Wavevector analysis of the jellium exchange-correlation surface energy in the random-phase approximation: detailed support for nonempirical density functionals

TL;DR

This paper presents a detailed wavevector analysis of jellium exchange-correlation surface energy using RPA, demonstrating the accuracy of nonempirical density functionals like TPSS meta-GGA in capturing long-range effects.

Contribution

It provides the first 3D wavevector analysis of jellium xc surface energy in RPA and evaluates the performance of various density functionals against these rigorous calculations.

Findings

RPA accurately captures long-range xc effects.

TPSS meta-GGA provides realistic wavevector analysis.

LSDA and PBE have specific limitations in different wavevector regions.

Abstract

We report the first three-dimensional wavevector analysis of the jellium exchange-correlation (xc) surface energy in the random-phase approximation (RPA). The RPA accurately describes long-range xc effects which are challenging for semi-local approximations, since it includes the universal small-wavevector behavior derived by Langreth and Perdew. We use these rigorous RPA calculations for jellium slabs to test RPA versions of nonempirical semi-local density-functional approximations for the xc energy. The local spin density approximation (LSDA) displays cancelling errors in the small and intermediate wavevector regions. The PBE GGA improves the analysis for intermediate wavevectors, but remains too low for small wavevectors (implying too-low jellium xc surface energies). The nonempirical meta-generalized gradient approximation of Tao, Perdew, Staroverov, and Scuseria (TPSS meta-GGA) gives a realistic wavevector analysis, even for small wavevectors or long-range effects. We also study the effects of slab thickness and of short-range corrections to RPA.