Asymptotics of the metal-surface Kohn-Sham exact exchange potential revisited

TL;DR

This paper investigates the asymptotic behavior of the exact exchange potential in metal surfaces, confirming previous analytical results and providing constraints for future functional development in density-functional theory.

Contribution

It offers a rigorous numerical analysis of the exchange potential's asymptotics, refutes a prior criticism, and informs the construction of better exchange-correlation functionals.

Findings

Confirmed $V_x(z) o e^2 rac{ ext{ln}(az)}{z}$ asymptotics

Refuted prior criticism of earlier work

Provided constraints for exchange-correlation functional development

Abstract

The asymptotics of the Kohn-Sham (KS) exact exchange potential $V_x(z)$ of a jelliumlike semi-infinite metal is investigated, in the framework of the optimized-effective-potential formalism of density-functional theory. Our numerical calculations clearly show that deep into the vacuum side of the surface $V_x(z) \propto e^2 \ln(az) / z$, with $a$ being a system-dependent constant, thus confirming the analytical calculations reported in Phys. Rev. B {\bf 81}, 121106(R) (2010). A criticism of this work published in Phys. Rev. B {\bf 85}, 115124 (2012) is shown to be incorrect. Our rigorous exchange-only results provide strong constraints both for the building of approximate exchange functionals and for the determination of the still unknown KS correlation potential.