Mixed Quantum/Classical Theory for Rotational Energy Exchange in Symmetric-Top-Rotor + Linear-Rotor Collisions and a Case Study of $ \rm ND_3 + \rm D_2$ System

The extension of mixed quantum/classical theory (MQCT) to describe collisional energy transfer is developed for symmetric-top-rotor + linear-rotor system type and is applied to $ \rm ND_3 + \rm D_2 $. State-to-state transition cross sections are computed in a broad energy range for all possible processes: when both $ \rm ND_3$ and $ \rm D_2$ molecules are excited or both are quenched, when one is excited while the other is quenched and vice versa, when $ \rm ND_3 $ state changes its parity while $ \rm D_2 $ is excited or quenched, and when $ \rm ND_3 $ is excited or quenched while $ \rm D_2 $ remains in the same state, ground or excited. In all these processes the results of MQCT are found to approximately satisfy the principle of microscopic reversibility. For a set of sixteen state-to-state transitions available from literature for collision energy $ \rm 800 cm^{-1} $ the values of cross sections predicted by MQCT are within 8% of accurate full-quantum results. A useful time-dependent insight is obtained by monitoring the evolution of state populations along MQCT trajectories. It is shown that, if before the collision, $ \rm D_2 $ is in its ground state, the excitation of to $ \rm ND_3 $ rotational states proceeds through a two-step mechanism in which the kinetic energy of molecule-molecule collision is first used to excite $ \rm D_2 $ and only then is transferred to the excited rotational states of to $ \rm ND_3 $. It is found that both potential coupling and Coriolis coupling play important roles in $ \rm ND_3 + \rm D_2 $collisions.