A simple, efficient, and general treatment of the singularities in Hartree-Fock and exact-exchange Kohn-Sham methods for solids

TL;DR

This paper introduces a simple, stable, and general scheme for correcting singularities in Hartree-Fock and exact-exchange Kohn-Sham methods for solids, improving convergence and stability across different lattice structures.

Contribution

The authors develop a universal correction scheme for singularities in EXX Kohn-Sham and HF methods that depends only on k-point count and lattice vectors, not atomic positions.

Findings

The correction scheme is stable and easy to implement.

Singularity corrections depend mainly on total k-points and lattice vectors.

The method improves volume optimization and k-point convergence in solids.

Abstract

We present a general scheme for treating the integrable singular terms within exact exchange (EXX) Kohn-Sham or Hartree-Fock (HF) methods for periodic solids. We show that the singularity corrections for treating these divergencies depend only on the total number and the positions of k-points and on the lattice vectors, in particular the unit cell volume, but not on the particular positions of atoms within the unit cell. The method proposed here to treat the singularities constitutes a stable, simple to implement, and general scheme that can be applied to systems with arbitrary lattice parameters within either the EXX Kohn-Sham or the HF formalism. We apply the singularity correction to a typical symmetric structure, diamond, and to a more general structure, trans-polyacetylene. We consider the effect of the singularity corrections on volume optimisations and k-point convergence. While the singularity corrections clearly depends on the total number of k-points, it exhibits a remarkably small dependence upon the choice of the specific arrangement of the k-points.