An analytic expression for the first shell of the radial distribution function

Abstract

A simple analytical expression for the first shell of the radial distribution function (RDF) is proposed. This expression, which has only three adjustable parameters, satisfies all the limiting cases of the hard-sphere RDF at high temperatures, the ideal gas RDF at zero density, the dilute-gas RDF at low densities, and the location of the peak in the first shell. The only requirement is the introduction of a potential function into the model. This theory has been applied to the Lennard Jones, Kihara, and square-well pair intermolecular potential energy functions. The first-shell RDF results are in good agreement with the available computer simulation data for the RDF of the Lennard Jones fluid and the experimental data for argon. By introducing the radius of truncation for the RDF, it is shown that information on the first shell of the RDF is sufficient to predict macroscopic properties of fluids. Calculations of radii of truncation of RDF for various properties indicate that they are always in the range of the first shell of RDF.