Semilocal density functional theory with correct surface asymptotics

TL;DR

This paper derives an exact condition for correct surface asymptotics within semilocal density functional theory and demonstrates its practical incorporation at the meta-GGA level, improving surface property predictions.

Contribution

It introduces a new exact condition for surface asymptotics in semilocal DFT and shows how to implement it practically at the meta-GGA level.

Findings

The derived condition accurately describes surface asymptotics.

Incorporation of the condition improves surface energy calculations.

The Airy-gas model relates closely to metal surface properties.

Abstract

Semilocal density functional theory is the most used computational method for electronic structure calculations in theoretical solid-state physics and quantum chemistry of large systems, providing good accuracy with a very attractive computational cost. Nevertheless, because of the non-locality of the exchange-correlation hole outside a metal surface, it was always considered inappropriate to describe the correct surface asymptotics. Here, we derive, within the semilocal density functional theory formalism, an exact condition for the image-like surface asymptotics of both the exchange-correlation energy per particle and potential. We show that this condition can be easily incorporated into a practical computational tool, at the simple meta-generalized-gradient approximation level of theory. Using this tool, we also show that the Airy-gas model exhibits asymptotic properties that are closely related to the ones at metal surfaces. This result highlights the relevance of the linear effective potential model to the metal surface asymptotics.