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We give a general method for finding the exact solution for the problem ofelectronic relaxation in solution, modeled by a particle undergoing diffusivemotion under a potential in the presence of a sink of finite width. Thesolution requires the knowledge of the Green's function in Laplace domain inthe absence of any sink. We find the exact solution for the case of parabolicpotential. This model has considerable improvement over the existing models forunderstanding non-radiative electonic relaxation of a molecule in solution, infact this is the first model where a simple analytical solution is possible inthe case of a sink of finite width.

Theory of Electronic relaxation in solution: Exact solution in case of parabolic potential with a sink of finite width