New formulation for non-equilibrium solvation: dielectric constant change during charging process and influence of slow response of polarization upon solvent reorganization energy of electron transfer

Based on continuous medium theory, a new expression for electrostatic free energy of non-equilibrium state is deduced. Considering the change of the dielectric constant of medium during the establishment of the non-equilibrium state, a less familiar but more rational formula is employed in calculating the difference of electrostatic free energy. Both the two-step method and the field superposition approach give a consistent result for non-equilibrium, that is, <f>G2non=(1/2)∫lower limit V dVρ2Φ2non.</f> The direct calculation of the electrostatic free energy has been performed for the polarization field, which can represent the non-equilibrium state in charge recombination process. The result of zero coincides with that judged by using the new expression. In the present form of <f>G2non,</f> no quantity of intermediate equilibrium is explicitly involved, hence it satisfies the request of the thermodynamics. Starting from the electrostatic free energy, generalized formulations for solvent reorganization energy of electron transfer (ET) have been deduced. Application to the two-sphere case yields new formulas estimating this quantity. A significant feature of the present two-sphere model is the dependency of solvent reorganization energy on the direction of reaction and the charges initially brought by the donor and acceptor spheres. Results in this work reveal that the previous theory seems to overestimate the solvent reorganization energy of ET by a factor of about two. A qualitative analysis indicates that the considerable discrepancies between the theoretical predication and the experimental observation in the literatures will be solved fairly well, if the new formulations are applied. [Copyright &y& Elsevier]