Although the dispersion and exchange-repulsive interactions between molecules can be calculated by quantum mechanics, we often resort to the force field description, a simple empirical expression, to perform molecular dynamics simulations. The prevalent form used in MD programs is to use Lennard-Jones potentials in Eq. (4) to describe the interaction between two particles
The Lennard-Jones equation may also be expressed in terms of the distance where the energy reaches a minimum . At this separation, the first derivative of the energy with respect to the internuclear distance is zero (i.e. ), from which it can easily be calculated that . We can rewrite the Lennard-Jones 12-6 potential function as follows
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The part comes from the dispersion energy, but there is no strong theoretical argument in favor of the repulsive form. Indeed, quantum mechanical calculations suggest an exponential form. The twelfth power term is found to be reasonable for rare gases but is probably too hard for other systems such as methane.
We will check the effect of the repulsive part of the Lennard-Jones potential in MD simulations, in particular, in the calculation of the PMF for two solutes in water.