南京大学结构化学双语教学教案CH5LEC1.ppt

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1、Chapter5Poly-atomicMoleculesMolecularOrbitalsandEnergylevelsWalshRuleandMolecularGeometry(Angular)ValenceBondOrbitalsandHybridizationHybridizationandGeometry(Bondlengths)VSPER(ValenceShellElectronpairRepulsion)5.1UnderstandingtheMolecularOrbitalsandEnergyLevels-Grou

2、pTheoreticalApproaches1.SymmetryinHamiltonian2.SymmetryinWavefunction3.FatorizationofSecularEquation（约化）OrthonormalityofBasisFunctionsTheoremVThebasisfunctionsoftheirreducibleREPsofagroupareorthogonaltoeachother.1-DREP---g=1.n-DREP---ghasn2values.4.6GroupTheoryandWa

3、veFunctionsSymmetryofwavefunctionsSymmetryinHamiltonian:Thesimilaritytransformationdoesnotchangethemolecularframe,themolecularenergyormolecularorbitaldistribution.Therefore,itdoesnotchangethehamiltonian.WehaveRĤR-1=Ĥ4.6GroupTheoryandWaveFunctionsSymmetryofwavefuncti

4、onsHamiltonian:Willnotchangeuponanysymmetryoperationofthemoleculepointgroupactingonit.4.6GroupTheoryandWaveFunctionsSymmetryofwavefunctionsSymmetryOperationonSchrödingerEq.Ĥy=EyRĤy=REyRRĤR-1Ry=ERyĤRy=ERyRyisalsoaneigenvectorofĤ,withthesameeigenvalueEasycorrespondsto

5、.4.6GroupTheoryandWaveFunctionsSymmetryofwavefunctionsIfeigenvalueEisnotdegenerate,thenRy=cyWhichmeansyisabasisforsome1-DI.R..4.6GroupTheoryandWaveFunctionsSymmetryofwavefunctionsIfeigenstateEisl-folddegenerate,thenWhichmeansset{y1,y2,…,yl}isabasisforthisl-DI.R.E{y1

6、,y2,…,yl}4.6GroupTheoryandWaveFunctionsSymmetryofwavefunctionsInLCAOapproachofMOtheory,weneedtosolvethesecularequation4.6GroupTheoryandWaveFunctionsSymmetryofwavefunctionsWecantransformtheoriginalbasesofAO’sintoLinearCombinationsofAO’swhichhavethesamepropertiesofsom

7、eI.R.s(SymmetryAdaptedLinearCombination),thereforetheSecularEquationisblockdiagonalized.AOSALC?4.6GroupTheoryandWaveFunctionsSymmetryofwavefunctionsH-ESG1G2......00BlockDiagonalizedAOSALCnnn2n2n1n1G4.6GroupTheoryandWaveFunctionsSymmetryofwavefunctionsStep1Reducet

8、heREPspannedbytheAObasis.Obtaintheni’sforeachI.R.Step2ConstructniSALCsforeachI.R..Step3Transformthehamiltonianmatrixintoblockdiagonalizedf