Transition state theory in liquids beyond planar dividing surfaces

The success of transition state theory (TST) in describing the rates of chemical reactions has been less-than-perfect in solution (and sometimes even in the gas phase) because conventional dividing surfaces are only approximately free of recrossings between reactants and products. Recent advances in dynamical systems theory have helped to identify the interconnected manifolds-“superhighways”-leading from reactants to products. The existence of these manifolds has been proven rigorously, and explicit algorithms are available for their calculation. We now show that these extended structures can be used to obtain reaction rates directly in dissipative systems. We also suggest a treatment for the substantially more general case in which the molecular solvent is fully specified by the positions of all its atoms. Specifically, we can construct effective solvent configurations for which the exact TST manifolds can be constructed and used to sample the rates of an open system.