Chapter 3.5 Extensions of the Ewald method for Coulomb interactions in crystals
Second Online Edition (2010)
Part 3. Dual bases in crystallographic computing
Published Online: 1 JUN 2010
© International Union of Crystallography 2006
International Tables for Crystallography
How to Cite
Darden, T. A. 2010. Extensions of the Ewald method for Coulomb interactions in crystals. International Tables for Crystallography. B:3:3.5:458–481.
- Published Online: 1 JUN 2010
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.
- Ewald method;
- Coulomb interactions;
- lattice sums;
- polarization response;
- smooth particle‐mesh Ewald method;
- Fourier Poisson method;