Small-curvature adiabatic approximation for reaction-path reduced-dimensionality effective Hamiltonian

Beginning with the Miller-Handy-Adams reaction-path Hamiltonian, which is applicable to chemical reactions and photodissociation processes, we classify the modes as one reaction coordinate, (f-1) strongly coupled modes, and (F-f) weakly coupled modes. We derive a reduced-dimensionality Hermitian Hamiltonian for f explicit modes such that the (F-f) weakly coupled modes are treated adiabatically and their coupling to the reaction coordinate due to reaction-path curvature is included implicitly. The reduction is achieved two ways: one based on a small-curvature-tunneling approximation and one based on a more general semiclassical-path assumption for the weakly coupled modes.