Combining rules
The combining rules are geometric expressions designed to provide the interaction energy between two dissimilar non-bonded atoms (here labelled ?UNIQ0f04d0997b4299f9-math-0000006C-QINU? and ?UNIQ0f04d0997b4299f9-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
?UNIQ0f04d0997b4299f9-ref-0000006E-QINU?
Diaz Peña-Pando-Renuncio
?UNIQ0f04d0997b4299f9-ref-0000006F-QINU? ?UNIQ0f04d0997b4299f9-ref-00000070-QINU?
Fender-Halsey
The Fender-Halsey combining rule for the Lennard-Jones model is given by ?UNIQ0f04d0997b4299f9-ref-00000071-QINU?
- ?UNIQ0f04d0997b4299f9-math-00000072-QINU?
Gilbert-Smith
The Gilbert-Smith rules for the Born-Huggins-Meyer potential?UNIQ0f04d0997b4299f9-ref-00000073-QINU??UNIQ0f04d0997b4299f9-ref-00000074-QINU??UNIQ0f04d0997b4299f9-ref-00000075-QINU?.
Good-Hope rule
The Good-Hope rule for Mie–Lennard‐Jones or Buckingham potentials ?UNIQ0f04d0997b4299f9-ref-00000076-QINU? is given by (Eq. 2):
- ?UNIQ0f04d0997b4299f9-math-00000077-QINU?
Hudson and McCoubrey
?UNIQ0f04d0997b4299f9-ref-00000078-QINU?
Hogervorst rules
The Hogervorst rules for the Exp-6 potential ?UNIQ0f04d0997b4299f9-ref-00000079-QINU?:
- ?UNIQ0f04d0997b4299f9-math-0000007A-QINU?
and
- ?UNIQ0f04d0997b4299f9-math-0000007B-QINU?
Kong rules
The Kong rules for the Lennard-Jones model are given by (Table I in ?UNIQ0f04d0997b4299f9-ref-0000007C-QINU?):
- ?UNIQ0f04d0997b4299f9-math-0000007D-QINU?
- ?UNIQ0f04d0997b4299f9-math-0000007E-QINU?
Kong-Chakrabarty rules
The Kong-Chakrabarty rules for the Exp-6 potential ?UNIQ0f04d0997b4299f9-ref-0000007F-QINU? are given by (Eqs. 2-4):
- ?UNIQ0f04d0997b4299f9-math-00000080-QINU?
- ?UNIQ0f04d0997b4299f9-math-00000081-QINU?
and
- ?UNIQ0f04d0997b4299f9-math-00000082-QINU?
Lorentz-Berthelot rules
The Lorentz rule is given by ?UNIQ0f04d0997b4299f9-ref-00000083-QINU?
- ?UNIQ0f04d0997b4299f9-math-00000084-QINU?
which is only really valid for the hard sphere model.
The Berthelot rule is given by ?UNIQ0f04d0997b4299f9-ref-00000085-QINU?
- ?UNIQ0f04d0997b4299f9-math-00000086-QINU?
These rules are simple and widely used, but are not without their failings ?UNIQ0f04d0997b4299f9-ref-00000087-QINU? ?UNIQ0f04d0997b4299f9-ref-00000088-QINU? ?UNIQ0f04d0997b4299f9-ref-00000089-QINU? ?UNIQ0f04d0997b4299f9-ref-0000008A-QINU?.
Mason-Rice rules
The Mason-Rice rules for the Exp-6 potential ?UNIQ0f04d0997b4299f9-ref-0000008B-QINU?.
Srivastava and Srivastava rules
The Srivastava and Srivastava rules for the Exp-6 potential ?UNIQ0f04d0997b4299f9-ref-0000008C-QINU?.
Sikora rules
The Sikora rules for the Lennard-Jones model ?UNIQ0f04d0997b4299f9-ref-0000008D-QINU?.
Tang and Toennies
?UNIQ0f04d0997b4299f9-ref-0000008E-QINU?
Waldman-Hagler rules
The Waldman-Hagler rules ?UNIQ0f04d0997b4299f9-ref-0000008F-QINU? are given by:
- ?UNIQ0f04d0997b4299f9-math-00000090-QINU?
and
- ?UNIQ0f04d0997b4299f9-math-00000091-QINU?
References
?UNIQ0f04d0997b4299f9-references-00000092-QINU? Related reading