The Rate Constant — Reaction Free Energy Dependence for the Electron Transfer Reactions in Solutions. The Way to Interpret the Experimental Data Correctly
From Firenze University Press Journal: Substantia
Lev I. Krishtalik, A.N. Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences
The relative influences of the reorganization energies of the classical and quantum modes on the maximum position of the rate constant — reaction free energy curve have been studied. In the framework of the continuum electrostatics, the electron transfer reorganization energies in methyltetrahydrofurane solutions for the system biphenylyl — spacer — acceptor were calculated. For different acceptors, the solvent reorganization energy varies from 1.0 to 1.1 eV. When added with the rather small reorganization energies for classical intra-molecular modes we obtain 1.13–1.34 eV. With account of possible errors this coincides practically with the experimental estimate of the energy at the maximum of the rate–free energy curve ΔGmax ≈ -1.2 eV. Hence, we can con-clude that the reorganization of quantum modes does not influence substantially the position of this maximum. To the contrary, in a non-polar solvent isooctane were the solvent reorganization does not play any role the reorganization of the quantum intra-reactants modes becomes determinant. These conclusions agree fully with the results of the general theoretical analysis and should be accounted for in the experimental data interpretation.
One of the fundamental problems of the chemical and electrochemical kinetics is the physical mechanism of the elementary act of the electron transfer, especially in condensed media. This question was intensively studied in many theoretical works. Electron transfer is connected with some reorganization of the reactant’s polar surroundings and reorganization of the molecules inner structure. These two processes are char-acterized by the corresponding parameters — the medi-um (solvent) reorganization energy λs and the intramolecular reorganization energy λv.The relative contribution of these processes has been many times discussed. In liquid solutions the kinetics of the electron transfer proper can be distorted by kinetics of the mutual diffusion of the reactants. Therefore, most suitable for the comparison of the experimental results with the theory are the systems in which the donor and the acceptor are connected by a rigid linker ensuring a constant distance between the reactants. In the pre-sent paper, a typical example of such a system will be considered. In many papers dealing with the problem in chemical and biochemical systems, it has been a priori accepted that both the parameters — λs and λv — contribute substantially to the final result. Accordingly, both parameters were found by fitting the experimental data to the theoretical equation derived under the same assumption. The results of such a fitting are not quite unequivocal. Therefore, it is highly desirable to estimate the reorganization energies, both λs and λv by independ-ent methods. As a vivid illustration of the possible problem the data of [7] can be mentioned. In this paper, the fitting for the system porphyrines — C2H4 — quinones in benzene and toluene has been performed with two sets of parameters — the first one λs = 0.18 eV, λV = 0.60 eV and the second λs = 0.60 eV, λV = 0.20 eV. The second set which is physically quite unrealistic gives the results almost so good as the first one. This shows again that one should use parameters obtained from the independent data. To emphasize this conclusion is the aim of the present paper.
DOI: https://doi.org/10.36253/Substantia-1872
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