Study on ‘‘regularity’’ of barrier recrossing motion

Abstract

A method to scrutinize ‘‘regularity’’ of barrier recrossing dynamics of chemical reactions in the vicinity of the transition state is developed by using Lie canonical perturbation theory (LCPT). As an example, the recrossing dynamics of a four-degrees of freedom Hamiltonian regarded as a model of proton transfer reaction of malonaldehyde is investigated. It is shown that the second order LCPT is essential to describe frequent saddle recrossings whose total number of crossings is greater than three, and reproduces the time-dependent transmission coefficient. It is found that the local recrossing dynamics can be regarded as quasiperiodic and a well-defined reaction coordinate along which no barrier recrossings occur, can be extracted in the phase space by using the second order LCPT Hamiltonian. We also formulate a new transition state theory which allows us to estimate the reaction rate constant taking account of the barrier recrossing effect if the recrossings are near-integrable in the short time but long enough to determine the final state of the recrossing dynamics.