Abstract
A fitting procedure is proposed to establish two analytic approximateexpressions for the complicated Barker-Henderson (BH) diameter withLennard-Jones potential in two temperature ranges. Considering that thedifferentiation is a process enlarging the errors and the integrationdecreasing the errors and that the derivative of BH diameter isimportant in the calculation of internal energy, we propose to fit thederivative directly, instead of usually fitting the original functionand subsequently deriving its derivative. The simplicity and precisionof two expressions developed are superior to the extensively usedexpressions in literature. The one with following form only has anaverage fitting 0.0063% in the reduced temperature range (0.4⩽kT/ε⩽15), and can be extrapolated to a widertemperature range (0.4⩽kT/ε⩽50) with anaverage error 0.13%, which is d/σ = 1.1755 + 0.02878ln τ-0.2072τ1/4 + 0.00463τ3/4.
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