# Ewald sum

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This technique, of a classical origin (Ref. 1) is widely used in order to simulate systems with long range interactions (typically, electrostatic interactions). Its aim is the computation of the interaction of a system with periodic boundary conditions with all its replicas. This is accomplished by the introduction of fictitious "charge clouds" that shield the charges. The interaction is then divided into a shielded part, which may be evaluated by the usual means, and a part that cancels the introduction of the clouds, which is evaluated in Fourier space.

## Particle mesh

#### Smooth particle mesh

## Related pages

## References

- Paul Ewald "Die Berechnung Optischer und Electrostatischer Gitterpotentiale", Annalen der Physik
**64**pp. 253-287 (1921) - S. W. de Leeuw, J. W. Perram and E. R. Smith "Simulation of Electrostatic Systems in Periodic Boundary Conditions. I. Lattice Sums and Dielectric Constants", Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
**373**pp. 27-56 (1980) - S. W. de Leeuw, J. W. Perram and E. R. Smith "Simulation of Electrostatic Systems in Periodic Boundary Conditions. II. Equivalence of Boundary Conditions", Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
**373**pp. 57-66 (1980) - W. Smith; D. Fincham "The Ewald Sum in Truncated Octahedral and Rhombic Dodecahedral Boundary Conditions", Molecular Simulation
**10**pp. 67-71 (1993) - Paul E. Smith and B. Montgomery Pettitt "Efficient Ewald electrostatic calculations for large systems", Computer Physics Communications
**91**pp. 339-344 (1995) - Christopher J. Fennell and J. Daniel Gezelter "Is the Ewald summation still necessary? Pairwise alternatives to the accepted standard for long-range electrostatics", Journal of Chemical Physics
**124**234104 (2006)