Editing Widom test-particle method
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[[Benjamin Widom]] proposed an elegant, general method to obtain | |||
the excess [[chemical potential]] of a system that is being | |||
simulated. A ''test particle'' is introduced in a random | |||
location, and <math>\Delta\Phi</math>, the difference | |||
in [[internal energy]] before and after the insertion, | |||
is computed. (For pairwise interactions, this would | |||
just be the interaction potential energy between the randomly | |||
placed test particle and the ''N'' 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 MC ]]). | |||
The excess chemical potential is given by | The excess chemical potential is given by | ||
:<math>\mu^{ | :<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 ''T'' 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]] |