Multidimensional transition state theory and the validity of Grote-Hynes theory

The Grote-Hynes theory of nonequilibrium solvation effects on reaction kine tics is examined using the perspective provided by multidimensional transit ion state theory. The analysis is performed for a model in which a solute r eaction coordinate is bilinearly coupled to a harmonic solvent bath, and we derive intermediate quantities that shed light on the ability of Grote-Hyn es theory to capture relevant physical features of the reaction dynamics. O ne example is a separatrix distribution, in particular, the distribution P( r) of Values of the solute reaction coordinate on the variationally optimiz ed transition state dividing surface for the multidimensional model. Anothe r example is the reactive probability density dp/dP(B) on a trial transitio n state dividing surface orthogonal to the solute reaction coordinate. The model is seen to be capable of producing wide P(r) distributions and bimoda l dp/dP(B) distributions. The bimodal distribution of the reactive probabil ity density can exist on a trial transition state dividing surface transver se to the solute reaction coordinate even if there is no solvent barrier. T he bimodality of the reactive probability density arises from the wings of the Gaussian solvent coordinate distribution in regions away from the saddl e point. The model is in good agreement with recent simulations of Na+Cl- i on pair dissociation in water. The deviations from conventional transition state theory can be interpreted as arising from solvent friction or from th e participation of the solvent in the reaction coordinate.