Introduction

The exact form of the interparticle potential u(r) for electrically neutral molecules and atoms has to be determined by a first principles quantum mechanical calculation. Such a calculation is very difficult, and for many purposes it is sufficient to choose a simple phenomenological form for u(r). The most important features of u(r) are a strong repulsion for small r and a weak attraction at large r. The most common phenomenological form of u(r) is the Lennard-Jones or 6-12 potential proposed by John Edward Lennard-Jones in 1924:

,

The values of σ and ε for argon are σ = 3.4 × 10^{-10} m and ε = 1.65 × 10^{-21} J.

The existence of many calculations and simulation results for the Lennard-Jones potential encourages us to consider it even though there are more accurate forms of the interparticle potential for real gas and liquids.

It is possible to simulate a system of Lennard-Jones particles using either molecular dynamics or Monte Carlo methods.

Problems

- Show that the minimum of the Lennard-Jones
potential is at
r
_{min}= 2^{1/6}σ and that u(r_{min}) = -ε. - At what value of r is the force f(r) = du(r)/dr a minimum?
- What is the value of the Lennard-Jones potential at r = 2.3 σ?

Updated 28 December 2009.