Nonequilibrium solvation energy by means of constrained equilibrium thermodynamics and its application to self-exchange electron transfer reactions.

This work presents a self-consistent thermodynamic approach to nonequilibrium solvation energy. By imposing an extra electric field onto the nonequilibrium solvation system, a constrained equilibrium state is prepared. New expressions of nonequilibrium solvation energy and solvent reorganization energy have been formulated. The numerical algorithm combining the new formulation with the dielectric polarizable continuum model has been implemented. As an application, self-exchange electron transfer (ET) reactions between tetramethylhydrazine, tetraethylhydrazine, and tetrapropylhydrazine and their corresponding radical cations have been investigated. The inner and solvent reorganization energies are calculated by the "four-point" method and the new method for nonequilibrium solvation, respectively. Besides, we also calculated the electronic coupling matrix. The rate constants for the three self-exchange ET reactions correlate well with experimental results. We have shown that the inner reorganization energies of these self-exchange ET are not very sensitive to compound size while the compound size has some effect on the solvent reorganization energy in acetonitrile. The new method for nonequilibrium solvation energy based on continuum model provides a reasonable result for the solvent reorganization energy.