Marcus reactions with self-exchange

The reversibility of the [Os(bpy)3]3+/2+ couple makes it useful for the determination of the electron self-exchange rates of other couples by application of the Marcus cross-reaction equation. Recently, this has been applied to the oxidation of S032- to S042- (622). The new rate constant for this reaction of 1.63 x 107 M-1 sec-1 is consistent with the... 

The second and far more common approach to testing the predicted dependence of kob on AG has been based on the so-called Marcus cross-reaction equation. The cross-reaction equation interrelates the rate constant for a net reaction, D+A- D++A ( el2), with the equilibrium constant (Kl2) and self-exchange rate constants for the two-component self-exchange reactions D+ 0 (Zen) and A0/- (k22). Its derivation is based on the assumption that the contributions to vibrational and solvent trapping for the net reaction from the individual reactants are simply additive (equation 63). The factors of one-half appear because only one of the two components of the self-exchange reactions is involved in the net reaction. The expression for A0 in equation (63) is an approximation. Note from equation (23) that k is a collective property of both reactants and the approximation in equation (63) is valid only if the reactants have similar radii. 

The success of the Marcus model is connected to the consistent description of self-exchange reactions and later to ET reactions with non-zero free energy. Using the easily measured free energy of reaction (-AGe) in the PES diagram, gives the Arrhenius rate ... 

What first strikes the eye in Table 12 is the variation in A, which is to be expected from an inspection of the individual values of A for self-exchange reactions that are listed in Table 6. No doubt the considerable scatter of data points in the Marcus plots reflects to a large extent this variation in X. It is therefore important to study series of closely similar compounds to test the theory, as was indeed pointed out very early by Marcus (1964). Preferably, one should work with compounds of known X, determined by independent measurements of self-exchange rate constants. 

However, with this E° value it is impossible to fit the data of entry no. 1 of Table 15 to the Marcus relation. Only by using a considerably higher E° for the SO4VSO4- couple, 3.08 V (or, of course, a set of lower values for ArH), can any reasonable fit be obtained. We then also have to postulate a rather small X value, 8.0 kcal mol, for the reaction. Knowing that X for self-exchange reactions of the compound types involved is around 10 kcal mol-1 (see Table 7) and assuming it to be small, 10 kcal mol-1, for SO4VSO4- too we can calculate X to be 9.0 kcal mol-1. 

Entry no. 2 presents another problem in that the electrostatic correction term for AG° in the solvent used, acetic acid, is very large, —15.3 kcal mol-1 (see Table 3 Z,Z2 = —2, rn = 7 A). Again, E° = 2.52 V is far too small to give any reasonable fit to the Marcus relation. With E° = 3.08 V, the result is at least consistent with that of entry no. 1. Entries nos. 3 and 4 have been treated with A values for self-exchange reactions of pyridine and acetate equal to 10 and 20 kcal mol-1 respectively fccalc comes out at 1010 M 1 s irrespective of the choice of E° = 2.52 or 3.08 V. For entry no. 5 X (CH3OH) was assumed to be > 20 kcal mol-1 and the quoted value of kcalc is estimated with E° = 3.08 V. It thus represents a maximum value and the reaction is certainly not feasible as an electron-transfer step. 

To sum up the survey of the past work on oxidation-reduction reactions the only experimental results obtained thus far which strongly indicate nonadiabatic effects are some obtained by Matteson and Bailey (22) and by Chan and Wahl (23) for self-exchange reactions. In addition, it is very likely that such effects are significant also for reactions of f electron redox agents, particularly on reaction with one another. Marcus has advocated consistently the position that nonadiabatic effects are relatively unimportant for the ordinary oxidation—reduction reactions which have been studied. But many experimentalists, including myself, have been much slower to arrive at it. Further work may show that a nonadiabatic factor is significant in many other processes, but at the present level of development of the subject, there are not many cases where it needs to be invoked. 

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