Boundary conditions: Difference between revisions
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Molecular simulation often tries to approximate the [[thermodynamic limit]], in which the systems are very large. Since this is impossible to achieve computationally, a simulation cell must be employed. This cell being finite, it would appear that it must be bounded in some way. However, finiteness does not imply boundaries, as the circle demonstrates. | Molecular simulation often tries to approximate the [[thermodynamic limit]], in which the systems are very large. Since this is impossible to achieve computationally, a simulation cell (or box) must be employed. This cell being finite, it would appear that it must be bounded in some way. However, finiteness does not imply boundaries, as the circle demonstrates. | ||
Thus, periodic boundary conditions are typically employed for the simulations of bulk materials (either disordered, or crystalline, in which case the cell must be carefully chosen.) In [[confined systems]] periodicity is only required in some spacial dimensions. Sometimes non-periodic boundary conditions are nevertheless employed (Ref. 3). | Thus, periodic boundary conditions are typically employed for the simulations of bulk materials (either disordered, or crystalline, in which case the cell must be carefully chosen.) In [[confined systems]] periodicity is only required in some spacial dimensions. Sometimes non-periodic boundary conditions are nevertheless employed (Ref. 3). | ||
==List of periodic boundary conditions== | ==List of periodic boundary conditions== | ||
===Cubic=== | ====Cubic==== | ||
===Orthorhombic=== | ====Orthorhombic==== | ||
===Parallelepiped=== | ====Parallelepiped==== | ||
===Truncated octahedral=== | ====Truncated octahedral==== | ||
#[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/10.1080/08927029308022499 W. Smith; D. Fincham "The Ewald Sum in Truncated Octahedral and Rhombic Dodecahedral Boundary Conditions", Molecular Simulation '''10''' pp. 67-71 (1993)] | ||
===Rhombic dodecahedral=== | ====Rhombic dodecahedral==== | ||
#[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/10.1080/08927029308022499 W. Smith; D. Fincham "The Ewald Sum in Truncated Octahedral and Rhombic Dodecahedral Boundary Conditions", Molecular Simulation '''10''' pp. 67-71 (1993)] | ||
===Slab=== | ====Slab==== | ||
===Hexagonal prism=== | ====Hexagonal prism==== | ||
==References== | ==References== | ||
# [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 (+computer codes on the [http://www.ccp5.ac.uk/librar.shtml CCP5 website]) | # [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 (+computer codes on the [http://www.ccp5.ac.uk/librar.shtml CCP5 website]) | ||
Revision as of 19:12, 22 October 2008
Molecular simulation often tries to approximate the thermodynamic limit, in which the systems are very large. Since this is impossible to achieve computationally, a simulation cell (or box) must be employed. This cell being finite, it would appear that it must be bounded in some way. However, finiteness does not imply boundaries, as the circle demonstrates. Thus, periodic boundary conditions are typically employed for the simulations of bulk materials (either disordered, or crystalline, in which case the cell must be carefully chosen.) In confined systems periodicity is only required in some spacial dimensions. Sometimes non-periodic boundary conditions are nevertheless employed (Ref. 3).
List of periodic boundary conditions
Cubic
Orthorhombic
Parallelepiped
Truncated octahedral
Rhombic dodecahedral
Slab
Hexagonal prism
References
- M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", Oxford University Press (1989) Section 1.5.2 (+computer codes on the CCP5 website)
- 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)