On the Theory of Oxidation-Reduction Reactions Involving Electron Transfer.

On the Theory of Oxidation-Reduction Reactions Involving Electron Transfer.

MAY, 1956 | R. A. Marcus
R. A. Marcus proposed a theory for electron transfer reactions in solution, focusing on a mechanism where there is minimal spatial overlap of electronic orbitals between reacting molecules in the activated complex. This theory explains the rates of oxidation-reduction reactions involving electron transfer, considering the solvent's electrical polarization in the intermediate state $ X^{*} $, which differs from the equilibrium value due to ionic charges. Using an equation for electrostatic free energy, the free energy of all possible intermediate states is calculated, and the most probable state is determined through the calculus of variations. The reaction rate is shown to depend on the formation of the intermediate state, with the rate expressed as the collision number multiplied by $ \exp(-\Delta F^{*}/kT) $. The theory accounts for the entropy of activation in isotopic exchange reactions, suggesting that the observed entropy is due to the low probability of electron tunneling through a solvation barrier. The paper also introduces a model for reactants as spheres surrounded by saturated dielectric regions, and calculates the electrostatic free energy of the activated complex, considering both electronic and atomic/orientation polarizations. The theory provides a quantitative framework for understanding electron transfer reactions, emphasizing the role of solvent polarization and the energy restrictions in the activated complex. The paper concludes with the derivation of rate constants for elementary steps, including the estimation of $ k_{-1} $ and $ k_{3} $, based on the probability of solvent fluctuations and electronic transitions.R. A. Marcus proposed a theory for electron transfer reactions in solution, focusing on a mechanism where there is minimal spatial overlap of electronic orbitals between reacting molecules in the activated complex. This theory explains the rates of oxidation-reduction reactions involving electron transfer, considering the solvent's electrical polarization in the intermediate state $ X^{*} $, which differs from the equilibrium value due to ionic charges. Using an equation for electrostatic free energy, the free energy of all possible intermediate states is calculated, and the most probable state is determined through the calculus of variations. The reaction rate is shown to depend on the formation of the intermediate state, with the rate expressed as the collision number multiplied by $ \exp(-\Delta F^{*}/kT) $. The theory accounts for the entropy of activation in isotopic exchange reactions, suggesting that the observed entropy is due to the low probability of electron tunneling through a solvation barrier. The paper also introduces a model for reactants as spheres surrounded by saturated dielectric regions, and calculates the electrostatic free energy of the activated complex, considering both electronic and atomic/orientation polarizations. The theory provides a quantitative framework for understanding electron transfer reactions, emphasizing the role of solvent polarization and the energy restrictions in the activated complex. The paper concludes with the derivation of rate constants for elementary steps, including the estimation of $ k_{-1} $ and $ k_{3} $, based on the probability of solvent fluctuations and electronic transitions.
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