Mathematical Analysis and Numerical Approximations of Density Functional Theory Models for Metallic Systems

TL;DR

This paper analyzes the energy minimization in density functional theory for metals, proposing new algorithms with proven convergence that outperform traditional methods in large-scale metallic system simulations.

Contribution

It introduces an adaptive double step size strategy and preconditioned conjugate gradient methods with proven global convergence for metallic systems.

Findings

Algorithms are efficient for large metallic systems.

Proposed methods converge where traditional SCF iterations fail.

Numerical experiments validate the effectiveness of the algorithms.

Abstract

In this paper, we investigate the energy minimization model of the ensemble Kohn-Sham density functional theory for metallic systems, in which a pseudo-eigenvalue matrix and a general smearing approach are involved. We study the invariance and the existence of the minimizer of the energy functional. We propose an adaptive double step size strategy and the corresponding preconditioned conjugate gradient methods for solving the energy minimization model. Under some mild but reasonable assumptions, we prove the global convergence of our algorithms. Numerical experiments show that our algorithms are efficient, especially for large scale metallic systems. In particular, our algorithms produce convergent numerical approximations for some metallic systems, for which the traditional self-consistent field iterations fail to converge.