m o l e c u l e of I n '

a toma i s 3n-6 (317-5 f o r r l i n e a r m o l e c u : e ) , s o t h a t

n ( n + 1 ) / 2 p o t e n t i a l e l l e r g y c o n s t a n t s w l i l be

r e q u i r e d t o d e s c r i b e a g e n e r a l quadratic v a l e n c e f o r c e

f i e l d . Due t o t h i s , no u n i q u e s o l u t l o n i s possible. I n

r u c h c a r e r , t h e s o l u t i o n i s o b t a i n e d by a d o p t ~ n g c e r t a l n

a p p r o x l m a t i o n a . In i a o t o p l c p a i r s of m o l e c u l e s , t h e

j ) o t e n t i a l f u n c t i o n may be assumed t o be t h e same, t o

a v e r y h i g h d e g r e e of a p p r o x l m a t l o n . Somet imes t h e

f o r c e c o n m t a n t v a l u e s c a n be t r a n s f e r r e d f rom one m o l e c u i e

l o a n o t h e r h a v i n g similar bond environments. R e c e n t l y

a d d i t i o n a l e x p e r ~ m e n t a l d a t a s u c h a s C o r l o l l s c o u p i l n g

r o n s t a n t r , r o t a t i o n a l distortion c o n s t a n t s and mean

a m p l l t u d e r of v i h r a t ~ o n have been s u c c e s s f u l l y used t o i l x

t h e m o l e c u l a r : o r c e f i e l d uniquely. khen a l l lice

r v a i l s b l e d a t a a r e no t s u f i i c l e n t t o p r o v l d e a u n l q u e

f o r c e f i e l d , t h e f ~ r o b l e m c a n be s o l v e d e l t h e r by t a k l n g

o n l y s e l e c t e d c r o s s t r r m a o r by p o s t u l a t i n g c e r t a i n

r ~ ~ e c ~ l i c f o r c e f l e l d s a p p r o p r i a t e t o t h e m o l e c u l e

where t h e number of f o r c e c o n s t a n t s l o be

t l r t e r m i n e d i s not l a r g e . Some of t h e f o r c e f i e i d s used I n

t h e e v a l u s l ~ o n o f f o r c e c o n s t a n l s a r e t h e c e n t r a l : o r c e

I ~ r l d ( l o ) , r i m p l e v a l e n c e f o r c e t i e i d ( l l ) , o r b r t a l t a i e n c e

force field (lZ), hybrid orbital force fleld (13, 14), urey-

Bradly force field (15-18) and general quadratlc valence

force field. In the prerent work, general quadratlc valence

force field ( G Q V F F ) ir adopted. It giver a more complete

picture o f the intermolecular forcer and takes into account

the varlour porrible interactions.

Another errential recent advance in the fleld of

vibrational spectroscopy i s the development and

incorporation of analytical derivative methods for the

determinalion of vibrational parameters In most standard

programr for r b initio molecular orbital caiculations (19).

As a rerult, the interpretation of frequencies and

lntenritirr in infrared and Raman spectra has b f 8 ,Ji?x

strongly interconnected with the appropriate quanturr

m c h a n i c a l crlculrtions. Needless to say, these deveiopments

have greatly enhanced the rellablllty and accuracy 01

vibrational spectral rtudies.

1 . 9 . 1 FOR= CONSTANTS

Wi l r o n ' s proup theorelleal melhcd (20) of analvsls of

molecular vlbrrtions has been of great servlce ln t h e s t ~ d )

of molrcular lorces. The procedure adopted i n the

rnveatigatlon presented In thls thesis follows kllson's t - G

matrix method (21). The flrst s t e p towards sol\inp the

cquatlons of mollon lies ln derlvlng expressions for the

kinetic and potential energles in terms of some convct41. nt

set of coordlnates. The chlef merit of group theoretical

method i r that i t leads t o a breaklng up of the vibrational

secular equatlon according to the symnetry species of the

molecule. By group theoretrcal considerations, the number of

Renuine vibrations In a molecule belonging to each mode 1s

lound. F r o m the internal coordlnates ( R j , the

orthonormalised llnear combinations vlz., symnetry

roordinaten ( S ) are formed. They are related as

5 = U H (1.14)

vhere U is the orthogonal transformation matrix. In terms of

the symnctry coordlnater, the potentla1 energy ( V ) becomes

where f is the valence force constants rcatrix and b 1 s the

n y m n t r l z e d force constant matrix.

Similarly the kinetic energy may also be given as

2 , i S c - ' S (1.10)

h e r e C l r the matrix ( 2 1 ) depending on the posltlon and

the reciprocal mass ( k ) o f the atoms consisting the

molecule.

The S m a t r i x i s r e l a t e d t o t h e C a r t e s i a n d ~ s p l a c e r n e n t

c o o r d i n a t e s ( X I t h r o u g h a t r a n s f o r m a t i o n (0) a s :

C c a n b e e v a l u a t e d u s i n g B m a t r i x t h r o u g h t h e r e l a t i o n

c; = B p X ( 1 . 1 8 )

1.9.2 KINETIC CONSTANTS

l h e a t t e n t i o n o f m o l e c u l a r s p e c t r o s c o p i s t s h a s b e e n

d r a w n t o t h e c o n c e p t o f k i n e t i c c o n s t a n t s I n m o l e c u l e s . l h e y

a r e t h e v i b r a t l o n a l i n e r t i a c o e f f i c l e n t s i n v o l v e d i n

W t l s o n l a e x p r e s b i o n f o r t h e k l n e t l c e n e r g y r e l a t l n g t o

n l o l e c u l e v i b r a t i o n a . They a r e given by

i h c e l e m e n t s of t h e m a t r i x h ' 5 a r c t h e i c i n e t i c c o : s t a n t s .

l h c s e c o n s t a n t s a r e f o u n d t o be b a s i c a l l y i r r p o r t a p , t l r , t h e

a r c h i t e c t u r e of m 3 l e c u l a r d v n a r n i c s . I n ana !og \ u l t h

p o t e n t i a l c o n s t n n t s , t h e s e c o n s t a n t s s a t i s i y t h e r e l a t i o n

w h e r e k'm a r e t h e v a l e n c e k i n e t i c c o n r t a n t s r r a t r i h . l h e

r t u d y o f k l n e t ~ c c o n a t a n t s i n d i c a t e s t h a t 0 1 1 - d i a g o n a l ~ o r c e

conslantn may I)c linked to the cor~cerned dlagonal force

constant8 through the reiatlon

F I F = K I K ( I < ] ) 11 I 1 11 I 3

( 1 . 2 1 )

provided the frequencies are ordered. The method of klnetlc

constants for solvlng the secular equatlon has been found to

give s a t ~ s f a c t o r y results In varlous types of polyatomrc

molecules (22-26).

1 . 9 . 3 COMPLIANCE CONSTANTS

'Ihe c o m p l ~ a n c e constants are the lnverse of the torce

constantc as introduced by L k c ~ u s (27).

where N sncl n are the compliance constant rnatrlces oerlned

wlth respect to the s y m m t r y and internal coorclnates

respectively.

1 . 9 . 4 YEAN SQUARE AMPLITUDES OF VIBRATION

The thermal vibrations of atoms wlthln the molecule can

best be r l u d ~ e d by evaluating the mean square amplituces of

vibration of !he atomlc dratarces. The mean square arplltude

for a particulmr atomic pair 1s defrned as the mar, r ~ , t ~ ~ a r e

v r 1 ue

( 1 . 2 3 )

where R and H' are the instantaneous and equilibrium 1 J 11

diltance between two atoms i and 1. A thorough study of the

problem of computing mean square amplitudes o f polyatomic

molecule# was carried out by Morino and his collaborators

( 2 8 - 2 9 ) . The symnetrized mean square amplitude quantities

Z I j are defined by the matrrx relation

r = < s s ' > ( 1 . 2 4 )

Ihe s y m t r y coordinates and the normal coordinates are

connected by the relation

S = L Q ( 1 . 2 5 )

where L Is the normal coordinate transformation matrix.

Hence

1 z LA'^ ( 1 . 2 6 )

wllere A la a nragonal matrix.

ul~rre h - p l a n k ' s cor,slant

k - Boltzmann's constant

7 - the abeolutc temperature

- 1 - the frequency in cm

ll~c non-bonded mean amplitudes arc expressed In r r r ~ b o f

I,rsnrled m n n amp1 ltudes. Ihe r i b r a t ~ o n a l amp11 tudt.5 can

r l a o be ol~ta~nctl f r o m electron cilflrnction c i a : > . i h e

romplaince constants and vrbrational m a n amplitudes a r e

reported I n the l a q t two chnlltcn of the thesis.

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