Long range electron transfer reactions in solution: An analytically solvable model

•Model for long range electron transfer is given.•Dirac delta coupling is used.•Parabolic potentials are considered.•Laplace transform of the Green's function is used.

We propose an analytical method for understanding the problem of long range electron transfer reaction in solution, modeled by a particle undergoing diffusive motion under the influence of large number of potentials which are involved (donor - long bridge - acceptor) in the process. The coupling between these potentials are assumed to be represented by Dirac delta functions. The diffusive motion in this paper is represented by the Smoluchowski equation. Our solution requires the knowledge of the Laplace transform of the Green's function for the motion in all the uncoupled potentials. For the case where all potentials are parabolic, we have derived a very simple expression for the Green's function of the whole process under the semi-infinite limit.

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