Diffusion-controlled reactions: A revisit of Noyes' theory

Noyes' theory of diffusion-controlled reactions is revisited in great detai ls. First, it is shown that this theory provides an interesting alternative approach to perform molecular dynamics simulations for diffusion-controlle d reactions. With this approach, reaction rate can be determined from simul ations of nonreactive equilibrium systems. No annihilation procedure is nee ded to simulate the reaction event. Provided that encounters with different reactants are strictly uncorrelated, the reaction rate can be determined m ore directly and accurately than by the methods that compute the survival p robability. We describe in detail the method for accurately determining the key quantity in Noyes' theory, i.e., the first recollision probability, fr om molecular dynamics simulations. It will also be shown that arguments sim ilar to those in Noyes' theory allow us to establish an exact relation (und er the same assumptions of absence of correlations) between the distributio n function of a reacting system at the encounter distance and that of a non reactive equilibrium system. This relation can be used to fix the boundary condition at the reaction distance in the approaches based on a diffusion e quation. New insights have been gained into the usefulness of the recollisi on probability. The recollision probability also provides a very useful too l for characterizing quantitatively some dynamic features of the cage effec t for reactions in dense liquids. Finally, the method presented here may al so be used to calculate reaction rates for diffusion-controlled reactions i n systems where the dynamics cannot be described by a diffusion equation. < (C)> 2001 American Institute of Physics.