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

The Grote-Hynes theory of nonequilibrium solvation effects on reaction kinetics is examined using the perspective provided by multidimensional transition state theory. The analysis is performed for a model in which a solute reaction coordinate is bilinearly coupled to a harmonic solvent bath, and we derive intermediate quantities that shed light on the ability of Grote-Hynes theory to capture relevant physical features of the reaction dynamics. One example is a separatrix distribution, in particular, the distribution P(r) of Values of the solute reaction coordinate on the variationally optimized transition state dividing surface for the multidimensional model. Another example is the reactive probability density dp/dP(B) on a trial transition state dividing surface orthogonal to the solute reaction coordinate. The model is seen to be capable of producing wide P(r) distributions and bimodal dp/dP(B) distributions. The bimodal distribution of the reactive probability density can exist on a trial transition state dividing surface transverse to the solute reaction coordinate even if there is no solvent barrier. The bimodality of the reactive probability density arises from the wings of the Gaussian solvent coordinate distribution in regions away from the saddle point. The model is in good agreement with recent simulations of Na+Cl- ion pair dissociation in water. The deviations from conventional transition state theory can be interpreted as arising from solvent friction or from the participation of the solvent in the reaction coordinate.