Dynamic salt effect on intramolecular charge-transfer reactions

Dielectric Polarization and Electric Displacement in Polar-Molecule Reactions

The aim of this work is to investigate the dielectric polarization in polar-molecule reactions in the liquid phase theoretically. On the basis of the modified Smoluchowski equation, the analytic expression of the polarization is derived. The result shows that the expression of the polarization in polar-molecule reactions is quite different from the one in the Debye model. For general reactions, two vectors, the rotational diffusion vector and the component concentration vector, are proposed to describe the polarization. For fast reactions, the conception of relative permittivity will be nonexistent due to the effect of the component concentration vector on the frequency of the applied field, and the dielectric behavior may only be analyzed in the time domain. On the contrary, for slow reactions, the relative permittivity will be concentration-dependent.

Solvent dynamics effect in condensed-phase electron-transfer reactions

Channel-based reaction-diffusion equations are solved analytically for two electron transfer (ET) models, where the fast inner-sphere coordinate leads to an ET reaction treated by Fermi's golden rule, and the slow solvent coordinate moves via diffusion. The analytic solution has let us derive an ET rate constant that modifies the Marcus-Jortner formula by adding a constant alpha which we call a dynamic correction factor. The dynamic correction factor measures the effect of solvent friction. When the relaxation of solvent dynamics is fast, the dynamic correction can be neglected and the ET rate constant reduces to the traditional Marcus-Jortner formula. If the solvent dynamic relaxation is slow, the dynamic correction can be very large and the ET rate can be reduced by orders of magnitude. Using a generalized Zusman-Sumi-Marcus model as a starting point, we introduce two variants, GZSM-A and GZSM-B, where in model A, only one quantum mode is considered for inner-sphere motion and in model B, a classical mode for inner-sphere motion is added. By comparing the two models with experimental data, it is shown that model B is better than model A. For the solvents that have a relaxation time ranging between 0 and 5 ps, our result agrees fairly well with experimental data; for the solvents that have a relaxation time ranging between 5 and 40 ps, our result deviates from the experimental values. After introducing an adjustable scaling index in the effective time correlation function of the reaction coordinate, good agreement is achieved between the experiment and the theory for model B for all of the solvents studied in this paper.

Ligand reorganization and activation energies in nonadiabatic electron transfer reactions

The activation energy and ligand reorganization energy for nonadiabatic electron transfer reactions in chemical and biological systems are investigated in this paper. The free energy surfaces and the activation energy are derived exactly in the general case in which the ligand vibration frequencies are not equal. The activation energy is derived by free energy minimization at the transition state. Our formulation leads to the Marcus-Hush [J. Chem. Phys. 24, 979 (1956); 98, 7170 (1994); 28, 962 (1958)] results in the equal-frequency limit and also generalizes the Marcus-Sumi [J. Chem. Phys. 84, 4894 (1986)] model in the context of studying the solvent dynamic effect on electron transfer reactions. It is found that when the ligand vibration frequencies are different, the activation energy derived from the Marcus-Hush formula deviates by 5%-10% from the exact value. If the reduced reorganization energy approximation is introduced in the Marcus-Hush formula, the result is almost exact.