Marcus equation (for electron transfer)

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.
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 [Terms] [Paper]