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Neutral atoms and molecules are subject to two distinct forces in the limit of large distance and short distance: an attractive force at long ranges (van der Waals force, or dispersion force) and a repulsive force at short ranges (the result of overlapping electron orbitals, referred to as Pauli repulsion from Pauli exclusion principle). The Lennard-Jones potential (also referred to as the L-J potential, 6-12 potential or, less commonly, 12-6 potential) is a simple mathematical model that represents this behavior. It was proposed in 1924 by John Lennard-Jones. The L-J potential is of the form
where is the depth of the potential well and is the (finite) distance at which the interparticle potential is zero.
These parameters can be fitted to reproduce experimental data or deduced from results of accurate quantum chemistry calculations. The term describes repulsion and the term describes attraction. The force function is the negative of the gradient of the above potential:
The lowest energy arrangement of an infinite number of atoms described by a Lennard-Jones potential is a hexagonal close-packing. On raising temperature, the lowest free energy arrangement becomes cubic close packing and then liquid. Under pressure the lowest energy structure switches between cubic and hexagonal close packing.
Other more recent methods, such as the Stockmayer equation and the so-called multi equation, describe the interaction of molecules more accurately. Quantum chemistry methods, Møller-Plesset perturbation theory, coupled cluster method or full configuration interaction can give extremely accurate results, but require large computational cost.
Additional recommended knowledge
The Lennard-Jones potential function is also often written as
= is the distance at the minimum of the potential.
The simplest formulation, often used internally by simulation software, is:
Molecular dynamics simulation: Truncated potential
To save computational time, the Lennard-Jones (LJ) potential is often truncated at the cut-off distance of where
i.e., at , the LJ potential is about 1/60th of its minimum value (depth of potential well). Beyond , the computational potential is set to zero. On the other hand, to avoid a jump discontinuity at , as shown in Eq.(1), the LJ potential is shifted upward a little so that the computational potential would be zero exactly at the cut-off distance .
For clarity, let denote the LJ potential as defined above, i.e.,
The computational potential is defined as follows 
It can be easily verified that , thus eliminating the jump discontinuity at .
Categories: Thermodynamics | Chemical bonding | Intermolecular forces | Computational chemistry
|This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Lennard-Jones_potential". A list of authors is available in Wikipedia.|