Oscillating reactivity of collinear symmetric heavy+light–heavy atom reactions

Abstract

The oscillatory reaction probability (as a function of energy) of collinear heavy+light–heavy systems (e.g., I+HI→IH+I) that has been seen in earlier quantum mechanical reactive scattering calculations is shown to be described quantitatively by a semiclassical WKB model. Because these reactions are highly vibrationally adiabatic they reduce to a two-state symmetric resonance system (analogous to symmetric charge transfer, e.g., H++H→H+H+) that involves only the phase shifts of the one-dimensional g (symmetric) and u (antisymmetric) combinations of the two states. Comparisons of the semiclassical and quantum mechanical reaction probabilities over a wide range of energy for the cases I+MuI→IMu+I and I+HI→IH+I show almost perfect agreement. The vibrationally adiabatic symmetric exchange problem is also solved classically (analytically) and is seen to have an interesting relation to the quantum/semiclassical result. The classical reaction probability is also an oscillatory function of energy, although the structure of the oscillations is different from the quantum/semiclassical ones (‘‘saw-tooth’’ rather than sinusoidal) and the phase of the classical oscillations is only approximately the same as that of the quantum/semiclassical case. (In the high energy limit, the phase of the oscillations increases roughly as the square root of collision energy.) Thus, though the classical (light atom hopping between two heavy atoms) and quantum mechanical (resonance interference of g and u collision channels) interpretations of the oscillatory reactivity seem at first to be quite different, they are seen in fact to be essentially the same.