Marcus Theory and The Condon Approximation Revisited I: E-SHAKE and Seam Sampling

Marcus theory is the workhorse of theoretical chemistry for predicting the rates of charge and energy transfer. Marcus theory overwhelmingly agrees with experiment -- both in terms of electron transfer and triplet energy transfer -- for the famous set of naphthalene-bridge-biphenyl and naphthalene-bridge-benzophenone systems studied by Piotrowiak, Miller, and Closs. That being said, the agreement is not perfect, and in this manuscript, we revisit one key point of disagreement: the molecule C-13-ae ([3,equatorial]-naphthalene-cyclohexane-[1,axial]-benzophenone). To better understand the theory-experiment disagreement, we introduce and employ a novel scheme to sample the seam between two diabatic electronic states (E-SHAKE) through which we reveal the breakdown of the Condon approximation and the presence of a conical intersection for the C-13-ae molecule; we also predict an isotopic effect on the rate of triplet-triplet energy transfer.