A connection between the density and temperature of the Lennard-Jones fluids at equilibrium and the first peak of the radial distribution function

A new method to obtain the density and temperature of the Lennard-Jones fluids at equilibrium from the height and the displacement of the first peak of the radial distribution function (RDF) is presented here. The density range and temperature range covered are 0.5< p* <1.2, 0.2< phi* <2.0 with p* = pa3 and fi* = e/kBT being the reduced density and temperature, respectively. Numerically, 152 state points (p*, if) are obtained with Delta p* = 0.1 and Delta r = 0.1 by molecular dynamics (MD) simulations. More than 10000 configurations are output for each state point. The RDFs are then obtained through classical distance histogram method. The stability of the RDF is found to be related to the number of configurations because of ensemble average. Two correlations establishing the relation of the height of the first peak of the RDF versus the density and temperature and the relation of the displacement of the first peak of the RDF versus the density and temperature are empirically constructed by fitting 40 state points out of 152. Other 112 state points are used to estimate the accuracy of the two correlations proposed. It is found that all of the 112 state points can be correctly predicted. These results indicate that the RDF can be conveniently used to assure the state point (p*, f) of the Lennard-Jones fluids at equilibrium. The importance of the present work is that a clear connection between a special point of the RDF, i.e., its first peak, and the state point (p*, p*) is firstly empirically built up. Their one to one map is observed.