# Self-referential method

The **self-referential method** is a 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 functions 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[edit]

## References[edit]

- Martin B. Sweatman and N. Quirke "Simulating Fluid-Solid Equilibrium with the Gibbs Ensemble", Molecular Simulation
**30**pp. 23-28 (2004) - Martin B. Sweatman "Self-referential Monte Carlo method for calculating the free energy of crystalline solids", Physical Review E
**72**016711 (2005) - 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) - Martin B. Sweatman "New techniques for simulating crystals", Molecular Simulation iFirst (2009)