Analysis of the Heyd-Scuseria-Ernzerhof density functional parameter space

TL;DR

This paper systematically explores the parameter space of HSE density functionals to optimize their accuracy and computational efficiency for semiconductor calculations, providing guidance for future functional development.

Contribution

It introduces a systematic analysis of the HSE functional parameters, identifying optimal choices like sX-PBE, HSE12, and HSE12s for balancing accuracy and computational cost.

Findings

sX-PBE approximates sX-LDA exchange functional

HSE12 minimizes overall error across tests

HSE12s reduces Fock exchange length scale without losing accuracy

Abstract

The Heyd-Scuseria-Ernzerhof (HSE) density functionals are popular for their ability to improve the accuracy of standard semilocal functionals such as Perdew-Burke-Ernzerhof (PBE), particularly for semiconductor band gaps. They also have a reduced computational cost compared to hybrid functionals, which results from the restriction of Fock exchange calculations to small inter-electron separations. These functionals are defined by an overall fraction of Fock exchange and a length scale for exchange screening. We systematically examine this two-parameter space to assess the performance of hybrid screened exchange (sX) functionals and to determine a balance between improving accuracy and reducing the screening length, which can further reduce computational costs. Three parameter choices emerge as useful: "sX-PBE" is an approximation to the sX-LDA screened exchange density functionals based on the local density approximation (LDA); "HSE12" minimizes the overall error over all tests performed; and "HSE12s" is a range-minimized functional that matches the overall accuracy of the existing HSE06 parameterization but reduces the Fock exchange length scale by half. Analysis of the error trends over parameter space produces useful guidance for future improvement of density functionals.