Combining rules: Difference between revisions

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<ref>[http://dx.doi.org/10.1007/BF01384663 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)]</ref>
<ref>[http://dx.doi.org/10.1007/BF01384663 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)]</ref>
==Waldman-Hagler rules==
==Waldman-Hagler rules==
<ref>[http://dx.doi.org/10.1002/jcc.540140909 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)]</ref>
The Waldman-Hagler rules <ref>[http://dx.doi.org/10.1002/jcc.540140909 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)]</ref> are given by:
 
:<math>r_{ij}^0 = \left( \frac{ (r_i^0)^6 + (r_j^0)^6 }{2} \right)^{1/6}</math>
 
and
 
:<math>\epsilon_{ij} = 2 \sqrt{\epsilon_i \cdot \epsilon_j} \left( \frac{ (r_i^0)^3 \cdot  (r_j^0)^3 }{ (r_i^0)^6  + (r_j^0)^6 }  \right)</math>
 
==References==
==References==
<references/>
<references/>

Revision as of 11:35, 10 April 2013

The combining 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. (See also Mixing rules).

Böhm-Ahlrichs

[1]

Diaz Peña-Pando-Renuncio

[2] [3]

Fender-Halsey

The Fender-Halsey combining rule for the Lennard-Jones model is given by [4]

Gilbert-Smith

The Gilbert-Smith rules for the Born-Huggins-Meyer potential[5][6][7].

Good-Hope rule

The Good-Hope rule for MieLennard‐Jones or Buckingham potentials [8] is given by (Eq. 2):

Hudson and McCoubrey

[9]

Kong rules

The Kong rules for the Lennard-Jones model are given by (Table I in [10]):

Lorentz-Berthelot rules

The Lorentz rule is given by [11]

which is only really valid for the hard sphere model.

The Berthelot rule is given by [12]

These rules are simple and widely used, but are not without their failings [13] [14] [15].

Mason-Rice rule

The Mason-Rice rule for the Exp-6 potential [16].

Sikora rules

The Sikora rules for the Lennard-Jones model [17].

Tang and Toennies

[18]

Waldman-Hagler rules

The Waldman-Hagler rules [19] are given by:

and

References

  1. Hans‐Joachim Böhm and Reinhart Ahlrichs "A study of short‐range repulsions", Journal of Chemical Physics 77 pp. 2028- (1982)
  2. 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)
  3. 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)
  4. 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)
  5. T. L. Gilbert "Soft‐Sphere Model for Closed‐Shell Atoms and Ions", Journal of Chemical Physics 49 pp. 2640- (1968)
  6. 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)
  7. Felix T. Smith "Atomic Distortion and the Combining Rule for Repulsive Potentials", Physical Review A 5 pp. 1708-1713 (1972)
  8. 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)
  9. 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)
  10. 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)
  11. H. A. Lorentz "Ueber die Anwendung des Satzes vom Virial in der kinetischen Theorie der Gase", Annalen der Physik 12 pp. 127-136 (1881)
  12. Daniel Berthelot "Sur le mélange des gaz", Comptes rendus hebdomadaires des séances de l’Académie des Sciences, 126 pp. 1703-1855 (1898)
  13. 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)
  14. 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)
  15. 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)
  16. Edward A. Mason and William E. Rice "The Intermolecular Potentials of Helium and Hydrogen", Journal of Chemical Physics 22 pp. 522- (1954)
  17. P. T. Sikora "Combining rules for spherically symmetric intermolecular potentials", Journal of Physics B: Atomic and Molecular Physics 3 pp. 1475- (1970)
  18. 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)
  19. 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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