Electrochemical solvent reorganization energies in the framework of the polarizable continuum model

Electron transfer reactions at electrochemical interfaces play a critical role in a wide range of catalytic processes. A key parameter in the rate constant expressions for such processes is the reorganization energy, which reflects the energetic cost of the solute and solvent rearrangements upon electron transfer. In this paper, we present dielectric continuum methods for calculating the solvent reorganization energy for electrochemical processes. We develop a method for calculating the electrochemical solvent reorganization energies with molecular-shaped cavities within the framework of the polarizable continuum model (PCM). The electronic and inertial responses of the solvent are separated according to their respective time scales, and two limiting cases of the relation between the solute and solvent electrons are examined. The effects of the electrode are included with the integral equations formalism PCM (IEF-PCM), in which the molecule-solvent boundary is treated explicitly, but the effects of the electrode-solvent boundary are included through an external Green's function. This approach accounts for the effects of detailed molecular charge redistribution in a molecular-shaped cavity, as well as the electronic and inertial solvent responses and the effects of the electrode. The calculated total reorganization energies are in reasonable agreement with experimental measurements for a series of electrochemical systems. Inclusion of the effects of the electrode is found to be essential for obtaining even qualitatively accurate solvent reorganization energies. These approaches are applicable to a wide range of systems and can be extended to include other types of boundaries, such as a self-assembled monolayer or double layer separating the electrode and the molecule.