Über die Erweiterung der Hartree-Fockschen Näherung durch Korrelationsfunktion

Abstract

To take into account the correlation between the valence electrons of an atom with N core electrons and two valence electrons we make use of the trial function suggested by FOCK WESSELOW and PETRASHEN (Here Ãis the antisymmetrisation operator, φ1, φ2,...,φN are the atomic core one-electron wave functions and Φ is the two-electron wave function of the valence electrons.) We study the question: which system of equations will provide us with the best determination of the functions φ1, φ2,...,Φ? With the aid of the energy minimum principle it is shown that if one neglects the effect of the valence electrons on the atomic core the core electron functions can be determined from the HARTREE-FOCK equations HF φi=Eiφi, (HF= HARTREE-FOCK HAMILTONian operator. i =1,2..... N) while the valence electron function satisfies the equation: {The operator [1— Ω(1,2)] is a projection operator with the following property: if one expands the function Φ(1,2) in terms of the functions of the operator HF (1) +HF (2) then the operator [1— Ω(1,2)] removes the core functions φ1,φ2,...,φN from the expansion.}