Franck-Condon energy transfer

AEth is the activation energy for the thermal electron transfer. AEop is the Franck-Condon energy for the photochemical electron transfer... 

EfC = C2W20 = Franck-Condon energy, an energy stabilization of the localized exciton in the absence of transfer. 

A similar conclusion follows from the more extensive data on charge transfer to solvent and vice versa. Quantities AG and AG calculated for these systems in Section II,G are not the Franck-Condon energies because they include the unknown interaction energies AGw and AGW which may vary from system to system nevertheless, the main sources of variation are likely to be AGFC and AGFC. ... 

In summary, it appears from this discussion that Franck-Condon energies can now be calculated for a diverse group of inorganic charge-transfer systems and that, although the accuracy of individual values is uncertain, it is possible qualitatively to rationalize the differences between analogous systems. Absolute predictions are much less satisfactory at the present time, and the electrostatic theory based on a dielectric continuum has only very limited applicability to the systems that have so far been studied. When inner-sphere reorganization... 

Forster, Th 211, 278, 282, 285 Forster resonance energy transfer, 282 Forster singlet energy transfer, 378 Franck-Condon factors, 23 Franck-Condon principle, 5 Franck-Condon transition, 5 French, C. S., 555 Friedman, G., 353 Fritzsche, J., 37 Frosch, R. P 252, 267, 269 Fumaronitrile, photodimerization in solid state, 478... 

Developed into a power series in R 1, where R is the intermolecular separation, H exhibits the dipole-dipole, dipole-quadrupole terms in increasing order. When nonvanishing, the dipole-dipole term is the most important, leading to the Forster process. When the dipole transition is forbidden, higher-order transitions come into play (Dexter, 1953). For the Forster process, H is well known, but 0. and 0, are still not known accurately enough to make an a priori calculation with Eq. (4.2). Instead, Forster (1947) makes a simplification based on the relative slowness of the transfer process. Under this condition, energy is transferred between molecules that are thermally equilibriated. The transfer rate then contains the same combination of Franck-Condon factors and vibrational distribution as are involved in the vibrionic transitions for the emission of the donor and the adsorptions of the acceptor. Forster (1947) thus obtains... 

We next consider the expression for k in the classical formalism. According to the Franck-Condon principle, internuclear distances and nuclear velocities do not change during the actual electron transfer. This requirement is incorporated into the classical electron-transfer theories by postulating that the electron transfer occurs at the intersection of two potential energy surfaces, one for the reactants... 

In the previous section, we alluded to the Franck Condon factors (FCF) in controlling electron transfer rates. For this topic, detailed reviews of theory and experiment are provided elsewhere. In sum, it is now well known that the reaction free energy required to transfer charge can be reduced by the reaction free energy, AG°, as summarized in the famous Marcus equation AG = (AG° — where X, the reorganization energy, is related to the degree of... 

Figure 8-1 shows the potential energy barrier for the transfer reaction of redox electrons across the interface of metal electrode. On the side of metal electrode, an allowed electron energy band is occupied by electrons up to the Fermi level and vacant for electrons above the Fermi level. On the side of hydrated redox particles, the reductant particle RED is occupied by electrons in its highest occupied molecular orbital (HOMO) and the oxidant particle OX, is vacant for electrons in its lowest imoccupied molecular orbital (LUMO). As is described in Sec. 2.10, the highest occupied electron level (HOMO) of reductants and the lowest unoccupied electron level (LUMO) of oxidants are formed by the Franck-Condon level sphtting of the same frontier oihital of the redox particles... 

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