Electron transfer in solution

Fast chemical reaction subsequent to the electron transfer in solution ... 

Fig. 12. Energy-reaction coordinate diagram for electron transfer in solution when there is only weak interaction between the initial and final energy states.

If, on the other hand, the electron transfer in solution is determined by some rearrangement within the ion-pair structure, it is crucial to investigate the feasibility of electron transfer for an immobilized ion-pair structure in the solid state. 

Most of the interest in mimicing aspects of photosynthesis has centered on a wide variety of model systems for electron transfer. Among the early studies were experiments involving photoinduced electron transfer in solution from chlorophyll a to p-benzoquinone (21, 22) which has been shown to occur via the excited triplet state of chlorophyll a. However, these solution studies are not very good models of the in vivo reaction center because the in vivo reaction occurs from the excited singlet state and the donor and acceptor are held at a fixed relationship to each other in the reaction-center protein. 

A. Z. Weller, Photoinduced electron transfer in solution Exciplex and radical ion pair formation free enthalpies and their solvent dependence, Z. Phys. Chem. Neue Folge, Wiesbaden 133, 93-98 (1982). 

Electron transfer reactions, treated by continuum theory, suggested that the Franck-Condon barrier (the barrier for the vertical transition of electrons), which is about four times the activation barrier for the isotopic electron transfer in solution, is due to Bom continuum solvation processes. Specific contributions for the activation of ions come from the solvent continuum far from the ion the important contribution from the solvent molecules oriented toward the central ion in the first and second solvation shells is neglected. ... 

Figure 7. Comparison of SH (thin solid line), MFT (dashed line), and quantum path-integral (solid line with dots) calculations (Ref. 198) obtained for Model Va describing electron transfer in solution. Shown is the time-dependent population probability Pf t) of the initially prepared diabatic electronic state.

Finally, we consider Model V by describing two examples of outer-sphere electron-transfer in solution. Figures 7 and 8 display results for the diabatic electronic population for Models Va and Vb, respectively. Similar to the mean-field trajectory calculations, for Model Va the SH results are in excellent agreement with the quantum calculations, while for Model Vb the SH method only is able to describe the short-time dynamics. As for the three-mode Model IVb discussed above, the SH calculations in particular predict an incorrect long-time limit for the diabatic population. The origin of this problem will be discussed in more detail in Section VI in the context of the mapping formulation. 

Figure 28. Time-dependent (a) adiabatic and (b) diabatic electronic excited-state populations as obtained for Model Vb describing electron transfer in solution. Quantum path-integral results [199] (big dots) are compared to mapping results for the limiting cases y = 0 (dashed lines) and Y = 1 (dotted lines) as well as ZPE-adjusted mapping results for Yi p, = 0.3 (full lines).

Titration according to this scheme showed that the treatment of Co Salen with excess amounts of sodium resulted in nonquantitative formation of [(Co°Salen) 2Na ]. Thus, catalytic and, especially, kinetic investigations of such complexes have to take into account the presence of Co Salen or (Co Salen) in the samples studied. The described convenient method of quantitative electron transfer in solutions is good at determining low-valence metallocomplexes. 

To study the role of ion pairs, it is necessary to investigate electron-transfer reversibility in a solution and compare the results obtained with redox potentials of a donor and an acceptor. As a rule, ion-pairing phenomena define electrode processes too (Baizer and Lund 1983). However, the known equations for equilibrium calculations cannot take ion pairing into consideration because the equations do not contain ion-pair terms. One has to rely on experiments, which are able to take into account the equilibrium of electron transfer in solutions. 

The total quantum yield [4>cs(total)] for CS is decreased to 0.17 in dimethyl-formamide (DMF) due to the competition of the CSH from Fc-ZnP-H2F+-C6o (1.63 eV) to Fc-ZnP- -HzP-Cso (1.34 eV) versus the decay of Fc-ZnP-Fl2P -C6o to the triplet states of the freebase porphyrin (1.40 eV) and the Ceo (1.50 eV) [47]. In contrast to the case of most donor-acceptor-linked systems, the decay dynamics of the charge-separated radical pair (Fc -ZnP-H2P-C6o ) does not obey first-order kinetics, but, instead, obeys second-order kinetics [47]. This indicates that the mframolecular electron transfer in Fc -ZnP-H2P-C6o" is too slow to compete with the diffusion-limited inter-molecular electron transfer in solution. 

The direct electrolysis of a number of organic substrates requires a considerable overvoltage in order to proceed at a reasonable rate. The rate of an electron transfer in solution is high when the standard potentials of the reacting systems have suitable values. 

At present the body of data on reactions in clusters is insufficient to test the above two microcanonical approaches. For electron transfers in solution it seems clear that the vibrational assistance approach, stemming from Eq. (1.2), with its extensions mentioned earlier, is the one that has been the most successful [27-30]. For slow isomerizations Sumi and Asano have pointed out that an analysis based on Eq. (1.2) was again needed [40]. An approach based on Eq. (1.1) or on its extension to include a frequency-dependent friction, they noted, led to unphysical correlation times [40]. In investigations of fast isomerizations the most commonly studied system has been the photoex-cited trans-stilbene [5, 41-43,46]. Difficulties encountered by a one-coordinate treatment for that system have been reported [4, 8]. Indeed, coherence results for photoexcited cw-stilbene have shown a coupling of a phenyl torsional mode to the torsional mode about the C=C bond [42, 47]. 

In the case of electron transfers in solution there appears to be a greater cohesiveness of views, and the need for vibrational assistance is well established for reactions accompanied by vibrational changes (e.g., changes in bond lengths). A detailed analysis of the experiments could be made because of the existence of independent data, which include X-ray crystallography, EXAFS, resonance Raman spectra, time-dependent fluorescence Stokes shifts, among others. 

Anderson. D.l. Composition of the Furth." Scienie, 367 [January 20. 1OS-1 Arnett. E.M.. et al. Chemical Bond-Making, Bond-Breaking, and Electron Transfer in Solution. Sconce. 423 (January 26. 1990),... 

The theory stems from the writer s work on simple electron transfer reactions of conventional reactants (5). A simple electron transfer reaction is defined as one in which no bonds are broken or formed during the redox step such a reaction might be preceded or followed by bondbreaking or bond-forming steps in a several-step reaction mechanism. Other chemical reactions involve rupture or formation of one or several chemical bonds, and only a few coordinates suffice to establish their essential features. In simple electron transfers in solution, on the other hand, numerous coordinates play a role. One cannot then use the usual two-coordinate potential energy contour diagram (4) to visualize the... 

Electron transfer processes are at the heart of electrochemistry, and often the focus is on events at electrode surfaces. While the theory for electron-transfer in solution [94], and at metal surfaces [95] is rather extensive, a comprehensive theory for electron transfer at metal oxide-organic interfaces [96, 97] is still under development. This section is devoted to a discussion of some of the key elements of the surface electron transfer in dye-sensitized solar cells, illustrated by results from recent calculations. 

A theory used to study and interpret the photo-induced electron transfer in solution was described by Marcus.19-25 In this theory, the electron transfer reaction can be treated by transition state theory where the reactant state is the excited donor and acceptor and the product state is the charge-separated state of the donor and acceptor (D+-A ), shown in Figure 15. 

Electrochemical studies on SAMs have proven invaluable in elucidating the impact of various molecular parameters such as bridge structure, molecular orientation or the distance between the electroactive species and electrode surface. As described above in Section 5.2.1, the kinetics of heterogeneous electron transfer have been studied as a function of bond length for many systems. Similarly, the impact of bridge structure and inter-site distances have been studied for various supramolecu-lar donor-acceptor systems undergoing photoinduced electron transfer in solution. In both types of study, electron transfer is observed to increase as the distance between the donor and acceptor decreases. As discussed earlier in Chapter 2, the functional relationship between the donor-acceptor distance and the electron transfer rate depends on the mechanism of electron transfer, which in turn depends on the electronic nature of the bridge. 

The - Marcus theory [vi-vii] gives a unified treatment of both heterogeneous electron transfer at electrodes and homogeneous electron transfer in solutions. 

Applications of Proton-Coupled Electron Transfer in Solution 209... 

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