Lennard Jones empirical potentials dispersion energy

The first two terms in Eq. (4) represent the dispersion and repulsion contribution to the van der Waals energy and are generally described in computer simulations by a semi-empirical Lennard-Jones (LJ) potential which is, in fact, a form of Mie s potential of Eq. (3) where m=12, n=6, B=4eo-, and C=4e(T . Even if an expression for the van der Waals energy is different from LJ it is convenient to approximate it by a 12-6 function [28] for computational convenience. 

The empirical XI potential (3.1) [248] consisting of a Lennard-Jones term for the nonelectrostatic part and a three-point-charge model for the electrostatics is used [140] to describe the N2-N2 interactions. The substrate-mediated dispersion energy as formulated by McLachlan [49, 225] is included... 

The derivation of the potential energy for London dispersion forces is quite involved, and usually such interactions are not quantitatively modeled by equations of the sort we have been presenting here. Typically, the empirically derived Lennard-Jones "6-12" potential discussed in Chapter 2 or a related function is used. To a first approximation, as with the dipole-induced-dipole, the energy of interaction can be considered to drop off with an dependence. 

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