Local self-interaction-free approximate exchange-correlation potentials in the variational density functional theory for individual excited states

Local self-interaction-free approximate exchange-correlation potentials are derived and applied in the Levy–Nagy variational density functional theory for individual excited states. The self-interaction-corrected (SIC) local von Barth–Hedin and Vosko–Wilk–Nusair potentials are studied for excited states of some atoms and ions. Accurate ionization energies and correct asymptotic decay of excited SIC potentials are observed. Approximate validity of Koopmans’ theorem for excited states are shown.