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

C M Horowitz,C R Proetto,J M Pitarke

doi:10.1103/physrevb.78.085126

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 imagelike $(\ensuremath{\sim}\ensuremath{-}{e}^{2}/z)$ but with a coefficient that differs from that of the classical image potential ${V}_{\text{im}}(z)=\ensuremath{-}{e}^{2}/4z$. 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.

Highlights

The analysis of the electronic structure of metal surfaces poses a big theoretical challenge; a suitable calculational tool is needed for large, interacting, and strongly inhomogeneous many-electron systems
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 imagelikeϳ−e2 / zbut with a coefficient that differs from that of the classical image potential Vimz = −e2 / 4z
We have reported benchmark exact-exchange selfconsistent calculations of the KS potential, surface energy, and work function of jellium slabs in the framework of the OEP scheme

Summary

INTRODUCTION

The analysis of the electronic structure of metal surfaces poses a big theoretical challenge; a suitable calculational tool is needed for large, interacting, and strongly inhomogeneous many-electron systems. Several advantages are associated with the use of the exact-exchange energy functional of DFT: ͑iit corrects the self-interaction problem inherent in approximate treatments of the exchange energy19 ͑this problem is acute for localized systems such as atoms and molecules, it is not relevant for extended systems like bulk solids and solid surfaces; ͑iiit yields great improvements in the study of the KS eigenvalue spectrum,[20] semiconductor band structures and excitations,[21] and nonlinear optical properties;22 ͑iiiit yields the correct asymptotics;23 ͑ivit reproduces the derivative discontinuity which should be present in the KS exchange potential each time the number of particles crosses through an integer value;[24,25,26,27,28] andvit yields the correct twodimensional2Dexchange energy per particle in the case of a quasi-2D electron gas.[29] It is the aim of this paper to provide benchmark exact-exchange OEP calculations for jellium slabs, with the expectation that more accurate DFT schemes that include correlation be developed by starting from a well founded exchange analysis and tested once reduced to their exchange-onlyx-onlycounterparts.

OEP APPROACH

ASYMPTOTICS OF THE EXACT-EXCHANGE KS POTENTIAL

SURFACE ENERGY

WORK FUNCTION

CONCLUSIONS