Explicit density-functional exchange potential with correct asymptotic behavior

Abstract

In this paper, a density-functional exchange potential is proposed. The suggested exchange potential reproduces the correct asymptotic behavior of finite systems: $\ensuremath{-}1∕r$, without significant increase in computational costs over a local-density approximation. Our model exchange potential, which is an explicit functional of a density and the gradient of the density, is given by a hybridization procedure of a Hartree potential and the homogeneous electron gas limit of the exchange potential. Since the Hartree potential behaves as $N∕r$ in an asymptotic region with $N$ number of electrons, it is utilized for achieving the correct $\ensuremath{-}1∕r$ asymptotic behavior in our model exchange potential. We found that the suggested exchange potential can yield very good estimates for the ionization potential of atoms and ions from the highest occupied orbital energies.