Lennard-Jones potential
From Academic Kids
Atoms of a noble gas reach an equilibrium distance from each other when an attracting van der Waals force balances a repelling force (the result of overlapping electron orbitals). The strength at which these two forces balance is the so-called Lennard-Jones potential (referred to as the L-J potential or 6-12 potential).
Subject to assumptions about the physical properties of the molecules, the L-J potential may be used to calculate an approximation for their separation. Other more recent methods, such as the Stockmayer equation and the so-called multi equation, describe the interaction of molecules more accurately.
The L-J potential is of the form <math> V(r) = 4\varepsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^{6} \right], <math> where <math>\epsilon<math> is the well depth and <math>\sigma<math> is the hard sphere radius.
The <math> \left(\frac{1}{r}\right)^{12} <math> term describes the repulsive force and the <math> \left(\frac{1}{r}\right)^{6} <math> term describes the attractive force.
The L-J potential is particularly useful for the calculation of solid-state properties of the rare gases.Template:Physics-stub
