Marcus cross-reaction equation

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... 

Experimental Tests The Marcus Cross-reaction Equation 355... 

The theoretical results obtained for outer-sphere electron transfer based on self-exchange reactions provide the essential background for discussing the interplay between theory and experiment in a variety of electron transfer processes. The next topic considered is outer-sphere electron transfer for net reactions where AG O and application of the Marcus cross reaction equation for correlating experimental data. A consideration of reactions for which AG is highly favorable leads to some peculiar features and the concept of electron transfer in the inverted region and, also, excited state decay. 

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 second and far more common approach to testing the predicted dependence of 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 (fci2), with the equilibrium constant (K12) and self-exchange rate constants for the two-component self-exchange reactions ( n) kii)- Its derivation is based on the assumption that the contributions to... 

Manganese(IV) complexes magnetic behavior, 272 Manganese(V) complexes magnetic behavior, 272 Mannich reaction metal complexes, 422 Marcus cross-reaction equation electron transfer, 355 Marcus Hush theory electron transfer, 340 Masking... 

Rate constants for outer-sphere electron transfer reactions that involve net changes in Gibbs free energy can be calculated using the Marcus cross-relation (Equations 1.24—1.26). It is referred to as a cross-relation because it is derived from expressions for two different self-exchange reactions. 

Another widely used result of Marcus theory deals with the extraction of useful kinetic relationships for cross reactions from parameters for self-exchange reactions. Consider the cross reaction, Equation (6.22), for which the rate... 

X 10 s ), the Marcus cross relation (Equation 6.26a) can be used to calculate the reaction rates for the reduction of Cu -stellacyanin by Fe(EDTA) and the oxidation of Cu -stellacyanin by Co(phen)3 +. E°(Cu ) for stellacyanin is 0.18 V vs. NHE, and the reduction potentials and self-exchange rate constants for the inorganic reagents are given in Table 6.3. For relatively small AE° values,/12 is 1 here a convenient form of the Marcus cross relation is log k,2 = 0.5[log kn + log 22 + 16.9AE°2]. Calculations with kn, 22, and AE°2 from experiments give k,2 values that accord quite closely with the measured rate constants. 

If the intrinsic barrier AGq could be independently estimated, the Marcus equation (5-69) provides a route to the calculation of rate constants. An additivity property has frequently been invoked for this purpose.For the cross-reaction... 

These results suggest that the Marcus equations can be applied quite successfully to gas phase displacement reactions, as suggested by Professor Brauman. We are currently generating more cross reactions and intend to test other rate-equilibrium relationships using our data. 

We now explore whether the pattern of reactivity predicted by the Marcus theory is found for methyl transfer reactions in water. We use equation (29) to calculate values of G from the experimental data where, from (27), G = j(JGlx + AG Y). The values of G should then be made up of a contribution from the symmetrical reaction for the nucleophile X and for the leaving group Y. We then examine whether the values of G 29) calculated for the cross reactions from (29) agree with the values of G(27) calculated from (27) using a set of values for the symmetrical reactions. The problem is similar to the proof of Kohlrausch s law of limiting ionic conductances. 

Table 13.8 summarizes results for a number of other outer sphere cross reactions. Confidence in the Marcus equation is high enough that, if it leads to a calculated rate constant that is in strong disagreement with an experimental value, a mechanism other than outer sphere should be considered. 

The reactions of the photochemically prepared [U02] ion with a series of chromium, ruthenium, and cobalt complexes have been studied/ An application of the Marcus equation to the cross-reaction data yields a [U02] self-exchange rate constant in the range of 1-15 s The reactions with the chromium and... 

Cross reactions of plastocyanins and azurins from various sources with cytochromes can be fitted to the Marcus equation using constant self-exchange rate constants of 6.6 x 10 s for the plastocyanins, 9.9 x 10 s for Ps. 

Equation (29) is also verified with several electron transfer reactions between coordinated metal ions [60,69]. The consideration of the role of the mixing entropy parameter can even explain anomalous "cross-reaction" estimates given by the theory of Marcus [60,70] and shines light on the controversy of the "inverted region" at low AG. 

Equation (9.41) is commonly known as the Marcus cross-relation. It will be expected to hold if the basic assumptions of Marcus theory (notably the parabolic energy-profile) and the assumed relation between the A. s (Equation (9.36)) are approximately correct. It is in fact much more accurately followed than the general Marcus equation (9.19) for the rate constant mn (cf. Section 9.1.3.2 below), as would be expected from the considerable cancellations among the IV terms. Some values are tabulated in Table 9.2 [13]. For 14 reactions out of the 17, the agreement is within a power of ten. In view of the wide range of rate constants (10 to 10 M s" ), this is satisfactory. 

Table 9.2 Test of the Marcus cross-relation Comparison of observed rate constants for electron-transfer reactions between metal complex ions with values calculated from rate constants observed for the related electron-exchange reactions (Equation (9.41)). Data from R.A. Marcus and N. Sutin, Ref. [13]...

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