Editing Periodic boundary conditions

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 techniques | 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 <ref>[http://www.atari.com/arcade/asteroids#!/arcade/asteroids/play play the official on-line version from Atari]</ref>, 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 transitions |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==
====Cubic====
====Orthorhombic====
====Parallelepiped====
====Truncated octahedral====
<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====
<ref name="multiple1">  </ref>
====Slab====
====Hexagonal prism====
==See also==
*[[Binder cumulant]]
*[[Finite size scaling]]
*[[Lees-Edwards boundary conditions]]
*[[System-size dependence]]
==References==
<references/>
'''Related reading'''
*[http://dx.doi.org/10.1007/BF01023055 M. J. Mandell "On the properties of a periodic fluid", Journal of Statistical Physics '''15''' pp. 299-305 (1976)]
*[http://dx.doi.org/10.1063/1.441276 Lawrence R. Pratt and Steven W. Haan "Effects of periodic boundary conditions on equilibrium properties of computer simulated fluids. I. Theory", Journal of Chemical Physics '''74''' pp. 1864- (1981)]
*[http://www.oup.com/uk/catalogue/?ci=9780198556459 M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids",  Oxford University Press (1989)] Section 1.5.2
* 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)]

==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)].
[[category: Computer simulation techniques]]