Correlated Wavefunctions for the Ground State of H−, He, and Li+

Energies are calculated variationally using a closed‐shell orbital product times the correlation function $$g_a{\text{\hspace{0.17em}=\hspace{0.17em}[1\hspace{0.17em}+\hspace{0.17em}λr}}_{12}{\mathrm{\hspace{0.17em}+\hspace{0.17em}\mu (r}}_1{\mathrm{\hspace{0.17em}-\hspace{0.17em}r}}_2{)}^2{\mathrm{\hspace{0.17em}+\hspace{0.17em}\nu r}}_{12}^2{\mathrm{(r}}_1{\mathrm{\hspace{0.17em}+\hspace{0.17em}r}}_2{)}^{\mathrm{-n}}{]}^{\text{1/2}}$$ $\text{(n\hspace{0.17em}=\hspace{0.17em}1}\mathrm{or}\text{2)}$ . Energy errors for H⁻, He, and Li⁺, respectively, are 0.00193, 0.00019, and 0.00021 a.u. when $\text{n\hspace{0.17em}=\hspace{0.17em}1}$ and 0.00229, 0.00025, and 0.00064 a.u. when $\text{n\hspace{0.17em}=\hspace{0.17em}2}$ or $\text{ν\hspace{0.17em}=\hspace{0.17em}0}$ . An explanation is proposed for the fact that $g_a$ is much more accurate for He and Li⁺ than for H⁻, whereas the opposite is true for the correlation function $g_b{\text{\hspace{0.17em}=\hspace{0.17em}1\hspace{0.17em}+\hspace{0.17em}λr}}_{12}{\mathrm{\hspace{0.17em}+\hspace{0.17em}\mu (r}}_1{\mathrm{\hspace{0.17em}-\hspace{0.17em}r}}_2{)}^2$ . For He, expectation values other than the energy are typically accurate to four figures.