In computational chemistry and molecular dynamics, the combination rules or combining rules are equations that provide the interaction energy between two dissimilar non-bonded atoms, usually for the part of the potential representing the van der Waals interaction. In the simulation of mixtures, the choice of combining rules can sometimes affect the outcome of the simulation.
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Combining rules for the Lennard-Jones potential
The Lennard-Jones Potential is a mathematically simple model for the interaction between a pair of atoms or molecules. One of the most common forms is
where ε is the depth of the potential well, σ is the finite distance at which the inter-particle potential is zero, r is the distance between the particles. The potential reaches a minimum, of depth ε, when r = 21/6σ ≈ 1.122σ.
Lorentz-Berthelot rules
The Lorentz rule was proposed by H. A. Lorentz in 1881:
The Lorentz rule is only analytically correct for hard sphere systems.
The Berthelot rule (Daniel Berthelot, 1898) is given by:
These rules are the most widely used and are the default in many molecular simulation packages, but are not without failings.
Waldman-Hagler rules
The Waldman-Hagler rules are given by:
and
Fender-Halsey
The Fender-Halsey combining rule is given by
Kong rules
The Kong rules for the Lennard-Jones potential are given by:
Others
Many others have been proposed, including those of Tang and Toennies Pena, Hudson and McCoubrey and Sikora(1970).
Good-Hope rule
The Good-Hope rule for Mie–Lennard‐Jones or Buckingham potentials is given by:
Hogervorst rules
The Hogervorst rules for the Exp-6 potential are:
and
Kong-Chakrabarty rules
The Kong-Chakrabarty rules for the Exp-6 potential are:
and
Other rules for that have been proposed for the Exp-6 potential are the Mason-Rice rules and the Srivastava and Srivastava rules (1956).