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We propose an analytical method for solving the problem of electronicrelaxation in solution in time domain, modelled by a particle undergoingdiffusion under the influence of two coupled potentials. The coupling betweenthe two potentials is assumed to be represented by a Dirac delta function ofarbitrary position and strength. Smoluchowskii equation is used model thediffusion motion on both the potentials. We report an analytical expression forsurvival probability in time domain. This is the first time analytical solutionin time domain is derived and this method can be used to solve problemsinvolving other potentials.

Barrierless electronic relaxation in solution -- two state model with exact analytical solution in time domain