南京大学结构化学双语课件ch5lec1

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1、Chapter5Poly-atomicMoleculesMolecularOrbitalsandEnergylevelsWalshRuleandMolecularGeometry(Angular)ValenceBondOrbitalsandHybridizationHybridizationandGeometry(Bondlengths)VSPER(ValenceShellElectronpairRepulsion)5.1UnderstandingtheMolecularOrbitalsandEnergyLevels-GroupTheoreticalApproaches1.Sy

2、mmetryinHamiltonian2.SymmetryinWavefunction3.FatorizationofSecularEquation（约化）OrthonormalityofBasisFunctionsTheoremVThebasisfunctionsoftheirreducibleREPsofagroupareorthogonaltoeachother.1-DREP---g=1.n-DREP---ghasn2values.4.6GroupTheoryandWaveFunctionsSymmetryofwavefunctionsSymmetryinHamilton

3、ian:Thesimilaritytransformationdoesnotchangethemolecularframe,themolecularenergyormolecularorbitaldistribution.Therefore,itdoesnotchangethehamiltonian.WehaveRĤR-1=Ĥ4.6GroupTheoryandWaveFunctionsSymmetryofwavefunctionsHamiltonian:Willnotchangeuponanysymmetryoperationofthemoleculepointgroupact

4、ingonit.4.6GroupTheoryandWaveFunctionsSymmetryofwavefunctionsSymmetryOperationonSchrödingerEq.Ĥy=EyRĤy=REyRRĤR-1Ry=ERyĤRy=ERyRyisalsoaneigenvectorofĤ,withthesameeigenvalueEasycorrespondsto.4.6GroupTheoryandWaveFunctionsSymmetryofwavefunctionsIfeigenvalueEisnotdegenerate,thenRy=cyWhichmeansyi

5、sabasisforsome1-DI.R..4.6GroupTheoryandWaveFunctionsSymmetryofwavefunctionsIfeigenstateEisl-folddegenerate,thenWhichmeansset{y1,y2,…,yl}isabasisforthisl-DI.R.E{y1,y2,…,yl}4.6GroupTheoryandWaveFunctionsSymmetryofwavefunctionsInLCAOapproachofMOtheory,weneedtosolvethesecularequation4.6GroupTheo

6、ryandWaveFunctionsSymmetryofwavefunctionsWecantransformtheoriginalbasesofAO’sintoLinearCombinationsofAO’swhichhavethesamepropertiesofsomeI.R.s(SymmetryAdaptedLinearCombination),thereforetheSecularEquationisblockdiagonalized.AOSALC?4.6GroupTheoryandWaveFunctionsSymmetryofwavefunctionsH-ESG1G2

7、......00BlockDiagonalizedAOSALCnnn2n2n1n1G4.6GroupTheoryandWaveFunctionsSymmetryofwavefunctionsStep1ReducetheREPspannedbytheAObasis.Obtaintheni’sforeachI.R.Step2ConstructniSALCsforeachI.R..Step3Transformthehamiltonianmatrixintoblockdiagonalizedf