SklogWiki - User contributions [en]

Combining rules

2015-01-15T21:19:29Z

38.105.236.163: Updated Lorentz reference

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==
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-QINUUNIQa5d53e6b5f34ffec-ref-00000074-QINUUNIQa5d53e6b5f34ffec-ref-00000075-QINU.
==Good-Hope rule==
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):

: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'''
*[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]]

Combining rules

2015-01-15T21:18:01Z

38.105.236.163:

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==
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-QINUUNIQf4e7a62258c5cdf7-ref-00000070-QINUUNIQf4e7a62258c5cdf7-ref-00000071-QINU.
==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):

: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'''
*[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]]

Combining rules

2015-01-15T21:15:44Z

38.105.236.163:

The '''combining rules''' are geometric expressions designed to provide the interaction energy between two dissimilar non-bonded atoms (here labelled UNIQ1d8d2241b28493a9-math-0000006C-QINU and UNIQ1d8d2241b28493a9-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==
UNIQ1d8d2241b28493a9-ref-0000006E-QINU
==Diaz Peña-Pando-Renuncio==
UNIQ1d8d2241b28493a9-ref-0000006F-QINU
UNIQ1d8d2241b28493a9-ref-00000070-QINU
==Fender-Halsey==
The Fender-Halsey combining rule for the [[Lennard-Jones model]] is given by UNIQ1d8d2241b28493a9-ref-00000071-QINU
:UNIQ1d8d2241b28493a9-math-00000072-QINU
==Gilbert-Smith==
The Gilbert-Smith rules for the [[Born-Huggins-Meyer potential]]UNIQ1d8d2241b28493a9-ref-00000073-QINUUNIQ1d8d2241b28493a9-ref-00000074-QINUUNIQ1d8d2241b28493a9-ref-00000075-QINU.
==Good-Hope rule==
The Good-Hope rule for [[Mie potential |Mie]]–[[Lennard-Jones model |Lennard‐Jones]] or [[Buckingham potential]]s UNIQ1d8d2241b28493a9-ref-00000076-QINU is given by (Eq. 2):

:UNIQ1d8d2241b28493a9-math-00000077-QINU
==Hudson and McCoubrey==
UNIQ1d8d2241b28493a9-ref-00000078-QINU
==Hogervorst rules==
The Hogervorst rules for the [[Exp-6 potential]] UNIQ1d8d2241b28493a9-ref-00000079-QINU:

:UNIQ1d8d2241b28493a9-math-0000007A-QINU

and

:UNIQ1d8d2241b28493a9-math-0000007B-QINU

==Kong rules==
The Kong rules for the [[Lennard-Jones model]] are given by (Table I in
UNIQ1d8d2241b28493a9-ref-0000007C-QINU):

:UNIQ1d8d2241b28493a9-math-0000007D-QINU

:UNIQ1d8d2241b28493a9-math-0000007E-QINU
==Kong-Chakrabarty rules==
The Kong-Chakrabarty rules for the [[Exp-6 potential]] UNIQ1d8d2241b28493a9-ref-0000007F-QINU are given by (Eqs. 2-4):

:UNIQ1d8d2241b28493a9-math-00000080-QINU

:UNIQ1d8d2241b28493a9-math-00000081-QINU

and

:UNIQ1d8d2241b28493a9-math-00000082-QINU

==Lorentz-Berthelot rules==
The Lorentz rule is given by UNIQ1d8d2241b28493a9-ref-00000083-QINU
:UNIQ1d8d2241b28493a9-math-00000084-QINU

which is only really valid for the [[hard sphere model]].

The Berthelot rule is given by UNIQ1d8d2241b28493a9-ref-00000085-QINU

:UNIQ1d8d2241b28493a9-math-00000086-QINU

These rules are simple and widely used, but are not without their failings UNIQ1d8d2241b28493a9-ref-00000087-QINU
UNIQ1d8d2241b28493a9-ref-00000088-QINU
UNIQ1d8d2241b28493a9-ref-00000089-QINU
UNIQ1d8d2241b28493a9-ref-0000008A-QINU.

==Mason-Rice rules==
The Mason-Rice rules for the [[Exp-6 potential]] UNIQ1d8d2241b28493a9-ref-0000008B-QINU.
==Srivastava and Srivastava rules==
The Srivastava and Srivastava rules for the [[Exp-6 potential]] UNIQ1d8d2241b28493a9-ref-0000008C-QINU.
==Sikora rules==
The Sikora rules for the [[Lennard-Jones model]] UNIQ1d8d2241b28493a9-ref-0000008D-QINU.
==Tang and Toennies==
UNIQ1d8d2241b28493a9-ref-0000008E-QINU
==Waldman-Hagler rules==
The Waldman-Hagler rules UNIQ1d8d2241b28493a9-ref-0000008F-QINU are given by:

:UNIQ1d8d2241b28493a9-math-00000090-QINU

and

:UNIQ1d8d2241b28493a9-math-00000091-QINU

==References==
UNIQ1d8d2241b28493a9-references-00000092-QINU
'''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)]
[[category: mixtures]]

Combining rules

2015-01-15T21:14:47Z

38.105.236.163:

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==
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-QINUUNIQ0f04d0997b4299f9-ref-00000074-QINUUNIQ0f04d0997b4299f9-ref-00000075-QINU.
==Good-Hope rule==
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==
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'''
*[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]]

Combining rules

2015-01-15T20:38:33Z

38.105.236.163: Undo revision 14463 by 38.105.236.163 (talk)

The '''combining rules''' are geometric expressions designed to provide the interaction energy between two dissimilar non-bonded atoms (here labelled UNIQ0460e71333a2b13d-math-0000006C-QINU and UNIQ0460e71333a2b13d-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==
UNIQ0460e71333a2b13d-ref-0000006E-QINU
==Diaz Peña-Pando-Renuncio==
UNIQ0460e71333a2b13d-ref-0000006F-QINU
UNIQ0460e71333a2b13d-ref-00000070-QINU
==Fender-Halsey==
The Fender-Halsey combining rule for the [[Lennard-Jones model]] is given by UNIQ0460e71333a2b13d-ref-00000071-QINU
:UNIQ0460e71333a2b13d-math-00000072-QINU
==Gilbert-Smith==
The Gilbert-Smith rules for the [[Born-Huggins-Meyer potential]]UNIQ0460e71333a2b13d-ref-00000073-QINUUNIQ0460e71333a2b13d-ref-00000074-QINUUNIQ0460e71333a2b13d-ref-00000075-QINU.
==Good-Hope rule==
The Good-Hope rule for [[Mie potential |Mie]]–[[Lennard-Jones model |Lennard‐Jones]] or [[Buckingham potential]]s UNIQ0460e71333a2b13d-ref-00000076-QINU is given by (Eq. 2):

:UNIQ0460e71333a2b13d-math-00000077-QINU
==Hudson and McCoubrey==
UNIQ0460e71333a2b13d-ref-00000078-QINU
==Hogervorst rules==
The Hogervorst rules for the [[Exp-6 potential]] UNIQ0460e71333a2b13d-ref-00000079-QINU:

:UNIQ0460e71333a2b13d-math-0000007A-QINU

and

:UNIQ0460e71333a2b13d-math-0000007B-QINU

==Kong rules==
The Kong rules for the [[Lennard-Jones model]] are given by (Table I in
UNIQ0460e71333a2b13d-ref-0000007C-QINU):

:UNIQ0460e71333a2b13d-math-0000007D-QINU

:UNIQ0460e71333a2b13d-math-0000007E-QINU
==Kong-Chakrabarty rules==
The Kong-Chakrabarty rules for the [[Exp-6 potential]] UNIQ0460e71333a2b13d-ref-0000007F-QINU are given by (Eqs. 2-4):

:UNIQ0460e71333a2b13d-math-00000080-QINU

:UNIQ0460e71333a2b13d-math-00000081-QINU

and

:UNIQ0460e71333a2b13d-math-00000082-QINU

==Lorentz-Berthelot rules==
The Lorentz rule is given by UNIQ0460e71333a2b13d-ref-00000083-QINU
:UNIQ0460e71333a2b13d-math-00000084-QINU

which is only really valid for the [[hard sphere model]].

The Berthelot rule is given by UNIQ0460e71333a2b13d-ref-00000085-QINU

:UNIQ0460e71333a2b13d-math-00000086-QINU

These rules are simple and widely used, but are not without their failings UNIQ0460e71333a2b13d-ref-00000087-QINU
UNIQ0460e71333a2b13d-ref-00000088-QINU
UNIQ0460e71333a2b13d-ref-00000089-QINU
UNIQ0460e71333a2b13d-ref-0000008A-QINU.

==Mason-Rice rules==
The Mason-Rice rules for the [[Exp-6 potential]] UNIQ0460e71333a2b13d-ref-0000008B-QINU.
==Srivastava and Srivastava rules==
The Srivastava and Srivastava rules for the [[Exp-6 potential]] UNIQ0460e71333a2b13d-ref-0000008C-QINU.
==Sikora rules==
The Sikora rules for the [[Lennard-Jones model]] UNIQ0460e71333a2b13d-ref-0000008D-QINU.
==Tang and Toennies==
UNIQ0460e71333a2b13d-ref-0000008E-QINU
==Waldman-Hagler rules==
The Waldman-Hagler rules UNIQ0460e71333a2b13d-ref-0000008F-QINU are given by:

:UNIQ0460e71333a2b13d-math-00000090-QINU

and

:UNIQ0460e71333a2b13d-math-00000091-QINU

==References==
UNIQ0460e71333a2b13d-references-00000092-QINU
'''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)]
[[category: mixtures]]

Combining rules

2015-01-15T20:28:11Z

38.105.236.163: /* Lorentz-Berthelot 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 [[Idealised models| 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-QINUUNIQ879f6b467d81d4c5-ref-00000093-QINUUNIQ879f6b467d81d4c5-ref-00000094-QINU.
==Good-Hope rule==
The Good-Hope rule for [[Mie potential |Mie]]–[[Lennard-Jones model |Lennard‐Jones]] or [[Buckingham potential]]s 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'''
*[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]]