Electron transfer processes fluctuations

Some authors have described the time evolution of the system by more general methods than time-dependent perturbation theory. For example, War-shel and co-workers have attempted to calculate the evolution of the function /(r, Q, t) defined by Eq. (3) by a semi-classical method [44, 96] the probability for the system to occupy state v]/, is obtained by considering the fluctuations of the energy gap between and 11, which are induced by the trajectories of all the atoms of the system. These trajectories are generated through molecular dynamics models based on classical equations of motion. This method was in particular applied to simulate the kinetics of the primary electron transfer process in the bacterial reaction center [97]. Mikkelsen and Ratner have recently proposed a very different approach to the electron transfer problem, in which the time evolution of the system is described by a time-dependent statistical density operator [98, 99]. 

With the intensive development of ultrafast spectroscopic methods, reaction dynamics can be investigated at the subpicosecond time scale. Femtosecond spectroscopy of liquids and solutions allows the study of sol-vent-cage effects on elementary charge-transfer processes. Recent work on ultrafast electron-transfer channels in aqueous ionic solutions is presented (electron-atom or electron-ion radical pairs, early geminate recombination, and concerted electron-proton transfer) and discussed in the framework of quantum theories on nonequilibrium electronic states. These advances permit us to understand how the statistical density fluctuations of a molecular solvent can assist or impede elementary electron-transfer processes in liquids and solutions. 

There are features of these reactions which have attracted a great deal of attention to the problem of the coupling between outer-sphere electron transfer processes and solvent relaxation processes (a) the electron-transfer potential-energy surface is presumably somewhat cusp-like in the surface-crossing region, and this makes the reactions unusually sensitive to solvent fluctuations (b) the electron transfer step is often very fast and the bulk solvent translational diffusion properties are often not pertinent to the observed frictional effects. 

Suppose the non-equilibrium solvent polarization around the D°A° pair can be produced as an equilibrium response to a DA state with hypothetical charges z + z and — z, which is labelled by D +A . By hypothetical charges , we mean the charges hypothetically put on the redox pair in order to produce a solvent polarization which is equivalent to the solvent fluctuation, or non-equilibrium polarization around the solute. In that sense, the hypothetical charges serve as an order parameter, or a reaction coordinate. It is convenient for an electron transfer process to define another reaction coordinate called solvent coordinate by... 

The diagram shown in Fig. 3.10 is now widely used to describe electron transfer processes at electrodes, and it has the merit that it can be extended readily to the discussion of electron transfer at semiconductor and insulator electrodes [16]. The theoretical basis for the diagram is to be found in the fluctuating energy level model of electron transfer which has been discussed by Marcus [12,13], Gerischer [17-19], Levich [20], and Dogonadze [21]. 

One should emphasize that the coordinates describing the vibrations of an inertial polarization should be considered as the reactive coordinates equivalent to intramolecular coordinates, and in the absence of the latter, the vibrations of an inertial polarization of the medium are the only factor which provides matching of the electronic energy levels of a donor and of an acceptor. However, as shown in Ref. [10], the effect of a medium in electron transfer reactions is not reduced to matching of the electronic energies only. There are some additional effects caused by the dynamical behaviour of a medium in the electronic transfer process. One of them consists in the fact that the vibration of polarization near an acceptor produces the electric field which is the interaction, additional with respect to the direct interaction between an electron and an acceptor, leading to electron transfer to an acceptor. In some cases this fluctuational interaction exceeds the direct interaction with an acceptor. 

THE EFFECT OF SOLVENT FLUCTUATIONS IN ELECTRON TRANSFER PROCESSES... 

In this paper we continue the study on fluctuations of the solvation energy of the tyrosine L162 residue by extending protein dynamics to different temperatures. The fluctuations are closely related to fluctuations of the energy difference between the initial (final) state and the intermediate bridging state located at the tyrosine residue These energies are governing the electron transfer process ... 

The model s important prediction is that of the influence of each of branches of the longitudinal polarizi ion fluctuation spectrum on the electron-transfer probability. The high-frequency electronic branches. Equation (2c), which are responsible for the photoemission relaxation energies, exert only a minor influence on electron-transfer by virtue of a temperature-independent prefactor. The low-frequency branches. Equation (2a), contribute to the activation energy for the electron transfer process as well as to the temperature-dependent widths of photoemission lines via Equation (6b). The IR branches. Equation (2b), cause the apparent activation energies to increase with increas-... 

In the catalyst reoxidation step, contrary to the electron-transfer step, the polymer ligand should shrink because of the formation of the Cu(II) complex. Therefore, the polymer chain may partially repeat are expansion and contraction occurring during the catalytic cycle. When one has a view of the polymer-Cu catalyst as a whole, each part of the polymer catalyst domain, which is drifted in solution, is seen to be fluctuating during the catalytic process [Fig. 32(b)]. The fluctuating shape of biopolymers in enzymic reactions has been pointed out, and the dynamically conformational change of a flexible polymer chain is considered to be one of the effects of the polymer catalyst. 

By contrast, electrolyte states are much more limited in their distribution than metal conduction band states so that in many cases electron transfer through surface states may be the dominant process in semiconductor-electrolyte junctions. On the other hand, in contrast to vacuum and insulators, liquid electrolytes allow substantial interaction at the interface. Ionic currents flow, adsorption and desorption take place, solvent molecules fluctuate around ions and reactants and products diffuse to and from the surface. The reactions and kinetics of these processes must be considered in analyzing the behavior of surface states at the semiconductor-electrolyte junction. Thus, at the semiconductor-electrolyte junction, surface states can interact strongly with the electrolyte but from the point of view of the semiconductor the reaction of surface states with the semiconductor carriers should still be describable by equations 1 and 2. 

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