Radiationless electron transfer, quantum

The first quantum mechanical treatment for the radiationless electron transfer was developed by Gurney [68] for hydrogen evolution on mercury. In his model, Gurney assumed that the intermediate H " is not... 

The basic idea of the theory of electron-transfer concerning the dynamic role of the solvent, first suggested by LIBBI /150/, has been developed by MARCUS /40a/ for outer-sphere redox processes on the basis of a classical continuum model for solvent polarization. A quantum-mechanical treatment of the same model was done by LEVICH and DO-GONADZE /40b,143/, making use of the theory of non-adiabatic radiationless electron transfer in polar crystals. 

Knowledge of photoiaduced electroa-transfer dyaamics is important to technological appUcations. The quantum efficiency, ( ), ie, the number of chemical events per number of photons absorbed of the desired electron-transfer photoreaction, reflects the competition between rate of the electron-transfer process, eg, from Z7, and the radiative and radiationless decay of the excited state, reflected ia the lifetime, T, of ZA ia abseace ofM. Thus,... 

Instead of the quantity given by Eq. (15), the quantity given by Eq. (10) was treated as the activation energy of the process in the earlier papers on the quantum mechanical theory of electron transfer reactions. This difference between the results of the quantum mechanical theory of radiationless transitions and those obtained by the methods of nonequilibrium thermodynamics has also been noted in Ref. 9. The results of the quantum mechanical theory were obtained in the harmonic oscillator model, and Eqs. (9) and (10) are valid only if the vibrations of the oscillators are classical and their frequencies are unchanged in the course of the electron transition (i.e., (o k = w[). It might seem that, in this case, the energy of the transition and the free energy of the transition are equal to each other. However, we have to remember that for the solvent, the oscillators are the effective ones and the parameters of the system Hamiltonian related to the dielectric properties of the medium depend on the temperature. Therefore, the problem of the relationship between the results obtained by the two methods mentioned above deserves to be discussed. 

In the quantum mechanical formulation of electron transfer (Atkins, 1984 Closs et al, 1986) as a radiationless transition, the rate of ET is described as the product of the electronic coupling term J2 and the Frank-Condon factor FC, which is weighted with the Boltzmann population of the vibrational energy levels. But Marcus and Sutin (1985) have pointed out that, in the high-temperature limit, this treatment yields the semiclassical expression (9). 

This case is shown in Fig. 10.6c and d where through absorption of light a photohole in the vb and a photoelectron in the cb are formed. The probability that interfacial electron transfer takes place, i.e. that a thermodynamically suitable electron donor is oxidized by the photohole of the vb depends (i) on the rate constant of the interfacial electron transfer, kET, (ii) on the concentration of the adsorbed electron donor, [Rads]. and (iii) on the rate constants of recombination of the electron-hole pair via radiative and radiationless transitions,Ykj. At steady-state of the electronically excited state, the quantum yield, Ox, ofinterfacial electron-transfer can be expressed in terms of rate constants ... 

Electron transfer reactions have also been treated from the quantum mechanical point of view in formal analogy to radiationless transitions, considering the weakly interacting states of a supermolecule AB the probability (rate constant) of the electron transfer is given by a golden rule expression of the type17... 

Electron transfer from the excited states of Fe(II) to the H30 f cation in aqueous solutions of H2S04 which results in the formation of Fe(III) and of H atoms has been studied by Korolev and Bazhin [36, 37]. The quantum yield of the formation of Fe(III) in 5.5 M H2S04 at 77 K has been found to be only two times smaller than at room temperature. Photo-oxidation of Fe(II) is also observed at 4.2 K. The actual very weak dependence of the efficiency of Fe(II) photo-oxidation on temperature points to the tunneling mechanism of this process [36, 37]. Bazhin and Korolev [38], have made a detailed theoretical analysis in terms of the theory of radiationless transitions of the mechanism of electron transfer from the excited ions Fe(II) to H30 1 in solutions. In this work a simple way is suggested for an a priori estimation of the maximum possible distance, RmSiX, of tunneling between a donor and an acceptor in solid matrices. This method is based on taking into account the dependence... 

The quantum mechanical treatment of non-adiabatic electron transfers are normally considered in terms of the formalism developed for multiphonon radiationless transitions. This formalism starts from Fermi s golden rule for the probability of a transition from a vibronic state Ay of the reactant (electronic state A with vibrational level v) to a set of vibronic levels B of the product... 

As far as kinetics is concerned, electron transfer processes can be described in terms of quantum mechanical [7-9] or classical [10-14] models. From a quantum mechanical viewpoint, both photoinduced electron transfer (Eq. 2) and charge recombination (Eq. 4) can be viewed as examples of radiationless transitions between... 

In the quantum-mechanical theories the intersection of the potential energy surfaces is deemphasized and the electron transfer is treated as a radiationless transition between the reactant and product state. Time dependent perturbation theory is used and the restrictions on the nuclear configurations for electron transfer are measured by the square of the overlap of the vibrational wave functions of the reactants and products, i.e. by the Franck-Condon factors for the transition. Classical and quantum mechanical description converge at higher temperature96. At lower temperature the latter theory predicts higher rates than the former as nuclear tunneling is taken into account. 

The participation of higher excited singlet states (Sn, n > 1) of molecules in photophysical (Sn SQ fluorescence (FL)) or photochemical (photoinduced electron transfer (PET), isomerization, etc.) processes, which compete with radiationless deactivation, manifests itself in the dependence of the quantum yield (q>) and FL spectra on the wavelength of the exciting light (the violation of the Vavilov law). Such processes were first shown for the FL of azulene solutions due to the transition from the second excited level to the ground state S2 -> S0. ... 

The quantum yield of DNA repair by photolyase (the number of cyclobutane pyrimidine dimers split by the enzyme for each photon absorbed by the enzyme in the enzyme-substrate complex) ranges from 0.7 to 1.0. It should be noted, however, that in photolyase FADH is the catalytic cofactor and MTHF (or 8-HDF) is the photoantenna. As a consequence, the quantum yield of photolyase is the product of three reactions (Payne and Sancar, 1990) energy transfer from MTHF (or 8-HDF) to FADH , electron transfer from (FADH ) to the PyrOPyr, and finally splitting of PyrOPyr °. The latter two reactions are very efficient and occur with nearly 100% efficiency, at least in the case of ToT. Therefore, the critical determinant of overall quantum yield of repair is the quantum yield of energy transfer from the photoantenna to the catalytic cofactor (Kim et aL, 1991, 1992). The efficiency of energy transfer by Forster radiationless... 

If the equilibrium of a semiconductor is disturbed by excitation of an electron from the valence to the conduction band, the system tends to return to its equilibrium state. Various recombination processes are illustrated in Fig. 1.16. For example, the electron may directly recombine with a hole. The excess energy may be transmitted by emission of a photon (radiative process) or the recombination may occur in a radiationless fashion. TTie energy may also be transferred to another free electron or hole (Auger process). Radiative processes associated with direct electron-hole recombination occur mainly in semiconductors with a direct bandgap, because the momentum is conserved (see also Section 1.2). In this case, the corresponding emission occurs at a high quantum yield. The recombination rate is given by... 

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