Fast method for force computations in electronic structure calculations

TL;DR

This paper introduces new efficient algorithms with O(N log N) complexity for computing key quantities in electronic structure calculations, especially suited for metallic systems, improving speed while maintaining accuracy.

Contribution

The paper develops and demonstrates a new set of algorithms for force and stress calculations in electronic structure methods, extending applicability to metallic systems with improved efficiency.

Findings

Algorithms achieve high accuracy and efficiency in metallic systems

Methods are systematically improvable

Effective for large-scale electronic structure calculations

Abstract

We present new efficient (O(N log N)) methods for computing three quantities crucial to electronic structure calculations: the ionic potential, the electron-ion contribution to the Born-Oppenheimer forces, and the electron-ion contribution to the stress tensor. The present methods are applicable to calculations in which the electronic charge density is represented on a uniform grid in real space. They are particularly well-suited for metallic extended systems, where other O(N) methodologies are not readily applicable. Based on a fast algorithm for determining the atomic structure factor, originally developed by Essmann et al. (U. Essmann, L. Perera, et al.,J. Chem. Phys. v.103, p.8577 (1995)) for fast Ewald energy and force computation, the present methods involve approximations that can be systematically improved. The methods are tested on a representative metallic system (bulk Al),and their ability to simultaneously achieve high accuracy and efficiency is demonstrated.