We present a perturbation theory that combines the use of a third-order Barker–Henderson expansion of the
Helmholtz energy with Mie-potentials that include first (Mie-FH1) and second-order (Mie-FH2) Feynman–
Hibbs corrections. The resulting equation of state (SAFT-VRQ Mie) is compared to molecular simulations,
and is seen to reproduce the thermodynamic properties of generic Mie-FH1 and Mie-FH2 fluids accurately.
SAFT-VRQ Mie is exploited to obtain optimal parameters for the potentials of neon, helium, deuterium,
ortho-, para- and normal-hydrogen for the Mie-FH1 and Mie-FH2 formulations. For helium, hydrogen and
deuterium, the use of either the first or second-order corrections yields significantly higher accuracy in the
representation of supercritical densities, heat capacities and speed of sounds when compared to classical Mie
fluids, although the Mie-FH2 is slightly more accurate than Mie-FH1 for supercritical properties. The MieFH1 potential is recommended for most of the fluids since it yields a more accurate representation of the
pure-component phase equilibria and extrapolates better to low temperatures. Notwithstanding, for helium,
where the quantum effects are largest, we find that none of the potentials give an accurate representation of
the entire phase envelope, and its thermodynamic properties are represented accurately only at temperatures
above 20 K. Overall, supercritical heat capacities are well represented, with some deviations from experiments
seen in the liquid phase region for helium and hydrogen.