LennardJonesi

LennardJonesi is a theoretical concept within molecular modeling and computational chemistry, representing an idealized pairwise interatomic potential. It is named after Sir John E. Lennard-Jones, who popularized its use. The Lennard-Jones potential describes the interaction between two neutral atoms or molecules that are not chemically bonded. It is composed of two terms: an attractive term and a repulsive term.

The attractive part of the potential, typically proportional to $r^{-6}$, accounts for van der Waals forces, such as London dispersion forces. These forces arise from temporary fluctuations in electron distribution, inducing dipoles in neighboring atoms or molecules. The repulsive part, typically proportional to $r^{-12}$, represents the Pauli exclusion principle, which dictates that electrons in different atoms cannot occupy the same quantum state. This term becomes significant at short distances, preventing atoms from overlapping.

The combined Lennard-Jones potential is expressed mathematically as $V(r) = 4\epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^{6} \right]$, where $r$ is the distance between the centers of the two particles, $\epsilon$ is the depth of the potential well (representing the strength of the attraction), and $\sigma$ is the finite distance at which the potential energy is zero. The $r^{-12}$ term is often used for simplicity as it is the square of the $r^{-6}$ term, making calculations more efficient.

While a simplification of real intermolecular interactions, the Lennard-Jones potential is widely used in molecular dynamics simulations and Monte Carlo methods to model the behavior of liquids, gases, and solids, particularly when detailed quantum mechanical calculations are computationally prohibitive. It provides a reasonable approximation for many non-polar molecules.