**Lennard-Jones potential**(rus. потенциал Леннарда-Джонса

*otherwise*потенциал 6–12) — the potential of interaction between two spherical nonpolar molecules which describes the dependence of the energy of interaction of two particles on the distance between them.

### Description

Lennard-Jones potential approximates the interaction between two particles, which repulse at short distances and attract at large. It is given in the following notation:

where is the distance between the centres of the particles, is the depth of the potential well, is the distance at which energy interaction becomes zero. Parameters

When the distance between the centres of particles is smaller than , repulsive forces exceed attractive forces, which corresponds to term of the formula. The disadvantage of such a representation of the interaction potential of two molecules is that the strength of the exchange interaction responsible for the repulsion of particles at short distances is only approximately described by exponential law. However, the exponential representation of the potential is useful for computer calculations. For this reason, Lennard-Jones potential is widely used in numerical simulations of the behaviour of matter. Since Lennard-Jones potential describes the pair interaction of nonpolar spherical molecules, it is not suitable for other types of molecules (non-spherical and/or those having permanent dipole moments).

Sometimes Lennard-Jones potential is used in the simulation of liquids and solids, but, strictly speaking, the interaction of molecules at high densities is not a pair interaction as the molecules of the environment begin to influence the pair of particles under consideration. In particular, for argon in the solid phase, contribution of triple interactions to the energy can reach 10 percent.

However, consideration of triple interactions is too complex, so for condensed media, the common approach is to use certain effective pair potential with parameters and differing from those for rare gases.

where is the distance between the centres of the particles, is the depth of the potential well, is the distance at which energy interaction becomes zero. Parameters

_{}are characterising the particles of the matter. When , attractive forces exceed repulsive forces, which corresponds to term of the formula. The attraction is caused by the van der Waals force (induced dipole-dipole interaction).

When the distance between the centres of particles is smaller than , repulsive forces exceed attractive forces, which corresponds to term of the formula. The disadvantage of such a representation of the interaction potential of two molecules is that the strength of the exchange interaction responsible for the repulsion of particles at short distances is only approximately described by exponential law. However, the exponential representation of the potential is useful for computer calculations. For this reason, Lennard-Jones potential is widely used in numerical simulations of the behaviour of matter. Since Lennard-Jones potential describes the pair interaction of nonpolar spherical molecules, it is not suitable for other types of molecules (non-spherical and/or those having permanent dipole moments).

Sometimes Lennard-Jones potential is used in the simulation of liquids and solids, but, strictly speaking, the interaction of molecules at high densities is not a pair interaction as the molecules of the environment begin to influence the pair of particles under consideration. In particular, for argon in the solid phase, contribution of triple interactions to the energy can reach 10 percent.

However, consideration of triple interactions is too complex, so for condensed media, the common approach is to use certain effective pair potential with parameters and differing from those for rare gases.

### Illustrations

#### Authors

- Goryacheva Irina G.
- Shpenеv Alexey G.

#### Sources

- Lennard-Jones potential // Wikipedia, the free encyclopedia. — http://en.wikipedia.org/wiki/Lennard-Jones_potential (reference date: 31.07.2010).
- Intermolecular force // Wikipedia, the free encyclopedia. — http://en.wikipedia.org/wiki/Intermolecular_force (reference date: 31.07.2010).