Hartree-Fock Procedure for Somensn′sS1Configurations

Abstract

A numerical Hartree-Fock procedure is described for computing wave functions for $\mathrm{ns}{n}^{\prime }s{}_{}{}^1{}_{}{}^{}S$ configurations in which the radial functions for the two $s$ electrons are not assumed to be orthogonal. When the two $s$ electrons are equivalent, this approach corresponds to the unrestricted Hartree-Fock approximation. The procedure was applied to some 2- and 4-electron systems. Results are reported for $1s1s^{\prime }{}_{}{}^1{}_{}{}^{}S$ of He, ${\mathrm{Li}}^{+}$, and ${\mathrm{Be}}^{2+}$ as well as $1s1s^{\prime }\left({}_{}{}^1{}_{}{}^{}S\right)2\mathrm{sns}{}_{}{}^1{}_{}{}^{}S$, $n=2, 3, 4$ of Be. The total energies are compared with those of other approximations, and the transition integrals for the unrestricted approximation are shown to differ only slightly from those of the Hartree-Fock approximation.