Semilocal exchange hole with an application to range-separation density functional

TL;DR

This paper introduces a semilocal exchange hole model based on the TPSS functional, improving the accuracy of range-separation density functionals for electronic properties while maintaining molecular energy accuracy.

Contribution

It proposes a novel semilocal exchange hole model tailored for the TPSS functional, enhancing the construction of range-separation functionals in density functional theory.

Findings

The exchange hole model closely mimics the exact exchange hole for atoms.

The TPSS-based range-separation functional improves band gaps and barrier heights.

Molecular atomization energies are preserved with minimal loss of accuracy.

Abstract

Exchange-correlation hole is a central concept in density functional theory. It not only provides justification for an exchange-correlation energy functional, but also serves as a local ingredient in nonlocal range-separation density functional. However, due to the nonlocal nature, modelig the conventional exact exchange hole presents a great challenge to density functional theory. In this work, we propose a semilocal exchange hole underlying the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA functional. The present model is distinct from previous models at small separation between an electron and the hole around the electron. It is also different in the way it interpolates between the rapidly varying iso-orbital density and the slowly varying density, which is determined by the wave vector analysis based on the exactly solvable infinite barrier model for jellium surface. Our numerical tests show that the exchange hole generated from this model mimics the conventional exact exchange hole quite well for atoms. Finally, as a simple application, we apply the hole model to construct a TPSS-based range-separation functional. Our tests show that this TPSS-based range-separation functional can substantially improve TPSS band gaps and barrier heights, without losing much accuracy of molecular atomization energies.