Reorganization energy correlation with rates

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. 

Some examples of correlations of electron transfer rate constants photo-induced from excited organic anions have been presented. In benzene solvent, intra ion pair electron transfer rates between borate anions and excited cyanine cation have been measured and correlated with the reaction free energy [93]. In a non polar medium such as benzene, the solvent reorganization energy is easily calculated to be nearly zero so that the 0.1 eV obtained from this correlation for dGo was attributed entirely to the inner contribution (dGo )v-... 

As one may expect from the electron transfer reactions catalyzed by peroxidases, the rates of Col and Coll reduction by a substrate series with different substituents correlated well with the oxidizability (i.e., the E value) of the substrates [33], However, in the case of structurally unrelated substrates, this is not the only factor to be taken in to account in determining the oxidation rate, since a certain degree of substrate specificity, controlled by the enzyme and the reorganization energies of electron transfer within the enzyme-substrate transition species complex, appears to be the determining factor [33],... 

Figure 14. Downhill exciton relaxation rates as a function of energy gap between two monomers, predicted by the Forster model (open triangles), the traditional Redheld model (open circles), and the modihed Redheld model (hlled circles). In (a) the electronic couphng, Ju = lOOcm and in b) Ju =20cm . The reorganization energy, if = lOOcm and the spectral density is represented by a Gaussian correlation function with Zg = 100 fs [163],...

Figure 6. Phase diagram of the RC compiled from QMC simulation data, correlating K 2 with E2 (thick lines). The proper reorganization energies are indicated on the phase diagram for those parameter sets that yield dynamics consistent with experiments (open circles), Nonadiabatic predictions for the yielding a room-temperature rate of (3ps) are also shown for comparison (dashed curve).

A different approach in terms of donicity has been used to explain some ligand effects in redox reactions. A correlation has been found between the energy of the first d-d bands of a number of Cr complexes and their rates of electron exchange with Cr +. The tetragonal distortion of the Cr complex was evaluated from an analysis of the electronic spectrum and is manifested as a lower reorganization energy of the precursor complex. 

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