LennardJonesPotenzials

Lennard-Jones potentials, often referred to as Lennard-Jones 12-6 potentials, are a class of simple pairwise interatomic potentials used to model the interactions between neutral atoms and nonpolar molecules. They are widely employed to represent van der Waals forces in a computationally efficient way, capturing short-range repulsion and long-range attraction.

The canonical form is V(r) = 4ε[(σ/r)^12 − (σ/r)^6], where r is the distance between two particles, ε is the depth of the potential well, and σ is the distance at which the potential is zero. The r^−12 term represents strong short-range repulsion, often attributed to Pauli exclusion, while the r^−6 term describes attractive dispersion forces. The potential is typically used as a pair potential in simulations of condensed matter, liquids, and nonpolar molecular systems.

In practice, Lennard-Jones potentials are used in molecular dynamics and Monte Carlo simulations to compute forces and energies. Simulations often employ a cutoff distance to limit calculations, with shifts or switching functions to avoid discontinuities at the cutoff. Variants include shifted, truncated, or truncated-and-shifted forms, and regional modifications to better reproduce specific properties. In some cases, long-range corrections or Ewald-like summation schemes are applied for improved accuracy in periodic systems.

Despite their simplicity, Lennard-Jones potentials have limitations. They do not describe directional bonding, polarization, or many-body effects, and are not suitable for ionic, covalent, or highly polar systems without extensions. Nevertheless, they remain a foundational tool in computational chemistry and materials science for modeling nonbonded interactions and serving as a benchmark for more complex potentials. The concept was introduced by John E. Lennard-Jones in 1924.