Electron Transfer Reactions In Polar Solvents Research Articles

Nonadiabatic dynamics of electron transfer in solution: explicit and implicit solvent treatments that include multiple relaxation time scales.

The development of efficient theoretical methods for describing electron transfer (ET) reactions in condensed phases is important for a variety of chemical and biological applications. Previously, dynamical dielectric continuum theory was used to derive Langevin equations for a single collective solvent coordinate describing ET in a polar solvent. In this theory, the parameters are directly related to the physical properties of the system and can be determined from experimental data or explicit molecular dynamics simulations. Herein, we combine these Langevin equations with surface hopping nonadiabatic dynamics methods to calculate the rate constants for thermal ET reactions in polar solvents for a wide range of electronic couplings and reaction free energies. Comparison of explicit and implicit solvent calculations illustrates that the mapping from explicit to implicit solvent models is valid even for solvents exhibiting complex relaxation behavior with multiple relaxation time scales and a short-time inertial response. The rate constants calculated for implicit solvent models with a single solvent relaxation time scale corresponding to water, acetonitrile, and methanol agree well with analytical theories in the Golden rule and solvent-controlled regimes, as well as in the intermediate regime. The implicit solvent models with two relaxation time scales are in qualitative agreement with the analytical theories but quantitatively overestimate the rate constants compared to these theories. Analysis of these simulations elucidates the importance of multiple relaxation time scales and the inertial component of the solvent response, as well as potential shortcomings of the analytical theories based on single time scale solvent relaxation models. This implicit solvent approach will enable the simulation of a wide range of ET reactions via the stochastic dynamics of a single collective solvent coordinate with parameters that are relevant to experimentally accessible systems.

Temperature- and Pressure-Dependence of the Outer-Sphere Reorganization Free Energy for Electron Transfer Reactions: A Continuum Approach

The outer-sphere reorganization free energy for electron-transfer reactions in polar solvents and its variations with temperature and pressure are studied in the dielectric continuum framework by extending the recent fluctuating cavity description [J. Chem. Phys. 2005, 123, 014504]. The diabatic free energies are obtained as a function of three variables, i.e., radii of two spherical cavities for the donor and acceptor moieties of an electron-transfer complex and a solvent coordinate that gauges an arbitrary configuration of solvent orientational polarization. Equilibrium cavities relevant to the reactant and product states are determined via the variational principle. This incorporates cavity size readjustment accompanying electron transfer and related electrostrictive effects. Another important consequence of the variational determination of equilibrium cavities is that their size depends on thermodynamic conditions. The application of the theoretical formulation presented here to electron self-exchange shows that in contrast to the prediction of the standard Marcus theory, the solvent reorganization free energy decreases with temperature. This is in excellent accord with a recent experiment on a mixed valence dinuclear iron complex in acetonitrile [J. Phys. Chem. A 1999, 103, 7888]. It is also found that electrostriction makes a significant contribution to outer-sphere reorganization. Model calculations for the dinuclear iron complex system show that about 25-30% of the total solvent reorganization free energy arises from cavity size changes, while solvent repolarization is responsible for the rest.

Solvent reorganization energy of electron-transfer reactions in polar solvents.

A microscopic theory of solvent reorganization energy in polar molecular solvents is developed. The theory represents the solvent response as a combination of the density and polarization fluctuations of the solvent given in terms of the density and polarization structure factors. A fully analytical formulation of the theory is provided for a solute of arbitrary shape with an arbitrary distribution of charge. A good agreement between the analytical procedure and the results of Monte Carlo simulations of model systems is achieved. The reorganization energy splits into the contributions from density fluctuations and polarization fluctuations. The polarization part is dominated by longitudinal polarization response. The density part is inversely proportional to temperature. The dependence of the solvent reorganization energy on the solvent dipole moment and refractive index is discussed.

Microscopic examination of free-energy relationships for electron transfer in polar solvents

A recently developed semiclassical trajectory (ST) approach is used to explore the microscopic free-energy relationship for electron-transfer reactions in polar solvents. The free-energy functional is evaluated by an adiabatic charging process based on the umbrella sampling method. The relevant energy fluctuations are generated by molecular dynamics simulation, representing the solvent molecules by the surface constrained all atom solvent (SCAAS) model. The specific model considered is composed of two benzene-like molecules with variable redox potentials. The simulation gives stable results with a relatively small convergence error. The results are compared to the free-energy profile predicted by the macroscopic Marcus' model. It is found that the solvent contribution to the activation barrier follows Marcus' relationship, provided that the reorganization energy parameter is evaluated from the microscopic simulation. The experimentally observed deviations from Marcus' relationship are shown, by realistic microscopic calculations, to be due to the solute vibronic channels. It is pointed out that the approximately quadratic behavior of the free-energy functional might reflect an inherent property of solvents with high dielectric constant.

Different energy gap laws for the three types of electron-transfer reactions in polar solvents

Different energy gap laws for the three types of electron-transfer reactions in polar solvents

Outer-sphere electron-transfer reactions in polar solvents

A model for outer-sphere electron-transfer reactions in polar solutions is suggested. It is based on the idea of dividing the system into two subsystems, a classical solvent and quantum mechanical interacting molecules. The solvent is looked upon as the source of an external field and is coupled parametrically to the reacting species. The model is analytically solved, under some approximations, for the transfer probability. Using a specific macroscopic model of the solvent a usable expression for the rate constant is given. Operational and physical criteria are developed regarding the problems of adiabaticity, nonadiabaticity, and independence on the solvent dynamics.