Pérez-Jordá JM. Variational solution of Poisson's equation using plane waves in adaptive coordinates.
PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014;
90:053307. [PMID:
25493904 DOI:
10.1103/physreve.90.053307]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2014] [Indexed: 06/04/2023]
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 H_{2} and H_{3}^{+} molecules, where Hartree-Fock energies with better than milli-Hartree accuracy require only a moderate number of plane waves.
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