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The '''self-referential method''' is a [[computer simulation techniques |computer simulation technique]] for calculating either the difference in the [[Helmholtz energy function]] between similar systems of differing sizes in the [[Canonical ensemble]], or for computing the [[Gibbs energy function]] when in the [[isothermal-isobaric ensemble]].
The '''self-referential method''' is a [[computer simulation techniques |computer simulation technique]] for calculating either the difference in the [[Helmholtz energy function]] between similar systems of differing sizes in the [[Canonical ensemble]], or for computing the [[Gibbs energy function]] when in the [[isothermal-isobaric ensemble]].
The most straightforward and efficient version of the self-referential method takes the large system to be twice the size of the small system. Starting with the small system at [[temperature]] T, the Helmholtz (or Gibbs) energy difference between this small system and a self-similar large (double-size) system at temperature 2T is easily found by comparing the [[partition function]]s of these systems. The self-similar double-size system is essentially two copies of the small system side-by-side which are identical, in terms of the positions, orientations etc. of the particles, to within a very small tolerance. The Helmholtz (or Gibbs) energy difference between this self-similar double-size system at temperature 2T and an ordinary double-size system at temperature T can be found efficiently using a form of [[thermodynamic integration]] that relaxes the tolerance constraint until it no longer has any effect on the system. The sum of these two contributions gives the desired Helmholtz (or Gibbs) energy difference.
==See also==
==See also==
*[[Computing the Helmholtz energy function of solids]]
*[[Computing the Helmholtz energy function of solids]]
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*[[Gibbs-Duhem integration]]
*[[Gibbs-Duhem integration]]
==References==
==References==
*[http://dx.doi.org/10.1080/08927020310001626238 Martin B. Sweatman and N. Quirke "Simulating Fluid-Solid Equilibrium with the Gibbs Ensemble", Molecular Simulation '''30''' pp. 23-28 (2004)]
#[http://dx.doi.org/10.1080/08927020310001626238 M. B. Sweatman and N. Quirke "Simulating Fluid-Solid Equilibrium with the Gibbs Ensemble", Molecular Simulation '''30''' pp. 23-28 (2004)]
*[http://dx.doi.org/10.1103/PhysRevE.72.016711 Martin B. Sweatman "Self-referential Monte Carlo method for calculating the free energy of crystalline solids", Physical Review E '''72''' 016711 (2005)]
#[http://dx.doi.org/10.1103/PhysRevE.72.016711 M. B. Sweatman "Self-referential Monte Carlo method for calculating the free energy of crystalline solids", Physical Review E '''72''' 016711 (2005)]
*[http://dx.doi.org/10.1063/1.2839881 Martin B. Sweatman, Alexander A. Atamas, and Jean-Marc Leyssale "The self-referential method combined with thermodynamic integration", Journal of Chemical Physics '''128''' 064102 (2008)]
#[http://dx.doi.org/10.1063/1.2839881 Martin B. Sweatman, Alexander A. Atamas, and Jean-Marc Leyssale "The self-referential method combined with thermodynamic integration", Journal of Chemical Physics '''128''' 064102 (2008)]
*[http://dx.doi.org/10.1080/08927020902769844 Martin B. Sweatman "New techniques for simulating crystals", Molecular Simulation iFirst (2009)]
[[category: computer simulation techniques]]
[[category: computer simulation techniques]]
[[category: Monte Carlo]]
[[category: Monte Carlo]]
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