Effect on the Energy of Increased Flexibility in the Separable Factor of Hylleraas-Type Atomic Wave Functions fromH−to O VII

Abstract

A number of wave functions of the form $f\left(r_1\right)f\left(r_2\right)g(r_1, r_2, r_{12})$ are applied to the two-electron systems from ${\mathrm{H}}^{-}$ to Ovii. Various analytic expressions for $f$ and $g$ are employed. The values of the various parameters in $f$ and $g$ are chosen to yield the minimum energy. The wave functions, the values of the parameters, and the minimum energies are tabulated. Twenty of the twenty-six functions tabulated are presented here for the first time. For five of the remaining six functions the values of the parameters and the energies have been recomputed. The energies obtained with these wave functions as well as with functions investigated by others are examined to ascertain what improvement in the energy results from considering other functional forms for $f\left(r\right)\mathrm{}$ than the customary negative exponential. In the case of ${\mathrm{H}}^{-}$, it is clear that certain types of flexibility in $f\left(r\right)\mathrm{}$ can substantially improve the energies obtained with the simpler functions. For larger nuclear charge the improvement is definite but smaller.