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2.FundamentalsofRamanscatteringspectroscopy
studyingofchemicalreactions,aswellasinter-andintramolecularbonding/in-
teractions.SimilarlytoIRspectroscopy,Ramanspectroscopyallowstoinvesti-
gatecompoundsinallphysicalstatesinawiderangeoftemperatureandpressure.
2010QuantumdescriptionofRamanscattering
TheclassicaltheoryproposedbyPlaczekexplainsthephenomenonofRamanscat-
teringbasedongenerationofscatteredlightbyinduceddipolemoment(2.1),which
isformedinmoleculesduetotheactionofincidentelectromagneticradiation:
(2.1)
whereaisapolarizabilitytensor,E
0-electricvectorofelectromagneticwave.
Polarizabilityrepresentsthetendencyofelectronsofmoleculestobedistortedby
anexternalelectricfield.
AsweexplainedinChapter1,molecularvibrationsarenever“frozen”andfrom
thisreasonpolarizabilitytensormustbeafectedbynormalmode.Hence,thein-
duceddipolemomentisalsomodulatedbyvibrationsofmolecules.Therefore,the
dipolemomentisgivenby(2.2):
(2.2)
Thisexpressionexplainshowtheinducedandalsooscillatingdipolemoment
simultaneouslygenerateselectromagneticradiationofthreefrequencies,corres-
pondingtoRayleigh(seeEq.2.2),Stokes(inblue)andanti-Stokes(ingreen)Raman
scattering.ThistheoryalsoexplainstheindependenceoftheRamanshiftonthe
wavelengthofexcitation,andfurtherdeterminesaselectionruleofRamanscat-
teringphenomenon.Specifically,Ramanspectrumexhibitsthepresenceofvibra-
tionsforwhichatleastonecomponentofthepolarizabilitytensorchangesdue
tovibration.
TheenergydiagraminFigure2.1showsthetwo-photonnatureofRayleigh
andRamanscatteringresultingfromquantumrules.Bothefectscanbedescribed
astwosingle-photonprocessesappearingsimultaneously.Firstly,absorptionof
photontoavirtualstatewithenergylowerthanthoseforexcitedelectronstate
occurs(fornormalRamanscattering),andthenemission(after~10
-14
s)ofanother
photonwiththesame(Rayleighscattering),lower(StokesRamanscattering)or
higherenergy(anti-StokesRamanscattering)isobserved.
Ramantransitionsareallowedwhentheirtransitionmomentisnon-zeroand
isdeterminedbythechangeofpolarizabilityduetotransitionfromntomvibra-
tionalstate(2.3):
(2.3)
Thequantumapproach,astheonlyone,properlydescribestheintensityofthe
scatteredradiationforagivenn→mtransition.TheintegralintensityoftheRaman