Widom test-particle method: Difference between revisions
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[[Benjamin Widom]] proposed an elegant, general | [[Benjamin Widom]] proposed an elegant, general [[Computer simulation techniques |simulation technique]] to obtain | ||
the excess [[chemical potential]] of a system | 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 | location, and <math>\Delta\Phi</math>, the difference | ||
in [[internal energy]] before and after the insertion, | in [[internal energy]] before and after the insertion, | ||
is computed. | is computed. For [[Intermolecular pair potential |pairwise interactions]], this would | ||
become be the interaction potential energy between the randomly | |||
placed test particle and the | placed test particle and the <math>N</math> particles that the system is comprised of. | ||
The particle is not actually inserted | 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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:<math>\mu^{ex} = -k_BT \log \langle e^{-\Delta\Phi/k_bT}\rangle_N ,</math> | :<math>\mu^{ex} = -k_BT \log \langle e^{-\Delta\Phi/k_bT}\rangle_N ,</math> | ||
where <math>k_B</math> is the [[Boltzmann constant]] and | where <math>k_B</math> is the [[Boltzmann constant]] and <math>T</math> is the [[temperature]]. | ||
==References== | ==References== | ||
#[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)] | #[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)] | ||
Revision as of 10:33, 30 January 2008
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Benjamin Widom proposed 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
- B. Widom "Some Topics in the Theory of Fluids", Journal of Chemical Physics 39 pp. 2808-2812 (1963)
- B. Widom "Potential-distribution theory and the statistical mechanics of fluids", Journal of Physical Chemistry 86 pp. 869 - 872 (1982)
- 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)