Systematic investigation of a family of gradient-dependent functionals for solids

TL;DR

This study systematically compares eleven density functionals, including new variations, for predicting lattice constants of solids, revealing that simple modifications to PBE improve performance, while PBE remains best for molecular atomization energies.

Contribution

The paper introduces and evaluates new PBE-based functionals with gradient and Lieb-Oxford bound modifications for solid-state properties.

Findings

Simple PBE modifications improve solid lattice constant predictions.

No single functional is best for all systems.

PBE performs best for molecular atomization energies.

Abstract

Eleven density functionals are compared with regard to their performance for the lattice constants of solids. We consider standard functionals, such as the local-density approximation and the Perdew-Burke-Ernzerhof (PBE) generalized-gradient approximation (GGA), as well as variations of PBE GGA, such as PBEsol and similar functionals, PBE-type functionals employing a tighter Lieb-Oxford bound, and combinations thereof. Several of these variations are proposed here for the first time. On a test set of 60 solids we perform a system-by-system analysis for selected functionals and a full statistical analysis for all of them. The impact of restoring the gradient expansion and of tightening the Lieb-Oxford bound is discussed, and confronted with previous results obtained from other codes, functionals or test sets. No functional is uniformly good for all investigated systems, but surprisingly, and pleasingly, the simplest possible modifications to PBE turn out to have the most beneficial effect on its performance. The atomization energy of molecules was also considered and on a testing set of six molecules, we found that the PBE functional is clearly the best, the others leading to strong overbinding.