Editing Widom test-particle method
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[[Benjamin Widom]] proposed 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== | ||
#[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/10.1021/j100395a005 B. Widom "Potential-distribution theory and the statistical mechanics of fluids", Journal of Physical Chemistry '''86''' pp. 869 - 872 (1982)] | |||
#[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)] | |||
[[category: computer simulation techniques]] | [[category: computer simulation techniques]] | ||