Fully Quantum Cross Second Virial Coefficients for the Three-Dimensional He–H$_{2}$ Pair

Abstract

A recent high-accuracy three-dimensional potential is used to compute the cross second virial coefficient $B_{12}(T)$ between helium and molecular hydrogen. These calculations fully account for both quantum effects (with the path-integral Monte Carlo method) and the flexibility of the hydrogen molecule. The effect of flexibility is relatively small (only slightly larger than the expanded uncertainty of our results), but the full quantum mechanical approach is essential to obtain correct results at cryogenic temperatures. Values are calculated from 8 K to 2000 K; the uncertainty of the potential is propagated into uncertainties of $B_{12}$. Similar calculations are performed for He with the isotopologues D$_{2}$, T$_{2}$, HD, HT, and DT. Comparison is made with the experimental data for the He/H$_{2}$ binary, and with the limited data available for He/D$_{2}$ and He/HD. The calculated $B_{12}(T)$’s are generally consistent with the experimental results, but have lower uncertainties.