Simple Analytic Expression with High Precision for the Barker-Henderson Diameter

A fitting procedure is proposed to establish two analytic approximate expressions for the complicated Barker-Henderson (BH) diameter with Lennard-Jones potential in two temperature ranges. Considering that the differentiation is a process enlarging the errors and the integration decreasing the errors and that the derivative of BH diameter is important in the calculation of internal energy, we propose to fit the derivative directly, instead of usually fitting the original function and subsequently deriving its derivative. The simplicity and precision of two expressions developed are superior to the extensively used expressions in literature. The one with following form only has an average fitting 0.0063% in the reduced temperature range (0.4 ≤ kT/ε ≤ 15), and can be extrapolated to a wider temperature range (0.4 ≤ kT/ε ≤ 50) with an average error 0.13%, which is d /σ = 1.1755 + 0.02878lnτ -0.2072τ^1/4+ 0.00463τ^3/4.