Electron transfer rate prediction

The pathway model makes a number of key predictions, including (a) a substantial role for hydrogen bond mediation of tunnelling, (b) a difference in mediation characteristics as a function of secondary and tertiary stmcture, (c) an intrinsically nonexponential decay of rate witlr distance, and (d) patlrway specific Trot and cold spots for electron transfer. These predictions have been tested extensively. The most systematic and critical tests are provided witlr mtlrenium-modified proteins, where a syntlretic ET active group cair be attached to the protein aird tire rate of ET via a specific medium stmcture cair be probed (figure C3.2.5). 

In Debye solvents, x is tire longitudinal relaxation time. The prediction tliat solvent polarization dynamics would limit intramolecular electron transfer rates was stated tlieoretically [40] and observed experimentally [41]. 

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-... 

Figure 2.5 Electron transfer rate as a function of the electronic interaction A. The full line is the prediction of first-order perturbation theory. The upper points correspond to a solvent with a low friction the lower points to a high friction. The data have been taken from Schmickler and Mohr [2002].

Electron Transfer Far From Equilibrium. We have shown how the Marcus Theory of electron transfer provides a quantitative means of analysis of outer-sphere mechanisms in both homogeneous and heterogeneous systems. It is particularly useful for predicting electron transfer rates near the equilibrium potential,... 

One striking prediction of the energy gap law and eq. 11 and 14 is that in the inverted region, the electron transfer rate constant (kjjj. = ket) should decrease as the reaction becomes more favorable (lnknr -AE). Some evidence has been obtained for a fall-off in rate constants with increasing -AE (or -AG) for intermolecular reactions (21). Perhaps most notable is the pulse radiolysis data of Beitz and Miller (22). Nonetheless, the applicability of the energy gap law to intermolecular electron transfer in a detailed way has yet to be proven. 

CV waves is taken as evidence that the Cu(III) state is high spin, which complicates the prediction one might make regarding its electron-transfer rate. 

Figure 6.24 Marcus theory predictions of the dependence of the electron-transfer rate on the thermodynamic driving force...

We have investigated the ferrocene/ferrocenium ion exchange to determine the effects of different solvents on electron-transfer rates. There is probably only a very small work term and very little internal rearrangement in this system. Thus the rates should reflect mostly the solvent reorganization about the reactants, the outer-sphere effect. We measured the exchange rates in a number of different solvents and did not find the dependence on the macroscopic dielectric constants predicted by the simple model [Yang, E. S. Chan, M.-S. Wahl, A. C. J. Phys. Chem. 1980, 84, 3094]. Very little difference was found for different solvents, indicating either that the formalism is incorrect or that the microscopic values of the dielectric constants are not the same as the macroscopic ones. 

Figure 2. Theoretical prediction for the temperature dependence of the electron transfer rate for activated and for activationless processes. Solid lines are calculated for a continuum of vibrational modes dotted lines represent the single-mode approximation (6, 8). Upper curve AE, —2000 cm 1 P, 20 and S, 20. Lower curves AE, —800 cm"1 P, 8 and S, 20.

Experimental evidence for long-range electron transfer in polypeptides and proteins had been early accrued.The value of using a metal center as a marker is apparent from the above. The approach can be extended to electron transfer between two proteins which are physiological partners. Metal substitution (e. g. Zn for Fe) can be used to alter the value of AG° and permit photoinduced initiation. The parabolic behavior predicted by (5.86) has been verified for the electron transfer rate constant vs AG° within the adduct between cyt c and cyt bj." ... 

In a stopped-flow study on cytochrome cdi from P. aeruginosa, the ferrous d heme-NO species was formed despite electron transfer from the c to the d heme being relatively slow, rate constant approximately 1 s , for the relatively short distance between the two hemes (32). Such a distance would normally predict much faster electron transfer. The relatively slow interheme electron transfer rate has been observed on a number of occasions, and before the structure of the protein was known was thought to reflect the relatively large interheme separation distance and/or relative orientation of the two hemes (30). The crystal structures provide no evidence for either of these proposals there is nothing unusual about the relative orientation of the c and di heme groups. 

A great benefit of the MH formalism is the fact that predictions of the electron transfer rates are possible based on molecular structure of the reactants and the reacting medium. 

The inverted region was initially predicted by Marcus and the decrease in the electron transfer rate constant with —AG° has been observed experimentally many times.18 This is an important and remarkable result both for natural and artificial photosynthesis and energy conversion it predicts that, following electron transfer quenching of the excited A -B, the back electron transfer in the inverted region for the charge-separated state A + -B becomes slower as the energy stored increases. 

Ao varies with (l/Z)op - 1/DS) and for polar solvents Dop 4 Ds, e.g. Dop = 2.028 and Ds = 8.9 for dichloromethane. As a consequence, dielectric continuum theory predicts electron transfer rates to be enhanced in solvents like CH2C12 which are electronically relatively highly polarizable. 

Many of the theoretical treatments predict that the electron transfer rate constant should be of the form... 

The pioneering applications of molecular mechanics to coordination compounds were conformational analyses127,281. Recent applications involving the computation of conformer equilibria discussed in this chapter are studies of solution structure refinements126,29 1, racemate separations131 3il and the evaluation of reaction pathways11 1,34,3S1. The importance of conformer equilibria in the areas of electron transfer rates and redox potentials is discussed in Chapter 10, and many examples discussed in the other chapters of Part II indicate how important the prediction of conformational equilibria is in various areas of coordination chemistry. 

Figure 5.2 Tafel plots of In k versus overpotential for a mixed self-assembled monolayer containing HS(CH2)i600C-ferrocene and HS(CH2)isCH3 in 1.0 M HCIO4 at three different temperatures V, 1 °C O/ 25 °C , 47°C. The solid lines are the predictions of the Marcus theory for a standard heterogeneous electron transfer rate constant of 1.25 s-1 at 25 °C, and a reorganization energy of 0.85 eV (= 54.8 kj moh1). Reprinted with permission from C. E. D Chidsey, Free energy and temperature dependence of electron transfer at the metal-electrolyte interface, Science, 251, 919-922 (1991). Copyright (1991) American Association for the Advancement of Science...

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