Difference between revisions of "Periodic boundary conditions"

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<ref name="multiple1">[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)]</ref>
 
<ref name="multiple1">[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)]</ref>
 
====Rhombic dodecahedral====
 
====Rhombic dodecahedral====
<ref name="multiple1"> </ref>
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<ref name="multiple1"></ref>
 
====Slab====
 
====Slab====
 
====Hexagonal prism====
 
====Hexagonal prism====
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* Daan Frenkel and Berend Smit "Understanding Molecular Simulation: From Algorithms to Applications", Second Edition pp. 32-35 (2002) ISBN 0-12-267351-4
 
* Daan Frenkel and Berend Smit "Understanding Molecular Simulation: From Algorithms to Applications", Second Edition pp. 32-35 (2002) ISBN 0-12-267351-4
 
*[http://dx.doi.org/10.1080/00268970600744768 Phil Attard "Non-periodic boundary conditions for molecular simulations of condensed matter", Molecular Physics '''104''' pp. 1951-1960 (2006)]
 
*[http://dx.doi.org/10.1080/00268970600744768 Phil Attard "Non-periodic boundary conditions for molecular simulations of condensed matter", Molecular Physics '''104''' pp. 1951-1960 (2006)]
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*[http://dx.doi.org/10.1063/1.4916294 Dhairyashil Ghatage, Gaurav Tomar and Ratnesh K. Shukla "Soft-spring wall based non-periodic boundary conditions for non-equilibrium molecular dynamics of dense fluids", Journal of Chemical Physics '''142''' 124108 (2015)]
  
 
==External resources==
 
==External resources==
 
*[ftp://ftp.dl.ac.uk/ccp5/ALLEN_TILDESLEY/F.01  Periodic boundary conditions in various geometries] 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.01  Periodic boundary conditions in various geometries] 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]]

Latest revision as of 13:27, 18 December 2017

A liquid, in the thermodynamic limit, would occupy an infinite volume. It is common experience that one can perfectly well obtain the thermodynamic properties of a material from a more modest sample. However, even a droplet has more atoms or molecules than one can possibly hope to introduce into ones computer simulation. Thus to simulate a bulk sample of liquid it is common practice to use a 'trick' known as periodic boundary conditions. If one has a cube of atoms/molecules, the molecule leaving one side enters on the diametrically opposite side. This is analogous to the arcade video game Asteriods [1], where one can imagine the action takes place on the surface of a torus. In general, a simulation box whose dimensions are several times the range of the interaction potential works well for equilibrium properties, although in the region of a phase transition, where long-range fluctuations play an important role, problems may arise. In confined systems periodicity is only required in some spacial dimensions.

List of periodic boundary conditions[edit]

Cubic[edit]

Orthorhombic[edit]

Parallelepiped[edit]

Truncated octahedral[edit]

[2]

Rhombic dodecahedral[edit]

[2]

Slab[edit]

Hexagonal prism[edit]

See also[edit]

References[edit]

Related reading

External resources[edit]