Lennard-Jones system of particles

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:

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    The attractive 1/r⁶ contribution to the Lennard-Jones potential is due to the induced dipole-dipole interaction of two atoms. Although each atom is electrically neutral, the instantaneous fluctuations in the charge distribution can have nonspherical symmetry. The resulting dipole in one atom can induce a dipole moment in the other atom. The resultant attractive potential is called the van der Waals potential.

    The repulsive interaction for small r is a consequence of the Pauli exclusion principle. The electron wave functions of the two molecules must distort to avoid overlap, causing some of the electrons to be in different quantum states. The net effect is an increase in kinetic energy and an effective repulsive interaction between the electrons. The 1/r¹² form of the repulsive potential is chosen only for convenience and is not derived from first principles.

    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.

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

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