Virial Coefficients of Helium‑4 from Ab Initio-Based Molecular Models

We examine the accuracy of virial coefficients Bn(T) for 4He for n = 2–7 and temperatures T from 20 to 1000 K while reporting new values from semiclassical and (for n = 5) path-integral Monte Carlo (PIMC) calculations. All coefficients are based on first-principles two- and three-body molecular models from the literature and have estimated stochastic and systematic uncertainty between 0.005 and 20%, depending on n and T (almost all of this due to estimated inaccuracy in the three-body model). The calculated Bn(T) are used to examine the virial equation of state (VEOS) against experimental data from the literature, from 223.15 to 500 K and pressures up to 38 MPa. First, the VEOS is used to calibrate the data, providing adjustments not exceeding the data’s estimated systematic uncertainty. Then, findings from the comparison include the following: (1) the VEOS based on the ab initio Bn(T) is fully consistent with the experimental data; (2) the series requires coefficients up to n = 5 in order to agree with experiment within all relevant uncertainties; (3) individual values Bk(T) can be regressed accurately from the experimental data if other coefficients Bn(T), n ≠ k, are given from the ab initio calculations; however, the uncertainty of these values is less than the coefficient magnitude only for k ≤ 5.