Semilocal approximations to the Kohn-Sham exchange potential as applied to a metal surface

TL;DR

This paper compares various semilocal exchange potentials in density-functional theory against the exact exchange OEP for a metal surface model, revealing their asymptotic behaviors and limitations in predicting ionization potentials.

Contribution

It provides a detailed analysis of three semilocal exchange potentials' asymptotics and their deviations from the exact OEP in a metal-vacuum interface context.

Findings

Semilocal potentials approach their asymptotes faster than OEP.

None of the potentials exactly match the OEP asymptotics of -e^2/z.

Some potentials overestimate ionization potentials due to their asymptotic behavior.

Abstract

Several semilocal exchange potentials usually employed in the framework of density-functional theory (DFT) are tested and compared with their exact counterpart, the exchange Optimized Effective Potential (OEP), as applied to the jellium-slab model of a metal-vacuum interface. Driven by their explicit dependence on the ground-state density, its gradient, and its kinetic-energy density, the three analyzed semilocal exchange potentials approach their respective asymptotic limits faster than in the case of the OEP, all of them having an asymptotic scaling of the form $-\alpha\,e^2/z + V_{\infty}$, with $\alpha < 1$. Here we provide the leading analytic asymptotics of the three model potentials under study, and we find that none of them exhibits the exact OEP slab asymptotics $-\;e^2/z$. While the so-called Becke-Roussel potential's leading asymptote is close to its exact OEP counterpart, the other two model potentials under study approach a material-dependent positive constant value far into the vacuum, resulting in considerably overestimated ionization potentials.