Equivalence of the Ehrenfest theorem and the fluid-rotor model for mixed quantum/classical theory of collisional energy transfer

The theory of two seemingly different quantum∕classical approaches to collisional energy transfer and ro-vibrational energy flow is reviewed: a heuristic fluid-rotor method, introduced earlier to treat recombination reactions [M. Ivanov and D. Babikov, J. Chem. Phys. 134, 144107 (2011)], and a more rigorous method based on the Ehrenfest theorem. It is shown analytically that for the case of a diatomic molecule + quencher these two methods are entirely equivalent. Notably, they both make use of the average moment of inertia computed as inverse of average of inverse of the distributed moment of inertia. Despite this equivalence, each of the two formulations has its own advantages, and is interesting on its own. Numerical results presented here illustrate energy and momentum conservation in the mixed quantum∕classical approach and open opportunities for computationally affordable treatment of collisional energy transfer.