A modified two-sphere model for solvent reorganization energy in electron transfer

In this work, the solvent reorganization energy is formulated within the framework of classical thermodynamics, by adding some external charges to construct a constrained equilibrium state. The derivation clearly shows that the reorganization energy is exactly the polarization cost for the inertial part of the polarization. We perform our derivation just within the framework of the first law of thermodynamics, and the final form of the reorganization energy is completely the same as that we gave in our recent work by defining a nonequilibrium solvation free energy. With the two-sphere model approximation, our solvent reorganization energy is derived as. This amends Marcus' model by a factor of (ε-1op - ε-1s)/(1 - ε-1s), which is coupled with the solvent polarity. Making use of the modified expression of solvent reorganization energy, two recently reported electron transfer processes are investigated in representative solvents. The results show that our formula can well reproduce the experimental observations.