Combining rules

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The combining rules (also known as mixing rules) are geometric expressions designed to provide the interaction energy between two dissimilar non-bonded atoms (here labelled and ). Most of the rules are designed to be used with a specific interaction potential in mind.

Admur and Mason

For the second virial coefficient of a mixture [1]

Böhm-Ahlrichs

[2]

Diaz Peña-Pando-Renuncio

[3] [4]

Fender-Halsey

The Fender-Halsey combining rule for the Lennard-Jones model is given by [5]

Gilbert-Smith

The Gilbert-Smith rules for the Born-Huggins-Meyer potential[6][7][8].

Good-Hope rule

The Good-Hope rule for MieLennard‐Jones or Buckingham potentials [9] is given by (Eq. 2):

Hudson and McCoubrey

[10]

Kong rules

[11]

Lorentz-Berthelot rules

The Lorentz rule is given by [12]

which is only really valid for the hard sphere model.

The Berthelot rule is given by [13]

These rules are simple and widely used, but are not without their failings [14] [15] [16].

Mason-Rice rule

The Mason-Rice rule for the Exp-6 potential [17].

Sikora rules

The Sikora rules for the Lennard-Jones model [18].

Tang and Toennies

[19]

Waldman-Hagler rules

[20]

References

  1. I. Amdur and E. A. Mason "Properties of Gases at Very High Temperatures", Physics of Fluids 1 pp. 370-383 (1958)
  2. Hans‐Joachim Böhm and Reinhart Ahlrichs "A study of short‐range repulsions", Journal of Chemical Physics 77 pp. 2028- (1982)
  3. M. Diaz Peña, C. Pando, and J. A. R. Renuncio "Combination rules for intermolecular potential parameters. I. Rules based on approximations for the long-range dispersion energy", Journal of Chemical Physics 76 pp. 325- (1982)
  4. M. Diaz Peña, C. Pando, and J. A. R. Renuncio "Combination rules for intermolecular potential parameters. II. Rules based on approximations for the long-range dispersion energy and an atomic distortion model for the repulsive interactions", Journal of Chemical Physics 76 pp. 333- (1982)
  5. B. E. F. Fender and G. D. Halsey, Jr. "Second Virial Coefficients of Argon, Krypton, and Argon-Krypton Mixtures at Low Temperatures", Journal of Chemical Physics 36 pp. 1881-1888 (1962)
  6. T. L. Gilbert "Soft‐Sphere Model for Closed‐Shell Atoms and Ions", Journal of Chemical Physics 49 pp. 2640- (1968)
  7. T. L. Gilbert, O. C. Simpson, and M. A. Williamson "Relation between charge and force parameters of closed‐shell atoms and ions", Journal of Chemical Physics 63 pp. 4061- (1975)
  8. Felix T. Smith "Atomic Distortion and the Combining Rule for Repulsive Potentials", Physical Review A 5 pp. 1708-1713 (1972)
  9. Robert J. Good and Christopher J. Hope "New Combining Rule for Intermolecular Distances in Intermolecular Potential Functions", Journal of Chemical Physics 53 pp. 540- (1970)
  10. G. H. Hudson and J. C. McCoubrey "Intermolecular forces between unlike molecules. A more complete form of the combining rules", Transactions of the Faraday Society 56 pp. 761-766 (1960)
  11. Chang Lyoul Kong "Combining rules for intermolecular potential parameters. II. Rules for the Lennard-Jones (12–6) potential and the Morse potential", Journal of Chemical Physics 59 pp. 2464-2467 (1973)
  12. H. A. Lorentz "Ueber die Anwendung des Satzes vom Virial in der kinetischen Theorie der Gase", Annalen der Physik 12 pp. 127-136 (1881)
  13. Daniel Berthelot "Sur le mélange des gaz", Comptes rendus hebdomadaires des séances de l’Académie des Sciences, 126 pp. 1703-1855 (1898)
  14. Jérôme Delhommelle; Philippe Millié "Inadequacy of the Lorentz-Berthelot combining rules for accurate predictions of equilibrium properties by molecular simulation", Molecular Physics 99 pp. 619-625 (2001)
  15. Dezso Boda and Douglas Henderson "The effects of deviations from Lorentz-Berthelot rules on the properties of a simple mixture", Molecular Physics 106 pp. 2367-2370 (2008)
  16. W. Song, P. J. Rossky, and M. Maroncelli "Modeling alkane+perfluoroalkane interactions using all-atom potentials: Failure of the usual combining rules", Journal of Chemical Physics 119 pp. 9145- (2003)
  17. Edward A. Mason and William E. Rice "The Intermolecular Potentials of Helium and Hydrogen", Journal of Chemical Physics 22 pp. 522- (1954)
  18. P. T. Sikora "Combining rules for spherically symmetric intermolecular potentials", Journal of Physics B: Atomic and Molecular Physics 3 pp. 1475- (1970)
  19. K. T. Tang and J. Peter Toennies "New combining rules for well parameters and shapes of the van der Waals potential of mixed rare gas systems", Zeitschrift für Physik D Atoms, Molecules and Clusters 1 pp. 91-101 (1986)
  20. M. Waldman and A. T. Hagler "New combining rules for rare-gas Van der-Waals parameters", Journal of Computational Chemistry 14 pp. 1077-1084 (1993)

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