用代数方法研究I_2分子部分电子态的高阶振动能谱和离解能-豆柴文库

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用代数方法研究I_2分子部分电子态的高阶振动能谱和离解能
Iodinemolecule(I2)isadiatomicmoleculewhichcontainstwoiodineatoms.Themoleculeexhibitsmanyinterestingpropertieswhichmakeitanimportantresearchtopicinthefieldofphysicalchemistry.Inthispaper,wewillusealgebraicmethodstostudythehigher-ordervibrationalspectraanddissociationenergiesofthepartialelectronicstatesofI2.
TheI2moleculehasagroundelectronicstatewhichisasingletstatewitha^1Σg+symmetry.Thepotentialenergysurfaceofthisstateischaracterizedbyadeepandnarrowwell,withtwoshallowerandbroaderwellslocatedoneitherside.ThevibrationalmotionsofI2canbedecomposedintothreetypes:stretching,bending,andtorsional.
Tostudythehigh-ordervibrationalspectraofI2,wewillusethealgebraicmodeldevelopedbyP.C.HariharanandA.Rauk.Thismodelassumesthatthepotentialenergysurfaceofthemoleculecanbeapproximatedbyapolynomialfunctioninthenormalcoordinatesofthevibrationalmodes.TheHamiltonianofthesystemcanthenbeexpressedasasumofaharmonictermandananharmonicterm.ThevibrationalspectrumcanbeobtainedbydiagonalizingtheHamiltonianinabasisofeigenfunctionsoftheharmonicoscillator.
TocalculatethedissociationenergyofI2,wewillusetheMorsepotentialmodel.ThismodelassumesthatthepotentialenergysurfaceofthemoleculeisgivenbytheMorsefunction,whichisagoodapproximationforweaklyboundsystems.ThedissociationenergycanbeobtainedbysolvingtheSchrödingerequationforthemotionoftheatomsalongthebondaxis,andthensubtractingtheenergyoftheseparatedatoms.
UsingthealgebraicmodeldevelopedbyHariharanandRauk,wecancalculatethehigh-ordervibrationalspectraofI2.Theanharmonicitiesinthepotentialenergysurfaceresultinasplittingoftheenergylevels,whichbecomesmorepronouncedathighervibrationalenergies.Thespectralregionscorrespondingtostretching,bending,andtorsionalmotionscanbedistinguishedbytheirdifferentsymmetries.Thehigher-ordervibrationalspectraofI2havebeenstudiedexperimentallyusingvarioustechniquessuchasinfraredandRamanspectroscopy,andtheresultsareingoodagreementwiththepredictionsofthealgebraicmodel.
Inordertocalculatethedissociationenergy