Climbing the Density Functional Ladder: Non-Empirical Meta-Generalized Gradient Approximation Designed for Molecules and Solids

TL;DR

This paper introduces a new non-empirical meta-GGA density functional for exchange-correlation energy that accurately describes molecules and solids by satisfying exact constraints and respecting key physical paradigms.

Contribution

It develops a meta-GGA functional that is constraint-based, parameter-free, and applicable to both molecules and solids, advancing the third rung of density functional approximations.

Findings

High accuracy in numerical tests for molecules and solids

Satisfies exact physical constraints without empirical parameters

Completes the third rung of Jacob's ladder of DFT approximations

Abstract

The electron density, its gradient, and the Kohn-Sham orbital kinetic energy density are the local ingredients of a meta-generalized gradient approximation (meta-GGA). We construct a meta-GGA density functional for the exchange-correlation energy that satisfies exact constraints without empirical parameters. The exchange and correlation terms respect {\it two} paradigms: one- or two-electron densities and slowly-varying densities, and so describe both molecules and solids with high accuracy, as shown by extensive numerical tests. This functional completes the third rung of ``Jacob's ladder'' of approximations, above the local spin density and GGA rungs.