Study of the Feynman-Hibbs effective potential against the path-integral formalism for Monte Carlo simulations of quantum many-body Lennard-Jones systems

Approximate quantum pair radial correlation functions and thermodynamic quantities for Lennard-Jones systems can be computed with Monte Carlo simulation involving Feynman-Hibbs potentials. A convolution approach to produce the quantum pair radial function from the direct Monte Carlo structural results is presented by analysing its connection with the path-integral instantaneous and linear response pair radial functions. Several Lennard-Jones systems with substantial quantum behaviour: methane, argon, neon, deuterium and helium-4 (eighteen state points) are studied. For the sake of comparison, new path-integral simulations of helium-4 and improved path-integral results for methane are also reported. The effective potential results are in close agreement with experimental and exact path-integral data over a wide range of de Broglie wavelengths, densities and temperatures.