Numerical solution of solvent reorganization energy and its application in electron transfer reaction

According to our recent studies on the nonequilibrium solvation, the solvent reorganization energy λ_s is found to be the cost of maintaining the residual polarization, which equilibrates with the constraining extra electric field. In this work, a matrix form of λ_s has been formulated based our new analytical expression of the solvent reorganization energy. By means of the integral equation formulation-polarizable continuum model (IEF-PCM), a new numerical algorithm for λ_s has been implemented as a subroutine coupled with the Q-Chem package. Then, we have performed a comparison of numerical results with analytical solution obtained by two-sphere model for λ_s in self-exchange electron transfer (ET) reaction of He-He⁺ system. The numerical results and analytical solution coincide as the distance between the donor and the acceptor. In order to compare with our pervious numerical algorithm with dielectric polarizable continuum model, self-exchange ET reactions between tetracyanoethylene, tetrathiafulvalene, and their corresponding ionic radicals in acetonitrile have been studied. Overall, the solvent reorganization energy calculated by IEF-PCM is more reasonable since IEF-PCM gives a better self-energy of surface element.