A rapidly converging algorithm for solving the Kohn-Sham and related equations in electronic structure theory

TL;DR

This paper introduces a fast-converging algorithm for solving Kohn-Sham equations in electronic structure calculations, directly computing electron density with minimal iterations, applicable to various inhomogeneous systems.

Contribution

The algorithm uniquely solves for electron density directly, reducing convergence time and computational effort compared to traditional methods.

Findings

Converges within few iterations from rough initial guesses.

Successfully applied to symmetric slabs and spherical jellium clusters.

Driven by static electric susceptibility for efficient convergence.

Abstract

We describe a rapidly converging algorithm for solving the Kohn--Sham equations and equations of similar structure that appear frequently in calculations of the structure of inhomogeneous electronic many--body systems. The algorithm has its roots the Hohenberg-Kohn theorem and solves directly for the electron density; single--particle wave functions are only used as auxiliary quantities. The method has been implemented for symmetric ``slabs'' of jellium as well as for spherical jellium clusters. Starting from very rough guesses for the initial electron density, convergence is reached within a few iterations. The iterations are driven by the static electric susceptibility.