On Mixed Quantum/Classical Theory for Rotationally Inelastic Scattering of Identical Collision Partners

TL;DR

This paper reviews a mixed quantum/classical theory for rotationally inelastic collisions of identical molecules, demonstrating that treating molecules as indistinguishable improves accuracy and computational efficiency, with results validated against full quantum calculations.

Contribution

It introduces an efficient approach for modeling identical molecular collisions using MQCT, including symmetrization and exchange effects, and provides a correction method to approximate indistinguishable treatment.

Findings

MQCT results agree within 5-10% with full quantum calculations

Indistinguishable treatment is eight times faster computationally

A posteriori correction improves accuracy of distinguishable treatment

Abstract

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 gives 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 for $H_2 + H_2$, CO + CO and $H_2O + H_2O$ systems, indicate good agreement of MQCT calculations with full-quantum calculations from literature and show that an a posteriori correction, applied after the treatment of collision partners as distinguishable, generally produces good results that agree well with the rigorous treatment of collision partners as indistinguishable. This correction for cross section includes either multiplication by 2, or summation over physically indistinguishable processes, depending on the transition type. After this correction, the results of 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 two treatments disappear. This interesting finding gives new insight into the collision process and indicates that indistinguishability of identical collision partners comes into play through the collision path itself, rather than through matrix elements of inelastic transitions.