The intermolecular potential

Our first goal is to identify the model we want to simulate. The first simplification is to consider the molecules spherical, chemically inert, and that they move according to the laws of classical mechanics. We also assume that the force between molecules depends only on the distance between them. The form of this potential for electrically neutral atoms can be constructed from a detailed first principles quantum mechanical calculation. Such calculation can be complicated, so we will consider a phenomenological form. The most important features are: strong repulsion at short distances, weak attraction at large separations. The repulsion originates from the electrostatic interaction between equally charged particles, and the long range attraction from the mutual polarization of the electronic clouds, known as ``van de Waals'' force.

Below we list some model potentials:

Hard Spheres

$V(r)=\infty$	if $r<r_{o}$
$V(r)=0$	if $r\geq r_{o}$

First approximation
in many applications

Lennard-Jones

$V(r)=4\epsilon \left[ \left( \frac{r}{\sigma }\right) ^{-12}-\left( \frac{r}{\sigma }\right) ^{-6}\right]$

Noble gas atoms;
nearly spherical
molecules

Harmonic

$V(r)=A(r-r_{o})^{2}$

Intramolecular bonds