Pair potential refers to a mathematical function used in computational physics and chemistry to describe the interaction energy between two particles as a function of their separation distance. It is commonly employed in molecular dynamics simulations and statistical mechanics to model systems at the atomic and molecular level. The pair potential is often denoted as \(V(r)\), where \(r\) is the distance between two interacting particles.
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A pair potential assigns interaction potential energy to two particles as a function of their separation, for example for an isotropic interaction. A pairwise-additive model then has , counting each unordered pair once. This reduces a many-particle energy calculation to repeated evaluation of one two-particle law.
A hard sphere model takes below the core diameter and zero outside it, forbidding overlap without adding attraction. A more general pair potential can contain both repulsion and attraction, producing competition between packing and binding. The associated radial force is where the derivative exists. Pairwise additivity is a modeling assumption: the interaction between two particles can be modified by their environment, requiring effective state-dependent interactions or explicit many-particle terms. Knowing supplies an input to statistical mechanics, not an immediate solution for every collective phase.