# Computing the Helmholtz energy function of solids

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There are various methods of computing the Helmholtz energy function of solid phases.
The most widely used is the procedure based on the techniques of thermodynamic integration.
The usual implementations derive from the paper by Frenkel and Ladd ^{[1]} which makes use of the Einstein crystal concept.
Recently, a more efficient formalism has been developed by N. G. Almarza ^{[2]}.

## See also[edit]

## References[edit]

- ↑ Daan Frenkel and Anthony J. C. Ladd, "New Monte Carlo method to compute the free energy of arbitrary solids. Application to the fcc and hcp phases of hard spheres", Journal of Chemical Physics
**81**pp. 3188-3193 (1984) - ↑ N. G. Almarza, "Computation of the free energy of solids", Journal of Chemical Physics
**126**211103 (2007)

**Related reading**

- William G. Hoover and Francis H. Ree "Use of Computer Experiments to Locate the Melting Transition and Calculate the Entropy in the Solid Phase", Journal of Chemical Physics
**47**pp. 4873-4878 (1967) - William G. Hoover and Francis H. Ree "Melting Transition and Communal Entropy for Hard Spheres", Journal of Chemical Physics
**49**pp. 3609-3617 (1968) - J. M. Polson, E. Trizac, S. Pronk, and D. Frenkel, "Finite-size corrections to the free energies of crystalline solids", The Journal of Chemical Physics
**112**, pp. 5339-5342 (2000) - Carlos Vega and Eva G. Noya "Revisiting the Frenkel-Ladd method to compute the free energy of solids: The Einstein molecule approach", Journal of Chemical Physics
**127**154113 (2007) - Enrique de Miguel, Ramona G. Marguta and Elvira M. del Río "System-size dependence of the free energy of crystalline solids", Journal of Chemical Physics
**127**154512 (2007) - Tai Boon Tan, Andrew J. Schultz, and David A. Kofke "Efficient calculation of temperature dependence of solid-phase free energies by overlap sampling coupled with harmonically targeted perturbation", Journal of Chemical Physics 133, 134104 (2010)
- Martin B. Sweatman "Comparison of absolute free energy calculation methods for fluids and solids", Molecular Physics
**113**pp. 1206-1216 (2015) - C. Calero1, C. Knorowski and A. Travesset "Determination of anharmonic free energy contributions: Low temperature phases of the Lennard-Jones system", Journal of Chemical Physics
**144**124102 (2016)