Abstract
We propose an analytical method for finding the time domain solution for the problem of electronic relaxation of a molecule in solution. The relaxation process is modeled by the decay of a diffusing probability distribution through an absorbing sink. In our model, the diffusive motion is modeled using the Smoluchowski equation for harmonic potential and the sink is represented by a Dirac Delta function of arbitrary strength and position. This has been an unsolved problem for a long time and is of immense importance as a model for understanding non-radiative electronic relaxation of a molecule in solution. Our solution can be used to understand various reaction-diffusion problems.
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