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

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

2006-03-23

arxiv.org/abs/cond-mat/0603632v2

Physics

Condensed Matter

Materials Science

24 pages, 5 Figures, re-submitted to Phys. Rev. B after revisions

Scientific paper

10.1103/PhysRevB.75.205126

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.

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