Electron transfer theory dependence

EPR studies on electron transfer systems where neighboring centers are coupled by spin-spin interactions can yield useful data for analyzing the electron transfer kinetics. In the framework of the Condon approximation, the electron transfer rate constant predicted by electron transfer theories can be expressed as the product of an electronic factor Tab by a nuclear factor that depends explicitly on temperature (258). On the one hand, since iron-sulfur clusters are spatially extended redox centers, the electronic factor strongly depends on how the various sites of the cluster are affected by the variation in the electronic structure between the oxidized and reduced forms. Theoret-... 

According to the Marcus theory [9], the electron transfer rate depends upon the reaction enthalpy (AG), the electronic coupling (V) and the reorganization energy (A). By changing the electron donor and the bridge we measured the influence of these parameters on the charge transfer rate. The re-... 

In addition, the determination of metal-ligand bond distances in solution and their oxidation state dependence is critical to the application of electron transfer theories since such changes can contribute significantly to the energy of activation through the so-called inner-sphere reorganizational energy term. 

Coming back to aromatic anion radicals, a more accurate comparison between the experimental reaction kinetics and the predictions of the dissociative electron transfer theory revealed that the agreement is good when steric hindrance is maximal (tertiary carbon acceptors) and that the reaction is faster and faster than predicted as steric hindrance decreases, as discussed in detail in Section 3.2.2 (see, particularly, Figure 3.1). These results were interpreted as indicating an increase in the ET character of the reaction as steric hindrance increases. Similar conclusions were drawn from the temperature dependence of the kinetics, showing that the entropy of activation increases with steric hindrance, paralleling the increase in the ET character of the reaction. 

In the preceding section, we have seen that the expressions given by electron transfer theories may depend on numerous variables. This is particularly true in biological systems which are characterized by a great number of degrees of freedom, and we first examine in this section the physical nature of the different parameters involved by the theory in these systems. The experimental determination of these parameters is the subject of intensive studies which are well represented in the various topics treated in the present volume. The following are some typical approaches that have been implemented ... 

Table II presents the vadues of v, the rate constant for the electron transfer reaction with the donor and acceptor in contact, calculated by deconvolution of the fluorescence decay curves for a number of excited porphyrin-cOkyl halide systems. It appears that the rate parauneter depends strongly on the calculated exothermicity for these reactions. Parauneter i/ contadns information about the Framck-Condon factor of the electron-tramsfer reaction, which is in itself dependent on the reaction exothermicity and reorgauiization energy (22.23). Whether the rate constauit for the electron-transfer reactions depends on the exothermicity in the manner predicted by theory, that is with a simple Gaussian dependence (22), cannot be ainswered at present because of the uncertainties in the energetics of the particular reactions studied here.

Excited state potentials can also be estimated from kinetic studies of electron transfer quenching reactions involving a series of acceptors and/or donors with varying potentials. By applying electron transfer theory to the quenching step, in conjunction with the predicted dependence of the quenching rate constant on AG° for the electron transfer reaction, estimates for the redox potentials may be obtained (2 ). These approaches have been used successfully in the evaluation of the redox properties of several metal complexes,... 

One particular example of the use of pulse radiolysis to general chemistry was the work of Miller and co-workers on the rates of electron-transfer reactions. These studies, which were begun using reactants captured in glasses, were able to show the distance dependence of the reaction of the electron with electron acceptors. Further work, where molecular frameworks were able to fix the distance between electron donors and acceptors, showed the dependence of electron-transfer rate on the energetics of the reaction. These studies were the first experimental confirmation of the electron transfer theory of Marcus. 

The lifetime of the MLCT excited state of [Ru(bipy)3] has been measured in several solvents and at different temperatures. Among the- conclusions drawn are that k, is only slightly solvent-dependent, that k , agrees quantitatively with predictions of energy gap law for radiationless transitions, and that the solvent dependence of kinetic parameters for MLCT —> d, dctransitions can be considered in the context of electron-transfer theory. These results may have implications for the use of [Ru(bipy)3] as sensitizer. The solvent dependence of the MLCT transitions of [Ru(bipy)3], [Os(bipy)3], [Os(bipy)2(py)2p, and [Os(bipy)2 l,2-(Ph2P)2CsH4 f has been interpreted in... 

It is commonly assumed that solvent reorganization will dominate electron transfer kinetically. Depending on the thermodynamics of the electron exchange, it is possible to quantitatively predict a relationship between the free energy of activation for electron transfer and the free energy associated with solvent reorganization based on Marcus theory. 

It is surprising that the rate of photodriven electron transfer in 17 is as great as it is. It was noted above that simple electron transfer theories predict an exponential dependence of electron transfer rates on donor-acceptor separation. Calculations based on an estimate of the donor-acceptor distance in 17 and the quantitative dependence of electron transfer on distance found for other porphyrin-quinone systems [27, 62-64] suggest that the quantum yield of formation of C-P -QA(OMe)2-Qr should be near zero. It seems likely, then, that the dimethoxynaphthalene 7t-electron system and perhaps the bicyclic bridge are playing some role in the electron transfer process. 

Contrary to outer sphere electron transfer reactions, the validity of the Butler-Volmer law for ion transfer reactions is doubtful. Conway and coworkers [225] have collected data for a number of proton and ion transfer reactions and find a pronounced dependence of the transfer coefficient on temperature in all cases. These findings were supported by experiments conducted in liquid and frozen aqueous electrolytes over a large temperature range [226, 227]. On the other hand, Tsionskii et al. [228] have claimed that any apparent dependence of the transfer coefficient on temperature is caused by double layer effects, a statement which is difficult to validate because double layer corrections, in particular their temperature dependence, depend on an exact knowledge of the distribution of the electrostatic potential at the interface, which is not available experimentally. Here, computer simulations may be helpful in the future. Theoretical treatments of ion transfer reactions are few they are generally based on variants of electron transfer theory, which is surprising in view of the different nature of the elementary act [229]. 

In Marcus electron transfer theory, the barrier also arises as a consequence of the intersection of the two diabatic potential energy curves. The barrier height depends mainly on the (solvent and reactant) reorganization energy. 

Neither the electron density dependence nor the shape (which is approximately stretched exponential) of the kinetics can be explained with second order reaction kinetics, where it is assumed that the reaction is controlled only by the concentrations of electrons and dye cations, nor are they consistent with simple electron transfer theory. An explanation was proposed by Nelson based on the continuous time random walk [109]. In the CTRW, electrons perform a random walk on a lattice, which contains trap sites distributed in energy, according to some distribution function, g E). In contrast to normal diffusion, where the mean time taken for each step is a constant, in the CTRW the time taken for each electron to move is determined by the time for thermal escape from the site currently occupied. 

One important question in the light of current electron transfer theories [85-87] is that of the transition between stepwise (electron transfer and bond cleavage as separate elementary steps) or concerted (dissociative electron transfer [88]) mechanisms. For the two extremes, one expects largely different activation parameters for the electron transfer at an electrode. In particular, in contrast to the simple Butler-Vohner relationship (Eq. 18) with a constant transfer coefficient, potential dependent a values become evident. The experimentally accessible apparent transfer coefficient... 

Time-dependent Theory of Electronic Spectroscopy Electronic Coupling Elements and Electron Transfer Theory Metal-metal Exchange Coupling Solvation... 

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