Numerical methods for the computation of densities of states of periodic operators

TL;DR

This paper compares various numerical methods for computing electronic densities of states in periodic systems, highlighting the strengths and limitations of each to guide practical applications.

Contribution

It provides a detailed analysis of the Brillouin complex deformation method and compares it with traditional approaches across different systems.

Findings

BCD offers exponential convergence without smearing.

Performance regimes vary for each method depending on system and accuracy.

Guidelines for choosing appropriate DOS computation methods are established.

Abstract

We present a comparative study of numerical methods for computingelectronic densities of states (DOS) in periodic systems. We provide a detailed analysis of the domain of validity of the Brillouincomplex deformation (BCD), a recently-proposed method promising exponential convergence without need for smearing. We compare on a range of systems the BCD with several methods, including the standard smearing and linear tetrahedron methods, as well as an adaptive integration method. Our results establish clear performance regimes for each method, offering practical guidance for DOS computations across a range of systems and accuracy requirements.