Hartree potential dependent exchange functional

TL;DR

This paper introduces a new non-local ingredient called the reduced Hartree parameter for exchange functionals, leading to a novel u-meta-GGA functional that is exact for one- and two-electron systems and improves accuracy across various systems.

Contribution

The paper develops a new exchange functional, u-meta-GGA, using the reduced Hartree parameter, enhancing non-empirical density functional design.

Findings

u-meta-GGA is exact for one- and two-electron systems

It outperforms many existing meta-GGA exchange functionals

It satisfies key theoretical constraints and scaling relations

Abstract

We introduce a novel non-local ingredient for the construction of exchange density functionals: the reduced Hartree parameter, which is invariant under the uniform scaling of the density and represents the exact exchange enhancement factor for one- and two-electron systems. The reduced Hartree parameter is used together with the conventional meta-generalized gradient approximation (meta-GGA) semilocal ingredients (i.e. the electron density, its gradient and the kinetic energy density) to construct a new generation exchange functional, termed u-meta-GGA. This u-meta-GGA functional is exact for {the exchange of} any one- and two-electron systems, is size-consistent and non-empirical, satisfies the uniform density scaling relation, and recovers the modified gradient expansion derived from the semiclassical atom theory. For atoms, ions, jellium spheres, and molecules, it shows a good accuracy, being often better than meta-GGA exchange functionals. Our construction validates the use of the reduced Hartree ingredient in exchange-correlation functional development, opening the way to an additional rung in the Jacob's ladder classification of non-empirical density functionals.