Corresponding-states framework for classical and quantum fluids—Beyond Feynman–Hibbs

Abstract

Effective potential methods, obtained by applying a quantum correction to a classical pair potential, are widely used for describing the thermophysical properties of fluids with mild nuclear quantum effects. In case of strong nuclear quantum effects, such as for liquid hydrogen and helium, the accuracy of these quantum corrections deteriorates significantly, but at present no simple alternatives are available. In this work, we solve this issue by developing a new, three-parameter corresponding-states principle that remains applicable in the regions of the phase diagram where quantum effects become significant. The new principle emerges from a mapping procedure, which shows that quantum-corrected pair potentials can be made conformal to their underlying classical pair potential by modifying the latter’s repulsive range. This mapping enables an accurate description of fluids with quantum-corrected interactions based on off-the-shelf methods for classical fluids (e.g., equations of state, classical density functional theory, and entropy scaling) using effective, mapped intermolecular-potential parameters. These effective parameters depend on temperature and molecular mass; simple analytic equations in case of a classical Mie potential with Feynman–Hibbs quantum corrections are presented. Using Mie Feynman–Hibbs force fields from the literature, we show that this procedure provides accurate predictions for the properties of fluids with mild nuclear quantum effects, such as neon or hydrogen at moderate temperatures. Moreover, by adjusting the functional form of the effective intermolecular-potential parameters to experimental data for helium and hydrogen, we are able to apply the corresponding-states principle for optimal quantum-corrected pair potentials that far surpass the accuracy of the Feynman–Hibbs correction.