Reaction coordinate in electron transfer: What physical quantity should we use for it?

Electrochemical Properties and Local Structure of the TEMPO/TEMPO+ Redox Pair in Ionic Liquids

Redox-active organic species play an important role in catalysis, energy storage, and biotechnology. One of the representatives is the 2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO) radical, used as a mediator in organic synthesis and considered a safe alternative to heavy metals. In order to develop a TEMPO-based system with well-controlled electrochemical and catalytic properties, a reaction medium should be carefully chosen. Being highly conductive, stable, and low flammability fluids, ionic liquids (ILs) seem to be promising solvents with easily adjustable physical and solvation properties. In this work, we give an insight into the local structure of ILs around TEMPO and its oxidized form, TEMPO⁺, underlining striking differences in the solvation of these two species. The analysis is coupled with a study of thermodynamics and kinetics of oxidation in the frame of Marcus theory. Our systematic investigation includes imidazolium, pyrrolydinium, and phosphonium families combined with anions of different size, polarity, and flexibility, opting to provide a clear and comprehensive picture of the impact of the nature of IL ions on the behavior of radical/cation redox pairs. The obtained results will help to explain experimentally observed effects and to rationalize the design of TEMPO/IL systems.

Projection of the Dynamics of Electron Transfer Reaction in Dual Space onto the One-Dimensional Slower Reaction Coordinate Axis

We have derived here for the first time an exact dynamical equation within the domain of classical mechanics for the time dependent density distribution function of one-dimensional reaction coordinate (RC) in the condensed phase for electron transfer reaction by projecting the dynamics of slower modes in multidimensional Liouville space starting with a given set of coordinates of the faster modes. After the faster modes were ensemble averaged, the dynamics of the whole system solely depends on the slower RC. To simplify the complicated equation into a tractable form, benchmark approximations are employed to reduce the formally exact equation into an equation similar to the Smoluchowski equation with a delocalized sink term. As a test case, a Hamiltonian for the solute-solvent system modeled by quadratic functions for fast-relaxing vibrational and slow-relaxing polarization modes, respectively, has been considered. Interestingly, our simplified kinetic equation corresponding to this model Hamiltonian is transformed into the well-known phenomenological Sumi-Marcus equation.

Time-resolved magnetic field effects distinguish loose ion pairs from exciplexes

We describe the experimental investigation of time-resolved magnetic field effects in exciplex-forming organic donor–acceptor systems. In these systems, the photoexcited acceptor state is predominantly deactivated by bimolecular electron transfer reactions (yielding radical ion pairs) or by direct exciplex formation. The delayed fluorescence emitted by the exciplex is magnetosensitive if the reaction pathway involves loose radical ion pair states. This magnetic field effect results from the coherent interconversion between the electronic singlet and triplet radical ion pair states as described by the radical pair mechanism. By monitoring the changes in the exciplex luminescence intensity when applying external magnetic fields, details of the reaction mechanism can be elucidated. In this work we present results obtained with the fluorophore-quencher pair 9,10-dimethylanthracene/N,N-dimethylaniline (DMA) in solvents of systematically varied permittivity. A simple theoretical model is introduced that allows discriminating the initial state of quenching, viz., the loose ion pair and the exciplex, based on the time-resolved magnetic field effect. The approach is validated by applying it to the isotopologous fluorophore-quencher pairs pyrene/DMA and pyrene-d₁₀/DMA. We detect that both the exciplex and the radical ion pair are formed during the initial quenching stage. Upon increasing the solvent polarity, the relative importance of the distant electron transfer quenching increases. However, even in comparably polar media, the exciplex pathway remains remarkably significant. We discuss our results in relation to recent findings on the involvement of exciplexes in photoinduced electron transfer reactions.

Polarization caging in diffusion-controlled electron transfer reactions in solution

In some bimolecular diffusion-controlled electron transfer (ET) reactions such as ion recombination (IR), both solvent polarization relaxation and the mutual diffusion of the reacting ion pair may determine the rate and even the yield of the reaction. However, a full treatment with these two reaction coordinates is a challenging task and has been left mostly unsolved. In this work, we address this problem by developing a dynamic theory by combining the ideas from ET reaction literature and barrierless chemical reactions. Two-dimensional coupled Smoluchowski equations are employed to compute the time evolution of joint probability distribution for the reactant (P((1))(X,R,t)) and the product (P((2))(X,R,t)), where X, as is usual in ET reactions, describes the solvent polarization coordinate and R is the distance between the reacting ion pair. The reaction is described by a reaction line (sink) which is a function of X and R obtained by imposing a condition of equal energy on the initial and final states of a reacting ion pair. The resulting two-dimensional coupled equations of motion have been solved numerically using an alternate direction implicit (ADI) scheme (Peaceman and Rachford, J. Soc. Ind. Appl. Math. 1955, 3, 28). The results reveal interesting interplay between polarization relaxation and translational dynamics. The following new results have been obtained. (i) For solvents with slow longitudinal polarization relaxation, the escape probability decreases drastically as the polarization relaxation time increases. We attribute this to caging by polarization of the surrounding solvent. As expected, for the solvents having fast polarization relaxation, the escape probability is independent of the polarization relaxation time. (ii) In the slow relaxation limit, there is a significant dependence of escape probability and average rate on the initial solvent polarization, again displaying the effects of polarization caging. Escape probability increases, and the average rate decreases on increasing the initial polarization. Again, in the fast polarization relaxation limit, there is no effect of initial polarization on the escape probability and the average rate of IR. (iii) For normal and barrierless regions the dependence of escape probability and the rate of IR on initial polarization is stronger than in the inverted region. (iv) Because of the involvement of dynamics along R coordinate, the asymmetrical parabolic (that is, non-Marcus) energy gap dependence of the rate is observed.