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Classical reactive scattering in a quantum spirit: Improving the shape of rotational state distributions in the quantum regime

For triatomic chemical reactions under single-collision conditions, we propose a new quasi-classical trajectory (QCT) approach to rotational-state distributions of particular interest in the quantum regime where only a few rotational states are available to the products. Our method is directly inspired from the amendments to be introduced in classical phase space theory (PST) in order to make it in exact agreement with quantum PST. The method is applied to the D$^+$ + H$_2$ and H$^+$ + D$_2$ reactions and the population of the rotational ground state is found to be in much closer agreement with the exact quantum one than the same population obtained by means of standard QCT calculations. The impact on the whole distribution is all the stronger as the number of available states is small. Last but not least, the shape of the distribution appears to be controlled to a large extent by three factors, respectively called parity, edge and rotational shift factors.