Marcus equation (for electron transfer)
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.
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.
PAC, 2007, 79, 293. (Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)) on page 368 [Terms] [Paper]