Widom test-particle method: Difference between revisions
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[[Benjamin Widom]] | The '''Widom test-particle method''', proposed by [[Benjamin Widom]] <ref>[http://dx.doi.org/10.1063/1.1734110 B. Widom "Some Topics in the Theory of Fluids", Journal of Chemical Physics '''39''' pp. 2808-2812 (1963)]</ref><ref>[http://dx.doi.org/10.1021/j100395a005 B. Widom "Potential-distribution theory and the statistical mechanics of fluids", Journal of Physical Chemistry '''86''' pp. 869-872 (1982)]</ref>, is an elegant, general [[Computer simulation techniques |simulation technique]] to obtain the excess [[chemical potential]] of a system. A so-called ''test particle'' is introduced in a [[Random numbers |random]] location, and <math>\Delta\Phi</math>, the difference in [[internal energy]] before and after the insertion, is computed. For [[Intermolecular pair potential |pairwise interactions]], this would become be the interaction potential energy between the randomly placed test particle and the <math>N</math> particles that the system is comprised of. The particle is not actually inserted, at variance with [[Monte Carlo in the grand-canonical ensemble|grand canonical Monte Carlo]]. | ||
The excess chemical potential is given by | The excess chemical potential is given by | ||
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where <math>k_B</math> is the [[Boltzmann constant]] and <math>T</math> is the [[temperature]]. | where <math>k_B</math> is the [[Boltzmann constant]] and <math>T</math> is the [[temperature]]. | ||
==References== | ==References== | ||
<references/> | |||
;Related reading | |||
*[http://dx.doi.org/10.1080/002689798169104 David S. Corti "Alternative derivation of Widom's test particle insertion method using the small system grand canonical ensemble", Molecular Physics '''93''' pp. 417-420 (1998)] | |||
*[http://dx.doi.org/10.1063/1.4968039 David M. Heyes and Andrés Santos "Chemical potential of a test hard sphere of variable size in a hard-sphere fluid", Journal of Chemical Physics '''145''' 214504 (2016)] | |||
[[category: computer simulation techniques]] | [[category: computer simulation techniques]] | ||
Latest revision as of 16:44, 12 December 2016
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The Widom test-particle method, proposed by Benjamin Widom [1][2], is an elegant, general simulation technique to obtain the excess chemical potential of a system. A so-called test particle is introduced in a random location, and , the difference in internal energy before and after the insertion, is computed. For pairwise interactions, this would become be the interaction potential energy between the randomly placed test particle and the particles that the system is comprised of. The particle is not actually inserted, at variance with grand canonical Monte Carlo.
The excess chemical potential is given by
where is the Boltzmann constant and is the temperature.
References[edit]
- Related reading
- David S. Corti "Alternative derivation of Widom's test particle insertion method using the small system grand canonical ensemble", Molecular Physics 93 pp. 417-420 (1998)
- David M. Heyes and Andrés Santos "Chemical potential of a test hard sphere of variable size in a hard-sphere fluid", Journal of Chemical Physics 145 214504 (2016)