多电子波函数算子参考chap3 wavefunction.pdfVIP

Many-ElectronWaveFunction

andoperators

Basicconcepts,techniques,andnotationsofQC:

ThestructureoftheHamiltonian,theformofthewave

function,thematrixelementsoftheHamiltonianbetween

determinants,theHartree-Fockmethod,etc.

Reference:

A.SzaboandN.S.Ostlund,ModernQuantumChemistry:

IntroductiontoAdvancedElectronicStructureTheory,

DoverPublications,.,NewYork,1996

Outline

2.1TheElectronicProblem

2.2Orbitals,Slaterdeterminants,and

basisfunctions

2.3Operatorsandmatrixelements

2.4Secondzation

2.5Spin-adaptedconfigurations

Amolecularcoordinatesystem:i,j=electrons;A,B=nuclei

2.1TheElectronicProblem

Ourmaininterestistofindapproximatesolutionstothetime-t

non-relativisticSchrödingerequation:

HE

HistheHamiltonianoperatorforasystemofnucleiandelectrons.

Inatomicunits,theHamiltonianforNelectronsandMnucleiis

N12NMZANN1M12MMZAZB

H



iA

2Rr2MR

i1i1A1iAi1jiiA1A1BA

jAAB

M:theratioofthemassofnucleusAtothemassofanelectron.

A

Z:theatomicnumberofnucleusA.

A

MainfeaturesoftheHamiltonian

N12NMzANN1MMzzM12

HAB

2i