Mixed quantum/classical theory for rotationally inelastic scattering of identical collision partners revised†

Mixed quantum/classical theory (MQCT) for the treatment of rotationally inelastic transitions during collisions of two identical molecules, described either as indistinguishable or distinguishable partners, is reviewed. The treatment of two molecules as indistinguishable includes symmetrization of rotational wavefunctions, introduces exchange parity, and leads to state-to-state transition matrix elements different from those in the straightforward treatment of molecules as distinguishable. Moreover, the treatment of collision partners as indistinguishable is eight times faster. Numerical results presented herein for H₂ + H₂, CO + CO and H₂O + H₂O systems indicate good agreement of MQCT calculations with full-quantum calculations from the literature and show that an a posteriori correction, applied after treatment of the collision partners as distinguishable, generally produces good results that agree well with the rigorous treatment of collision partners as indistinguishable. This correction for the cross section includes either multiplication by 2 or a summation over physically indistinguishable processes, depending on the transition type. After this correction, the results of the two treatments agree within 5% for most but may reach 10–20% for some transitions. At low collision energies dominated by scattering resonances, these differences can be larger, but they tend to decrease as collision energy is increased. It is also shown that if the system is artificially forced to follow the same collision path in the indistinguishable and distinguishable treatments, then all differences between the results of the two treatments disappear. This interesting finding gives new insight into the collision process and indicates that the indistinguishability of identical collision partners comes into play through the collision path itself, rather than through matrix elements of inelastic transitions.