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: \[k_{\mathrm{ET}}=\frac{\kappa _{\mathrm{ET}}\ k\ T}{h}\ \exp (- \frac{\Delta G^{\ddagger }}{R\ T})\] 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: \[\Delta G^{\ddagger} = \frac{(\lambda\,+\,\Delta _{\text{ET}}G^{\,\unicode{x26ac}})^{2}}{4\ \lambda }\] where ΔET.Go 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 (https://doi.org/10.1351/pac200779030293)