On the dynamics of exothermic triatomic exchange reactions

Abstract

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.