Lennard-Jones potential
/ LEN-ard JOHNZ /
Imagine two people approaching each other in the dark. From far away they feel a slight pull to come closer; but if they bump too hard, they shove apart. There is one comfortable distance in between where neither pulling nor pushing wins. The Lennard-Jones potential is a simple formula that captures exactly this give-and-take between two neutral atoms or molecules.
The Lennard-Jones potential is a mathematical model for the energy between two particles as a function of how far apart they are. It has two parts: a gentle attraction that pulls them together at moderate range (the dispersion force, falling off as the sixth power of distance) and a steep repulsion that kicks in hard when their electron clouds start to overlap (rising as the twelfth power). Together they make an energy curve with a single low point — the equilibrium distance, where the two particles sit most comfortably.
Why it matters: this one tidy curve, set by just two numbers (how deep the well is and how big the particle is), is the workhorse of computer simulations of liquids, gases, and proteins. The honest caveat is that it is a deliberate simplification: the steep repulsion uses a twelfth power mainly because it is easy to compute, and the model ignores permanent dipoles, hydrogen bonds, and charges, so it fits noble gases best.
In a molecular-dynamics simulation of liquid argon, every pair of atoms feels a Lennard-Jones force: a gentle pull at long range and a hard push the instant they get too close, reproducing argon's real density and boiling point.
A simple two-parameter curve modeling attraction and repulsion at once.
The Lennard-Jones potential is a model, not a law. Its sixth-power attraction is physically grounded in dispersion theory, but its twelfth-power repulsion was chosen mainly for mathematical convenience; it neglects polarity, hydrogen bonds, and charge, so it suits noble gases best.