Electron transfer models for

The POs identified above can also be used for the analysis of other observables of our simple electron-transfer model. For example, it has been shown that a calculation employing two POs qualitatively reproduce the short-time evolution of the probability distribution P(x, t) = (f) /2) x) (x ( i2 l I (O)... 

The Arrhenius plot shows an apparent overall activation energy of about 8 kcal/mol, well below the initiation by a hydrogen abstraction [(Eq. (7)] and more consistent with an electron transfer model for initiation reaction [(Eq. (8)]. 

Tanaka, S. and Marcus, R.A. (1997) Electron transfer model for electric field effect on quantum yield of charge separation in bacterial photosynthetisc reaction centers, J. Phys. Chem. 101, 5031-5045. 

As mentioned above, the formation of excited states in chemical reactions may be understood in the context of an electron transfer model for chemiluminescence, first proposed by Marcus [2]. According to this model the formation of excited states is competitive with the formation of the ground state, even though the latter is strongly favored thermodynamically. Thus, understanding the factors that determine the electron transfer rate is of considerable importance. The theory of electron transfer reactions in solution has been summarized and reviewed in many reviews (e.g., [30-36]). Therefore, in this chapter the relevant ideas and equations are only briefly summarized, to serve as a basis for description of the ECL experiments. 

The ECL mechanism for both Ru(bpy)3" and Ru(dph) + complexes seems to be parallel, with one important difference. In the case of Ru(bpy)3 , the efficiency increases as temperature decreases. The opposite trend is observed for Ru(dph) " . The effects are rather small, but certainly greater than the experimental errors. The trivial explanation that the observed difference is caused by medium effects can be simply excluded. Our unpublished results indicate that the ECL behavior of Ru(bpy)3+ in both solvents (ACN and BN) is nearly the same. The observed difference can be understood by kinetic analysis in terms of the electron transfer model for ECL processes. According to this model, the yield of the emissive excited state is given by the ratio of the rate constants for the electron transfer processes producing the excited-state and the ground-state products, respectively. Unfortunately, the values of the appropriate parameters, which are necessary for the calculation of these rates, are not available. However, some qualitative conclusions are possible they are summarized below. 

Computations of ketene-alkene [2 - - 2] cycloaddition using an electron transfer model for formation of an initial radical cation/radical anion pair correctly predict " the maior product regio- and stereoselectivity (Scheme 4.28). " "... 

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. 

Molecular modeling treatments of electron transfer kinetics for reactions involving bond breaking were developed much earlier than the continuum theories originated by Weiss in 1951. Gurney in 193l published a landmark paper (the foundation of quantum electrochemistry) on a molecular and quantum mechanical model of proton and electron transfer... 

The calculation of the transmission coefficient for adiabatic electron transfer modeled by the classical Hamiltonian Hajis based on a similar procedure developed for simulations of general chemical reactions in solution. The basic idea is to start the dynamic trajectory from an equilibrium ensemble constrained to the transition state. By following each trajectory until its fate is determined (reactive or nonreactive), it is possible to determine k. A large number of trajectories are needed to sample the ensemble and to provide an accurate value of k. More details... 

Figure 22 shows the same quantities for the intramolecular electron-transfer Model IVb. Similar to what occurs in the pyrazine model, the classical level density obtained with y = 1 overestimates the total and state-specific level density while for y = 0 the classical level densities are too small. Employing a ZPE correction of y = 0.8 results in a very good agreement with the total quantum mechanical level density, while the criterion to reproduce the state-specific level density results in a ZPE correction of y = 0.6. 

Finally, we discuss applications of the ZPE-corrected mapping formalism to nonadiabatic dynamics induced by avoided crossings of potential energy surfaces. Figure 27 shows the diabatic and adiabatic electronic population for Model IVb, describing ultrafast intramolecular electron transfer. As for the models discussed above, it is seen that the MFT result (y = 0) underestimates the relaxation of the electronic population while the full mapping result (y = 1) predicts a too-small population at longer times. In contrast to the models... 

Figure 29. Comparison of quantum path-integral results (thick tines) and ZPE-corrected mapping results (thin lines) for the diabatic electronic populations of a three-state electron transfer model describing (a) sequential and (b) superexchange electron transfer.

The semiclassical mapping approach outlined above, as well as the equivalent formulation that is obtained by requantizing the classical electron-analog model of Meyer and Miller [112], has been successfully applied to various examples of nonadiabatic dynamics including bound-state dynamics of several spin-boson-type electron-transfer models with up to three vibrational modes [99, 100], a series of scattering-type test problems [112, 118, 120], a model for laser-driven... 

In addition, these thin films have been important in studies of electron transfer, relevant for catalytic systems [64], molecular recognition [65], biomaterial interfaces [66], cell growth [67], crystallization [68], adhesion [69], and many other aspects [70]. SAMs provide ideal model systems, because fine control of surface functional group concentration is possible by preparing mixed SAM systems of two or more compounds, evenly distributed over the surface [71, 72], as two- or... 

Most of the modern theories of the photoconductivity sensitization consider that local electron levels play the decisive role in filling up the energy deficit The photogeneration of the charge carriers from these local levels is an essential part of the energy transfer model. Regeneration of the ionized sensitizer molecule due to the use of the carriers on the local levels takes place in the electron transfer model. The existence of the local levels have now been proved for practically all sensitized photoconductors. The nature of these levels has to be established in any particular material. A photosensitivity of up to 1400 nm may be obtained for the known polymer semiconductors. There are a lot of sensitization models for different types of photoconductors and these will be examined in the corresponding sections. 

This latter electron transfer (Donor-Acceptor -Accepto ) triplex is reminiscent of solution phase models of energy transfer within excited triplexes (35) and of simple synthetic (D-D-A) photoinduced electron transfer systems, for example, 6,... 

Thus, the model incorporating the direct hole trapping by adsorbed dichloroacetate molecules, which has been proposed by Bahnemann and co-workers, appears to be probable [7]. Moreover, calculations using the Marcus electron transfer theory for adiabatic processes which result in a reorientation energy of 0.64 eV suggest that also in the case of SCN- the hole transfer occurs in the adsorbed state [7]. 

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