Fast method for force computations in electronic structure calculations

We present efficient [O(N ln 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 [J. Chem. Phys. 103, 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.