## Wikipedia - Teoria di Marcus (it) Marcus equation (for electron transfer)

https://doi.org/10.1351/goldbook.M03702
Relation between the rate of @[email protected] and the thermodynamics of this process. Essentially, the @[email protected] within the @[email protected] (or the @[email protected] of @[email protected] 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 @[email protected], $$h$$ the @[email protected], $$R$$ the @[email protected] and $$\kappa _{\text{ET}}$$ the so-called electronic @[email protected] ($$\kappa _{\text{ET}}\sim 1$$ for @[email protected] and $$<<1$$ for @[email protected]). For @[email protected] 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]