Spin-Projected Hartree-Fock Calculations on the He-Like Ions Using General Spin Orbitals

Abstract

Spin-projected Hartree-Fock (PHF) wave functions are obtained for the isoelectronic series ${\mathrm{H}}^{-}$, He, ${\mathrm{Li}}^{+}$, and ${\mathrm{Be}}^{++}$, using different orbitals for different spins and general spin-orbitals (GSO), in both cases of pure $s$ character. The GSO energy for He is -2.87887 a.u., accounting for 99.1% of the radial correlation energy. A natural orbital analysis of the GSO function shows that it corresponds to a configuration interaction function with three $s^2$ configurations. The one-electron energies obtained from the PHF equations are given an interpretation as ionization energies. In the GSO case, the one-electron energies are not unique, but an upper limit is obtained.