Self-consistent calculations of atomic properties using self-interaction-free exchange-only Kohn-Sham potentials

Abstract

The spin-unrestricted optimized-effective-potential (OEP) method and an approximation to it due to the authors (KLI) have been applied to atoms from Li (Z=3) to Ba (Z=56) plus Au (Z=79) and Hg (Z=80) within the exchange-only scheme. Calculations were performed for the term with the lowest energy in the ground-state configuration. For a few transition elements, terms in the low-lying excited-energy-state configuration are also self-consistently calculated. We have compared our OEP and KLI results with each other and with those obtained from the spin-unrestricted Hartree-Fock (SUHF) method and the local-spin-density exchange-only (LSDX) approximation. As the spin-restricted OEP, the spin-unrestricted OEP yields nearly identical results as the corresponding SUHF. The relative difference of the total energy from that of the SUHF is only 40 ppm for ${}_{}{}^3{}_{}{}^{}\mathrm{Li}$ and monotonically decreases as Z increases to less than 2 ppm for ${}_{}{}^{80}{}_{}{}^{}\mathrm{Hg}$. The highest occupied energy eigenvalues of each spin projection, ${\mathrm{\varepsilon }}_{\mathit{m}\mathrm{\sigma }}$, and the various expectation values for the operators ${\mathit{r}}^2$, ${\mathit{r}}^{\mathrm{-}1}$, and δ(r) are all very similar to the SUHF theory.