Thermodynamics for nonequilibrium solvation and numerical evaluation of solvent reorganization energy

This work presents a thermodynamic method for treating nonequilibrium solvation. By imposing an extra electric field onto the nonequilibrium solvation system, a virtual constrained equilibrium state is prepared. In this way, the free energy difference between the real nonequilibrium state and the con-strained equilibrium one is simply the potential energy of the nonequilibrium polarization in the extra electronic field, according to thermodynamics. Further, new expressions of nonequilibrium solvation energy and solvent reorganization energy have been formulated. Analysis shows that the present formulations will give a value of reorganization energy about one half of the traditional Marcus theory in polar solvents, thus the explanation on why the traditional theory tends to overestimate this quantity has been found out. For the purpose of numerical determination of solvent reorganization energy, we have modified Gamess program on the basis of dielectric polarizable continuum model. Applying the procedure to the well-investigated intramolecular electron transfer in biphenyl-androstane-naphthyl and biphenyl-androstane-phenanthryl systems, the numerical results of solvent reorganization energy have been found to be in good agreement with the experimental fittings.