Self-consistency test for the exchange-only Kohn-Sham potential

Abstract

The relationship, recently derived by Krieger, Li, and Iafrate [Phys. Lett. A 148, 470 (1990)], that ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{m}\mathrm{\ensuremath{\sigma}}}$, the exchange-only Kohn-Sham (KS) single-particle energy eigenvalue corresponding to the highest occupied orbital, exactly equals \ensuremath{\epsilon}${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathit{m}\mathrm{\ensuremath{\sigma}}}^{\mathrm{HF}}$, the expectation value of the Hartree-Fock (HF) single-particle Hamiltonian averaged over this Kohn-Sham orbital, is employed to test the accuracy of the local-spin-density (LSD) exchange-only potential as well as the recent results of Wang et al. [Phys. Rev. A 41, 78 (1990)]. For the eleven atoms with closed subshells from He to Xe we find that in the LSD approximation ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{m}\mathrm{\ensuremath{\sigma}}}$ is only approximately equal to 60% of \ensuremath{\epsilon}\ifmmode\bar\else\textasciimacron\fi{} $_{\mathit{m}\mathrm{\ensuremath{\sigma}}}^{\mathrm{HF}}$, whereas the potential of Wang et al. yields ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{m}\mathrm{\ensuremath{\sigma}}}$\ensuremath{\simeq}\ensuremath{\epsilon}\ifmmode\bar\else\textasciimacron\fi{} $_{\mathit{m}\mathrm{\ensuremath{\sigma}}}^{\mathrm{HF}}$ to within 0.5%, providing further evidence that it closely approximates the exact KS exchange-only potential.