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Cited by 6,081Photochemistry and Electron Transfer StudiesAdvanced Physical and Chemical Molecular InteractionsChemical Reaction Mechanisms

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

Marcus, R. A.·1956·The Journal of Chemical Physics
DOI 10.1063/1.1742723
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Abstract

A mechanism for electron transfer reactions is described, in which there is very little spatial overlap of the electronic orbitals of the two reacting molecules in the activated complex. Assuming such a mechanism, a quantitative theory of the rates of oxidation-reduction reactions involving electron transfer in solution is presented. The assumption of ``slight-overlap'' is shown to lead to a reaction path which involves an intermediate state X* in which the electrical polarization of the solvent does not have the usual value appropriate for the given ionic charges (i.e., it does not have an equilibrium value). Using an equation developed elsewhere for the electrostatic free energy of nonequilibrium states, the free energy of all possible intermediate states is calculated. The characteristics of the most probable state are then determined with the aid of the calculus of variations by minimizing its free energy subject to certain restraints. A simple expression for the electrostatic contribution to the free energy of formation of the intermediate state from the reactants, ΔF*, is thereby obtained in terms of known quantities, such as ionic radii, charges, and the standard free energy of reaction. This intermediate state X* can either disappear to reform the reactants, or by an electronic jump mechanism to form a state X in which the ions are characteristic of the products. When the latter process is more probable than the former, the over-all reaction rate is shown to be simply the rate of formation of the intermediate state, namely the collision number in solution multiplied by exp(—ΔF*/kT). Evidence in favor of this is cited. In a detailed quantitative comparison, given elsewhere, with the kinetic data, no arbitrary parameters are needed to obtain reasonable agreement of calculated and experimental results.

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Crossref · 10.1063/1.1742723

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15 of 15 references verified0 citation errors · 0 not checkable

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  • The dynamics described by the past quantum mechanical models of photosynthesis, respiration and vision are often exponential and follow from the application of Fermi's Golden Rule.

    “The dynamics described by these models are often 'exponential' and follow from the application of Fermi's Golden Rule [1,2].”

    From The future of quantum biology (2018) · cites this paper as [2]

  • While Marcus' theory of electron transfer neglects nuclear tunnelling and can therefore underestimate the electron transfer rate at low temperatures, semi-classical Marcus theory can be extended to a fully quantum-mechanical treatment based on the theory of nonradiative transitions that includes nuclear tunnelling, and which gives a good prediction for the increasing rate of charge separation with

    “While Marcus' theory of electron transfer neglects nuclear tunnelling [2], and can therefore underestimate the electron transfer rate at low temperatures, semi-classical Marcus theory can be extended to a fully quantum-mechanical treatment based on the theory of nonradiative transitions that includes nuclear tunnelling, and which gives a good prediction for the increasing rate of charge separation”

    From The future of quantum biology (2018) · cites this paper as [2]

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Authors
Marcus, R. A.
Affiliations
Department of Chemistry, Polytechnic Institute of Brooklyn, Brooklyn, New York
Corresponding author
Marcus, R. A.
ORCID
Marcus, R. A.
Venue
The Journal of Chemical Physics
Publisher
AIP Publishing
Published
1956-05-01
Volume
24
Issue
5
Pages
966-978
ISSN
  • 0021-9606 (ISSN-L)
  • 1089-7690
DOI
10.1063/1.1742723
OpenAlex
W2001270915
Cited by
6,081
References
15
Citations by year
2026: 218 · 2025: 256 · 2024: 231 · 2023: 222 · 2022: 200 · 2021: 220 · 2020: 247 · 2019: 231 · 2018: 215 · 2017: 221 · 2016: 219 · 2015: 206 · 2014: 240 · 2013: 157 · 2012: 202
FWCI
4.78
Type
journal article
Language
en
Open access
closed
Locations
  • The Journal of Chemical Physics (publishedVersion)
  • CaltechAUTHORS (California Institute of Technology) (submittedVersion)
Topics
  • Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Photochemistry and Electron Transfer Studies
  • Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
  • Physical Sciences › Chemistry › Organic Chemistry › Chemical Reaction Mechanisms
Keywords
electron transfer, redox reactions, reaction mechanism, transition state, orbital overlap, solvent polarization, electrostatic free energy, non-equilibrium states, reaction rate theory, intermediate state, collision number, ionic radius

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