Reaction path Hamiltonian analysis of the dynamics for Cl− + CH3Br → ClCH3 + Br− SN2 nucleophilic substitution Original Research Article

Coupling terms in the reaction path Hamiltonian (RPH) provide a qualitative interpretation of the non-statistical effects observed in classical trajectory simulations and experiments for the Cl− + CH3Br → ClCH3 + Br− SN2 nucleophilic substitution reaction. The small couplings between the Cl− + CH3Br relative translational, which is the reaction coordinate as the reactants collide, and the CH3Br vibrational modes explain why translation to vibration (T → V) energy transfer is unimportant for Cl− ⋯CH3Br complex formation and, instead, the complex is formed by T → R energy transfer. A large coupling term between the ClCBr symmetric stretch and the reaction coordinate leads to a large reaction path curvature at regions along the reaction path separating the central barrier and the pre- and post-reaction complexes. Such sharp values for the curvature can trap trajectories in the vicinity of the central barrier, which is consistent with the central barrier recrossings observed in classical trajectory simulations. Because of singularities in the RPH it is difficult to use it in classical trajectory simulations. Numerical difficulties in evaluating the long-time flux-flux autocorrelation function for the RPH precludes using this approach for calculating the quantum mechanical rate constant for Cl− + CH3Br SN2 nucleophilic substitution. Also, since the RPH does not include overall rotation and rotational/vibrational coupling and assumes a quadratic expansion for displacements away from the reaction path, this Hamiltonian may not give an accurate quantum mechanical rate constant even if a converged flux-flux autocorrelation function could be evaluated.