Ewald method for polytropic potentials in arbitrary dimensionality

• Published in: Molecular physics Vol. 110; no. 4; pp. 227 - 247
• Main Authors: Osychenko, O.N., Astrakharchik, G.E., Boronat, J.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Group 20-02-2012; Taylor & Francis Ltd
• Subjects: Computer simulation; Ewald summation; Jellium; Mathematical models; Molecular physics; Optimization; power-law potentials; Simulation; Studies; Sums
• ISSN: 0026-8976; 1362-3028
• DOI: 10.1080/00268976.2011.640291

The Ewald summation technique is generalized to power-law 1/|
r
|
k
potentials in three-, two- and one-dimensional geometries with explicit formulae for all the components of the sums. The cases of short-range, long-range and 'marginal' interactions are treated separately. The jellium model, as a particular case of a charge-neutral system, is discussed and the explicit forms of the Ewald sums for such a system are presented. A generalized form of the Ewald sums for a non-cubic (non-square) simulation cell for three- (two-) dimensional geometry is obtained and its possible field of application is discussed. A procedure for the optimization of the involved parameters in actual simulations is developed and an example of its application is presented.