Donor Franck-Condon principle

The basic theory of the kinetics of charge-transfer reactions is that the electron transfer is most probable when the energy levels of the initial and final states of the system coincide [5] following the Franck-Condon principle. Thus, the efficiency of the redox reaction processes is primarily controlled by the energy overlap between the quantum states in the energy bands of the semiconductor and the donor and acceptor levels of the reactants in the electrolyte (Fig. 1). In the ideal case, the anodic current density is given by the... 

In line with the Franck-Condon principle, the electron transfer occurs at the seam of the crossing between diabatic (localized) states of donor and acceptor. The electronic coupHng is the off-diagonal matrix element of the Hamiltonian defined at the crossing point. 

Franck-Condon principle. That means in other words that the time for electron transfer from a molecule to an electrode is short compared with the time of atomic movements in vibrations or rotations. This has the consequence that for electron transfer reactions the energy terms E of the electrons in the donors or acceptors are different from the thermodynamic energy levels °E which we have discussed in the preceding section. 

Electron transfer is a fast reaction ( 10-12s) and obeys the Franck-Condon Principle of energy conservation. To describe the transfer of electron between an electrolyte in solution and a semiconductor electrode, the energy levels of both the systems at electrode-electrolyte interface must be described in terms of a common energy scale. The absolute scale of redox potential is defined with reference to free electron in vacuum where E=0. The energy levels of an electron donor and an electron acceptor are directly related to the gas phase electronic work function of the donor and to the electron affinity of the acceptor respectively. In solution, the energetics of donor-acceptor property can be described as in Figure 9.6. 

According to the Franck-Condon principle, the photoexcitation triggers a vertical transition to the excited state, which is followed by a rapid nuclear equilibration. Without donor excitation, the electron transfer process would be highly endothermic. However, after exciting the donor, electron transfer occurs at the crossing of the equilibrated excited state surface and the product state. 

Employing the Franck-Condon principle, i.e. preservation of the nuclear configuration of reactant and product at the point of transition, we can assume a horizontal transition between the donor (D) and acceptor (A). In terms of the... 

On the basis of the Franck-Condon principle, photoelectron transfer between a donor and acceptor molecule proceeds as follows (Fig. 10). Initially, the donor and acceptor are dispersed randomly in a solution. On light absorption, the donor (or acceptor) undergoes a rapid transition to form a Franck-Condon state, which rapidly undergoes nuclear relaxation to an equilibrated state. A further nuclear reorganization takes place before electron transfer. After electron transfer, there is nuclear relaxation to the final, equilibrated product state. 

According to the Franck-Condon principle, electron transition from donor to acceptor takes place while the atomic positions can be regarded as fixed on the reaction coordinate Q. This means that it takes place at the crossing point between the diabatic potentials KiQ) and Fp(0 for the reactant and product states, respectively, because energy conservation is satisfied only at that point under this principle. This situation can be formulated by... 

As shown in Scheme 2, an electron is transferred from an electron donor (D) to an acceptor (A) instantaneously according to the Franck-Condon principle when the reactant pair (D-A) is activated to reach the nuclear configurations which include the solvation, where the energy before and after the electron transfer is the same. Figure 2 shows the dependence of logfcgt on AG°et based on Eq. 1. The k i value increases with decreasing (a) AG°et or/and (b) X (Figure 2). Thus, in order to accelerate the rate of electron transfer, the AG°et or/and X values should be decreased. 

The time-dependent perturbation theory of the rates of radiative ET is based on the Born-Oppenheimer approximation [59] and the Franck Condon principle (i.e. on the separation of electronic and nuclear motions). The theory predicts that the ET rate constant, k i, is given by a golden rule -type equation, i.e., it is proportional to the product of the square of the donor-acceptor electronic coupling (V) and a Franck Condon weighted density of states FC) ... 

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... 

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