Tunnel electron transfer processes

Regularities of Photoinduced Tunnel Electron Transfer Processes... 

Fig. 2 (a) Schematic representation of the energy levels diagrams for a DBA system and a MBM junction in which the electron transfer process is dominated (b) by superexchange or non-resonant tunnelling, (c) by resonant tunnelling or (d) by hopping ... 

To summarize, in this article we have discussed some aspects of a semiclassical electron-transfer model (13) in which quantum-mechanical effects associated with the inner-sphere are allowed for through a nuclear tunneling factor, and electronic factors are incorporated through an electronic transmission coefficient or adiabaticity factor. We focussed on the various time scales that characterize the electron transfer process and we presented one example to indicate how considerations of the time scales can be used in understanding nonequilibrium phenomena. 

There is currently much interest in electron transfer processes in metal complexes and biological material (1-16, 35). Experimental data for electron transfer rates over long distances in proteins are scarce, however, and the semi-metheme-rythrin disproportionation system appears to be a rare authentic example of slow electron transfer over distances of about 2.8 nm. Iron site and conformational changes may also attend this process and the tunneling distances from iron-coordinated histidine edges to similar positions in the adjacent irons may be reduced from the 3.0 nm value. The first-order rate constant is some 5-8 orders of magnitude smaller than those for electron transfer involving some heme proteins for which reaction distances of 1.5-2.0 nm appear established (35). 

These predictions can provide an experimental test of the mechanism for quantum-mechanical tunneling effects on electron transfer processes in solution and in glasses over a wide temperature range. 

All through this chapter, we have avoided the terminology electron transfer by tunneling which is rather confusing though it often appears in the literature [14]. The nature of the different tunneling effects involved in electron transfer processes is discussed in the previously cited reviews [4, 22, 23]. 

Our data show that in all hybrids, the thermal electron transfer process (Eq (2)) is remarkably insensitive to temperature, suggesting that ET proceeds by quantum mechanical tunnelling to quite high temperatures. Figure 8 shows the temperature dependence of k, the rate constant for the thermal Fe (CN )P-> (MP) electron transfer for M = Mg and Zn. For [(ZnP), Fe (CN )P], kb decreases by less than a factor of three from 300 K to 100 K ... 

By the same token, electron transfer involves transfer of a particle between electronically coupled chemical sites and can be described as a tunneling process. In that sense, every electron transfer process involves electron tunneling with a tunneling frequency given, in the classical limit, by equation (31). 

Secondly, the model of thermal diffusion does not allow one to explain the independence of the reaction rate on temperature observed for many low-temperature electron transfer processes. Indeed, the thermal diffusion of molecules in liquids and solids is known to be an activated process and its rate must be dependent on temperature. True, at low temperatures when activated processes are very slow, diffusion itself can be assumed to become a non-activated process going on via a mechanism of nuclear tunneling, i.e. by tunneling transitions of atoms over very short (less than 1 A) distances. A sequence of such transitions can, in principle, result in a diffusional approach of reagents in the matrix. Direct tunneling of the electron, whose mass is less than that of an atom by a factor of 10 or 104, can, however, be expected to proceed much faster. 

The results of experimental research have also stimulated the appearance of theoretical papers devoted to the analysis of an elementary act of electron tunneling reactions in terms of the theory of non-radiative electron transitions in condensed media and to the derivation of the kinetic equations of long-range electron transfer processes [19-30],... 

R [15]. For particles Ag with R = 5nm this correction lifts Fermi level to 0.22 eV in comparison with level for bulk metal [15]. The surface-determined size effect for Fermi energy of metal nanoparticles results in mutual charging of nanoparticles of different sizes by the tunnel electron transfer between nanoparticles. Such charging processes, as it will be shown below (Subsection 4.4), greatly influence catalytic reactions induced by assembly of metal nanoparticles with size distribution immobilized in solid dielectric matrix. 

Unusually small value of pc in this system speaks that the true concentration of Ag in the areas of a film, where Ag nanocrystals are formed, strongly differs from the average concentration determined in experiment. Systems with concentration of M/SC nanoparticles close to pc are of special interest. In such systems the essential increase in conductivity as compared to that of pure polymer results from processes of tunnel electron transfer between nanoparticles. Conductivity of composite system with regard to electron tunneling between M/SC nanoparticles has been considered in work [88] on the basis of the following model. In the model, the spherical particle of radius Rq is surrounded with the sphere of radius Rd describing the delocalization for conductivity electrons of the particle and partial transition of electronic density in an environment (Figure 10.6a). 

Figure 2.9 Schematics illustrating an adsorbate-electrode interface in aqueous solution, plus the corresponding thermal activation and electron tunneling steps associated with a heterogeneous electron transfer process...

Electron-phonon interaction in a semiconductor is the main factor for relaxation of a transferred electron. There are two different relaxation processes that decrease the efficiency of light conversion in a solar system (1) relaxation of an electron from a semiconductor conduction band to a valence band and (2) a backward electron transfer reaction. The forward and backward electron transfer processes have been already included in the tunneling interaction, HSm-qd, described by Eq. (108). However, the effect of SM e-ph interaction is important for the correct description of electron transfer in the SM-QD solar cell system. In the previous section, we have gradually considered different types of interactions in the quantum dot and obtained the exact expression for the photocurrent (128) where the exact nonequilibrium QD Green s functions determined from Eq. (127) have been used. However, in... 

The constrained nature of the copper center in BCB domains reduces its reorganization energy, which is considered an important feature for their function in long-range electron transfer processes. They are capable of tunneling electrons, usually over 10- to 12-A distances, intramolecu-larly within the same protein (in the case of multicopper oxidases and nitrite reductases) or intermolecularly between a donor and an acceptor protein (in the case of cupredoxins) in a thermodynamically favorable environment. 

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