The cross second virial coefficients \(B_{12}\) for interactions of molecular nitrogen (N2) with molecular hydrogen (H2), of molecular oxygen (O2) with H2, and of carbon dioxide (CO2) with H2 were obtained at temperatures ranging from 36 K to 2000 K for the former two systems and from 100 K to 2000 K for the latter system from new rigid-rotor intermolecular potential energy surfaces (PESs) for the three molecule pairs. Each PES is based on interaction energies calculated for a large number of pair configurations employing high-level quantum-chemical ab initio methods up to coupled cluster with single, double, triple, and perturbative quadruple excitations [CCSDT(Q)]. Core-core and core-valance correlation and relativistic effects were accounted for as well. \(B_{12}\) values were extracted from the PESs classically and semiclassically using the Mayer-sampling Monte Carlo approach. The deficiencies of the semiclassical calculations at the lowest temperatures were partly remedied by a more rigorous treatment of translational quantum effects using the phase-shift method. The results for the N2–H2 and CO2–H2 systems are in excellent agreement with the most accurate experimental data. For the O2–H2 system, there are no experimental \(B_{12}\) data because this mixture is highly explosive. There are, however, previous first-principles results for \(B_{12}\) of this system by Van Tat and Deiters [Chem. Phys. 457, 171–179 (2015)], which were obtained at a much lower level of sophistication for both the PES and the method to extract \(B_{12}\) and differ significantly from the present \(B_{12}\) values.
