combustionchemistryandpropulsion(激光诊断)

Lecture4:PolyatomicSpectraAmmoniamolecule1.Fromdiatomictopolyatomic2.Classificationofpolyatomicmolecules3.Rotationalspectraofpolyatomicmolecules4.Vibrationalbands,vibrationalspectraA-axisNHRotation–Diatomics21.FromdiatomictopolyatomicRecall:FordiatomicmoleculesIchcmB218,Centrifugaldistortionconstant22..111,JDJJBJcmJFRREnergy:Rotationalconstant:SelectionRule:Lineposition:311412JDJBJJ11'JJJNotes:1.Dvissmall,i.e.,2.E.g.,forNO,62210319007.144eNOBBD1/4/2vibBBD01.0~/2JBD→Even@J=60,Whataboutpolyatomics(≥3atoms)?3D-bodyrotation31.FromdiatomictopolyatomicABC3principalaxes(orthogonal):A,B,C3principalmomentsofinertia:IA,IB,ICMoleculesareclassifiedintermsoftherelativevaluesofIA,IB,ICConvention:A-axisisthe“unique”or“figure”axis,alongwhichliesthemolecule’sdefiningsymmetryTypesofmolecules42.ClassificationofpolyatomicmoleculesTypeLinearMoleculesSymmetricTopsSphericalTopsAsymmetricRotorsRelativemagnitudesofIA,B,CIB=IC;IA≈0*IB=IC≠IAIA≠0IA=IB=ICIA≠IB≠ICExamplesCO2C2H2OCSNH3CH3FBCl3CH4H2ONO2*Actuallyfinite,butquantizedmomentummeansitisinloweststateofrotationRelativelysimpleNodipolemomentNotmicrowaveactiveLargestcategoryMostcomplexCarbonoxysulfideAcetyleneBorontrichlorideLinearmolecules52.ClassificationofpolyatomicmoleculesE.g.,Carbonoxy-sulfide(OCS)OCSCenterofmassrCOrCSrCO=1.165ÅrCS=1.558ÅrCrS161232IB=IC;IA≈0cIhcmBB218,ABCABCSymmetrictops62.ClassificationofpolyatomicmoleculesProlateIAIB=IC,AB=CE.g.,CH3FC.M.11219IB=IC≠IA;IA≠0cIhcmBB218,cIhcmAA218,cIhcmCC218,CFHTripod-like(tetrahedralbonding)HHABCABCSymmetrictops72.ClassificationofpolyatomicmoleculesOblateIAIB=IC,AB=CE.g.,BCl3(Planar)C.M.35.511BClPlanarviewClClABCABCIB=IC≠IA;IA≠0cIhcmBB218,cIhcmAA218,cIhcmCC218,Noelec.dipolemom.→noQMselectionruleABCSphericaltopsAsymmetricrotors82.ClassificationofpolyatomicmoleculesC.M.IA=IB=ICE.g.,CH4(methane)CHHHHCubew/CatcenterandHatdiagonalcornersSymmetric,butNodipolemomentNorotationalspectrumIA≠IB≠ICE.g.,H2OC.M.OHHBAC104.45oComplexandnotaddressedhereLinearmolecules(IB=IC;IA≈0)ExamplesEnergiesandlinepositions93.RotationalspectraofpolyatomicmoleculesOCSHCNCO2C2H2HC2ClSymmetric,nodipolemomentMustbeasymmetrictohaveelectricdipolemoment(isotopicsubstitutiondoesn’tchangethisasbondlengthsremainfixed)Note:LargerI,smallerB(&linespacing)thandiatomicsCantreatlikediatomic(1valueofI)→samespectrum322141211JDJBJJDJJBJJFRotationalconst.Centrifugaldistortionconst.(“issuppressed,i.e.J=J”)_Linearmolecules(IB=IC;IA≈0)Bondlengths103.RotationalspectraofpolyatomicmoleculesNatomsN-1bondlengthstobefoundAbs./Emis.spectraB1valueofIBUseN-1isotopesN-1valuesofIBExample:OCS(carbonoxy-sulfide)OCSCenterofmassrCOrCSrCrSO16C12S321.165Å1.558ÅUse2isotopesfor2equations:CSCOSCOCSCOSCOrrmassesIrrmassesI,,,,321218321216FFSolveforrCO,rCSSymmetrictops(IB=IC≠IA;IA≠0)2maindirectionsofrotation→2quantumnumbersQuantizedangularmomentumEnergylevels113.RotationalspectraofpolyatomicmoleculesJ(totalangularmomentum):0,1,2,…K(angularmomentumaboutA):J,J-1,…,1,0,-1,…-J+&-allowed,w/ochangeinenergy2J+1possibilitiesofKforeachJNotedegeneracy,i.e.,independentofsignofKAsbefore:Plusnew:222222222221KIJJIIIAACCBBAAiiiKJIE2,2121,KBAJBJKJFJKSymmetrictops(IB=IC≠IA;IA≠0)Q.M.SelectionrulesLinepositions123.Rotationalspectraofpolyatomicmolecules∆J=+1RememberthatJ=J’–J”∆K=0NodipolemomentforrotationaboutA-axisNochangeinKwilloccurwithabs./emis.Note:IndependentofKforarigidrotorSameasrigiddiatomic!K-dependenceintroducedfornon-rigidrotation1.12,,1cmJBJKJFKJFKJSymmetrictops(IB=IC≠IA;IA≠0)Non-rigidrotation133.RotationalspectraofpolyatomicmoleculesEffectofextendingbondlengths(w/changesinK)ChangeenergiesofrotationCentrifugaldistortionconst.DJ,DK,DJK122.422221212111,cmKDJDBJKDKJJDJJDKBAJBJKJFJKJKJKJKJE.g.,CH3F,MethylFluorideC.M.CFHHHANote:EachJhas2J+1components,butonlyJ+1frequencies151611047.1102851.0cmDcmDcmBJKJIfJ≈20,J2≈400,2DJ2≈1.6x10-3,2DJ2/B≈.2%J123ν,cm-1345672B~1.7cm-1K2102DJK(J+1)K2~10-4cm-12DJK(J+1)K2~4x10-4cm-13linesforJ=2K=2,1,0Symmetrictops(IB=IC≠IA;IA≠0)getscomplexfast!143.RotationalspectraofpolyatomicmoleculesOblateIAIB=IC,AB=CProlateIAIB=IC,AB=C21,KBAJBJKJF01182BAIIchBA21,KBAJBJKJF01182BAIIchBAExampleenergylevelsLinearSymmetrictopSphericaltopAsymmetricrotorB=C;IA≈0B=C≠A;IA≠0A=B=CA≠B≠CRotationalpartitionfunction153.RotationalspectraofpolyatomicmoleculeshcBkTQrot321hckTABQrot331hckTBQrot31hckTABCQrotMoleculeσMoleculeTypeCO22LinearNH33SymmetricTopCH412SphericalTopH2O2AsymmetricRotorσ–molecule-dependentsymmetryfactorcIhcmBB218,cIhcmAA218,cIhcmCC218,Linear(diatomic&polyatomic)andsymmetrictopmoleculesgivesimilar(equalspacing)spectraatrigidrotorlevelHighresolutionneededtodetectcorrections/splittingsSpectra→microscopicparameters(re,angles)Isotopesusefulforspectralstudies163.Rotation