https://doi.org/10.1351/goldbook.M03702
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 \(\kappa _{\rm{ET}}\) the so-called electronic transmission factor (\(\kappa _{\rm{ET}}\sim 1\) for adiabatic and \(<<1\) for diabatic electron transfer). For outer-sphere electron transfer the barrier height can be expressed as: \[\Delta G^{\ddagger} = \frac{(\lambda\,+\,\Delta _{\rm{ET}}G^{\,\unicode{x26ac}})^{2}}{4\ \lambda }\] where \(\Delta _{\rm{ET}}G^{\,\unicode{x26ac}}\) is the standard Gibbs energy change accompanying the electron-transfer reaction and \(\lambda \) 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.