Nonrelativistic variationally optimized exchange potentials for Ne-like atomic ions having large atomic number

Abstract

In an earlier study, the exchange energy density ${\ensuremath{\epsilon}}_{x}(r)$ has been calculated analytically for Ne-like atomic ions in the nonrelativistic limit of large atomic number Z. Here, though now by numerical methods based on the optimized exchange potential approximation, corresponding results are obtained for ${V}_{x}(r)$ for such ten-electron ions at large Z. The approach to the bare Coulomb limiting form of the $1/Z$ expansion is considered in some detail, as are corrections to the Slater potential ${V}_{x}^{\mathrm{Sl}}(r),$ given in terms of the exchange energy density and ground-state density $\ensuremath{\rho}(r)$ by $2{\ensuremath{\epsilon}}_{x}(r)/\ensuremath{\rho}(r).$