Adiabatic separatrix crossing theory for heavy–light–heavy chemical reactions in three dimensions

Abstract

The beautifully regular dynamics observed for the collinear I+HI reaction appears to be largely irrelevant for the three-dimensional reaction. The pronounced oscillations in the collinear reaction probability and other variables are suppressed in three dimensions due to the extreme instability of the collinear dynamics in directions orthogonal to the collinear subspace. A new theory is formulated for the three-dimensional classical dynamics of heavy–light–heavy (HLH) reactions. This theory is based on three ideas. First, the fastest time scale motion can be adiabatically eliminated with high accuracy. The fast motion corresponds to diatomic vibration in the asymptotic channels and to asymmetric stretch motion in the strong collision region. A composite set of ‘‘α’’ and ‘‘β’’ channel Jacobi coordinates properly captures the correct separation of time scales. Second, the reactive separatrix can be easily defined within the adiabatic approximation and is crucial in modeling the reactive dynamics. The separatrix is the boundary in phase space between the trajectories where the light atom is dynamically bound to one of the heavy atoms and those trajectories where the light atom is exchanging back and forth between the two heavy atoms. Third, trajectories which cross the separatrix behave statistically in three dimensions. For the I+HI reaction with J=0, it is found that the reaction probability is very accurately modeled by PR= (1)/(2) Px, where Px is the probability for trajectories to cross the separatrix in the adiabatic approximation. Numerical simulations on the I+HI reaction strongly support a statistical adiabatic separatrix crossing theory and suggest widespread chaotic scattering for reactive orbits.