Self-exchange rates

A powerful application of outer-sphere electron transfer theory relates the ET rate between D and A to the rates of self exchange for the individual species. Self-exchange rates correspond to electron transfer in D/D (/cjj) and A/A (/c22)- These rates are related through the cross-relation to the D/A electron transfer reaction by the expression... 

This is the origin of the various values for self-exchange rate constants. We may now attempt to rationalize some of these in terms of the /-electron configurations of the various oxidation states. Consider the self-exchange rate constants for some iron complexes. 

In the present case, the electron hopping chemistry in the polymeric porphyrins is an especially rich topic because we can manipulate the axial coordination of the porphyrin, to learn how electron self exchange rates respond to axial coordination, and because we can compare the self exchange rates of the different redox couples of a given metallotetraphenylporphyrin polymer. To measure these chemical effects, and avoid potentially competing kinetic phenomena associated with mobilities of the electroneutrality-required counterions in the polymers, we chose a steady state measurement technique based on the sandwich electrode microstructure (19). 

Fig. 5. Plot of apparent electron self exchange rate constants kf P, derived from polymer De values for films containing the indicated metals, mixed valent states, and ligands, all in acetonitrile, using Equation 2, vs. literature heterogeneous electron transfer rate constants k° for the corresponding monomers in nitrile solvents. See Ref. 6 for details. (Reproduced from Ref. 6. Copyright 1987 American Chemical Society.)...

The difference in the self-exchange rates of the two cobalt couples favors the oxidative pathway by a factor of 300. (For a further discussion of the above and other self-exchange rates, see B. S. Brunschwig, C. Creutz, D. H. Macartney, T.-K. Sham, and N. Sutin, Faraday Discuss. Chem. Soc., No 74, in press). Evidently the difference in the intrinsic barriers is large enough to compensate for the less favorable driving force for the oxidative pathway. As a result the latter pathway can compete favorably with the reductive pathway. 

The NO/NO+ and NO/NO- self-exchange rates are quite slow (42). Therefore, the kinetics of nitric oxide electron transfer reactions are strongly affected by transition metal complexes, particularly by those that are labile and redox active which can serve to promote these reactions. Although iron is the most important metal target for nitric oxide in mammalian biology, other metal centers might also react with NO. For example, both cobalt (in the form of cobalamin) (43,44) and copper (in the form of different types of copper proteins) (45) have been identified as potential NO targets. In addition, a substantial fraction of the bacterial nitrite reductases (which catalyze reduction of NO2 to NO) are copper enzymes (46). The interactions of NO with such metal centers continue to be rich for further exploration. 

Rotzinger then evaluated and H t as a function of the distance between the two reactant metal centers. He used the Fuoss equation to calculate the ion-pairing equilibrium constant to form the precursor complex at these internuclear distances. Assembly of these data then allowed the calculation of the self-exchange rate constants as a function of the internuclear distance in the transition state, the maximum rate being taken as the actual rate. 

If self-exchange rate constants for the Cu(II/I) couple are calculated by applying the Marcus cross relationship to the observed second-order... 

When the Marcus analysis is corrected to use rate constants and driving forces characteristic of the CuL species the derived self-exchange rate constants are much more self consistent. We caution, however, that the CuL + complex likely has all six thiaether atoms coordinated to the Cu11 center, while the CuLj complex is probably four coordinate. Since it is rather unlikely that electron transfer occurs in concert with this change in coordination number, a further correction will probably be required in order to obtain physically meaningful self-exchange rate constants. 

A literature value for E° for the SCH2COO / SCH2COO redox couple (0.74 V) was then used in conjunction with the cross relationship of Marcus theory to derive a self-exchange rate constant of 1.5 x 105 M-1 s-1 for the SCH2COO / SCH2COO redox couple. 

Although the proposed Tl1 intermediate has never been detected, an analogous species is found in the classical Hg2+ cation, which also has a metal-metal bond. Further support for this proposal is the observation that low concentrations of Cl- and Br- decrease the self-exchange rate such ligands are expected to stabilize Tl3+ more than Tl2+. 

Here, i is the faradaic current, n is the number of electrons transferred per molecule, F is the Faraday constant, A is the electrode surface area, k is the rate constant, and Cr is the bulk concentration of the reactant in units of mol cm-3. In general, the rate constant depends on the applied potential, and an important parameter is ke, the standard rate constant (more typically designated as k°), which is the forward rate constant when the applied potential equals the formal potential. Since there is zero driving force at the formal potential, the standard rate constant is analogous to the self-exchange rate constant of a homogeneous electron-transfer reaction. 

Experimental values of AG and the pre-exponential factor were obtained from a plot of In k,. vs 1/T under the assumption that the slope is — AG /R, and the hidden assumption that AG is temperature independent (AS is zero). Comparison between the calculated and observed pre-exponential factor was used to infer significant non-adiabaticity, but one may wonder whether inclusion of a nonzero AS would alter this conclusion. From an alternative perspective, reasonable agreement was noted for the values of ke and the homogeneous self-exchange rate constant after a standard Marcus-type correction was made for the differing reaction types. 

The variations of the symmetry factor, a, with the driving force are much more difficult to detect in log k vs. driving force plots derived from homogeneous experiments than in electrochemical experiments. The reason is less precision on the rate and driving force data, mostly because the self-exchange rate constant of the donor couple may vary from one donor to the other. It nevertheless proved possible with the reaction shown in Scheme 3.3.11... 

The rate constants may be expressed as functions of the self-exchange rate constant, k0, and the potential difference, linearizing the activation-driving force law and taking a value of 0.5 for the symmetry factor. Thus,... 

As for the difference observed for the sepulchrate complex, that may have to do with strain in the ligand. A student of mine has done some calculations considering the fact that the ligand itself may change the preferred distance and change the frequencies. This could account for a large part of the difference between the self-exchange rate constants for the sepulchrate and trisethylenediamine complexes. 

DR. SUTIN I think that this is always a problem with exchange reactions involving aquometal ions. The manganese system bears out what Dr. Taube said we have to be sure of the numbers which we are attempting to interpret. In this regard, I believe that the manganese self-exchange rate constant which you referred to was not measured directly. 

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