Gradient-dependent density functionals of the PBE type for atoms, molecules and solids

TL;DR

This paper introduces new members of a family of density functionals based on PBE, evaluates their performance on atoms, molecules, and solids, and provides guidelines for functional development and application.

Contribution

It constructs and tests three new functionals within the PBE family, revealing that PBE and PBEsol are not always optimal for all systems and offering insights for future functional design.

Findings

PBE is not always the best for solids or molecules.

PBEsol is not universally optimal for solids.

Performance depends on constraints from infinite systems.

Abstract

One of the standard generalized-gradient approximations (GGAs) in use in modern electronic-structure theory, PBE, and a recently proposed modification designed specifically for solids, PBEsol, are identified as particular members of a family of functionals taking their parameters from different properties of homogeneous or inhomogeneous electron liquids. Three further members of this family are constructed and tested, together with the original PBE and PBEsol, for atoms, molecules and solids. We find that PBE, in spite of its popularity in solid-state physics and quantum chemistry, is not always the best performing member of the family, and that PBEsol, in spite of having been constructed specifically for solids, is not the best for solids. The performance of GGAs for finite systems is found to sensitively depend on the choice of constraints steaming from infinite systems. Guidelines both for users and for developers of density functionals emerge from this work.