DOI: 10.1063/1.2790426. Revisiting the Frenkel-Ladd method to compute the free energy of solids: The Einstein molecule approach

Revisiting the Frenkel-Ladd method to compute the free energy of solids: The Einstein molecule approach

10.1063/1.2790426

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

In this paper a new method to evaluate the free energy of solids is proposed. The method can be regarded as a variant of the method proposed by Frenkel and Ladd [J. Chem. Phys. 81, 3188 (1984)]. The main equations of the method can be derived in a simple way. The method can be easily implemented within a Monte Carlo program. We have applied the method to determine the free energy of hard spheres in the solid phase for several system sizes. The obtained free energies agree within the numerical uncertainty with those obtained by Polson et al. [J. Chem. Phys. 112, 5339 (2000)]. The fluid-solid equilibria has been determined for several system sizes and compared to the values published previously by Wilding and Bruce [Phys. Rev. Lett. 85, 5138 (2000)] using the phase switch methodology. It is shown that both the free energies and the coexistence pressures present a strong size dependence and that the results obtained from free energy calculations agree with those obtained using the phase switch method, which constitutes a cross-check of both methodologies. From the results of this work we estimate the coexistence pressure of the fluid-solid transition of hard spheres in the thermodynamic limit to be p*=11.54(4), which is slightly lower than the classical value of Hoover and Ree (p*=11.70) [J. Chem. Phys. 49, 3609 (1968)]. Taking into account the strong size dependence of the free energy of the solid phase, we propose to introduce finite size corrections, which allow us to estimate approximately the free energy of the solid phase in the thermodynamic limit from the known value of the free energy of the solid phase with N molecules. We have also determined the free energy of a Lennard-Jones solid by using both the methodology of this work and the finite size correction. It is shown how a relatively good estimate of the free energy of the system in the thermodynamic limit is obtained even from the free energy of a relatively small system.

Bibliography

Vega, C., & Noya, E. G. (2007). Revisiting the Frenkel-Ladd method to compute the free energy of solids: The Einstein molecule approach. The Journal of Chemical Physics, 127(15).

Authors 2

Carlos Vega (first)
Eva G. Noya (additional)

References 43 Referenced 156

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Dates

Type	When
Created	17 years, 10 months ago (Oct. 19, 2007, 8:08 a.m.)
Deposited	2 years ago (July 31, 2023, 4:47 p.m.)
Indexed	3 weeks ago (July 30, 2025, 6:49 a.m.)
Issued	17 years, 10 months ago (Oct. 18, 2007)
Published	17 years, 10 months ago (Oct. 18, 2007)
Published Online	17 years, 10 months ago (Oct. 18, 2007)
Published Print	17 years, 10 months ago (Oct. 21, 2007)

Funders 0

None

BibTeX

@article{Vega_2007, title={Revisiting the Frenkel-Ladd method to compute the free energy of solids: The Einstein molecule approach}, volume={127}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.2790426}, DOI={10.1063/1.2790426}, number={15}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Vega, Carlos and Noya, Eva G.}, year={2007}, month=oct }

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  "subject": [],
  "published-other": {
    "date-parts": [
      [
        2007,
        10,
        21
      ]
    ]
  },
  "published": {
    "date-parts": [
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        10,
        18
      ]
    ]
  },
  "article-number": "154113"
}