Non-empirical hyper-generalized-gradient functionals constructed from the Lieb-Oxford bound

TL;DR

This paper derives a new, general representation of the exact exchange-correlation functional in density-functional theory from the Lieb-Oxford bound, enabling the construction of non-empirical hyper-generalized-gradient approximations that outperform current methods.

Contribution

It introduces a novel, non-empirical approach to constructing hyper-generalized-gradient functionals based on the Lieb-Oxford bound, offering a new paradigm in density-functional theory.

Findings

HGGAs match or outperform existing correlation functionals

Simple HGGAs perform well on atomic and molecular energies

Provides a theoretical basis for hybrid functional construction

Abstract

A simple and completely general representation of the exact exchange-correlation functional of density-functional theory is derived from the universal Lieb-Oxford bound, which holds for any Coulomb-interacting system. This representation leads to an alternative point of view on popular hybrid functionals, providing a rationale for why they work and how they can be constructed. A similar representation of the exact correlation functional allows to construct fully non-empirical hyper-generalized-gradient approximations (HGGAs), radically departing from established paradigms of functional construction. Numerical tests of these HGGAs for atomic and molecular correlation energies and molecular atomization energies show that even simple HGGAs match or outperform state-of-the-art correlation functionals currently used in solid-state physics and quantum chemistry.