Calculation of thermodynamic properties of helium using path integral Monte Carlo simulations in the <i>NpT</i> ensemble and <i>ab initio</i> potentials

We apply the methodology of Lustig, with which rigorous expressions for all thermodynamic properties can be derived in any statistical ensemble, to derive expressions for the calculation of thermodynamic properties in the path integral formulation of the quantum-mechanical isobaric-isothermal (NpT) ensemble. With the derived expressions, thermodynamic properties such as the density, speed of sound, or Joule-Thomson coefficient can be calculated in path integral Monte Carlo simulations, fully incorporating quantum effects without uncontrolled approximations within the well-known isomorphism between the quantum-mechanical partition function and a classical system of ring polymers. The derived expressions are verified by simulations of supercritical helium above the vapor-liquid critical point at selected state points using recent highly accurate ab initio potentials for pairwise and nonadditive three-body interactions. We observe excellent agreement of our results with the most accurate experimental data for the density and speed of sound and a reference virial equation of state for helium in the region where the virial equation of state is converged. Moreover, our results agree closer with the experimental data and virial equation of state than the results of semiclassical simulations using the Feynman-Hibbs correction for quantum effects, which demonstrates the necessity to fully include quantum effects by path integral simulations. Our results also show that nonadditive three-body interactions must be accounted for when accurately predicting thermodynamic properties of helium by solely theoretical means.