Rate constant Fermi Golden Rule, electron-transfer

The first type of interaction, associated with the overlap of wavefunctions localized at different centers in the initial and final states, determines the electron-transfer rate constant. The other two are crucial for vibronic relaxation of excited electronic states. The rate constant in the first order of the perturbation theory in the unaccounted interaction is described by the statistically averaged Fermi golden-rule formula... 

Royea W. J., Fajardo A. M. and Lewis N. S. (1997), Fermi golden rule approach to evaluating outer-sphere electron-transfer rate constants at semiconductor/liquid interfaces , J. Phys. Chem. B 101, 11152-11159. 

The following generalized rate expression, derived from Fermi s golden rule (see e.g., [9,11]), is useful for discussing the effects of cofactor structure changes on the electron transfer rate constant (kgj) ... 

Recently, the electron-transfer kinetics in the DSSC, shown as a schematic diagram in Fig. 10, have been under intensive investigation. Time-resolved laser spectroscopy measurements are used to study one of the most important primary processes—electron injection from dye photosensitizers into the conduction band of semiconductors [30-47]. The electron-transfer rate from the dye photosensitizer into the semiconductor depends on the configuration of the adsorbed dye photosensitizers on the semiconductor surface and the energy gap between the LUMO level of the dye photosensitizers and the conduction-band level of the semiconductor. For example, the rate constant for electron injection, kini, is given by Fermi s golden rule expression ... 

The Fermi Golden rule describes the first-order rate constant for the electron transfer process, according to equation (11), where the summation is over all the vibrational substates of the initial state i, weighted according to their probability Pi, times the square of the electron transfer matrix element in brackets. The delta function ensures conservation of energy, in that only initial and final states of the same energy contribute to the observed rate. This treatment assumes a weak coupling between D and A, also known as the nonadiabatic limit. 

From a quanmm mechanical viewpoint, both the photoinduced and back-electron transfer processes can be viewed as radiationless transitions between different, weakly interacting electronic states of the A-L-B supermolecule (Fig. 2.6). The rate constant of such processes is given by an appropriate Fermi golden rule expression ... 

This is the most direct experimental manifestation of the existence of an electronic interaction. It can occur spontaneously in mixed-valence complexes, but also in bimetallic systems after a photochemical excitation (photoinduced electron transfer). The general theory considers electron transfer as a special case of radiationless transition, with a perturbative treatment based on Fermi s Golden Rule [42]. In the nonadiabatic case, the rate constant can be written as [43] ... 

In such a case, the rate constant of electron transfer is given by Fermi s golden rule ... 

---