Simplified Self-Consistent Field Equations with Correlations

It is pointed out that the correlation hole has, qualitatively, features analogous to the exchange one; and to the correlation, there corresponds a potential of the conventional electrical character. We can further obtain---in the case of the free-electron gas---the correlation potential averaged over all the electron states, in close correspondence with the average exchange potential of Slater. It is further reasonable to use this potential as the averaged correlation potential of the arbitrary many-electron system where the density of the free-electron gas is replaced by the density of actual charge in the system.Adding the average correlation potential as well as the averaged exchange correlation potential to the Hartree-Fock operators, we obtain the self-consistent field equations with correlations.