Meta-generalized gradient approximation: non-empirical construction and performance of a density functional

Abstract

The local ingredients of a meta-generalized gradient approximation (meta-GGA) include the electron density, its gradient, and the Kohn–Sham orbital kinetic energy density. We discuss the strategy of constructing a successful meta-GGA density functional for the exchange-correlation energy that satisfies exact constraints without empirical parameters. The new feature of this functional is that it simultaneously respects the two paradigms of electronic structure theory: one- or two-electron densities and slowly-varying densities, and so is uniformly accurate for atoms, molecules and solids. Results of extensive numerical tests of the new functional are summarized and evaluated.

Acknowledgments

The authors thank Ernest R. Davidson for suggesting several interesting tests of the LSDA–PBE–PKZB–TPSS functional ladder. J.T. and J.P.P. were supported by the National Science Foundation under Grant No. DMR-01-35678. A.R. was supported in part by the Pro Progressio Foundation. V.N.S. and G.E.S. acknowledge support from the National Science Foundation (NSF) under Grant No. CHE-99-82156 and the Welch Foundation. A.R. and G.I.C. acknowledge support from OTKA under Grant No. T034764. The authors thank Tony Gonis for organizing the workshop on Electron Correlation and Materials Properties 3.