Marcus theory

Marcus theory posits that the rate of an outer-sphere electron transfer reaction is governed by the free energy change (ΔG°) and the reorganization energy (λ), which represents the energy required to reorganize the nuclear coordinates of the reactants and their surrounding solvent to the product state without electron transfer. The rate constant is given by k = (2π/ħ) |V|² (4πλk_BT)^-1/2 exp[-(ΔG° + λ)²/(4λk_BT)], where V is the electronic coupling matrix element. This equation predicts a parabolic dependence of the rate on ΔG°, leading to three regimes: normal, activationless, and inverted.

Marcus theory is applied to a wide range of electron transfer processes, including photosynthesis, respiration, and enzymatic reactions. In photosynthesis, it explains the efficient charge separation in reaction centers. In electrochemistry, it underpins the understanding of electrode kinetics. The theory also guides the design of molecular wires, solar cells, and organic semiconductors. Its predictions have been verified experimentally in numerous systems, from simple metal complexes to proteins.

Extensions of Marcus theory include the semiclassical treatment of nuclear tunneling, the inclusion of quantum mechanical effects for high-frequency vibrational modes, and the development of the Marcus–Levich–Jortner theory. These refinements account for deviations in the inverted region and for temperature-dependent rates. The theory has also been extended to proton-coupled electron transfer and to electron transfer in proteins, where the reorganization energy is influenced by the protein matrix.

Marcus theory was initially met with skepticism; the inverted region was not experimentally confirmed until 1984 by Miller, Calcaterra, and Closs using intramolecular electron transfer in rigid donor-bridge-acceptor molecules. Marcus also contributed to the theory of unimolecular reactions (RRKM theory) and to the development of the mean spherical approximation in statistical mechanics. The theory's name is sometimes extended to 'Marcus–Hush' theory in electrochemistry, acknowledging Noel Hush's parallel work.

Reorganization energy

Energy needed to reorganize nuclear coordinates and solvent without electron transfer.

Inverted region

Regime where increasing thermodynamic driving force decreases the rate.

Electronic coupling

Matrix element V that quantifies the interaction between donor and acceptor orbitals.