Chapter 4 - Raman Spectroscopy.pdf

Raman

1. Raman spectra
Thisisbasedonscatteringofradiationandnot
ontheabsorptionofradiationbythesample.

2. RAMAN SPECTRA
GENERAL INTRODUCTION
Itisatypeofspectroscopywhichdealsnotwiththe
absorptionofelectromagneticradiationbutdealswiththe
scatteringoflightbythemolecules.Whenasubstance
whichmaybegaseous,liquidorevensolidisirradiatedwith
monochromaticlightofadefinitefrequencyv,asmall
fractionofthelightisscattered.Rayleighfoundthatifthe
scatteredlightisobservedatrightanglestothedirectionof
theincidentlight,thescatteredlightisfoundtohavethe
samefrequencyasthatoftheincidentlight.Thistypeof
scatteringiscalledRayleighscattering.

3. energy absorbed by molecule
from photon of light
not quantized
No change in
electronic states
Infinite number
of virtual states

4. Whenasubstanceisirradiatedwithmonochromaticlightofa
definitefrequencyv,thelightscatteredatrightanglestothe
incidentlightcontainedlinesnotonlyoftheincidentfrequency
butalsooflowerfrequencyandsometimesofhigher
frequencyaswell.Thelineswithlowerfrequencyarecalled
Stokes'lineswhereaslineswithhigherfrequencyarecalled
anti-Stokes'lines.
Ramanfurtherobservedthatthedifferencebetweenthe
frequencyoftheincidentlightandthatofaparticularscattered
linewasconstantdependingonlyuponthenatureofthe
substancebeingirradiatedandwascompletelyindependentof
thefrequencyoftheincidentlight.Ifv
iisthefrequencyofthe
incidentlightandv
sthatofparticularscatteredline,the
differencev=v
i-v
siscalledRamanfrequencyorRaman
shift.

5. -some scattered emissions occur at the same energy while others return
in a different state
Rayleigh Scattering
no change in energy
hn
in= hn
out
Elastic: collision between photon and molecule results in no change in energy
Inelastic: collision between photon and molecule results in a net change in energy
Raman Scattering
net change in energy
hn
in<> hn
out

6. Anti-Stokes: E = hn+ DE
Two Types of Raman Scattering
Stokes: E = hn-DE
DE –the energy of the first vibration level of the ground state–IR vibration absorbance
Raman frequency shiftand IR absorption peak frequencyare identical

8. EXPLANATION FOR OBSERVING RAYLEIGH
LINEAND RAMAN LINES
•Elasticandinelasticcollisionsbetweenthe
radiationsandinteractingmoleculesresultsin
theformationofRayleighandRamanlines.
•Intermsofexcitationofelectrons
• v
abs=v
eRayleighline
• v
abs>v
eStokesline
• v
abs<v
eAntiStokesline

10. POLARIZABILITYOFMOLECULES
ANDRAMANSPECTRA
•TheRamaneffectarisesonaccountofthe
polarization(distortionoftheelectroncloud)ofthe
scatteringmoleculesthatiscausedbytheelectric
vectoroftheelectromagneticradiation.Theinduced
dipolemoment(μ)dependsuponthemagnitudeofthe
appliedfield,E,andtheeasewithwhichthemolecule
canbedistorted.Wemaywrite
μ=αE
whereαisthepolarizabilityofthemolecule.

11. ConsiderfirstthediatomicmoleculeH
2placedinanelectric
field,whichshowsend-onandsidewaysorientation,
respectively.Theelectronsformingthebondaremoreeasily
displacedbythefieldalongthebondaxis(Figure:b)than
thatacrossthebond(Figure:a)andthepolarizabilityisthus
saidtobeanisotropic.Thepolarizabilityofamoleculein
variousdirectionsisconventionallyrepresentedbydrawing
apolarizabilityellipsoid(Figurec&d).
Figure: The hydrogen molecule in an electric field and its polarizability
ellipsoid seen along and across the bond axis.

12. Alldiatomicmoleculeshaveellipsoidsofthesame
generaltangerineshapeasH
2,asdolinearpolyatomic
molecules,suchasCO
2,H
2C
2,etc.Theydifferonlyinthe
relativesizesoftheirmajorandminoraxes.
Whenasampleofsuchmoleculesissubjectedtoabeam
ofradiationoffrequencyʋtheelectricfieldexperienced
byeachmoleculevariesaccordingtotheequation
E=E
0sin2πʋt (1)
andthustheinduceddipolealsoundergoesoscillationsof
frequencyʋ:
μ=αE=αE
0sin2πʋt (2)
Eq.(3)istheclassicalexplanationofRayleighscattering.

13. Ifthemoleculeundergoessomeinternalmotion,suchas
vibrationorrotation,whichchangesthepolarizability
periodically,thentheoscillatingdipolewillhave
superimposeduponitthevibrationalorrotational
oscillation.Consideravibrationoffrequencyʋ
vibwhich
changesthepolarizabilty:wecanwrite
α=α
0+βsin2πʋ
vibt (3)
whereα
0istheequilibriumpolarizabilityandβrepresents
therateofchangeofpolarizabilitywiththevibration.Then
wehave:
μ=αE=(α
0+βsin2πʋ
vibt)E
0sin2πʋt
or,expandingandusingthetrigonometricrelation:
sinAsinB=½{cos(A–B)–cos(A+B)}

14. Wehave
μ=α
0E
0sin2πʋt+½βE
0{cos2π(ʋ–ʋ
vib)t–cos2π(ʋ+ʋ
vib)t} (4)
andthustheoscillatingdipolehasfrequencycomponents(ʋ±ʋ
vib)as
wellastheexcitingfrequency(ʋ).
Thegeneralrule:InordertobeRamanactiveamolecularrotationor
vibrationmustcausesomechangeinacomponentofthemolecular
polarizability.Achangeinpolarizabilityisreflectedbyachangeineither
themagnitudeorthedirectionofthepolarizabilityellipsoid.

15. Figure: The water molecule and its polarizabilityellipsoid seen
along the three coordinate axes.

16. Figure: The chloroform molecule and its polarizabilityellipsoid
seen from across and along the symmmetryaxis.

17. Types of molecules showing Rotational Raman Spectra
•Amoleculescatterslightbecauseitispolarizable.Hencethe
grossselectionruleforamoleculetogivearotationalRaman
spectrumisthatthepolarizabilityofthemoleculemustbe
anisotropici.e.thepolarizabilityofthemoleculemustdependupon
theorientationofthemoleculewithrespecttothedirectionofthe
electricfield.
•Hencealldiatomicmolecules,linearmoleculesandnon-spherical
moleculesgiveRamanspectrai.e.theyarerotationallyRaman
active.Ontheotherhand,sphericallysymmetricmoleculessuch
asCH
4,SF
6etc.donotgiverotationalRamanspectrumi.e.they
arerotationallyRamaninactive.(Thesemoleculesarealso
rotationallymicrowaveinactive).

18. PURE ROTATIONAL RAMAN SPECTRA
Linear Molecules
Therotationalenergylevelsoflinearmoleculeshavealreadybeen
statedbytheequation
Ɛ
J=BJ(J+1)–DJ
2
(J+1)
2
cm
–1
(J=0,1,2,…..)
InRamanspectroscopytheprecisionofthemeasurementsdoesnot
normallywarranttheterminvolvingthecentrifugaldistortionconstant,
D.Thuswetakethesimplerexpression:
Ɛ
J=BJ(J+1)cm
–1
(J=0,1,2,…..)
torepresenttheenergylevels.

19. Transitionsbetweentheselevelsfollowtheformalselectionrule:
ΔJ=0,or±2only
TheselectionruleΔJ=0correspondstoRayleighscattering
whereasselectionruleΔJ=±2givesrisetoRamanlinesas
explained.
Asexplainedearlier,theintensitiesoflinesdependuponthe
populationofinitiallevelfromwherethemoleculesareexcitedor
de-excitedtothefinallevel.Sincethepopulationofrotational
energylevelsisasshowninFig.thereforetheintensitiesofthe
Stokes'andanti-Stokes'linesvaryinasimilarmanner.

21. Symmetric top molecule
Onlyend-over-endrotationsproduceachangeinthepolarizability
inthecaseofthesymmetrictopmolecules(amoleculeinwhich
twomomentsofinertiaarethesame).
Theenergylevels:
Ɛ
J,K=BJ(J+1)+(A–B)K
2
cm
–1
(J=0,1,2,…..;K=±J,±(J–1),….)
The Raman selection rules for a symmetric top molecule are:
ΔK= 0
ΔJ= 0, ±1, ±2 (except for K=0 states, when ΔJ = ±2 only)

22. (1) ΔJ = ±1 (R branch)
Lines at ΔE
R= 2B(J+1) J = 1, 2, .. but J ≠ 0
(2) ΔJ = ±2 (S branch)
Lines at ΔE
S= 2B(2J+3) J = 0, 1, 2, ..
Thespectrumshowsacomplexintensity
structure(nottobeconfusedwithnuclear
spineffects),butthebasiclinespacingis
now2B,ratherthan4Basinthecaseof
linearmolecules.
Asymmetrictopmoleculehasanisotropicpolarizability.Thisselectionrule
holdsforanyK.Therearetwocases:
TherotationalRamanspectrum
ofasymmetrictopmolecule

23. VIBRATIONAL RAMAN SPECTRA
Raman Activity of Vibration
Thechangeinsize,shapeor
directionofthepolarizability
ellipsoidofthewatermolecule
duringeachofthethree
vibrationalmodes.Thecenter
columnshowstheequilibrium
positionofthemolecule,whileto
rightandleftaretheextremesof
eachvibration.

24. Thechangesinpolarizability
ellipsoidofcarbondioxide
duringitsvibrations,anda
graphshowingthevariation
ofthepolarizability,α,with
thedisplacementcoordinate,
ξ,duringeachvibration.

25. Raman Activity

26. 1-Atomic number Z:
P the amount of electrons,
Electrons become less control by nuclear charge.
2-Bond Length:
P Bond Length
3-Atomic or Molecular Size:
P Size,
4-Molecular orientation with respect to an electric field
Parallel or perpendicular (Exp: Parallel has more effect)
5-Bond Strength (Bond order):
P 1/strength of bond C=C, and C≡C, C≡N bonds are
strong scatterers, bonds undergo polarization.
6-Electronegativity difference:
P 1/ difference in electronegativity
7-Covalent bonds more polarizable than ionic bonds.
Factors affect Polarizability

27. Structure of Vibrational Raman Spectra
Foreveryvibrationalmodeofthemolecule,theenergyofthe
modeisgivenby
Ɛ=ϖ
e(ʋ+
1
2
)–ϖ
ex
e(ʋ+
1
2
)
2
cm
–1
(ʋ=0,1,2,…..) (1)
where,ϖ
eistheequilibriumvibrationalfrequencyexpressedin
wavenumbersandx
eistheanharmonicityconstant.The
selectionrule:
Δʋ=0,±1,±2,…. (2)
whichisthesameforRamanasforinfra-redspectroscopy,the
probabilityofΔʋ=±2,±3,….decreasingrapidly.

28. ForRamanactivemodes,wecanapplytheselectionrule(eq.2)
totheenergylevelexpression(eq.1)andobtainthetransition
energies:
ʋ=0→ʋ=1:Δɛ
fundamental=ϖ
e(1–2x
e)cm
–1
ʋ=0→ʋ=2:Δɛ
overtone=2ϖ
e(1–3x
e)cm
–1
ʋ=1→ʋ=2:Δɛ
hot =ϖ
e(1–4x
e)cm
–1
However,sincetheRamanScatteringProcessisveryweak,we
canignoreallprocessessuchasOvertonesandHotbands
sincetheseareweakeveninIRspectra.Soweonlyneedto
considerthefundamentaltransitionsʋ=0→ʋ=1.Inother
wordswecanwrite
ʋ
fundamental=ʋ
ex.±Δɛ
fundamentalcm
–1
wheretheminussignrepresentstheStokes’linesandtheplus
signreferstotheanti-Stokes’lines.

29. Example:CHCl
3molecule.
Symmetrictopmoleculewith5atoms⇒3N-6
=15-6=9vibrationalmodes,however,dueto
symmetry3modesaredegenerate⇒6
vibrationalmodes.
Modesareseenat262,366,668,761,1216
and3019cm-1.AllsixmodesarebothIRand
Ramanactive.ExcitingsourceisAr488nm
laserline.
IntheRamanspectrumontheleftthe
wavenumberoftheincident(laser)radiationis
settozero,sox-axisshowswavenumbersof
thevibrationalmodes(andnotabsolutevalues).
VibrationalRamanSpectra

30. IngeneralforpolyatomicmoleculesitisusuallynecessarytoapplyGroup
Theoryinordertodecidewhetheraparticularvibrationofthemoleculeis
Ramanactiveornot.Butsomegeneralrulesapply:
Ifthemoleculehasnosymmetry(e.g.HCN)thenusuallyallofits
vibrationalmodesareRamanactive.
Inmoleculesthatpossesssymmetry(e.g.CO
2,H
2O)then
SymmetricvibrationsgiverisetointenseRamanlines,nonsymmetric
vibrationsareusuallyweakandsometimesunobservable.Inparticular
bendingmodesusuallyyieldaveryweakRamanline.
Raman Activity in Polyatomic Molecules

31. RuleofMutualExclusion:
Ifthemoleculehasacentreofsymmetry,then
Ramanactivevibrationsareinfraredinactiveand
viceversa.Ifthereisnocentreofsymmetryinthe
moleculethensomeorallofthevibrationsmaybe
bothRamanandIRactive.

32. Vib. Raman Spectra: Example CCl
4

33. Comparison of Raman and IR Spectra

34. Vibrational-Rotational Raman spectroscopy
The fine structure is rarely resolved except in the case of diatomic
molecules. We can write the vib-rot energy levels as:
Ɛ
J,ʋ= ϖ
e(ʋ+
1
2
)–ϖ
ex
e(ʋ+
1
2
)
2
+ BJ(J+1) cm
–1
(ʋ= 0, 1, 2,…..; J = 0, 1, 2,……)
wherewehaveignoredthecentrifugaldistortion(Dterm).
FordiatomicmoleculesΔJ=0,±2andcombiningthiswiththe
fundamentaltransitionʋ=0→ʋ=1gives
Q-BranchΔJ=0:ΔƐ
Q=ʋ
0cm
–1
(forallJ)
S-BranchΔJ=+2:ΔƐ
S=ʋ
0+B(4J+6)cm
–1
(J=0,1,2,….)
O-BranchΔJ=–2:ΔƐ
O=ʋ
0–B(4J+6)cm
–1
(J=2,3,4,….)

35. Stokeslines,lyingatlowfrequency(wavenumber)sideofexciting
radiationwilloccuratwavenumbersgivenby:
ʋ
Q=ʋ
ex.–ΔƐ
Q=ʋ
ex.–ʋ
0cm
–1
(forallJ)
ʋ
O=ʋ
ex.–ΔƐ
O=ʋ
ex.–ʋ
0+B(4J+6)cm
–1
(J=2,3,4,….)
ʋ
S=ʋ
ex.–ΔƐ
S=ʋ
ex.–ʋ
0–B(4J+6)cm
–1
(J=0,1,2,….)
ʋ
ex.isthefrequencyoftheincident(exciting)radiation,e.g.laser
frequency
(ʋ
ex.–ʋ
0)
ʋ
0
Figure:The pure rotation and the rotation vibration spectrum of a diatomic molecule having a fundamental
frequency of ʋ
0 cm
–1
. Stokes’ lines only are shown.

36. InstrumentationforRamanSpectroscopy
Schematic diagram of a Raman spectrometer

37. FourierTransformRamanSpectroscopy