Lennard-Jones-Potential

The Lennard -Jones potential (after John Lennard -Jones ) is used in physical chemistry and atomic and molecular physics. It approximates the interaction between uncharged, not chemically bound to each other atoms.

Description

For large distances between two particles outweigh the attractive forces. It is in the attractive forces mainly to van der Waals forces, but also by permanent dipole -dipole interactions. Approaching the respective particles, so outweighs beyond a certain distance ( see figure) between them, the repulsive part and the potential energy increases rapidly. These repulsive forces arise from the fact that the electrons have to resort in part to higher energy orbitals when approaching the atomic shells, because they can not occupy the same state more after the Pauli principle.

The attractive component of the Lennard- Jones potential is derived from the London formula ( after Fritz London), it is

Wherein the potential of the distance between the particles, and a relatively complicated term. This contains substance-specific constants such as the ionization energy for both particles under consideration. However, the equation is just an approximation.

The repulsive portion is described by a similar equation:

Here is. In the Lennard-Jones (n, 6 ) potential, the two formulas above are combined to

Is chosen for practical reasons, often 12 because only needs to be in the calculation of the squared value is then. The result is the Lennard-Jones ( 12.6 ) potential, which is typically written into one of the two following forms:

Here, the "depth" of the potential well caused by the two factors. The distance in the first form is the distance at which the Lennard -Jones potential having a zero point, that is valid. The distance in the second form, the distance from the origin of the energy minimum. It applies here. For large distances (ie, when goes to infinity ), the potential from below the zero line is approaching.

Others

Lennard -Jones potential is a special case of the Mie potential

Which was introduced in 1903 by Gustav Mie.

A further form of the Lennard- Jones potential, the Lennard-Jones (exp, 6 ) potential, wherein the repellent is an exponential term. It is a special case of Buckingham potential:

With

• , The zero point of the potential
• , The depth of the energy minimum
• , "Steepness" of the repulsive force