Electron transfer process golden rule expression

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 rate constant for the energy transfer process is thus given by a golden rule expression similar to that seen above (Eq. 5) for electron transfer. 

Next consider the rate of such electron transfer process. The golden-rule expression for this rate is... 

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 ... 

Finally, it may be useful to note that the Fermi golden rule and time correlation function expressions often used (see ref. 12, for example) to express the rates of electron transfer have been shown [13], for other classes of dynamical processes, to be equivalent to LZ estimates of these same rates. So, it should not be surprising that our approach, in which we focus on events with no reorganization energy requirement and we use LZ theory to evaluate the intrinsic rates, is closely related to the more common approach used to treat electron transfer in condensed media where the reorganization energy plays a central role in determining the rates but the z factor plays a second central role. 

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