Comparison of Radial Distribution Functions from Integral Equations and Monte Carlo

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Abstract
The radial distribution functions g for a system of particles interacting with the Lennard-Jones 6–12 potential have been found by solving the Percus—Yevick (PY) equation, convolution approximation or hypernetted chain equation (CHNC), and the Born—Green—Yvon (BGY) equation, for four particle densities already investigated by Monte Carlo (MC) techniques by Wood and Parker. The thermodynamic quantities p/nkT, E/NkT, and nkTK have also been computed from the g's. A comparison shows that the PY quantities agree best with MC, CHNC quantities agree next best, and BGY agree most poorly, particularly at high densities. A comparison of nkTK computed by differentiating p/nkT and by direct integration involving g gives approximately consistent results for the PY g but not for the CHNC g. The asymptotic form of g for high densities for the PY and CHNC equations is found to agree with that obtained by Kirkwood.