Tunneling electron transfer

In tunneling electron transfer, the transfer rate Vt at the energy level e can be given by the product of the state density occupied by electrons in the initial state, the state density vacant for electrons hi the final state of the step, the tunneling probability Wt, and the transmission coefficient K( as expressed in Eqn. 7-30 ... 

Publications [30-32] have played an essential stimulating role in the development of broader research on tunnel electron transfer reactions. However, ref. 30 did not contain any experimental data that could reliably exclude the possibility of a diffusion mechanism for the decay of etr. Nor did... 

In conclusion, let us summarize briefly the main evidence suggesting that the recombination of the trapped electron, etr, with the anion radical, 0, in water-alkaline matrices proceeds via long-range tunnel electron transfer. From the analysis of the EPR lines of etr it follows that, under the conditions... 

N.M. Chernyavskaya and D.S. Chernyavskii, Tunnel Electron Transfer in Photosynthesis, MGU, Moscow, 1977 (in Russian). 

Numerical calculations of the dependences of the efficiency of tunnel electron transfer in triethylamine solutions of P on the concentration of mediator molecules calculated in Ref. [85] using Eq. (37), for various values of parameter A are presented in Fig. 15. From comparison of these results with the experimental data, it is seen that the best fit corresponds to A = 0.5 eV. So one can suppose that the nearest vacant level of CC14 in triethylamine is 0.5 eV distant from the energy of the tunneling electron. 

Regularities of Photoinduced Tunnel Electron Transfer Processes... 

The rate of photoinduced tunnel electron transfer may depend on the mutual orientation of the reagents. This dependence may result from the angular dependence of the electronic wave functions involved in electron transfer. Examples... 

Chapter 3 describes radiationless transitions in the tunneling electron transfers in multi-electron systems. The following are examined within the framework of electron Green s function approach the dependence on distance, the influence of crystalline media, and the effect of intermediate particles on the tunneling transfer. It is demonstrated that the Born-Oppenheimer approximation for the wave function is invalid for longdistance tunneling. 

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). 

The question arises, naturally, about the limiting size of external sphere in the considered model. This size can be estimated, recognizing that a tunnel current should exceed thermionic one. Therefore, value Rd depends on temperature and height of a barrier for tunnel electron transfer. Comparison of tunnel and thermionic currents has shown that at room temperature and a barrier of height 1 eV the tunnel current will prevail over the thermionic one at a spacing between particles no more than 5-6 nm, i.e., at values Rd -Rq < 2-3 nm [90]. 

The increase in catalytic activity with the rise of metal content can be explained by the mutual charging of Cu nanoparticles by tunnel electron transfer between particles of different size. Presumably, negative charged particles formed in this case, among positively charged ones, facilitate initiation of the chain reaction (I) via dissociation of CC14. 

The specific low-frequency dielectric losses are found out in composite films, containing M nanoparticles. It is assumed that these losses are caused by interaction of an electromagnetic field with the dipoles reorientation in the environment connected with tunnel electrons transfer between the nanoparticles or traps of the environment. 

Theoretical and experimental studying of the tunnel electrons transfer in relation to the size distribution of nanoparticles in a film and to mutual charging of particles of various sizes. 

Let us compare the probabilities of tunnel electron transfer from singly and doubly charged metallic nanoparticles (Z — —l and Z = —2) to an adsorbed molecule. In the general case, tunnel electron transfer occurs in three stages (i) thermal activation of an electron in the metal, (ii) tunneling of the electron through the barrier to a molecular level, and (iii) transformation of the adiabatic potential of the molecule. 

When it is a viable pathway, nuclear tunneling tends to dominate at low temperatures, at which the probability of the system reaching the intersection point, S, is low. At the same time, nuclear tunneling rates are independent of temperature. This is because, in tunneling, electron transfer occurs at energies near the zero-point... 

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