An integral equation approximation for the dynamics of reversible electron‐transfer reactions

Dynamic salt effect on intramolecular charge-transfer reactions

The dynamic salt effect in charge-transfer reactions is investigated theoretically in this paper. Free-energy surfaces are derived based on a nonequilibrium free-energy functional. Reaction coordinates are clearly defined. The solution of the reaction-diffusion equation leads to a rate constant depending on the time correlation function of the reaction coordinates. The time correlation function of the ion-atmosphere coordinate is derived from the solution of the Debye-Falkenhagen equation. It is shown that the dynamic salt effect plays an important role in controlling the rate of charge-transfer reactions in the narrow-window limit but is balanced by the energetics and the dynamics of the polar-solvent coordinate. The simplest version of the theory is compared with an experiment, and the agreement is fairly good. The theory can also be extended to charge-transfer in the class of electrolytes that has come to be called "ionic fluids."

Photosynthetic electron transfer controlled by protein relaxation: analysis by Langevin stochastic approach

Relaxation processes in proteins range in time from picoseconds to seconds. Correspondingly, biological electron transfer (ET) could be controlled by slow protein relaxation. We used the Langevin stochastic approach to describe this type of ET dynamics. Two different types of kinetic behavior were revealed, namely: oscillating ET (that could occur at picoseconds) and monotonically relaxing ET. On a longer time scale, the ET dynamics can include two different kinetic components. The faster one reflects the initial, nonadiabatic ET, whereas the slower one is governed by the medium relaxation. We derived a simple relation between the relative extents of these components, the change in the free energy (DeltaG), and the energy of the slow reorganization Lambda. The rate of ET was found to be determined by slow relaxation at -DeltaG < or = Lambda. The application of the developed approach to experimental data on ET in the bacterial photosynthetic reaction centers allowed a quantitative description of the oscillating features in the primary charge separation and yielded values of Lambda for the slower low-exothermic ET reactions. In all cases but one, the obtained estimates of Lambda varied in the range of 70-100 meV. Because the vast majority of the biological ET reactions are only slightly exothermic (DeltaG > or = -100 meV), the relaxationally controlled ET is likely to prevail in proteins.