Ab initiolocal-density potential for atoms: The modifiedΞmethod

In the $\Xi$ method, the self-interaction part of the total exchange-correlation potential in atoms is evaluated exactly and the remaining "pure exchange" is approximated using a Fermi-hole formalism. A theoretical derivation of an ab initio exchange potential for atoms using a simple model of this pure exchange hole is presented. This model of the exchange hole satisfies, unlike an earlier treatment, the necessary condition that the total charge removed from the exchange hole is zero. The orbital eigenvalues and the total energies of the ground-state multiplets for various atoms and ions are reported and found to be in close agreement with the Hartree-Fock values.