Combining rules: Difference between revisions
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The '''combining rules''' are geometric expressions designed to provide the interaction energy between two dissimilar non-bonded atoms (here labelled | 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 [[Idealised models| interaction potential]] in mind. (''See also'' [[Mixing rules]]). | ||
==Böhm-Ahlrichs== | ==Böhm-Ahlrichs== | ||
| UNIQ0f04d0997b4299f9-ref-0000006E-QINU | ||
==Diaz Peña-Pando-Renuncio== | ==Diaz Peña-Pando-Renuncio== | ||
| UNIQ0f04d0997b4299f9-ref-0000006F-QINU | ||
| UNIQ0f04d0997b4299f9-ref-00000070-QINU | ||
==Fender-Halsey== | ==Fender-Halsey== | ||
The Fender-Halsey combining rule for the [[Lennard-Jones model]] is given by | The Fender-Halsey combining rule for the [[Lennard-Jones model]] is given by UNIQ0f04d0997b4299f9-ref-00000071-QINU | ||
: | :UNIQ0f04d0997b4299f9-math-00000072-QINU | ||
==Gilbert-Smith== | ==Gilbert-Smith== | ||
The Gilbert-Smith rules for the [[Born-Huggins-Meyer potential]] | The Gilbert-Smith rules for the [[Born-Huggins-Meyer potential]]UNIQ0f04d0997b4299f9-ref-00000073-QINUUNIQ0f04d0997b4299f9-ref-00000074-QINUUNIQ0f04d0997b4299f9-ref-00000075-QINU. | ||
==Good-Hope rule== | ==Good-Hope rule== | ||
The Good-Hope rule for [[Mie potential |Mie]]–[[Lennard-Jones model |Lennard‐Jones]] or [[Buckingham potential]]s | The Good-Hope rule for [[Mie potential |Mie]]–[[Lennard-Jones model |Lennard‐Jones]] or [[Buckingham potential]]s UNIQ0f04d0997b4299f9-ref-00000076-QINU is given by (Eq. 2): | ||
: | :UNIQ0f04d0997b4299f9-math-00000077-QINU | ||
==Hudson and McCoubrey== | ==Hudson and McCoubrey== | ||
| UNIQ0f04d0997b4299f9-ref-00000078-QINU | ||
==Hogervorst rules== | ==Hogervorst rules== | ||
The Hogervorst rules for the [[Exp-6 potential]] | The Hogervorst rules for the [[Exp-6 potential]] UNIQ0f04d0997b4299f9-ref-00000079-QINU: | ||
: | :UNIQ0f04d0997b4299f9-math-0000007A-QINU | ||
and | and | ||
: | :UNIQ0f04d0997b4299f9-math-0000007B-QINU | ||
==Kong rules== | ==Kong rules== | ||
The Kong rules for the [[Lennard-Jones model]] are given by (Table I in | 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== | ==Kong-Chakrabarty rules== | ||
The Kong-Chakrabarty rules for the [[Exp-6 potential]] | 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 | and | ||
: | :UNIQ0f04d0997b4299f9-math-00000082-QINU | ||
==Lorentz-Berthelot rules== | ==Lorentz-Berthelot rules== | ||
The Lorentz rule is given by | The Lorentz rule is given by UNIQ0f04d0997b4299f9-ref-00000083-QINU | ||
: | :UNIQ0f04d0997b4299f9-math-00000084-QINU | ||
which is only really valid for the [[hard sphere model]]. | which is only really valid for the [[hard sphere model]]. | ||
The Berthelot rule is given by | 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 | 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== | ==Mason-Rice rules== | ||
The Mason-Rice rules for the [[Exp-6 potential]] | The Mason-Rice rules for the [[Exp-6 potential]] UNIQ0f04d0997b4299f9-ref-0000008B-QINU. | ||
==Srivastava and Srivastava rules== | ==Srivastava and Srivastava rules== | ||
The Srivastava and Srivastava rules for the [[Exp-6 potential]] | The Srivastava and Srivastava rules for the [[Exp-6 potential]] UNIQ0f04d0997b4299f9-ref-0000008C-QINU. | ||
==Sikora rules== | ==Sikora rules== | ||
The Sikora rules for the [[Lennard-Jones model]] | The Sikora rules for the [[Lennard-Jones model]] UNIQ0f04d0997b4299f9-ref-0000008D-QINU. | ||
==Tang and Toennies== | ==Tang and Toennies== | ||
| UNIQ0f04d0997b4299f9-ref-0000008E-QINU | ||
==Waldman-Hagler rules== | ==Waldman-Hagler rules== | ||
The Waldman-Hagler rules | The Waldman-Hagler rules UNIQ0f04d0997b4299f9-ref-0000008F-QINU are given by: | ||
: | :UNIQ0f04d0997b4299f9-math-00000090-QINU | ||
and | and | ||
: | :UNIQ0f04d0997b4299f9-math-00000091-QINU | ||
==References== | ==References== | ||
| UNIQ0f04d0997b4299f9-references-00000092-QINU | ||
'''Related reading''' | '''Related reading''' | ||
*[http://dx.doi.org/10.1021/ja00046a032 Thomas A. Halgren "The representation of van der Waals (vdW) interactions in molecular mechanics force fields: potential form, combination rules, and vdW parameters", Journal of the American Chemical Society '''114''' pp. 7827-7843 (1992)] | *[http://dx.doi.org/10.1021/ja00046a032 Thomas A. Halgren "The representation of van der Waals (vdW) interactions in molecular mechanics force fields: potential form, combination rules, and vdW parameters", Journal of the American Chemical Society '''114''' pp. 7827-7843 (1992)] | ||
[[category: mixtures]] | [[category: mixtures]] | ||
Revision as of 23:14, 15 January 2015
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