Efficient Evaluation of Exact Exchange for Periodic Systems via Concentric Atomic Density Fitting

TL;DR

This paper introduces a new efficient method for calculating exact exchange in periodic systems using concentric atomic density fitting, significantly reducing computational costs while maintaining accuracy.

Contribution

The paper presents a novel CADF-based formulation for periodic HF exchange that avoids four-center integral evaluations, improving efficiency in electronic structure calculations.

Findings

Reduces computational cost compared to conventional methods.

Achieves sub-millihartree/atom accuracy in Hartree-Fock energies.

Demonstrates good error cancellation in relative energies.

Abstract

The evaluation of exact (Hartree--Fock, HF) exchange operator is a crucial ingredient for the accurate description of electronic structure in periodic systems through ab initio and hybrid density functional approaches. An efficient formulation of periodic HF exchange in LCAO representation presented here is based on the concentric atomic density fitting (CADF) approximation, a domain-free local density fitting approach in which the product of two atomic orbitals (AOs) is approximated using a linear combination of fitting basis functions centered at the same nuclei as the AOs in that product. Significant reduction in the computational cost of exact exchange is demonstrated relative to the conventional approach due to avoiding the need to evaluate four-center two-electron integrals, with sub-millihartree/atom errors in absolute Hartree-Fock energies and good cancellation of fitting errors in relative energies. Novel aspects of the evaluation of the Coulomb contribution to the Fock operator, such as the use of real two-center multipole expansions and spheropole-compensated unit cell densities are also described.