The distance dependence of electron transfer rates

In this case the donor acceptor coupling may be obtained by using (16.97)-(16.99) to estimate the couplings Fab and Fbd from spectroscopic parameters obtained from charge transfer donor-to-ligand and acceptor-to-ligand transitions. 

To end this section it should be mentioned that another route to the nonadiabatic electronic coupling can be found in theory. Ab initio quantum chemical calculations of this coupling in medium-size systems are now feasible,and semi-empirical calculations are also becoming increasingly reliable. 

Newton, Quantum chemical probes of electron-transfer kinetics—the nature of donor-acceptor interactions, Chem. Rev. 91, 767 (1991). 

Skourtis and D. Beratan, Theories for structure-function relationships for bridge-mediated electron transfer reactions, in Electron Transfer—From Isolated Molecules to Biomolecules, edited by M. Bixon and J. Jortner, Advances in Chemical Physics, Vol. 106 (Wiley, New York, 1999), Part I, p. 377. 

As usual, most of the work on the contributions of electronic factors to electron transfer rates has dealt with the transfer of electrons between widely separated donors and acceptors. Most of the literature in the time period surveyed has dealt with elegant experimental studies of synthetic, modified metalloenzyme or of photosynthetic donor-acceptor systems. 

The theoretical aspects of long-range electron transfer have been reviewed in a recent monograph. Mikkelsen and Ratner have used their density matrix approach to examine the effects of a molecular species (H2O) placed between the benzene radical anion donor and the benzene molecule acceptor and of the relative 

The authors interpret this in terms of a hyperconjugative component of the through-bond coupling and its solvational perturbation. That the ratio of k2 is approximately correlated with the static dielectric constant of the solvent (see Table 1.1) could arise from a more mundane dependence of the electron transfer relaxation rate constant on k u. Thus, when Eq. (2) holds the nuclear contribution to the rate constant ratio becomes the relationship in Eq. (3). One does not 

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Four Aspects of the Distance Dependence of Electron-Transfer Rates... 

Fig.6 The distance dependence of electron-transfer rates in DNA hairpins [51]. The acceptor is a photoexcited derivatized stilbene (SA) or phenanthrene (PA) the electron donor is guanine (G), deazaguanine (Z), or inosine (I). The decay is much more rapid in the Z-PA couple compared to the G-SA couple because the tunneling energy is further from the bridge states in the case of Z-PA...

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) ... 

Recent theoretical developments have been directed at incorporating the distance dependence of electron-transfer rate constants into the kinetic equations for diffusion-controlled reactions on the micelle surface, rather than assuming that these are collisional processes [82]. Both forward and back electron-electron transfers have been considered, with fitting of experimental data by numerical integration of appropriate differential equations. A standard Marcus-type expression was used to describe the electron-transfer rate constants. In the particular case of electron transfer from a donor to a single acceptor located initially at 0, one has instead of Eq. 10 [82c]... 

In Equation (6.28), Hab is the electronic coupling at close contact (d°), and fi is the rate of decay of coupling with distance (d). Studies of the distance dependence of electron-transfer rates in donor-acceptor complexes, and of randomly oriented donors and acceptors in rigid matrices, have suggested 0.8 iS<1.2... 

This has grown to form a considerable area of chemistryIt includes such varied topics as the ab initio calculation of electronic matrix elements/ the effect of bridging groups,electron tunneling theories,selection rules for electron transfer, and the distance dependence of electron transfer rates/ ... 

Key to electrical communication between glucose oxidase and the electrodes is the spacing, i.e., the density, of relays. The relays must be sufficiently close to both the FAD/FADH2 centers and to the metal electrodes (and possibly also to each other) for the electron transfer to be rapid. The distance-dependence of electron transfer rates in biosystems has been the subject of intensive theoretical and experimental research in recent years . It is now evident that for distances greater than 8 A electron transfer rates (k) within and between molecules, as well as between electrodes and ions or molecules in their proximity, or between the ions themselves, decay exponentially with the distance (d) between the involved centers, i.e., k = In proteins the electron... 

Boxer has written a very good review of the distance dependence of electron transfer rates in proteins.This article presents a detailed overview of theoretical and experimental studies of electron transfer processes in proteins and in modified protein systems. The major focus of this review is on the fast, primary, photoinduced processes in the reaction centers of Rhodobacter sphaeroides and Rhodopseudomonas viridis. 

Issues related to the preferred pathways and the distance dependence of electron transfer in biological systems have been addressed by covalently linking electron-transfer donors or acceptors (e.g. a ruthenium complex) to specific sites (e.g. a histidine) of a protein or an enzyme.The distance dependence of the electron-transfer rate constants is generally fitted to equation (44), with most values of for proteins falling in the range of 1.0 to 1.3 A The protein in... 

Figure 18.7. Distance Dependence of Electron-Transfer Rate. The rate of electron transfer decreases as the electron donor and the electron acceptor move apart. In a vacuum, the rate decreases by a factor of 10 for every increase of 0.8 A. In proteins, the rate decreases more gradually, hy a factor of 10 for every increase of 1.7 A. This rate is only approximate because variations in the structure of the intervening protein medium can affect the rate.

Figure 18.19 Distance dependence of electron-transfer rate. The...

Along with the distances associated with proton transfer, the distance-dependence of electron transfer on PCET reactions of phenols has also been of considerable interest. To study the effect of distance on the rates of phenol oxidation, Wenger and coworkers synthesized a series of heteroleptic ruthenium polypyridine complexes where the distance from the metal to the distal phenol was varied as a function of the... 

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