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 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]]).
The '''combining rules'''  are geometric expressions designed to provide the interaction energy between two dissimilar non-bonded atoms (here labelled UNIQa5d53e6b5f34ffec-math-0000006C-QINU and UNIQa5d53e6b5f34ffec-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==
UNIQf4e7a62258c5cdf7-ref-0000006A-QINU
UNIQa5d53e6b5f34ffec-ref-0000006E-QINU
==Diaz Peña-Pando-Renuncio==
==Diaz Peña-Pando-Renuncio==
UNIQf4e7a62258c5cdf7-ref-0000006B-QINU
UNIQa5d53e6b5f34ffec-ref-0000006F-QINU
UNIQf4e7a62258c5cdf7-ref-0000006C-QINU
UNIQa5d53e6b5f34ffec-ref-00000070-QINU
==Fender-Halsey==
==Fender-Halsey==
The Fender-Halsey combining rule for the [[Lennard-Jones model]] is given by UNIQf4e7a62258c5cdf7-ref-0000006D-QINU
The Fender-Halsey combining rule for the [[Lennard-Jones model]] is given by UNIQa5d53e6b5f34ffec-ref-00000071-QINU
:UNIQf4e7a62258c5cdf7-math-0000006E-QINU
:UNIQa5d53e6b5f34ffec-math-00000072-QINU
==Gilbert-Smith==
==Gilbert-Smith==
The Gilbert-Smith rules for the [[Born-Huggins-Meyer potential]]UNIQf4e7a62258c5cdf7-ref-0000006F-QINUUNIQf4e7a62258c5cdf7-ref-00000070-QINUUNIQf4e7a62258c5cdf7-ref-00000071-QINU.
The Gilbert-Smith rules for the [[Born-Huggins-Meyer potential]]UNIQa5d53e6b5f34ffec-ref-00000073-QINUUNIQa5d53e6b5f34ffec-ref-00000074-QINUUNIQa5d53e6b5f34ffec-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 UNIQf4e7a62258c5cdf7-ref-00000072-QINU is given by (Eq. 2):
The Good-Hope rule for [[Mie potential |Mie]]–[[Lennard-Jones model |Lennard‐Jones]] or [[Buckingham potential]]s UNIQa5d53e6b5f34ffec-ref-00000076-QINU is given by (Eq. 2):


:UNIQf4e7a62258c5cdf7-math-00000073-QINU
:UNIQa5d53e6b5f34ffec-math-00000077-QINU
==Hudson and McCoubrey==
==Hudson and McCoubrey==
UNIQf4e7a62258c5cdf7-ref-00000074-QINU
UNIQa5d53e6b5f34ffec-ref-00000078-QINU
==Hogervorst rules==
==Hogervorst rules==
The Hogervorst rules for the [[Exp-6 potential]] UNIQf4e7a62258c5cdf7-ref-00000075-QINU:
The Hogervorst rules for the [[Exp-6 potential]] UNIQa5d53e6b5f34ffec-ref-00000079-QINU:


:UNIQf4e7a62258c5cdf7-math-00000076-QINU
:UNIQa5d53e6b5f34ffec-math-0000007A-QINU


and
and


:UNIQf4e7a62258c5cdf7-math-00000077-QINU
:UNIQa5d53e6b5f34ffec-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  
UNIQf4e7a62258c5cdf7-ref-00000078-QINU):
UNIQa5d53e6b5f34ffec-ref-0000007C-QINU):


:UNIQf4e7a62258c5cdf7-math-00000079-QINU
:UNIQa5d53e6b5f34ffec-math-0000007D-QINU


:UNIQf4e7a62258c5cdf7-math-0000007A-QINU
:UNIQa5d53e6b5f34ffec-math-0000007E-QINU
==Kong-Chakrabarty  rules==
==Kong-Chakrabarty  rules==
The Kong-Chakrabarty rules for the [[Exp-6 potential]] UNIQf4e7a62258c5cdf7-ref-0000007B-QINU are given by (Eqs. 2-4):
The Kong-Chakrabarty rules for the [[Exp-6 potential]] UNIQa5d53e6b5f34ffec-ref-0000007F-QINU are given by (Eqs. 2-4):


:UNIQf4e7a62258c5cdf7-math-0000007C-QINU
:UNIQa5d53e6b5f34ffec-math-00000080-QINU


:UNIQf4e7a62258c5cdf7-math-0000007D-QINU
:UNIQa5d53e6b5f34ffec-math-00000081-QINU


and
and


:UNIQf4e7a62258c5cdf7-math-0000007E-QINU
:UNIQa5d53e6b5f34ffec-math-00000082-QINU


==Lorentz-Berthelot rules==
==Lorentz-Berthelot rules==
The Lorentz rule is given by UNIQf4e7a62258c5cdf7-ref-0000007F-QINU
The Lorentz rule is given by UNIQa5d53e6b5f34ffec-ref-00000083-QINU
:UNIQf4e7a62258c5cdf7-math-00000080-QINU
:UNIQa5d53e6b5f34ffec-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 UNIQf4e7a62258c5cdf7-ref-00000081-QINU
The Berthelot rule is given by UNIQa5d53e6b5f34ffec-ref-00000085-QINU


:UNIQf4e7a62258c5cdf7-math-00000082-QINU
:UNIQa5d53e6b5f34ffec-math-00000086-QINU


These rules are simple and widely used, but are not without their failings UNIQf4e7a62258c5cdf7-ref-00000083-QINU
These rules are simple and widely used, but are not without their failings UNIQa5d53e6b5f34ffec-ref-00000087-QINU
UNIQf4e7a62258c5cdf7-ref-00000084-QINU
UNIQa5d53e6b5f34ffec-ref-00000088-QINU
UNIQf4e7a62258c5cdf7-ref-00000085-QINU.
UNIQa5d53e6b5f34ffec-ref-00000089-QINU
UNIQa5d53e6b5f34ffec-ref-0000008A-QINU.


==Mason-Rice rules==   
==Mason-Rice rules==   
The Mason-Rice rules for the [[Exp-6 potential]] UNIQf4e7a62258c5cdf7-ref-00000086-QINU.
The Mason-Rice rules for the [[Exp-6 potential]] UNIQa5d53e6b5f34ffec-ref-0000008B-QINU.
==Srivastava and Srivastava rules==
==Srivastava and Srivastava rules==
The Srivastava and Srivastava rules for the [[Exp-6 potential]] UNIQf4e7a62258c5cdf7-ref-00000087-QINU.
The Srivastava and Srivastava rules for the [[Exp-6 potential]] UNIQa5d53e6b5f34ffec-ref-0000008C-QINU.
==Sikora rules==
==Sikora rules==
The Sikora rules for the [[Lennard-Jones model]] UNIQf4e7a62258c5cdf7-ref-00000088-QINU.
The Sikora rules for the [[Lennard-Jones model]] UNIQa5d53e6b5f34ffec-ref-0000008D-QINU.
==Tang and Toennies==
==Tang and Toennies==
UNIQf4e7a62258c5cdf7-ref-00000089-QINU
UNIQa5d53e6b5f34ffec-ref-0000008E-QINU
==Waldman-Hagler rules==
==Waldman-Hagler rules==
The Waldman-Hagler rules UNIQf4e7a62258c5cdf7-ref-0000008A-QINU are given by:
The Waldman-Hagler rules UNIQa5d53e6b5f34ffec-ref-0000008F-QINU are given by:


:UNIQf4e7a62258c5cdf7-math-0000008B-QINU
:UNIQa5d53e6b5f34ffec-math-00000090-QINU


and
and


:UNIQf4e7a62258c5cdf7-math-0000008C-QINU
:UNIQa5d53e6b5f34ffec-math-00000091-QINU


==References==
==References==
UNIQf4e7a62258c5cdf7-references-0000008D-QINU
UNIQa5d53e6b5f34ffec-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 22:19, 15 January 2015

The combining rules are geometric expressions designed to provide the interaction energy between two dissimilar non-bonded atoms (here labelled ?UNIQa5d53e6b5f34ffec-math-0000006C-QINU? and ?UNIQa5d53e6b5f34ffec-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

?UNIQa5d53e6b5f34ffec-ref-0000006E-QINU?

Diaz Peña-Pando-Renuncio

?UNIQa5d53e6b5f34ffec-ref-0000006F-QINU? ?UNIQa5d53e6b5f34ffec-ref-00000070-QINU?

Fender-Halsey

The Fender-Halsey combining rule for the Lennard-Jones model is given by ?UNIQa5d53e6b5f34ffec-ref-00000071-QINU?

?UNIQa5d53e6b5f34ffec-math-00000072-QINU?

Gilbert-Smith

The Gilbert-Smith rules for the Born-Huggins-Meyer potential?UNIQa5d53e6b5f34ffec-ref-00000073-QINU??UNIQa5d53e6b5f34ffec-ref-00000074-QINU??UNIQa5d53e6b5f34ffec-ref-00000075-QINU?.

Good-Hope rule

The Good-Hope rule for Mie–Lennard‐Jones or Buckingham potentials ?UNIQa5d53e6b5f34ffec-ref-00000076-QINU? is given by (Eq. 2):

?UNIQa5d53e6b5f34ffec-math-00000077-QINU?

Hudson and McCoubrey

?UNIQa5d53e6b5f34ffec-ref-00000078-QINU?

Hogervorst rules

The Hogervorst rules for the Exp-6 potential ?UNIQa5d53e6b5f34ffec-ref-00000079-QINU?:

?UNIQa5d53e6b5f34ffec-math-0000007A-QINU?

and

?UNIQa5d53e6b5f34ffec-math-0000007B-QINU?

Kong rules

The Kong rules for the Lennard-Jones model are given by (Table I in ?UNIQa5d53e6b5f34ffec-ref-0000007C-QINU?):

?UNIQa5d53e6b5f34ffec-math-0000007D-QINU?
?UNIQa5d53e6b5f34ffec-math-0000007E-QINU?

Kong-Chakrabarty rules

The Kong-Chakrabarty rules for the Exp-6 potential ?UNIQa5d53e6b5f34ffec-ref-0000007F-QINU? are given by (Eqs. 2-4):

?UNIQa5d53e6b5f34ffec-math-00000080-QINU?
?UNIQa5d53e6b5f34ffec-math-00000081-QINU?

and

?UNIQa5d53e6b5f34ffec-math-00000082-QINU?

Lorentz-Berthelot rules

The Lorentz rule is given by ?UNIQa5d53e6b5f34ffec-ref-00000083-QINU?

?UNIQa5d53e6b5f34ffec-math-00000084-QINU?

which is only really valid for the hard sphere model.

The Berthelot rule is given by ?UNIQa5d53e6b5f34ffec-ref-00000085-QINU?

?UNIQa5d53e6b5f34ffec-math-00000086-QINU?

These rules are simple and widely used, but are not without their failings ?UNIQa5d53e6b5f34ffec-ref-00000087-QINU? ?UNIQa5d53e6b5f34ffec-ref-00000088-QINU? ?UNIQa5d53e6b5f34ffec-ref-00000089-QINU? ?UNIQa5d53e6b5f34ffec-ref-0000008A-QINU?.

Mason-Rice rules

The Mason-Rice rules for the Exp-6 potential ?UNIQa5d53e6b5f34ffec-ref-0000008B-QINU?.

Srivastava and Srivastava rules

The Srivastava and Srivastava rules for the Exp-6 potential ?UNIQa5d53e6b5f34ffec-ref-0000008C-QINU?.

Sikora rules

The Sikora rules for the Lennard-Jones model ?UNIQa5d53e6b5f34ffec-ref-0000008D-QINU?.

Tang and Toennies

?UNIQa5d53e6b5f34ffec-ref-0000008E-QINU?

Waldman-Hagler rules

The Waldman-Hagler rules ?UNIQa5d53e6b5f34ffec-ref-0000008F-QINU? are given by:

?UNIQa5d53e6b5f34ffec-math-00000090-QINU?

and

?UNIQa5d53e6b5f34ffec-math-00000091-QINU?

References

?UNIQa5d53e6b5f34ffec-references-00000092-QINU? Related reading

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