A Discussion of Analytic and Hartree-Fock Wave Functions for1s2Configurations fromH−to C v

Two simple analytic expressions are presented, both of which are excellent approximations to a Hartree-Fock $1s$ wave function in a $1s^2$ configuration. One of these expressions is a two-parameter function and the other a three-parameter one. The parameters were chosen variationally and their values are given for the various members of the isoelectronic sequence from ${\mathrm{H}}^{-}$ to C v. The energies were also computed, and the energies and the wave functions are compared with the corresponding Hartree-Fock quantities where the latter are known. Both the two- and the three-parameter functions approximate the numerical functions closely and give energies as low, or almost as low, as the more reliable of the Hartree-Fock energies. The three-parameter wave function proves to be the better, particularly in the case of ${\mathrm{H}}^{-}$. Some comments are made on the existing numerical functions and their energies.