The correlated Hartree-Fock equations and the generalised density matrices

Abstract

The paper deals with a study of correlation effects in many-electron systems. Coulomb correlation is introduced into the theory by multiplying the Slater determinant formed from the one-electron orbitals by a correlation factor which is a symmetric and increasing function of the inter-electronic distances. The integro-differential equations satisfied by the best one-electron orbitals have been been deduced for non-stationary systems. From the extended Hartree-Fock equations given by Löwdin, the integro-differential equations satisfied by the density matrices have been derived. An expression for the energy-matrix of the system which is helpful in deriving a correlated Thomas-Fermi charge distribution, has also been given.