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 ?UNIQ0460e71333a2b13d-math-0000006C-QINU? and ?UNIQ0460e71333a2b13d-math-0000006D-QINU?). Most of the rules are designed to be used with a specific interaction potential in mind. (See also Mixing rules).

Böhm-Ahlrichs

?UNIQ0460e71333a2b13d-ref-0000006E-QINU?

Diaz Peña-Pando-Renuncio

?UNIQ0460e71333a2b13d-ref-0000006F-QINU? ?UNIQ0460e71333a2b13d-ref-00000070-QINU?

Fender-Halsey

The Fender-Halsey combining rule for the Lennard-Jones model is given by ?UNIQ0460e71333a2b13d-ref-00000071-QINU?

?UNIQ0460e71333a2b13d-math-00000072-QINU?

Gilbert-Smith

The Gilbert-Smith rules for the Born-Huggins-Meyer potential?UNIQ0460e71333a2b13d-ref-00000073-QINU??UNIQ0460e71333a2b13d-ref-00000074-QINU??UNIQ0460e71333a2b13d-ref-00000075-QINU?.

Good-Hope rule

The Good-Hope rule for MieLennard‐Jones or Buckingham potentials ?UNIQ0460e71333a2b13d-ref-00000076-QINU? is given by (Eq. 2):

?UNIQ0460e71333a2b13d-math-00000077-QINU?

Hudson and McCoubrey

?UNIQ0460e71333a2b13d-ref-00000078-QINU?

Hogervorst rules

The Hogervorst rules for the Exp-6 potential ?UNIQ0460e71333a2b13d-ref-00000079-QINU?:

?UNIQ0460e71333a2b13d-math-0000007A-QINU?

and

?UNIQ0460e71333a2b13d-math-0000007B-QINU?

Kong rules

The Kong rules for the Lennard-Jones model are given by (Table I in ?UNIQ0460e71333a2b13d-ref-0000007C-QINU?):

?UNIQ0460e71333a2b13d-math-0000007D-QINU?
?UNIQ0460e71333a2b13d-math-0000007E-QINU?

Kong-Chakrabarty rules

The Kong-Chakrabarty rules for the Exp-6 potential ?UNIQ0460e71333a2b13d-ref-0000007F-QINU? are given by (Eqs. 2-4):

?UNIQ0460e71333a2b13d-math-00000080-QINU?
?UNIQ0460e71333a2b13d-math-00000081-QINU?

and

?UNIQ0460e71333a2b13d-math-00000082-QINU?

Lorentz-Berthelot rules

The Lorentz rule is given by ?UNIQ0460e71333a2b13d-ref-00000083-QINU?

?UNIQ0460e71333a2b13d-math-00000084-QINU?

which is only really valid for the hard sphere model.

The Berthelot rule is given by ?UNIQ0460e71333a2b13d-ref-00000085-QINU?

?UNIQ0460e71333a2b13d-math-00000086-QINU?

These rules are simple and widely used, but are not without their failings ?UNIQ0460e71333a2b13d-ref-00000087-QINU? ?UNIQ0460e71333a2b13d-ref-00000088-QINU? ?UNIQ0460e71333a2b13d-ref-00000089-QINU? ?UNIQ0460e71333a2b13d-ref-0000008A-QINU?.

Mason-Rice rules

The Mason-Rice rules for the Exp-6 potential ?UNIQ0460e71333a2b13d-ref-0000008B-QINU?.

Srivastava and Srivastava rules

The Srivastava and Srivastava rules for the Exp-6 potential ?UNIQ0460e71333a2b13d-ref-0000008C-QINU?.

Sikora rules

The Sikora rules for the Lennard-Jones model ?UNIQ0460e71333a2b13d-ref-0000008D-QINU?.

Tang and Toennies

?UNIQ0460e71333a2b13d-ref-0000008E-QINU?

Waldman-Hagler rules

The Waldman-Hagler rules ?UNIQ0460e71333a2b13d-ref-0000008F-QINU? are given by:

?UNIQ0460e71333a2b13d-math-00000090-QINU?

and

?UNIQ0460e71333a2b13d-math-00000091-QINU?

References

?UNIQ0460e71333a2b13d-references-00000092-QINU? Related reading