Cage and Entropy Effects in the Dynamics of Dissociative Electron Transfer

Abstract

Dissociative electron transfers in condensed phases occur in two steps. The fragments are first formed within a solvent cage from which they further diffuse. The formation of caged, rather than free-moving, fragments is taken into account in an improved version of the dissociative electron transfer theory where entropic aspects are emphasized. A more detailed treatment than previously available of the fragmentation and solvent reorganization factors is given in terms of both energies and free energies. The reason that the bond dissociation energy, rather than the bond dissociation free energy, represents the contribution of fragmentation to the intrinsic barrier ensues. The resulting equations that relate the activation free enthalpy and entropy, as well as the symmetry factor, to the standard free enthalpy and entropy of the reaction are given for electrochemical, bimolecular, and intramolecular reactions. Solvation radii change upon electron transfer triggered bond cleavage. An iterative procedure is proposed for adapting the estimation of the solvent reorganization factor to the ensuing coupling of the fragmentation and solvent reorganization coordinates. Experimental examples illustrating applications of the theory are discussed.

MD simulations of heterogeneous reduction of the tert-butyl bromide molecule

“…The fundamental experimental data about kinetics of such reaction were provided by the group of Savéant in a series of papers [1][2][3][4][5][6], who also proposed the simple theoretical model for description of such processes. In this model [3] the Morse potential was used to describe the C-X bond rupture and combined with the Marcus-Hush theory [7][8][9][10].…”

“…Unfortunately, the lack of experimental data due to the extremely high overpotentials necessary for the latter compound did not allow for a satisfactory comparison and verification of the model. This is not the case for the electrochemical reduction of the tert-butyl bromide molecule, which was analyzed in detail by Savéant's group in the past [1][2][3]5,6].…”

Passage from Stepwise to Concerted Dissociative Electron Transfer through Modulation of Electronic States Coupling

“…Assuming a concerted dissociative electron-transfer mechanism, the transfer coefficient is given by the dissociative electrontransfer model [Eq. (3)]: [6] …”

“…Experimental data were then analyzed in the framework of the concerted dissociative electron-transfer model, [6] for which a quadratic activation/driving force relationship applies [Eq. (6)]…”

“…Thus, in borderline situations, the system may pass from one mechanism to the other on variation of the electrode potential or the standard potential of the homogeneous electron donor, [3] and this possibly results in systems that undergo concerted electrochemical and stepwise photoinduced electron-transfer reactions. [4] The classical Marcus-Hush model of outer-sphere electron transfer [5] is applicable to the electron-transfer step of the stepwise reaction, whereas Morse-curve models can be used for the concerted pathway [6] and for cleavage of the intermediate radical anion in the stepwise case. [7] All three reactions are characterized by a quadratic activation/driving force relationship.…”