Quantum transition probabilities in multidimensional systems with potential barriers

The probabilities of bimolecular chemical reactions are studied, taking account of vibrational transitions. A special curvilinear coordinate system is introduced, coinciding with the normal vibrational modes of reactants or products in the asymptotic regions and describing their gradual transformation along the reaction coordinate. It provides a generalization of a two-dimensional ‘natural collision coordinate system’ introduced by Marcus. In terms of these coordinates a model hamiltonian is defined, neglecting the curvature of the reaction coordinate and with a special potential, for which an exact adiabatic solution is found. Using its eigenfunctions as a basic, the Born perturbation expansion is given, being capable of treating vibrational transitions in the course of the elementary reaction act and including the curvature as a perturbation. The zero-order adiabatic hamiltonian is in fact that of the activated complex theory.