LennardJones

Lennard-Jones, often referred to as the Lennard-Jones potential, is a simplified model that describes the interaction between a pair of neutral atoms or nonpolar molecules. It is named after John Edward Lennard-Jones, who introduced the formulation in 1924. The potential energy as a function of the interparticle distance r is U(r) = 4ε[(σ/r)^12 − (σ/r)^6], where ε sets the depth of the potential well and σ is the distance at which the potential is zero.

The potential captures two competing effects: at very short distances, the repulsive r^−12 term dominates, preventing particles from coming too close; at intermediate distances, the attractive r^−6 term lowers the energy and promotes cohesion. The potential has a minimum of −ε at r = 2^(1/6) σ.

Lennard-Jones potentials are widely used in molecular simulations because of their simplicity and reasonable accuracy for nonpolar interactions. They are commonly applied to noble gases, simple liquids, and hydrocarbon systems, and they form a foundational tool in molecular dynamics and Monte Carlo methods for estimating thermodynamic and structural properties.

Limitations include neglecting many-body effects and anisotropy; the model assumes pairwise additivity and isotropy, which reduces accuracy for polar species, hydrogen bonding, or complex condensed phases. In practice, LJ potentials are often truncated and shifted at a cutoff distance (for example, 2.5σ) to improve computational efficiency, sometimes with long-range dispersion corrections or extensions for more complex systems. Variants include truncated, shifted, or damped LJ forms, and the 12-6 notation remains the most common reference.