Efficient Computation of the Long-Range Exact Exchange using an Extended Screening Function

TL;DR

This paper presents a new extended screening function that enables efficient computation of long-range exact exchange in hybrid functionals, maintaining accuracy while reducing computational cost.

Contribution

It introduces a first-order Taylor expansion of the screening function to approximate long-range Coulomb interactions efficiently.

Findings

Achieves computational speeds similar to HSE06

Accurately predicts energy gaps and energies with reduced cost

Validates approach on semiconductors and organic crystals

Abstract

We introduce a computationally efficient screening for the Coulomb potential that also allows calculating approximated long-range exact exchange contributions with an accuracy similar to an explicit full-range evaluation of the exact exchange. Starting from the screening function of the HSE functional, i.e., the complementary error function, as zeroth order, a first-order Taylor expansion in terms of the screening parameter {\omega} is proposed as an approximation of the long-range Coulomb potential. The resulting extended screening function has a similar spatial extend as the complementary error function leading to a computational speed comparable to screened hybrid functionals such as HSE06, but with long-range exact exchange contributions included. The approach is tested and demonstrated for prototypical semiconductors and organic crystals using the PBE0 functional. Predicted energy band gaps, total energies, cohesive energies, and lattice energies from the first-order approximated PBE0 functional are close to those from the unmodified PBE0 functional, but are obtained at significantly reduced computational cost.