Exact-exchange Kohn-Sham potential, surface energy, and work function of jellium slabs

TL;DR

This paper presents exact-exchange self-consistent calculations of the Kohn-Sham potential, surface energy, and work function for jellium slabs using the OEP scheme, revealing image-like potentials and quantum size effects absent in LDA.

Contribution

It provides the first detailed analysis of the exact-exchange Kohn-Sham potential and related surface properties of jellium slabs within the OEP framework, highlighting differences from LDA results.

Findings

Exchange potential is image-like but with a different coefficient than classical image potential.

Surface energy oscillates with slab thickness due to quantum size effects.

Work function exhibits large quantum size effects related to the derivative discontinuity.

Abstract

Exact-exchange self-consistent calculations of the Kohn-Sham potential, surface energy, and work function of jellium slabs are reported in the framework of the Optimized Effective Potential (OEP) scheme of Density Functional Theory. In the vacuum side of the jellium surface and at a distance $z$ that is larger than the slab thickness, the exchange-only Kohn-Sham potential is found to be image-like ($\sim -e^2/z$) but with a coefficient that differs from that of the classical image potential $V_{im}(z)=-e^2/4z$. The three OEP contributions to the surface energy (kinetic, electrostatic, and exchange) are found to oscillate as a function of the slab thickness, as occurs in the case of the corresponding calculations based on the use of single-particle orbitals and energies obtained in the Local Density Approximation (LDA). The OEP work function presents large quantum size effects that are absent in the LDA and which reflect the intrinsic derivative discontinuity of the exact Kohn-Sham potential.