Kohn-Sham Exchange Potential for a Metallic Surface

TL;DR

This paper derives and analyzes the exact exchange potential at a metallic surface within density functional theory, revealing its asymptotic behavior and structural features near the interface.

Contribution

It provides the first exact numerical and analytical results for the exchange component of the Kohn-Sham potential at a metal-vacuum interface.

Findings

The exchange potential approaches -e^2/z at large distances.

A shoulder-like structure appears near the interface.

The asymptotic behavior is unaffected by correlation effects.

Abstract

The behavior of the surface barrier that forms at the metal-vacuum interface is important for several fields of surface science. Within the Density Functional Theory framework, this surface barrier has two non-trivial components: exchange and correlation. Exact results are provided for the exchange component, for a jellium metal-vacuum interface, in a slab geometry. The Kohn-Sham exact-exchange potential $V_{x}(z)$ has been generated by using the Optimized Effective Potential method, through an accurate numerical solution, imposing the correct boundary condition. It has been proved analytically, and confirmed numerically, that $V_{x}(z\to \infty)\to - e^{2}/z$; this conclusion is not affected by the inclusion of correlation effects. Also, the exact-exchange potential develops a shoulder-like structure close to the interface, on the vacuum side. The issue of the classical image potential is discussed.