Lennard-Jones Potential - Explanation

Explanation

The r−12 term, which is the repulsive term, describes Pauli repulsion at short ranges due to overlapping electron orbitals and the r−6 term, which is the attractive long-range term, describes attraction at long ranges (van der Waals force, or dispersion force). Whereas the functional form of the attractive term has a clear physical justification, the repulsive term has no theoretical justification. It is used because it approximates the Pauli repulsion well, and is more convenient due to the relative computational efficiency of calculating r12 as the square of r6.

The Lennard-Jones (12,6) potential can be further approximated by the (exp-6) potential later proposed by R. A. Buckingham, in which the repulsive part is exponential:

The L-J potential is a relatively good approximation and due to its simplicity is 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.

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. Real materials include BCC structures as well.

Other more recent methods, such as the Stockmayer potential, 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.