a complexity barrier due to the rapid increase of the number of channels involved in calculations, while memory and CPU requirements scale as the square and the cube of this number, respectively. Resorting to quantum CS or IOS approximations is inaccurate, because the energy is close to threshold for high-$J_1$ channels. In the meanwhile, the accuracy of classical approximations improves for higher collisional energies. For the energy range where $J_1 > 15$ channels are open *and* for deexcitation processes involving those channels, we employ a Quasi-Classical Trajectory (QCT) method, which has been shown at several instances to be a valid approximation for higher collisional energies and large rates [@chapman77; @lepp95; @mandy04; @faure06].

For Monte-Carlo QCT methods, we must devise a way of defining an ensemble of initial conditions for classical trajectories, on the one hand, and of analyzing the final state of each trajectory, on the other hand. Contrary to the asymmetric rotor case [like water, see @faure04], the analysis of final conditions for a linear molecule is straightforward. Using the simplest quantization approximation, we bin the final classical angular momentum $J'_1$ of [$\mathrm{HC_3N}$]{}to the nearest integer. While the quantum formalism goes through a microcanonical calculation —calculating $\sigma_{J_1J_1'}(E)$ for fixed 