Lennard-Jones potential

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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 van der Waals force, or dispersion force, at long ranges, and a repulsion force, the result of overlapping electron orbitals, referred to as Pauli repulsion (from Pauli exclusion principle). The Lennard-Jones potential (referred to as the L-J potential or 6-12 potential) is a simple mathematical model that represents this behavior. It was proposed in 1931 by John Lennard-Jones of Bristol University. Image:Argon dimer potential and Lennard-Jones.png The L-J potential is of the form

<math>

V(r) = 4\varepsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^{6} \right], </math>

where <math>\epsilon</math> is the well depth and <math>\sigma</math> is the hard sphere radius. These parameters can be fitted to reproduce experimental data or deduced from results of accurate quantum chemistry calculations. The <math> \left(\frac{1}{r}\right)^{12} </math> term describes the repulsive force and the <math> \left(\frac{1}{r}\right)^{6} </math> term describes the attractive force.

The L-J potential is approximate and the form of the repulsion term has no theoretical justification (the repulsion force depends exponentially on the distance). The attractive long-range potential, however, is derived from dispersion interactions. The L-J potential is a relatively good approximation and due to its simplicity often used to describe the properties of gases, and to model dispersion and overlap interactions in molecular models. It is particularly accurate for noble gas atoms and is a good approximation at long and short distances for neutral atoms and molecules. On the graph, Lennard-Jones potential for argon dimer is shown. Small deviation from the accurate empirical potential due to incorrect long range part of the repulsion term can be seen.

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.

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