Variational solution of Poisson's equation using plane waves in adaptive coordinates

José M. Pérez-Jordá
Phys. Rev. E 90, 053307 – Published 13 November 2014

Abstract

A procedure for solving Poisson's equation using plane waves in adaptive coordinates (u) is described. The method, based on Gygi's work, writes a trial potential ξ as the product of a preselected Coulomb weight μ times a plane-wave expansion depending on u. Then, the Coulomb potential generated by a given density ρ is obtained by variationally optimizing ξ, so that the error in the Coulomb energy is second-order with respect to the error in ξ. The Coulomb weight μ is chosen to provide to each ξ the typical long-range tail of a Coulomb potential, so that calculations on atoms and molecules are made possible without having to resort to the supercell approximation. As a proof of concept, the method is tested on the helium atom and the H2 and H3+ molecules, where Hartree-Fock energies with better than milli-Hartree accuracy require only a moderate number of plane waves.

  • Received 30 May 2014

DOI:https://doi.org/10.1103/PhysRevE.90.053307

©2014 American Physical Society

Authors & Affiliations

José M. Pérez-Jordá*

  • Departament de Química Física, Universitat d'Alacant E-03080, Alacant, Spain

  • *jmpj@ua.es

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Issue

Vol. 90, Iss. 5 — November 2014

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