We systematically test how the Duschinsky mixing of normal coordinate vibrations affects transition rates for electron transfer (ET). We find that ET rates in the inverted region can increase many orders of magnitude from Duschinsky mixing, and both totally symmetric and nontotally symmetric vibrations are very important. The Duschinsky effect arises when two electronic states have vibrational normal mode coordinate systems that are rotated and translated relative to each other. We use a conventional quantum rate model for ET, and the examples include 6-8 vibrations, where two vibrational modes are mixed with different amounts of coordinate rotation. The multidimensional Franck-Condon factors (FCF) are computed with standard algorithms and recently developed recursion relations. When displaced, totally symmetric modes are involved, rates with Duschinsky mixing can increase several orders of magnitude for inverted electron transfer reactions and modest mixing. The peak location in a rate vs energy gap plot can depend on the degree of Duschinsky mixing, and therefore it corresponds to a sum of solvent and an effective vibrational reorganization energy that is not predictable by simple models that exclude mixing. In addition, for some examples of inverted region ET we observe significant flattening of the usual parabolic curve at large degrees of mixing. We demonstrate that large rate effects can occur with very little change in either the calculated absorption or emission spectra, depending on the details of the Duschinsky mixing. The origin of the rate effect is the increased FCF between the initial vibrational state and the higher lying final vibrational states when the Duschinsky effect is taken into account. The rate effect of totally symmetric modes is greater than nontotally symmetric modes, but since there are many nontotally symmetric modes, in real molecules these modes can make a large total contribution to ET rates.
Journal of Physical Chemistry a, 2001, Vol 105, Issue 22, p. 5317-5325