International Tables for Crystallography

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International Tables for Crystallography (). Vol. , ch.
Extensions of the Ewald method for Coulomb interactions in crystals
T. A. Darden. International Tables for Crystallography (2010). Vol. B, ch. 3.5, pp. 458-481  [ doi:10.1107/97809553602060000772 ]

Abstract

The electrostatic energy per unit cell of a large but finite crystal of point charges that is immersed in a dielectric medium can be efficiently calculated using the Ewald-sum technique (assuming a neutral unit cell). The form of this sum is derived here in a manner that generalizes to other interactions, such as long-range dispersion interactions, that depend on higher inverse powers of distance. The Ewald method is then generalized to finite crystals of model charge densities using Hermite Gaussian basis functions. Finally, efficient methods to accelerate the Ewald sum for these charge densities to near-linear scaling (i.e. scaling as N log N with system size N) are derived and tested.


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About International Tables for Crystallography

International Tables for Crystallography is the definitive resource and reference work for crystallography. The multi-volume series comprises articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials.