Theory of electron correlation in atoms and molecules

Abstract

Corrections to the Hartree-Fock (H.F.) wave function, $\Phi_0$, and energy of a many-electron system are given. By the use of operator techniques in perturbation theory, the first-order w.f., $X'_1$, is obtained in terms of pair functions. These satisfy equations just like those of an actual two-electron system, except that now each electron moves in the H.F. field of the entire N-electron `medium' added to the field of nuclei. Every pair function must be orthogonalized to each of the two H.F. orbitals associated with it to get the complete $X'_1$. This $X'_1$ determines both E$_2$ and E$_3$. The second-order energy. E$_2$, comes out as the sum of pair interactions and three- and four-body correlations due to the exclusion principle. The latter may be incorporated into the pair energies if each pair function is orthogonalized also to the remaining H.F. orbitals of $\Phi_0$. The approach allows the valence and inner shells, etc., to be discussed separately and extends some of the concepts of quantum chemistry based on orbital approximations so as to include correlation.