Condon approximation, electron-transfer

EPR studies on electron transfer systems where neighboring centers are coupled by spin-spin interactions can yield useful data for analyzing the electron transfer kinetics. In the framework of the Condon approximation, the electron transfer rate constant predicted by electron transfer theories can be expressed as the product of an electronic factor Tab by a nuclear factor that depends explicitly on temperature (258). On the one hand, since iron-sulfur clusters are spatially extended redox centers, the electronic factor strongly depends on how the various sites of the cluster are affected by the variation in the electronic structure between the oxidized and reduced forms. Theoret-... 

The rate constant of an electrode reaction does not measure the rate of electron transfer itself, as this is an adiabatic process, following the Franck-Condon principle, and occurs in approximately 10 16s. What it does measure is the time needed for the species, once they have reached the interfacial region, to arrange themselves and their ionic atmospheres into position for electron transfer to be able to occur. 

Figure 12. Plot of the logarithm of the Franck-Condon factors for the electron transfer reaction calculated using the classical expression, Eq. 23 two-mode expression, Eq. 62 three-mode expression, Eq. 64 and the approximate three-mode expression, Eq. 65 vs driving force. The parameters used (As, Ac,/ Vc,Ah,/ Vh in cm" ) for the calculations are classical (3200) two-mode, (1200, 2000, 600) three-mode (600, 600, 200, 2000, 600) and the temperature is 80 K. The sohd line (inverted parabola), dotted line, oscillating solid line and the dashed line are for the classical expression, Eq. 23, the two-mode expression, Eq. 62, the full three-mode expression, Eq. 64, and the approximate three-mode expression, Eq. 65, respectively.

It should be emphasized here that the electron transfer in the activated state is a very fast process which occurs within a time interval of about 10" s. The relaxation times for the solvent and the reacting nuclei are much longer, typically 10"" to 10" - s for vibrational motion and 10" to 10"" s for rotational motion. Accordingly, it is a reasonable approximation that the positions of the nuclei are unchanged in the course of the electron transfer. This condition is called the Franck-Condon principle. It is well known from studies of absorption and emission of light by molecules. 

Relaxation of the commonly applied Condon approximation in schemes of separating electronic and nuclear dynamics. This is important for long-range interfacial electron transfer. 

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