Relative efficacy of vibrational vs. translational excitation in promoting atom-diatom reactivity: rigorous examination of Polanyi's rules and proposition of sudden vector projection (SVP) model.

To provide a systematic and rigorous re-examination of the well-known Polanyi's rules, excitation functions of several A + BC(v = 0, 1) reactions are determined using the Chebyshev real wave packet method on accurate potential energy surfaces. Reactions with early (F + H2 and F + HCl), late (Cl + H2), and central (H∕D∕Mu + H2, where Mu is a short-lived light isotope of H) barriers are represented. Although Polanyi's rules are in general consistent with the quantum dynamical results, their predictions are strictly valid only in certain energy ranges divided by a cross-over point. In particular, vibrational excitation of the diatomic reactant typically enhances reactivity more effectively than translational excitation at high energies, while reverse is true at low energies. This feature persists irrespective of the barrier location. A sudden vector projection model is proposed as an alternative to Polanyi's rules. It is found to give similar, but more quantitative, predictions about mode selectivity in these reactions, and has the advantage to be extendible to reactions involving polyatomic molecules.