Electron transfer donor-acceptor separation

One expects the impact of the electronic matrix element, eqs 1 and 2, on electron-transfer reactions to be manifested in a variation in the reaction rate constant with (1) donor-acceptor separation (2) changes in spin multiplicity between reactants and products (3) differences in donor and acceptor orbital symmetry etc. However, simple electron-transfer reactions tend to be dominated by Franck-Condon factors over most of the normally accessible temperature range. Even for outer-... 

Examples of electron tunneling reactions on the surface of heterogeneous catalysts have been discussed in Chap. 7. These reactions provide electron transfer between spatially separated donor and acceptor centres on the surface of heterogeneous catalysts as well as between the centres one of which is on the surface of the catalyst and the other is in the subsurface layer. Such processes are expected to be important for photocatalytic reactions, as well as for thermal catalytic reactions proceeding at low temperatures by heterolytic mechanisms. 

The pre-exponential factor A in Eq. 1 is a weak function of the temperature and the reorganization energy, and strongly dependent upon the electronic coupling matrix element V. In the simplest case, V may be assumed to be exponentially dependent upon the through-space donor-acceptor separation r. This yields a distance dependence for electron transfer of ... 

The FEG law was checked and confirmed experimentally but only for intramolecular electron transfer when the donor-acceptor separation r is fixed and what is measured is really W(r) (Fig. 3.3). The results were reviewed and discussed in Ref. 83 and in other articles published in the same special issue of the Journal of Physical Chemistry. Similar results were obtained in solids where the reactants are also immobile. 

Until recently very little quantitative experimental data concerning the distance dependence of electron-transfer rates were available. From experiments on electron transfer between statistically distributed donor and acceptor species in an inert glassy matrix it had been concluded (Miller et al., 1984) that the rate falls of sharply with increasing donor-acceptor separation and that at a given edge-to-edge separation Re (in A) the fastest rate (k in s ) achievable under optimally exothermic conditions would be given by the exponential expression eq. (1) ... 

Other theoretical activity has centered on the dependence of reaction non-adiabaticity upon the structure of the intervening medium as well as the donor-acceptor separation for intramolecular electron transfer [50], i.e. between donor and acceptor sites contained within a single species such as a binuclear complex. The electron-tunneling probability is predicted to be enhanced substantially by the presence of delocalized electron groups, such as aromatic ligands, between the reacting centers [50]. This is consistent with experimental studies of thermal and optically induced electron transfer within binuclear complexes [51]. 

The electronic coupling of the reactant state with the product state, F, is a function of the overlap of the donor and acceptor orbitals. This in turn depends on energetic, spatial, geometric, and symmetry factors. At relatively large donor acceptor separations, it can be assumed that the relevant orbitals decay exponentially with distance. In these cases, the electron transfer rate constant will depend on this separation as per Eq. 2, where Rda is the donor-acceptor separation and y is a constant that expresses the sensitivity of the... 

The majority of the research on the photochemistry of porphyrins linked to other moieties has been in the area of photoinduced electron transfer, and the systems studied are all in some sense mimics of the photosynthetic process described above. The simplest way to prepare a system in which porphyrin excited states can act as electron donors or acceptors is to mix a porphyrin with an electron acceptor or donor in a suitable solvent. Experiments of this type have been done for years, and a good deal about porphyrin photophysics and photochemistry has been learned from them. Although these systems are easy to construct, they have serious problems for the study of photoinduced electron transfer. In solution, donor-acceptor separation and relative orientation cannot be controlled. As indicated above, electron transfer is a sensitive function of these variables. In addition, because electron transfer requires electronic orbital overlap, the donor and acceptor must collide in order for transfer to occur. As this happens via diffusion, electron transfer rates and yields are often affected or controlled by diffusion. As mentioned above, porphyrin excited singlet states typically have lifetimes of a few nanoseconds. Therefore, efficient photoinduced electron transfer must occur on a time scale shorter that this. This is difficult or impossible to achieve via diffusion. Thus, photoinduced electron transfer between freely diffusing partners is confined mainly to electron transfer from excited triplet states, which have the required long lifetimes (on the micro to the millisecond time scale). 

Problems associated with precursor formation and successor dissociation are circumvented when the nonspecific interaction between donor and acceptor in Eq. 1, represented by, is replaced by a covalent linker. As the many chapters of this Series attest, the restriction of electron transfer to an intramolecular process, where the distance between donor and acceptor is fixed, has led, in the past two decades, to an explosion in our knowledge of electron transfer processes and the factors that control them. These include the donor-acceptor separation distance the nature of the intervening medium and the relative orientation between the donor and acceptor sites (all of which influence electronic coupling) the driving force of the reaction (AG°) and the nuclear reorganization of reactants and solvent (2). 

Figure 5.38. Dependence of the light-induced electron transfer on donor-acceptor separation R and upon solvation characterized by the distance between solvent molecules and donor-acceptor system (by permission from Ramunni and Salem, 1976).

The longer lifetime noted for IS relative to 16 may be ascribed to the enhanced donor-acceptor separation in IS. Direct electron transfer from Qg to C should be slow because of the large distance involved, and a multistep charge recombination such as was observed in some of the triad systems discussed above would require slow endergonic electron transfer to yield either C-P -Qa-Q or C -P-Qa -Qb followed by direct recombination of these states or a second endergonic electron transfer to yield C-P -Qg -Qg. 

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. 

Fig. 16.8 Charge recombination lifetimes in the compounds shown in the inset in dioxane solvent. (J. M. Warman, M. P. de Haas, J. W. Verhoeven, and M. N. Paddon-Row, Adv. Chem. Phys. 106, Electron transfer—from isolated molecules to bio-molecules, Part I, edited by J. JortnerandM. Bixon (Wiley, New York, 1999). The technique used is time-resolved microwave conductivity (TRMC), in which the change in dielectric response of a solution is monitored following photoinduced electron transfer—a charge separation process that changes the solute molecular dipole. The lifetimes shown as a function of bridge length (number of a-bonds separating the donor and acceptor sites in the compounds shown in the inset) are for the back electron transfer (charge recombination) process.

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