Ewald sum: Difference between revisions

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The '''Ewald sum''' technique, of a classical origin (Ref. 1) is widely used in order to simulate systems with
The '''Ewald sum''' technique <ref>[http://dx.doi.org/10.1002/andp.19213690304  Paul Ewald "Die Berechnung Optischer und Electrostatischer Gitterpotentiale", Annalen der Physik '''64''' pp. 253-287 (1921)]</ref>  is widely used in order to simulate systems with
[[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]].
[[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==
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*[[Reaction field]]
*[[Reaction field]]
==References==
==References==
#[http://dx.doi.org/10.1002/andp.19213690304  Paul Ewald "Die Berechnung Optischer und Electrostatischer Gitterpotentiale", Annalen der Physik '''64''' pp. 253-287 (1921)]
<references/>
#[http://dx.doi.org/10.1063/1.1727895 S. G. Brush, H. L. Sahlin and E. Teller "Monte Carlo Study of a One-Component Plasma. I", Journal of Chemical Physics  '''45''' pp. 2102- (1966)]
'''Related reading'''
#[http://dx.doi.org/10.1098/rspa.1980.0135 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)]
*[http://dx.doi.org/10.1063/1.1727895 S. G. Brush, H. L. Sahlin and E. Teller "Monte Carlo Study of a One-Component Plasma. I", Journal of Chemical Physics  '''45''' pp. 2102- (1966)]
#[http://dx.doi.org/10.1098/rspa.1980.0136 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)]
*[http://dx.doi.org/10.1098/rspa.1980.0135 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)]
#[http://dx.doi.org/10.1080/08927029308022499 W. Smith; D. Fincham "The Ewald Sum in Truncated Octahedral and Rhombic Dodecahedral Boundary Conditions", Molecular Simulation '''10''' pp. 67-71 (1993)]
*[http://dx.doi.org/10.1098/rspa.1980.0136 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)]
#[http://dx.doi.org/10.1016/0010-4655(95)00058-N  Paul E. Smith and B. Montgomery Pettitt  "Efficient Ewald electrostatic calculations for large systems", Computer Physics Communications  '''91''' pp. 339-344 (1995)]
*[http://dx.doi.org/10.1080/08927029308022499 W. Smith; D. Fincham "The Ewald Sum in Truncated Octahedral and Rhombic Dodecahedral Boundary Conditions", Molecular Simulation '''10''' pp. 67-71 (1993)]
#[http://dx.doi.org/10.1063/1.2206581    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)]
*[http://dx.doi.org/10.1016/0010-4655(95)00058-N  Paul E. Smith and B. Montgomery Pettitt  "Efficient Ewald electrostatic calculations for large systems", Computer Physics Communications  '''91''' pp. 339-344 (1995)]
*[http://dx.doi.org/10.1063/1.2206581    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)]
==External resources==
==External resources==
*[ftp://ftp.dl.ac.uk/ccp5/ALLEN_TILDESLEY/F.22    Routines to perform the Ewald sum] sample FORTRAN computer code from the book [http://www.oup.com/uk/catalogue/?ci=9780198556459 M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", Oxford University Press (1989)].
*[ftp://ftp.dl.ac.uk/ccp5/ALLEN_TILDESLEY/F.22    Routines to perform the Ewald sum] sample FORTRAN computer code from the book [http://www.oup.com/uk/catalogue/?ci=9780198556459 M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", Oxford University Press (1989)].
[[category: Computer simulation techniques]]
[[category: Computer simulation techniques]]
[[category: electrostatics]]
[[category: electrostatics]]

Revision as of 12:11, 13 August 2010

The Ewald sum technique [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 (SPME)

Related pages

References

Related reading

External resources