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 UNIQf4e7a62258c5cdf7-math-00000068-QINU and UNIQf4e7a62258c5cdf7-math-00000069-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== | ||
| UNIQf4e7a62258c5cdf7-ref-0000006A-QINU | ||
==Diaz Peña-Pando-Renuncio== | ==Diaz Peña-Pando-Renuncio== | ||
| UNIQf4e7a62258c5cdf7-ref-0000006B-QINU | ||
| UNIQf4e7a62258c5cdf7-ref-0000006C-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 UNIQf4e7a62258c5cdf7-ref-0000006D-QINU | ||
: | :UNIQf4e7a62258c5cdf7-math-0000006E-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]]UNIQf4e7a62258c5cdf7-ref-0000006F-QINUUNIQf4e7a62258c5cdf7-ref-00000070-QINUUNIQf4e7a62258c5cdf7-ref-00000071-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 UNIQf4e7a62258c5cdf7-ref-00000072-QINU is given by (Eq. 2): | ||
: | :UNIQf4e7a62258c5cdf7-math-00000073-QINU | ||
==Hudson and McCoubrey== | ==Hudson and McCoubrey== | ||
| UNIQf4e7a62258c5cdf7-ref-00000074-QINU | ||
==Hogervorst rules== | ==Hogervorst rules== | ||
The Hogervorst rules for the [[Exp-6 potential]] | The Hogervorst rules for the [[Exp-6 potential]] UNIQf4e7a62258c5cdf7-ref-00000075-QINU: | ||
: | :UNIQf4e7a62258c5cdf7-math-00000076-QINU | ||
and | and | ||
: | :UNIQf4e7a62258c5cdf7-math-00000077-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 | ||
| UNIQf4e7a62258c5cdf7-ref-00000078-QINU): | ||
: | :UNIQf4e7a62258c5cdf7-math-00000079-QINU | ||
: | :UNIQf4e7a62258c5cdf7-math-0000007A-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]] UNIQf4e7a62258c5cdf7-ref-0000007B-QINU are given by (Eqs. 2-4): | ||
: | :UNIQf4e7a62258c5cdf7-math-0000007C-QINU | ||
: | :UNIQf4e7a62258c5cdf7-math-0000007D-QINU | ||
and | and | ||
: | :UNIQf4e7a62258c5cdf7-math-0000007E-QINU | ||
==Lorentz-Berthelot rules== | ==Lorentz-Berthelot rules== | ||
The Lorentz rule is given by | The Lorentz rule is given by UNIQf4e7a62258c5cdf7-ref-0000007F-QINU | ||
: | :UNIQf4e7a62258c5cdf7-math-00000080-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 UNIQf4e7a62258c5cdf7-ref-00000081-QINU | ||
: | :UNIQf4e7a62258c5cdf7-math-00000082-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 UNIQf4e7a62258c5cdf7-ref-00000083-QINU | ||
| UNIQf4e7a62258c5cdf7-ref-00000084-QINU | ||
| UNIQf4e7a62258c5cdf7-ref-00000085-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]] UNIQf4e7a62258c5cdf7-ref-00000086-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]] UNIQf4e7a62258c5cdf7-ref-00000087-QINU. | ||
==Sikora rules== | ==Sikora rules== | ||
The Sikora rules for the [[Lennard-Jones model]] | The Sikora rules for the [[Lennard-Jones model]] UNIQf4e7a62258c5cdf7-ref-00000088-QINU. | ||
==Tang and Toennies== | ==Tang and Toennies== | ||
| UNIQf4e7a62258c5cdf7-ref-00000089-QINU | ||
==Waldman-Hagler rules== | ==Waldman-Hagler rules== | ||
The Waldman-Hagler rules | The Waldman-Hagler rules UNIQf4e7a62258c5cdf7-ref-0000008A-QINU are given by: | ||
: | :UNIQf4e7a62258c5cdf7-math-0000008B-QINU | ||
and | and | ||
: | :UNIQf4e7a62258c5cdf7-math-0000008C-QINU | ||
==References== | ==References== | ||
| UNIQf4e7a62258c5cdf7-references-0000008D-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 23:18, 15 January 2015
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
?UNIQf4e7a62258c5cdf7-ref-0000006A-QINU?
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 Mie–Lennard‐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):
- ?UNIQf4e7a62258c5cdf7-math-0000007C-QINU?
- ?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