On the dynamics of exothermic triatomic exchange reactions

Analytic expressions are derived for the population of vibrational states for triatomic exchange reactions. The predictions are in good accord with the so-called ’’Polanyi rules.’’ The results are expressed in terms of the masses, frequencies, exothermicity, interaction length, and the attractive part of the potential A⊥E*. Comparison with exact quantum-mechanical calculations is made for a series of light-heavy-heavy (LHH) reactions. An almost linear relation between the attractive part of the potential and the product vibrational energy is obtained. For the LHH-mass combination the slope is almost one. For other mass combinations like HHL, HLL, or HLH the final vibrational energy is relatively insensitive to A⊥, showing always strong population inversion. The width of the vibrational energy distribution is smallest for the HLH mass combination.