An accurate expression for radial distribution function of the Lennard-Jones fluid

Abstract

A simple and accurate expression for radial distribution function (RDF) of the Lennard-Jones fluid is presented. The expression explicitly states the RDF as a continuous function of reduced interparticle distance, temperature, and density. It satisfies the limiting conditions of zero density and infinite distance imposed by statistical thermodynamics. The distance dependence of this expression is expressed by an equation which contains 11 adjustable parameters. These parameters are fitted to 353 RDF data, obtained by molecular dynamics calculations, and then expressed as functions of reduced distance, temperature and density. This expression, having a total of 65 constants, reproduces the RDF data with an average root-mean-squared deviation of 0.0152 for the range of state variables of 0.5 ⩽ T ∗ ⩽ 5.1 and 0.35 ⩽ ρ ∗ ⩽ 1.1 ( T ∗ = kT / ε and ρ ∗ = ρσ 3 are reduced temperature and density, respectively). The expression predicts the pressure and the internal energy of the Lennard-Jones fluid with an uncertainty that is comparable to that obtained directly from the molecular dynamics simulations.