Separated Wavefunctions for the Ground State of Two-Electron Atoms

Abstract

Partially separated wavefunctions of the form ${\mathrm{U(r}}_1{\mathrm{,\; r}}_2{\mathrm{)W(r}}_{12})$ yield helium ground‐state energies in error by as little as 4 × 10⁻⁴ a.u. Completely separated functions ${\mathrm{F(r}}_1{\mathrm{)F(r}}_2{\mathrm{)W(r}}_{12})$ give distinctly poorer results. The correlation function ${\mathrm{W(r}}_{12}{\text{)\hspace{0.17em}=\hspace{0.17em}(1\hspace{0.17em}+\hspace{0.17em}Br}}_{12}{)}^{\text{1\hspace{0.17em}/\hspace{0.17em}2}}$ yields energy errors of less than 1 × 10⁻³ a.u. for H⁻, He, and Li⁺.