Improved tetrahedron method for the Brillouin-zone integration applicable to response functions

TL;DR

This paper presents an improved linear tetrahedron method that reduces systematic errors in Brillouin-zone integrations, applicable to various response function calculations and demonstrated on phonon calculations in MgB₂ and lithium.

Contribution

The authors develop a modified tetrahedron method that corrects overestimations and underestimations in integrals, extending applicability beyond total energy and density calculations to response functions.

Findings

Reduced systematic errors in Brillouin-zone integrations

Effective for calculating phonons in MgB₂ and lithium

Applicable to diverse response function calculations

Abstract

We improve the linear tetrahedron method to overcome systematic errors due to overestimations (underestimations) in integrals for convex (concave) functions, respectively. Our method is applicable to various types of calculations such as the total energy, the harge (spin) density, response functions, and the phonon frequency, in contrast with the Bl\"ochl correction, which is applicable to only the first two. We demonstrate the ability of our method by calculating phonons in MgB$_2$ and fcc lithium.