R aman sp e ctr osc opy XI-1 XI. RAMAN SPECTR …

1 ,SymmetryandSpectroscopy,OxfordUniversit yPress, ,ModernSpectroscopy,Wiley,Chichester, , , ths,Ed.'s,Wiley, ,InfraredandRamanSpectra,VanNostrand, ,ConstantsofDiatomicMolecules,VanNostran d, ,MolecularQuantumMechanics,OxfordUnivers ityPress, ,IntroductiontotheTheoryofMolecularVibra tionsandVibrationalSpectroscopy,Clarendo nPress, , ,MolecularVibrations,McGraw-Hill,1955.(E nnyupplaga:Dover,1980). ,VibrationalStates,Wiley, , ,AcademicPress, ,IntroductiontoMolecularEnergiesandSpect ra,Holt&Winston, ,Spektrometrisettaulukot,Otakustantamo, , , RAMAN /infraredatlasoforganiccompounds,V CH,Weinheim, ,TheRamane edtreatmentofthetheoryofRamanscatteringb ymolecules,Wiley,Chichester, ,however,di , , ' ' (forthesakesimplicityone) eldF=F0cos( 0t)(XI:1)inducesadipolemoment = F0cos( 0t):(XI:2)Thequantity ,Nature,121(1928)501-502, Anewtypeofsecondaryradiation ; ,IndianJournalofPhysics2(1928)399-419.

2 , (1928) , (1923) k,k=1;2;:::; = 0+MXk=1 kcos( kt+ k):(XI:3)Aphasefactor 0F0cos( 0t)+MXk=1 kF0cos( 0t)cos( k+ k)= 0F0cos( 0t)+MXk=1 kF0 cos[( 0+ k)t+ k]+cos[( 0 k)t+ k] :(XI:4)Theclassicaltheoryofelectromagnet ismstatesthatanoscillatingdipoleemitsrad iationoftheintensityI= 4012 0c3jpj2:(XI:5)Asimpleinsertiongivesthere sultI= 4012 0c3 20F20cos2( 0t)Rayleigh+112 0c3 PMk=1 2kF20 f( 0+ k)4cos2[( 0+ k)t+ k]anti Stokes+( 0 k)4cos2[( 0 k)t+ k]gStokes+:::(XI:6)Anoscillatingdipolemo mentemitsthereforewiththefrequencyofthei ncident eld(Ray-leighscattering)inphasewiththein cident ,themoleculeradiateswithtwofrequenciesth ataremodulatedbythefrequencyoftheexcited normalvibrationandphaseshifted(Ramanscat tering).TheRamanscatteredlighthasalowerf requencythantheincidentlight(Stokes-rama nscattering)orahigherfrequency(anti-Stok es-Ramanscattering).

3 Oneofthefailuresoftheclassicalpictureist hattheratiooftheStokesandanti-Stokesinte nsitiesshouldtheoreticallybeI(Stokes)I(a nti Stokes)=( 0 k)4( 0+ k)4;(XI:7) ectTherelevantquantummechanicalsystemist hemoleculeplusthe dingerequationofthesystemissolvedbyusing perturbationtheory,basicallyinthesameway theEinsteintransitionrateiscalculated, 2 20c4( 0 k)4j<njmijm>j2(XI:8)withthematrixelementsoftheinduce ddipolemoment<njmijm>= hXjXrf<nj^ ijr> <rj^ i^F0jjm> rm 0+<nj^ i^F0jjr> <rj^ ijm> nr 0g:(XI:9)Themomentaneousdipolemoment^ 'seigenstates(somewhatperturbed)thesyste malsohas(anin nitenumberof) eldtothemolecule("dressedmolecule") scatteringh = h 0h 0h UVvis absorptionStokes scatteringh = h 0 - h k kh 0h Anti-Stokes scatteringh = h 0 + h kh 0h (Stokes)I(anti Stokes)=( 0 k)4( 0+ k)4ehc~ k=kT:(XI:10) ~ k 1:43879[lnfI(anti Stokes)I(Stokes)g+4lnf 0 k 0+ kg]:(XI.)

4 11) frequency (cm-1) RAMAN intensity -> , 0 ( ; ; ), , ( ,from1064to532nm) , ( , , , , ).Ifonedoesnotusea ,inparticulartheargonlaserthathastwostro nemissionlinesat514and488nm, , ,inparticular976, angle(backscattering). ,theportionofRamanscatteringofallthescat teredlightislargerin90 geometrythanin180 (90 )IRayleigh(90 )=1:32 IRaman(180 )IRayleigh(180 ):(XI:12)Inthe180 .ForgaseousnitrogenIRaman(180 )IRaman(90 )=1:50:(XI:13) ,PRayleigh( )=0:75 (1+cos2 )PRaman( )= 34+8 1+3 +(1 )cos2 :(XI:14)Here , = (180 )IRayleigh(180 ))=4:9 10 4:(XI:15) , (1972) ,however, cantlymoresensitive(byafactoroftentohund red) ectscanbeusedandtherebysensitivesamplesa rea ( ,random uctuationsofthechargecarriersintheelectr oniccircuits) , , (oralargeportionofit) (upto1m) (SolarTIIDM160).

5 'sMcTripleLEmonochromator,7thetwo (McPhersonMcTrippleLE). , :YAGlaseremittingnearinfraredlightandwit hane ,thedetectorwillbeover , lterwithanopticaldenistyofatleast68andab andwidthof 100cm lterthatisspeci nedhereasOD= log10(Transmission).Analternativede nitionisOD= log10(Transmission)= ( m)876543210 Optical ,however, *Wavelength ( m)PbSe (300 K)PbSe (196 K)PbS (77 K)PbS (196 K)InSb (77 K)InAs (77 K)InGaAs (300 K)Ge (77 K) ,the detectorTransmission gratingRaman signalFilterRaman and Rayleigh erentialscatteringcrosssec-tion ( ; ). ectthepolarizabilityandthereforedi erentvibrationalmodesgivedi ( ; )(~ 0 ~ k) (cm 1) ( ; )(~ 0 ~ k) 410 48cm6= , , J=0; 1,whichgiverisetotheP, J=0; 2andthelabelsofthebranchesarethenO, erentfromthoseofinraredspectroscopybecau sethephysicalprocessesgivinrisetothespec traaredi , 1 RamanIRNaphtalene1630-1595wm1580-1570vsv w1510-1500vwm1390-1350vsmsAnthracene1630 -1620msms1560-1550vss1400-1390vsvwFenant rene1620-1600mm1520-1500ms1460-1440sm135 0-1300vswOneapplicationwhereRamanspectro scopycanbeparticularlyusefulisidenti cationofinorganiccompoundsthatoftenhavel owvibrationalfrequencieslyingclosetoorev enbelow400cm ,fourand 1band,cm 1 2band,cm 1 Molecule(vibration,symmetry)(vibration,s ymmetry)(puktgrupp)inH2 OpowderRIRinH2 OpowderRIRD1h s( +) ( )

6 NO 313501380-1320vs635660-630NO+21400vs570 FHF 610-585vs12051260-1200mmC1vOCN 1292,12051215-1200sw615640-600mSCN 745sw470490-420mmC2v s(A1) (A2)NO 213301380-1320ss815635-825msD3h s(A01) (A002)BO3 3910p1000-925vs700760-680sNO 31050p1060-1020vs825835-780wsCO2 21060p1090-1050vs880890-850mC3v s(A1) (A1)SO2 3965p990-950vss615p650-620wmClO 3930p935-915s625p625-600 BrO 3800p805-770s440p445-420IO 3780p780-695s390p415-400OH+33380-3280mvs 1180-1150Td s(A1) (E)NH+43040ps1680ND+42215ps1215PO3 4935p975-960vs565600-540wmSO2 4980p1010-970vs615680-610wmClO 4930p940-930vs625IO 4790pvs325 MnO 4840p860-840vs430 CrO 4850p860-840vs370 AsO3 4810pvs340 AlH 41740p1640ss800900-800wmBF 4770pvss525wsRamanspectroscopyXI-19 1band,cm 1 2band,cm 1 Molecule(vibration,symmetry)(vibration,s ymmetry)(puktgrupp)inH2 OpowderRIRinH2 OpowderRIRD1h as( +)NO 320702190-2010vsNO+22360vsFHF 15351700-1400vsC1vOCN 2190p2220-2130ssSCN 2065p2160-2040vssC2v as(B1)NO 212301260-1230mvsD3h as(E0) (E0)BO3 31460-1240vs680-590mmNO 31400mvs720740-710mwCO2 214151495-1380wvs680740-610wmC3v as(E) (E)

7 SO2 3950970-890ms470520-470smClO 3980990-965ms480500-460 BrO 3830830-800ms350IO 3825830-760ms350OH+33380-3270mvs1700-160 0msTd as(T2) (T2)NH+43145s14001430-1390sND+42350s1065 PO3 410801100-1080s420500-400SO2 411001140-1080wvs450wClO 411301140-1080460IO 4850255 MnO 4920940-880355 CrO 4885915-870350 AsO3 4810vs400 AlH 417401785vs745800-700ssBF (ortheelectricvectoroftheincidentradiati on,~E), ,parallelwiththepolarizationplaneofthein cidentlight,Ik,andperpendiculartoit,I?,o necandeterminethedepolarizationratio as =I?Ik:(XI:16)Thepolarizationdirectionsar ede cellLaser inEAnalyserOpticalaxisSpectrometerI||I = = ,respectively, I|| ~ni=ez= (ki)andEiy(?i). anglewillpropagateinthedirection~ns= (ks)andpy(?s).Thescatteredelectricvector isparallelwithorperpendiculartothescatte ringplane, 'sapproximation( ,assumingthatthepolarizabilitytensorisad iabatic)as(py)=( yy)Ey(pz)=( zy)Ey(XI:17) , ,byreplacing( yy)2by<( yy)2>.

8 Theisotropicmeanvalueisexpressedbyusingi nvariantquantitiesthatcanbede nedinseveraldi (i)XI-22 MolecularspectroscopyzyxOni = ezEy( i)Ex(||i)ns = expz(||s)py( s) ( xx+ yy+ zz);(XI:18)(ii)anisotropy 2=12 j xx alphayyj2+j yy alphazzj2+j zz alphaxxj2 +34 j xy+ yxj2+j xz+ zxj2+j yz+ zyj2 ;(XI:19)(iii)antisymmetricanisotropy 2=34 j xy yxj2+j yz zyj2+j zx xzj2 :(XI:20)Theintensityofanoscillatingdipol eattheangle totheaxisofthedipoleisI=K!!4(p)2sin2 :(XI:21)Hereonlyscatteringat90 angleisconsidered, .e., = = ( =2;?s;?i)=K!N!4<( yy)2>E2y:(XI:22)Similarlyonecanobtaintheinten sityI( =2;ks;?i)=K!N!4<( zy)2>E2y:(XI:23)Usingtheisotropicinvariantqua ntitiestheintensitiescanbewrittenasI( =2;?s;?i)=K!N!4 45a2+4 245 E2y(XI:24)9 Foradiscussionoftheinvariantquantitiesan dtheirrelationtothepolarizabilitytensor, seeanyadvancedtextbookinelectrodynamics, ( =2;ks;?)

9 I)=K!N!4 215 E2y:(XI:25)Usingthesenotations,thedepola rizationratiocanbewrittenas ( =2;?i)=I( =2;ks;?i)I( =2;?s;?i)=3 245a2+4 2:(XI:26) ' ; ' , (cm-1)Intensity (arbitrary units)NH4 ReO4 (NH4) (ReO4) (ReO4)50 100 150 200 250 Wavenumber (cm-1)Intensity (arbitrary units)Lattice , ,17(1986) , bresand ,typicallyapproximately10 lmscanbestudied, ,byusingasampleholderwherethelightisre ectedonthe thick lmsoflong-chainedorganicmolecules,of75 thickphospholipids,of6nmthicktitaniumoxi de lmsorof1 mthickpolymer substrateGlassFilmLaser uselightandphotographthesurfacethroughan otch , ,whichisastrongscatterer, ,inparticularresonanceRamanandSERS, uorescence, ,infraredlightisoftenusedinpar-ticularin FT-Ramaninstrumentsbecauseoflowprobabili tyof uorescenceisobserved, uorescenceoccursoneshould,ifpossible, ' (9-vinylcarbazol)

10 Uorescentlightonemaytrytouseahighlaserpo werandseetheveryweakRamansignalsontopoft hestrongbroad (cm-1)Intensity (arbitrary units)830 nm514 (9-vinylcarbazol)attwoincidentlaserwavel engthsofwhichoneinduces inSlitSampleSampleLaser , , ,thewavelengthofanelectronic transitiontheRamansignalofthestretchingv ibrationofthe bondwillbea , (PEP) (cm-1)Intensity (arbitrary units)244 nm514 nm** rsttermoftheKramers-Heisenbergequationwh eretheenergydenominatorcontainsthedi erenceoffrequencies(seeAppendixI).Thisdi , ,68(2995) ,SERS) ,goldinparticular, ,2-bis(4-pyridyl)-ethylene(BPE) (cm-1)Intensity (arbitrary units) , ,82(2004) ,CARS).Oneofthemhasa xedfrequence 1andtheotherisadyelaseroranotherlaserlig htsourcewithadjustablefrequency eldswillinteractandastrongscatteredlaser beamwiththefrequency 3=2 1- , , laserDye laserScattered eldofapplicationisthevibrationspectrosco pyofmoleculesin 1and 2interactandcreatethetwovirtualstatesja> andjb> (3).