Localized versus extended systems in density-functional theory: some lessons from the Kohn-Sham exact exchange potential

TL;DR

This paper rigorously analyzes the asymptotic behavior of the Kohn-Sham exact exchange potential at metal surfaces, revealing it decays as ln(z)/z in extended systems, contrasting with localized systems, and constrains approximate functionals.

Contribution

It proves the asymptotic decay of the Kohn-Sham exchange potential in extended systems, providing insights into long-range behavior in density-functional theory.

Findings

Kohn-Sham exchange potential decays as ln(z)/z at metal surfaces

Decay behavior differs between extended and localized systems

Provides constraints for approximate correlation-energy functionals

Abstract

A long-standing puzzle in density-functional theory is the issue of the long-range behavior of the Kohn-Sham exchange-correlation potential at metal surfaces. As an important step towards its solution, it is proved here, through a rigurouos asymptotic analysis and accurate numerical solution of the Optimized-Effective-Potential integral equation, that the Kohn-Sham exact exchange potential decays as $\ln(z)/z$ far into the vacuum side of an {\it extended} semi-infinite jellium. In contrast to the situation in {\it localized} systems, like atoms, molecules, and slabs, this dominant contribution does not arise from the so-called Slater potential. This exact-exchange result provides a strong constraint on the suitability of approximate correlation-energy functionals.