System-bath decomposition of the reaction path Hamiltonian for polyatomic scattering: Quantum perturbative treatment

An approach to quantum mechanical reactive scattering in polyatomic molecular systems is described. The formulation is based on the reaction path Hamiltonian of Miller, Handy, and Adams [J. Chem. Phys. 72, 99 (1980)]. The essential physical idea is that the reaction coordinate in even polyatomic systems may be coupled strongly to only a few (one or two) of the vibrational modes orthogonal to it, and rather weakly coupled to the (perhaps many) remaining modes. This leads naturally to a "system-bath" decomposition of the reaction process, and this paper shows how this is carried through for the reaction path Hamiltonian. If only one transverse mode is included with the reaction coordinate to form the "system," for example, then the overall model is that of a collinearlike reaction, whose dynamics are treated accurately, taking place in a (harmonic) "bath" to which it is weakly coupled.