Quantum effects on the static structure factor of Lennard-Jones fluids

Abstract

The classical and quantum static structure factors of Lennard-Jones fluids (liquid neon, deuterium gas and helium-4 gas) far from exchange are computed. The starting point is the usual Ornstein–Zernike equation which is known to be valid for classical as well as for moderately quantum (i.e. Feynman-Hibbs) disordered fluids. Monte Carlo simulations provide the basic pair radial distribution functions used to formulate three different versions of the Ornstein–Zernike equation: classical, quantum particle 'centre of mass' and true quantum particle linear response. These Ornstein–Zernike equations are solved with the use of Baxter's partition and the Dixon–Hutchinson variational procedure. A study of the stability of this variational procedure against the Monte Carlo sample size and run length is presented, giving measures for safe applications. As regards the evaluation of quantum effects, the results cover the following quantities: Baxter's Q'-functions and their features, direct correlation functions, static structure factors and isothermal compressibilities. The consistency of the quantum results is checked by comparing the linear response and 'centre of mass' results. The classical and quantum atom-atom structure factors of deuterium gas also are computed by describing the diatomic molecule as a classical free rotor. Comparison with experiment is made wherever possible, and the results indicate that the range of applicability of the present method for computing quantum structure factors is the same as that of the Feynman–Hibbs picture for representing quantum fluids.