Choly, NicholasKaxiras, Efthimios2019-09-202003Choly, Nicholas, and Efthimios Kaxiras. 2003. “Fast Method for Force Computations in Electronic Structure Calculations.” Physical Review B 67 (15). https://doi.org/10.1103/physrevb.67.155101.1098-01211550-235Xhttp://nrs.harvard.edu/urn-3:HUL.InstRepos:41384085We 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.en-USJournal Article2019-09-2010.1103/PhysRevB.67.155101