Monte Carlo study of perturbation theory for the radial distribution function

Publisher Website
Google Scholar
Abstract
Monte Carlo calculations are reported for the radial distribution function g 2(r; λ) of a fluid in which the intermolecular pair potential is [u ref(r) + λu p(r)], u ref(r) being the Weeks-Chandler-Andersen (WCA) reference fluid, and [u ref(r) + u p(r)] being the Lennard-Jones (6, 12) fluid. The calculations are performed for λ values in the range 0 to 1, at the state condition ρσ3 = 0·80, kT/ε = 0·719. It is shown that at high densities the perturbation expansion of g 2(r; λ = 1) about g 2(r; λ = 0) is rapidly convergent, but that the corresponding expansion for y 2(r; λ) = exp [βu(r; λ)] × g 2(r; λ) is not. In addition Monte Carlo estimates of the individual terms that contribute to the first-order perturbation term, (∂g 2/∂λ)λ=0, are presented. It is shown that these terms are individually large, but that (∂g 2/∂λ)λ=0 is small because there is strong cancellation between the various terms. Consequently, the calculation of (∂g 2/∂λ)λ=0 is highly sensitive to the approximation used to evaluate the individual terms.