Optimized local basis set for Kohn-Sham density functional theory

TL;DR

This paper introduces an optimized local basis set for Kohn-Sham density functional theory that improves accuracy and efficiency in electronic structure calculations for both insulators and metals.

Contribution

It presents a new method for generating optimized local basis functions that reduces computational cost while maintaining high accuracy in DFT calculations.

Findings

Achieves high accuracy with fewer basis functions per atom.

Systematically controls Pulay force, eliminating the need for its calculation.

Effective in both insulating and metallic systems.

Abstract

We develop a technique for generating a set of optimized local basis functions to solve models in the Kohn-Sham density functional theory for both insulating and metallic systems. The optimized local basis functions are obtained by solving a minimization problem in an admissible set determined by a large number of primitive basis functions. Using the optimized local basis set, the electron energy and the atomic force can be calculated accurately with a small number of basis functions. The Pulay force is systematically controlled and is not required to be calculated, which makes the optimized local basis set an ideal tool for ab initio molecular dynamics and structure optimization. We also propose a preconditioned Newton-GMRES method to obtain the optimized local basis functions in practice. The optimized local basis set is able to achieve high accuracy with a small number of basis functions per atom when applied to a one dimensional model problem.