Approximations of the Green's Function in Multiple Scattering Theory for Crystalline Systems

TL;DR

This paper investigates various approximations of the scattering path matrix in multiple scattering theory for crystalline systems, demonstrating convergence and supporting the approach with numerical experiments.

Contribution

It introduces and justifies new approximations of the scattering path matrix that enable linear-scaling in multiple scattering calculations for crystalline materials.

Findings

Convergence of SPM approximations is established.

Numerical experiments confirm the theoretical results.

Approximations facilitate efficient electronic structure calculations.

Abstract

The multiple scattering theory (MST) is a Green's function method that has been widely used in electronic structure calculations for crystalline disordered systems. The key property of the MST method is the scattering path matrix (SPM) that characterizes the Green's function within a local solution representation. This paper studies various approximations of the SPM, under the condition that an appropriate reference is used for perturbation. In particular, we justify the convergence of the SPM approximations with respect to the size of scattering region and the length of scattering path, which are the central numerical parameters to achieve a linear-scaling MST method. We present numerical experiments on several typical systems to support the theory.