Self-consistent approximation to the Kohn-Sham exchange potential

Abstract

A scheme of approximation of the Kohn-Sham exchange potential ${\mathit{v}}_{\mathit{x}}$ is proposed, making use of a partitioning of ${\mathit{v}}_{\mathit{x}}$ into the long-range Slater ${\mathit{v}}_{\mathit{S}}$ and the short-range response ${\mathit{v}}_{\mathrm{resp}}$ components. A model potential ${\mathit{v}}_{\mathrm{resp}}^{\mathrm{mod}}$ has been derived from dimensional arguments. It possesses the proper short-range behavior and the atomic-shell stepped structure characteristic for ${\mathit{v}}_{\mathrm{resp}}$. When combined with the accurate ${\mathit{v}}_{\mathit{S}}$, ${\mathit{v}}_{\mathrm{resp}}^{\mathrm{mod}}$ provides an excellent approximation to the exchange potential of the optimized potential model ${\mathit{v}}_{\mathit{x}}^{\mathrm{OPM}}$. With the generalized-gradient approximation to ${\mathit{v}}_{\mathit{S}}$ ${\mathit{v}}_{\mathrm{resp}}^{\mathrm{mod}}$ provides an efficient density-functional-theory approach that fits closely the form of the accurate exchange potential and yields reasonably accurate exchange and total energies as well as the energy of the highest occupied orbital.