Periodic boundary conditions: Difference between revisions
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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 play the official on-line version from Atari]</ref>, where one can imagine the action takes place on the surface of a torus. | 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. | 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== | ==List of periodic boundary conditions== | ||
Revision as of 14:11, 2 April 2014
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
Cubic
Orthorhombic
Parallelepiped
Truncated octahedral
Rhombic dodecahedral
Slab
Hexagonal prism
See also
References
Related reading
- M. J. Mandell "On the properties of a periodic fluid", Journal of Statistical Physics 15 pp. 299-305 (1976)
- 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)
- 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
- Phil Attard "Non-periodic boundary conditions for molecular simulations of condensed matter", Molecular Physics 104 pp. 1951-1960 (2006)
External resources
- Periodic boundary conditions in various geometries sample FORTRAN computer code from the book M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", Oxford University Press (1989).