Simple calculation of Madelung constants

Walter A. Harrison
Phys. Rev. B 73, 212103 – Published 7 June 2006

Abstract

It is found that direct Madelung sums within a sphere of large radius R obtained with a laptop converge rapidly if, and only if, one calculates also the charge Q of the cluster, and adds a shell of charge Q at radius R. A simple program running through the lattice provides Madelung potentials within a part in a thousand of the correct values in a few seconds of computation. It is illustrated for perovskite lattices. The corresponding calculation for a metal, positive charges embedded in a constant compensating negative charge distribution, is similarly successful.

  • Figure
  • Received 16 February 2006

DOI:https://doi.org/10.1103/PhysRevB.73.212103

©2006 American Physical Society

Authors & Affiliations

Walter A. Harrison

  • Applied Physics Department, Stanford University, Stanford, California 94305-4045, USA

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Issue

Vol. 73, Iss. 21 — 1 June 2006

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