What is reorganization energy?

It is the energy that would be needed to distort the nuclei of the reactants and the surrounding solvent from their equilibrium reactant geometry to the equilibrium product geometry without transferring the electron; it sets the height of the electron-transfer barrier.

How does Marcus theory relate to the Butler–Volmer equation?

Both describe electron-transfer rates, but Marcus theory derives the potential dependence from a microscopic free-energy model and predicts a non-constant transfer coefficient, whereas Butler–Volmer assumes a constant coefficient and is recovered as a limiting case near the equilibrium potential.

Marcus Electron Transfer Theory

Marcus theory provides a microscopic account of electron-transfer rates, expressing the activation barrier in terms of the reaction free energy and a reorganization energy that captures the nuclear rearrangement accompanying charge transfer.

Definition

A theory of electron-transfer kinetics in which the activation free energy is a quadratic function of the reaction free energy and the reorganization energy required to distort nuclei and solvent into the transition-state configuration.

Scope

This topic covers the Marcus model of outer-sphere electron transfer: the parabolic free-energy surfaces of reactant and product, the reorganization energy and its inner-sphere and solvent (outer-sphere) contributions, the quadratic dependence of activation energy on driving force, and the prediction of the inverted region. It includes the connection to electrode reactions and the distinction from the empirical Butler–Volmer picture.

Core questions

What nuclear and solvent rearrangements must occur for an electron to transfer between species?
How does the rate of electron transfer depend on the thermodynamic driving force?
Why can increasing the driving force eventually slow electron transfer in the inverted region?
How does reorganization energy decompose into inner-sphere and outer-sphere contributions?

Key theories

Marcus free-energy relation: Representing reactant and product as intersecting parabolas of equal curvature, the activation energy becomes (λ + ΔG°)²/4λ, where λ is the reorganization energy, giving a quadratic dependence of the barrier on driving force.
Inverted region: The quadratic form predicts that beyond an optimal driving force equal to the reorganization energy, the rate decreases as the reaction becomes more exergonic, a counterintuitive result later confirmed experimentally.

Clinical relevance

Marcus theory explains electron-transfer rates in photosynthesis and respiration, the design of molecular electronics and dye-sensitized solar cells, the kinetics of redox catalysis, and the curvature seen in Tafel plots of fast electrode reactions.

History

Rudolph Marcus formulated the theory in a series of papers beginning in 1956, with parallel contributions by Hush; the predicted inverted region was experimentally verified by Miller, Calcaterra, and Closs in 1984, and Marcus received the 1992 Nobel Prize in Chemistry.

Key figures

Rudolph A. Marcus
Noel Hush
Joshua Jortner

Seminal works

marcus1956
marcus1993
bard2001

Frequently asked questions

What is reorganization energy?: It is the energy that would be needed to distort the nuclei of the reactants and the surrounding solvent from their equilibrium reactant geometry to the equilibrium product geometry without transferring the electron; it sets the height of the electron-transfer barrier.
How does Marcus theory relate to the Butler–Volmer equation?: Both describe electron-transfer rates, but Marcus theory derives the potential dependence from a microscopic free-energy model and predicts a non-constant transfer coefficient, whereas Butler–Volmer assumes a constant coefficient and is recovered as a limiting case near the equilibrium potential.