Equation that emperically models the van der Waals forces between two atoms. It usually takes on the form:

1 1
E = a * ( --- - b --- )
r^{x} r^{y}

The values of x and y are usually 12 and 6 (known as the 12-6 Lennard Jones potential - surprisingly). The r

^{12} term is a repulsive term that gets very high at small values of r. This represents the

electron orbitals coming too close to each other. The r

^{6} term represents

dipole-dipole interactions generally. The values of a and b depend on the types of atoms interacting. Combining this with

Coulomb's law to model charge-charge interactions is often sufficient for a rudimentary

force field to describe molecular interactions. The shape of a 12-6 Lennard-Jones potential shows the equilibrium distance of a particular interaction:

| *
| *
| *
| *
| *
| *
| *
| *
E | *
| *
-----*-----------------********------- r
| * *****
| * ***
| ** **
| ****
r_{eq}
E = energy
r = distance between two objects
r_{eq} = equilibrium distance for system.

I apologize that this graph looks horrible, but the essential elements are as follows: At very short distances (the left end of the graph), the two molecules are repelling each other very strongly. As this distances approaches zero, the energy goes to infinity. At some distance r

_{eq}, the repulsion 1/r

^{12} term and the attractive 1/r

^{6} term are balanced such that an energy minimum is achieved. This is the most stable distance for the system to lie in. As r increases, the attractive force (which follows a 1/r

^{6} dependence) drops off gradually and the energy converges to zero.