Combining rules
The combining rules are geometric expressions designed to provide the interaction energy between two dissimilar non-bonded atoms (here labelled ?UNIQ879f6b467d81d4c5-math-0000008B-QINU? and ?UNIQ879f6b467d81d4c5-math-0000008C-QINU?). Most of the rules are designed to be used with a specific interaction potential in mind. (See also Mixing rules).
Böhm-Ahlrichs
?UNIQ879f6b467d81d4c5-ref-0000008D-QINU?
Diaz Peña-Pando-Renuncio
?UNIQ879f6b467d81d4c5-ref-0000008E-QINU? ?UNIQ879f6b467d81d4c5-ref-0000008F-QINU?
Fender-Halsey
The Fender-Halsey combining rule for the Lennard-Jones model is given by ?UNIQ879f6b467d81d4c5-ref-00000090-QINU?
- ?UNIQ879f6b467d81d4c5-math-00000091-QINU?
Gilbert-Smith
The Gilbert-Smith rules for the Born-Huggins-Meyer potential?UNIQ879f6b467d81d4c5-ref-00000092-QINU??UNIQ879f6b467d81d4c5-ref-00000093-QINU??UNIQ879f6b467d81d4c5-ref-00000094-QINU?.
Good-Hope rule
The Good-Hope rule for Mie–Lennard‐Jones or Buckingham potentials ?UNIQ879f6b467d81d4c5-ref-00000095-QINU? is given by (Eq. 2):
- ?UNIQ879f6b467d81d4c5-math-00000096-QINU?
Hudson and McCoubrey
?UNIQ879f6b467d81d4c5-ref-00000097-QINU?
Hogervorst rules
The Hogervorst rules for the Exp-6 potential ?UNIQ879f6b467d81d4c5-ref-00000098-QINU?:
- ?UNIQ879f6b467d81d4c5-math-00000099-QINU?
and
- ?UNIQ879f6b467d81d4c5-math-0000009A-QINU?
Kong rules
The Kong rules for the Lennard-Jones model are given by (Table I in ?UNIQ879f6b467d81d4c5-ref-0000009B-QINU?):
- ?UNIQ879f6b467d81d4c5-math-0000009C-QINU?
- ?UNIQ879f6b467d81d4c5-math-0000009D-QINU?
Kong-Chakrabarty rules
The Kong-Chakrabarty rules for the Exp-6 potential ?UNIQ879f6b467d81d4c5-ref-0000009E-QINU? are given by (Eqs. 2-4):
- ?UNIQ879f6b467d81d4c5-math-0000009F-QINU?
- ?UNIQ879f6b467d81d4c5-math-000000A0-QINU?
and
- ?UNIQ879f6b467d81d4c5-math-000000A1-QINU?
Lorentz-Berthelot rules
The Lorentz rule is given by ?UNIQ879f6b467d81d4c5-ref-000000A2-QINU?
- ?UNIQ879f6b467d81d4c5-math-000000A3-QINU?
which is only really valid for the hard sphere model.
The Berthelot rule is given by ?UNIQ879f6b467d81d4c5-ref-000000A4-QINU?
- ?UNIQ879f6b467d81d4c5-math-000000A5-QINU?
These rules are simple and widely used, but are not without their failings ?UNIQ879f6b467d81d4c5-ref-000000A6-QINU? ?UNIQ879f6b467d81d4c5-ref-000000A7-QINU? ?UNIQ879f6b467d81d4c5-ref-000000A8-QINU? ?UNIQ879f6b467d81d4c5-ref-000000A9-QINU?.
Mason-Rice rules
The Mason-Rice rules for the Exp-6 potential ?UNIQ879f6b467d81d4c5-ref-000000AA-QINU?.
Srivastava and Srivastava rules
The Srivastava and Srivastava rules for the Exp-6 potential ?UNIQ879f6b467d81d4c5-ref-000000AB-QINU?.
Sikora rules
The Sikora rules for the Lennard-Jones model ?UNIQ879f6b467d81d4c5-ref-000000AC-QINU?.
Tang and Toennies
?UNIQ879f6b467d81d4c5-ref-000000AD-QINU?
Waldman-Hagler rules
The Waldman-Hagler rules ?UNIQ879f6b467d81d4c5-ref-000000AE-QINU? are given by:
- ?UNIQ879f6b467d81d4c5-math-000000AF-QINU?
and
- ?UNIQ879f6b467d81d4c5-math-000000B0-QINU?
References
?UNIQ879f6b467d81d4c5-references-000000B1-QINU? Related reading