Marienhagen, Philipp

The method of Lustig [J. Chem. Phys. 100, 3048–3059 (1994)] is applied to the path integral formulation of the quantum-mechanical canonical ensemble to derive equations for the calculation of all common thermodynamic properties in a rigorous and systematic way. Using these equations, thermodynamic properties such as the pressure, the isochoric and isobaric heat capacity, the speed of sound, or the Joule–Thomson coefficient can be calculated in path integral Monte Carlo simulations, fully incorporating quantum effects without uncontrolled approximations. The equations are derived for primitive and virial estimators. For the virial estimators, we generalize the finite-difference approach of Yamamoto [J. Chem. Phys. 123, 104101 (2005)] to arbitrary thermodynamic properties. We verify the derived equations by Monte Carlo simulations of supercritical helium-4 above the vapor–liquid critical point at selected state points on the 80 K isotherm using recent, highly accurate ab initio pair and nonadditive three-body potentials. The results of these simulations agree with our previous simulation results in the isobaric-isothermal ensemble, a virial equation of state of metrological quality, and the most accurate experimental data for the speed of sound in helium within their mutual uncertainties. We suppose that our results for the density are more accurate than the available experimental data in this region of the phase diagram.

In the project H2MIXPROP, highly accurate data for several thermophysical properties of gaseous mixtures containing molecular hydrogen are obtained by state-of-the-art theoretical approaches and experimental methods. Such data are required for many technical applications in the transition of the energy supply system to renewable energy sources, in which hydrogen is expected to play a prominent role. This contribution describes theoretical results for cross second virial coefficients of several binary mixtures, the development and validation of a path integral Monte Carlo code for the simulation of quantum gases, and the current status of the experimental tasks.

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.

We provide third to eighth virial coefficients of oblate, hard ellipsoids of revolution and hard lenses in dependence on their aspect ratio ν. Employing an algorithm optimized for hard anisotropic shapes, highly accurate data are accessible with comparatively small numerical effort. For both geometries, reduced virial coefficients B[over ̃]_{i}(ν)=B_{i}(ν)/B_{2}^{i-1}(ν) are in first approximation proportional to the inverse excess contribution α^{-1} of their excluded volume. The latter quantity is directly accessible from second virial coefficients and analytically known for convex bodies.