Difference between revisions of "Ewald sum"

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(Some more info on this fine method)
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{{Stub-general}}
 
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This technique, of a classical origin [1] is widely used in order to simulate systems with
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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_analysis | Fourier space]].
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[[long range interactions]] (typically, [[Electrostatics |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_analysis | Fourier space]].
 
 
 
==Particle mesh==
 
==Particle mesh==
 
*[http://dx.doi.org/10.1063/1.464397    Tom Darden, Darrin York, and Lee Pedersen "Particle mesh Ewald: An N·log(N) method for Ewald sums in large systems", Journal of Chemical Physics '''98''' pp. 10089-10092 (1993)]
 
*[http://dx.doi.org/10.1063/1.464397    Tom Darden, Darrin York, and Lee Pedersen "Particle mesh Ewald: An N·log(N) method for Ewald sums in large systems", Journal of Chemical Physics '''98''' pp. 10089-10092 (1993)]

Revision as of 10:57, 5 February 2008

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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

  1. Paul Ewald "Die Berechnung Optischer und Electrostatischer Gitterpotentiale", Annalen der Physik 64 pp. 253-287 (1921)
  2. 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)
  3. 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)
  4. W. Smith; D. Fincham "The Ewald Sum in Truncated Octahedral and Rhombic Dodecahedral Boundary Conditions", Molecular Simulation 10 pp. 67-71 (1993)
  5. Paul E. Smith and B. Montgomery Pettitt "Efficient Ewald electrostatic calculations for large systems", Computer Physics Communications 91 pp. 339-344 (1995)
  6. 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)