Feynman-Hibbs potentials and path integrals for quantum Lennard-Jones systems: Theory and Monte Carlo simulations

Publisher Website
Google Scholar
Abstract
This paper addresses unexplored aspects of the Feynman-Hibbs Gaussian picture and the ħ2- and ħ4-effective potentials obtainable from that model. Thermodynamic and structural properties are compared with their path-integral counterparts. In particular, a closed formula for the self-correlation (intranecklace) radial distribution function is derived from the Feynman-Hibbs model in view of, first, its importance in determining quantum structure factors and, second, the great difficulty in computing it accurately via path-integral calculations. In order to assess the reliability of the ħ2- and ħ4-potentials, neon liquid and helium-4 gas are studied for new state points with the corresponding semiclassical and ‘exact’ path-integral Monte Carlo simulations. As regards thermodynamics, energies, pressures and also specific heats at constant volume are reported. Structural results cover necklace radii of gyration, and instantaneous, linear response and self-correlation radial distribution functions. Comparison with experiment is made wherever possible, and the results indicate better performances for the ħ2-potential.