Marcus equation (for electron transfer)

Relation between the rate of outer-sphere electron transfer and the thermodynamics of this process. Essentially, the rate constant within the encounter complex (or the rate constant of intramolecular transfer) is given by the Eyring equation:

$k ET = κ ET k T h exp ( − Δ G ‡ R T )$

where $k$ is the Boltzmann constant, $h$ the Planck constant, $R$ the gas constant and $κ ET$ the so-called electronic transmission factor ( $κ ET ∼ 1$ for adiabatic and $<< 1$ for diabatic electron transfer). For outer-sphere electron transfer the barrier height can be expressed as:

$Δ G ‡ = ( λ + Δ ET G o ) 2 4 λ$

where $Δ ET G o$ is the standard Gibbs energy change accompanying the electron-transfer reaction and $λ$ the total reorganization energy.

Note:

Whereas the classical Marcus equation has been found to be quite adequate in the normal region, it is now generally accepted that in the inverted region a more elaborate formulation, taking into account explicitly the Franck–Condon factor due to quantum mechanical vibration modes, should be employed.

Source:

PAC, 2007, 79, 293 (Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)) on page 368