https://doi.org/10.1351/goldbook.M03702

Relation between the rate of @O04351@ and the thermodynamics of this process. Essentially, the @O04322@ within the @E02087@ (or the @O04322@ of @I03130@ 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 @B00695@, \(h\) the @P04685@, \(R\) the @G02579@ and \(\kappa _{\text{ET}}\) the so-called electronic @T06482@ (\(\kappa _{\text{ET}}\sim 1\) for @A00141@ and \(<<1\) for @D01659@). For @O04351@ the barrier height can be expressed as: \[\Delta G^{\ddagger} = \frac{(\lambda\,+\,\Delta _{\text{ET}}G^{\,\unicode{x26ac}})^{2}}{4\ \lambda }\] where \(\Delta _{\text{ET}}G^{\,\unicode{x26ac}}\) is the standard Gibbs energy change accompanying the electron-transfer reaction and \(\lambda \) the total reorganization energy.

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.

**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.