Combining rules

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The combining rules are geometric expressions designed to provide the interaction energy between two dissimilar non-bonded atoms (here labelled ?UNIQf4e7a62258c5cdf7-math-00000068-QINU? and ?UNIQf4e7a62258c5cdf7-math-00000069-QINU?). Most of the rules are designed to be used with a specific interaction potential in mind. (See also Mixing rules).

Böhm-Ahlrichs

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Diaz Peña-Pando-Renuncio

?UNIQf4e7a62258c5cdf7-ref-0000006B-QINU? ?UNIQf4e7a62258c5cdf7-ref-0000006C-QINU?

Fender-Halsey

The Fender-Halsey combining rule for the Lennard-Jones model is given by ?UNIQf4e7a62258c5cdf7-ref-0000006D-QINU?

?UNIQf4e7a62258c5cdf7-math-0000006E-QINU?

Gilbert-Smith

The Gilbert-Smith rules for the Born-Huggins-Meyer potential?UNIQf4e7a62258c5cdf7-ref-0000006F-QINU??UNIQf4e7a62258c5cdf7-ref-00000070-QINU??UNIQf4e7a62258c5cdf7-ref-00000071-QINU?.

Good-Hope rule

The Good-Hope rule for MieLennard‐Jones or Buckingham potentials ?UNIQf4e7a62258c5cdf7-ref-00000072-QINU? is given by (Eq. 2):

?UNIQf4e7a62258c5cdf7-math-00000073-QINU?

Hudson and McCoubrey

?UNIQf4e7a62258c5cdf7-ref-00000074-QINU?

Hogervorst rules

The Hogervorst rules for the Exp-6 potential ?UNIQf4e7a62258c5cdf7-ref-00000075-QINU?:

?UNIQf4e7a62258c5cdf7-math-00000076-QINU?

and

?UNIQf4e7a62258c5cdf7-math-00000077-QINU?

Kong rules

The Kong rules for the Lennard-Jones model are given by (Table I in ?UNIQf4e7a62258c5cdf7-ref-00000078-QINU?):

?UNIQf4e7a62258c5cdf7-math-00000079-QINU?
?UNIQf4e7a62258c5cdf7-math-0000007A-QINU?

Kong-Chakrabarty rules

The Kong-Chakrabarty rules for the Exp-6 potential ?UNIQf4e7a62258c5cdf7-ref-0000007B-QINU? are given by (Eqs. 2-4):

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?UNIQf4e7a62258c5cdf7-math-0000007D-QINU?

and

?UNIQf4e7a62258c5cdf7-math-0000007E-QINU?

Lorentz-Berthelot rules

The Lorentz rule is given by ?UNIQf4e7a62258c5cdf7-ref-0000007F-QINU?

?UNIQf4e7a62258c5cdf7-math-00000080-QINU?

which is only really valid for the hard sphere model.

The Berthelot rule is given by ?UNIQf4e7a62258c5cdf7-ref-00000081-QINU?

?UNIQf4e7a62258c5cdf7-math-00000082-QINU?

These rules are simple and widely used, but are not without their failings ?UNIQf4e7a62258c5cdf7-ref-00000083-QINU? ?UNIQf4e7a62258c5cdf7-ref-00000084-QINU? ?UNIQf4e7a62258c5cdf7-ref-00000085-QINU?.

Mason-Rice rules

The Mason-Rice rules for the Exp-6 potential ?UNIQf4e7a62258c5cdf7-ref-00000086-QINU?.

Srivastava and Srivastava rules

The Srivastava and Srivastava rules for the Exp-6 potential ?UNIQf4e7a62258c5cdf7-ref-00000087-QINU?.

Sikora rules

The Sikora rules for the Lennard-Jones model ?UNIQf4e7a62258c5cdf7-ref-00000088-QINU?.

Tang and Toennies

?UNIQf4e7a62258c5cdf7-ref-00000089-QINU?

Waldman-Hagler rules

The Waldman-Hagler rules ?UNIQf4e7a62258c5cdf7-ref-0000008A-QINU? are given by:

?UNIQf4e7a62258c5cdf7-math-0000008B-QINU?

and

?UNIQf4e7a62258c5cdf7-math-0000008C-QINU?

References

?UNIQf4e7a62258c5cdf7-references-0000008D-QINU? Related reading