Franck-Condon factors electron transfer processes

A decrease of the theoretical value of kq in this exothermic region is due to a decrease of the k23-value which is ascribed to small values of Franck-Condon factors in this process. A similar theoretical consideration was given by Levich and Dogonadze, using the polaron model (5). A quantum mechanical treatment of electron transfer was developed by Kestner et al. (6). These results indicated a similar bell-shaped curve for the relation between log kq and AG23. None of the treatments can interpret the experimental results. 

Due to the complicated kinetics for both processes no attempt was made in ref. 83 to treat the data quantitatively. It was estimated, however, that the back electron transfer reaction is slower by about 3 orders of magnitude than that of the forward electron transfer. At the same time, the free energy change for the forward reaction (AG° = - 0.4 eV) is smaller than that for the back electron transfer (AG° = — 1.7 eV). This decrease of the reaction rate at large exothermicity was attributed [83] to the decrease of the Franck-Condon factors with increasing J in the situation when J > Er (see Chap. 3, Sect. 5). 

In Equation 6.88, K0 is the equilibrium constant for the formation of the collision complex, (V) 2 is the electronic coupling, and F is the Franck-Condon factor. In contrast to the radiationless relaxation, the energy transfer process cannot be rationalized only in the limit of the strong and weak coupling limits shown in Figure 6.16. 

Again, //()" is the electronic coupling between the two excited states intercon-verted by the energy transfer process and FCWDen is an appropriate Franck-Condon factor. 

The theory for this intermolecular electron transfer reaction can be approached on a microscopic quantum mechanical level, as suggested above, based on a molecular orbital (filled and virtual) approach for both donor (solute) and acceptor (solvent) molecules. If the two sets of molecular orbitals can be in resonance and can physically overlap for a given cluster geometry, then the electron transfer is relatively efficient. In the cases discussed above, a barrier to electron transfer clearly exists, but the overall reaction in certainly exothermic. The barrier must be coupled to a nuclear motion and, thus, Franck-Condon factors for the electron transfer process must be small. This interaction should be modeled by Marcus inverted region electron transfer theory and is well described in the literature (Closs and Miller 1988 Kang et al. 1990 Kim and Hynes 1990a,b Marcus and Sutin 1985 McLendon 1988 Minaga et al. 1991 Sutin 1986). 

Electron transfer reactions and spectroscopic charge-transfer transitions have been extensively studied, and it has been shown that both processes can be described with a similar theoretical formalism. The activation energy of the thermal process and the transition energy of the optical process are each determined by two factors one due to the difference in electron affinity of the donor and acceptor sites, and the other arising from the fact that the electronically excited state is a nonequilibrium state with respect to atomic motion (P ranck Condon principle). Theories of electron transfer have been concerned with predicting the magnitude of the Franck-Condon barrier but, in the field of thermal electron transfer kinetics, direct comparisons between theory and experimental data have been possible only to a limited extent. One difficulty is that in kinetic studies it is generally difficult to separate the electron transfer process from the complex formation... 

Most LRET processes in biological systems are nonadiabatic. In quantum-mechanical electron-transfer theory, the rate constant for nonadiabatic ET from a donor to acceptor can be expressed as the product of the square of an electronic coupling matrix element (Hp ) and a nuclear Franck-Condon factor (FC) kpy = (27t/h)[Hpj2(FC).The [HpJ is a measure ofthe... 

The description of the radiationless processes which lead to the transfer of excitation energy from one excited state to another in heavy metal complexes has been discussed by several authors (JI, 17, 22). Spin-orbit coupling must be included in the description of the initial and final states for the radiationless process but may also contribute to the coupling terms responsible for this process (II, 17). There are also vibronic coupling terms which arise from breakdown of the Bom-Oppen-heimer approximation which presumably play some role in radiationless energy transfer processes in both heavy- and light-atom molecules (II, 17). Beyond these electronic terms, there are vibrational contributions to the rate constant for a radiationless process, and these contributions are generally expressed as Franck-Condon factors (II). 

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