Hartree-Fock Calculations for Atoms with Inner-Shell Vacancies

For configuration states such as 2p⁵3p⁵¹S, ³P, ¹D the Hartree-Fock method produces total wave functions with an incorrect form as the atomic number Z→∞. It is shown how a correct form can be obtained, with similar accuracy as the Hartree-Fock wave function, for a statistically weighted average of 2p⁵3p⁵³S, ¹P, ³D.