First-Principles Calculation of ortho-para Effects in the Second Virial Coefficients of H₂ and D₂ at Low Temperatures

We report ab initio calculations of the second virial coefficient B(T) of molecular hydrogen isotopologues in the rigid-rotor approximation using the path-integral Monte Carlo method. We present a novel method for efficient sampling of rotational degrees of freedom based on Doob's h-transform that can be used with any spin isomer, including those for which the quantum mechanical propagator in imaginary time is negative, e.g., ortho-H₂. Additionally, we extend the theory to evaluate the contribution to B(T) due to quantum statistical effects, relevant at low temperatures. This allows us to compute the difference in B(T) between para-H₂ and normal H₂; our calculation of this difference near 20 K is in qualitative agreement with the only available experimental measurements.