Mixed Quantum/Classical Theory for Rotational Energy Exchange in Symmetric-Top-Rotor + Linear-Rotor Collisions and a Case Study of $\mathrm{N}{\mathrm{D}}_3+{\mathrm{D}}_2$ 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 $\mathrm{N}{\mathrm{D}}_3+{\mathrm{D}}_2$. State-to-state transition cross sections are computed in a broad energy range for all possible processes: when both $\mathrm{N}{\mathrm{D}}_3$ and ${\mathrm{D}}_2$ molecules are excited or both are quenched, when one is excited while the other is quenched and vice versa, when $\mathrm{N}{\mathrm{D}}_3$ state changes its parity while ${\mathrm{D}}_2$ is excited or quenched, and when $\mathrm{N}{\mathrm{D}}_3$ is excited or quenched while ${\mathrm{D}}_2$ 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 $800\mathrm{c}{\mathrm{m}}^{-1}$ 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, ${\mathrm{D}}_2$ is in its ground state, the excitation of to $\mathrm{N}{\mathrm{D}}_3$ rotational states proceeds through a two-step mechanism in which the kinetic energy of molecule-molecule collision is first used to excite ${\mathrm{D}}_2$ and only then is transferred to the excited rotational states of to $\mathrm{N}{\mathrm{D}}_3$. It is found that both potential coupling and Coriolis coupling play important roles in $\mathrm{N}{\mathrm{D}}_3+{\mathrm{D}}_2$collisions.