Solvent Reorganization Energy Of Electron Transfer Research Articles

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, G 2 non =(1/2) ∫ V dVρ 2Φ 2 non . 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 G 2 non, 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.

Proton-coupled electron transfer in a model for tyrosine oxidation in photosystem II.

Theoretical calculations of a model for tyrosine oxidation in photosystem II are presented. In this model system, an electron is transferred to ruthenium from tyrosine, which is concurrently deprotonated. This investigation is motivated by experimental measurements of the dependence of the rates on pH and temperature (Sjödin et al. J. Am. Chem. Soc. 2000, 122, 3932). The mechanism is proton-coupled electron transfer (PCET) at pH < 10 when the tyrosine is initially protonated and is single electron transfer (ET) for pH > 10 when the tyrosine is initially deprotonated. The PCET rate increases monotonically with pH, whereas the single ET rate is independent of pH and is 2 orders of magnitude faster than the PCET rate. The calculations reproduce these experimentally observed trends. The pH dependence for the PCET reaction arises from the decrease in the reaction free energies with pH. The calculations indicate that the larger rate for single ET arises from a combination of factors, including the smaller solvent reorganization energy for ET and the averaging of the coupling for PCET over the reactant and product hydrogen vibrational wave functions (i.e., a vibrational overlap factor in the PCET rate expression). The temperature dependence of the rates, the solvent reorganization energies, and the deuterium kinetic isotope effects determined from the calculations are also consistent with the experimental results.

A Failure of Continuum Theory: Temperature Dependence of the Solvent Reorganization Energy of Electron Transfer in Highly Polar Solvents

The temperature dependence of the solvent reorganization energy for intramolecular electron transfer (ET) in acetonitrile is measured experimentally and calculated theoretically. The Stokes shifts for the charge transfer, optical transitions of (tetrahydro-4H-thiopyran-4-ylidene)propanedinitrile indicate that the solvent reorganization energy for ET decreases with temperature, whereas dielectric continuum theories of solvent reorganization predict an increase with temperature. A molecular alternative to the continuum description is proposed that models the solvent as a fluid of polarizable, dipolar hard spheres. Good agreement between the molecular theory and experiment is achieved for both the ET reorganization energy and equilibrium energy gap. The negative temperature slope of the solvent reorganization energy is understood in terms of its dissection into components arising from different solute−solvent interaction potentials and contributions from different solvent modes activating ET. In the first approach, we consider reorganization energy components from permanent and induced dipoles. In the second dissection, the orientational and density solvent fluctuations are considered. The analyses show that the molecular nature of the solvent, embodied in density fluctuations and associated translational motions of the solvent permanent dipoles, is the principal source of the negative temperature dependence of the solvent reorganization energy. This component is absent in the continuum picture. Its absence is the reason the continuum model fails to correctly predict the sign of the reorganization energy temperature dependence in polar solvents.