The limits of Feynman–Hibbs corrections in capturing quantum-nuclear contributions to thermophysical properties

Abstract

Feynman–Hibbs (FH) corrected interaction potentials provide an efficient route to approximating quantum-nuclear effects on properties of fluids and solids at cryogenic temperatures. In this study, we aim to provide insight into which FH order to choose, in what temperature range the FH corrections are reliable, and whether they can be applied outside of equilibrium. We study argon, neon, hydrogen, and helium using accurate ab initio interaction potentials combined with FH corrections up to 14th order. By comparing to full quantum mechanical calculations, we find that the second virial coefficient is predicted within 2% with first-order FH corrections at temperatures above ≈10K for argon and neon, and within 10% above 23 K for hydrogen. At cryogenic temperatures, first-order FH corrections offer a significant improvement compared to classical interaction potentials. Increasing to second-order FH corrections yields a small improvement in the case of neon and helium, while higher-order corrections give systematically less accurate predictions. At sufficiently low temperatures, the accuracy of the FH corrections deteriorates rapidly due to the increasingly relevant impact of the discretization of energy states when the thermal energy is small compared to the energy gaps between bound dimer states. By comparing to full quantum mechanical calculations, we show that FH corrections decrease the accuracy in the prediction of transport properties at infinite dilution. This shows that the qualitative picture of “quantum swelling” only applies when considering a large number of particles and not for binary collision dynamics.