The extended Hartree-Fock equations for atoms

The consequences of adopting a precise definition of the extended Hartree-Fock scheme proposed in an earlier paper are examined. It is shown that the extended Hartree-Fock scheme can correct for the zero-order mixing of configurations for certain, but not all, states of small atoms. An earlier calculation of the second-order extended Hartree-Fock energy of the ground states of beryllium-like ions is shown to be in error and the correct value is calculated by an alternative but more accurate and yet simpler method. The extended Hartree-Fock scheme is shown to give an augmented significance to the perturbation treatment of Hartree-Fock equations. It is also shown that in this scheme the purely variationally determined mixing coefficients for configurations depend, in general, on the nuclear charge Z .