Widom test-particle method

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The excess chemical potential is given by

\mu^{ex} = -k_BT \ln \langle e^{-\Phi/k_bT}\rangle_N

where k_B is the Boltzmann constant, T is the temperature, N is the number of particles within the system and \Phi is the interaction potential energy between the randomly placed test particle and the N particles that the system is comprised of.


  1. B. Widom "Some Topics in the Theory of Fluids", Journal of Chemical Physics 39 pp. 2808-2812 (1963)
  2. B. Widom "Potential-distribution theory and the statistical mechanics of fluids", Journal of Physical Chemistry 86 pp. 869 - 872 (1982)
  3. 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)