New formulation for nonequilibrium solvation: a consistent expression of electrostatic free energy by different methods and its application to solvent reorganization energy and spectral shifts in solution

We present an overview of the current status of the theories of nonequilibrium solvation and their generalizations in modern chemistry. Based on the continuous medium theory, the nonequilibrium electrostatic free energy has been reformulated. We adopt three different methods, the multi-step charging approach, the field superposition principle, and the interaction energy method, to achieve the consistent expression of electrostatic free energy of nonequilibrium. The misunderstandings on the interaction energy between the polarization field and its source (free) charge have been made clear. Derivations reveal a significant feature that this interaction energy is quite different from that between two independent fields. In the present work, the solvation free energy is found entirely contributed from the interaction between the solvent polarization and its source charge, whereas the self-energy of the polarization field is deduced to zero. The spectral shifts for light absorption and emission, and solvent reorganization energy for electron transfer in solution, have been derived to new forms differing from the conventional ones. The newly developed two-sphere model for electron transfer has been employed to investigation of the intramolecular electron transfer in Closs-Miller system.