Barrierless Reactions in Solution: An Analytically Solvable Model

We propose an analytical method for solving the problem of barrierless reactions in solution, modeled by a particle undergoing diffusive motion under the influence of both reactant and product potentials. The coupling between these two potentials is taken to be a Dirac Delta function. The diffusive motion in this paper is described by the Smoluchowskii equation. Our solution requires only the knowledge of the Laplace transform of the Green's function for the motion in both the uncoupled potentials. Our model is more general than all the earlier models, because we are the first one to consider the potential energy surfaces of both the reactant and product explicitly.