Marcus cross relationship

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

A number of ostensibly outer-sphere reactions involving the O2 /02 redox couple were considered to have anomalous rates that were inconsistent with the Marcus model, but many of these deviations are now recognized to arise from size disparities between the small 02 radical and the large reaction partners these size disparities affect the solvent reorganization energies in ways that are not accounted for in the simple Marcus cross relationship.74... 

Coordinated ligands can also undergo one-electron reduction when C02 is the reducing agent. This occurs for the coordinated bpz ligand in [Ru(bpz)3]2 +, 192 and also for an extensive series of related complexes.193 The rates of these reactions depend on driving force in conformity with the Marcus cross relationship. 

The acid dependence observed in the reduction of trans-[Co(Me4[14]tetraeneN4)(N3)2] by Fe (aq) is attributed to the greater reactivity of the oxidant upon protonation of an azide ligand. The application of the Marcus cross-relationship to the data for the reduction of [Co(tmen)3] (tmen = tetramethylethylenediamine) by [Ru(H20)6] " yields a self-exchange rate constant of 10 s for the [Co(tmen)3] couple. Studies of the spectroscopic... 

The electron exchange rate constants [Rh(dmpe)3]" / " couples have been determined to be 2 x 10 and 4 x 10 M" s", respectively, from the appliction of the Marcus cross-relationship to the reactions with several ruthenium(II) pentaammine complexes. The relative values are consistent with the differences in the M—P bond distance changes (Ado = 0.068 A for Tc and 0.054 A for Re) determined by EXAFS measurements. 

Electrochemical measurements of the Cu(II/I) potentials with the nS4 ligands (n = 12-16) indicate that the Cu(II) and Cu(I) species each exist in two different conformational states [170]. Conformational rearrangement may either precede or succeed electron transfer. Rorabacher and coworkers interpreted their results in light of a square mechanistic scheme that neatly reconciles the sweep rate dependence of the cyclic voltammograms with the requisite change in coordination geometry at Cu. Kinetic studies on the electron transfer [149, 170, 176-177] support this scheme application of the Marcus cross relationship to reduction of Cu(II) and oxidation of Cu(I) yields widely discrepant values, presumably because of the different conformational states involved. 

One of the most important results to evolve from the theoretical treatment of Marcus is now referred to as the Marcus cross relationship. This important relationship was developed later by Ratner and Levine from a thermodynamic perspective, and this formulation provides a simple basis for understanding some of the concepts and assumptions in the more microscopic molecular theory of Marcus that is described later. 

This is the Marcus cross relationship in terms of Ifree energies. 

This is the cross relationship in terms of rate constants. There is often reason to believe (or need to assume) that = 1, and then Eq. (6.20) reduces to what is often called the simplified Marcus cross relationship. This is particularly useful because a knowledge of any three of the values, AB AA BB o " AB Hows One to predict the fourth. 

Table 63. Comparison of Some Obsaved Rate Constants (M s", 25 C) with Those Calculated from the Marcus Cross Relationship...

Table 6. Self-Exchange Rate Constants (25°C) for Various Reactions of Calculated from the Marcus Cross Relationship"...

The equilibrium constant for this last reaction, obtained from emf measurements, is Ki2- For reactants and products of the same size and charge type the simplest form of the Marcus cross-relationship is... 

A thermodynamic derivation of the Marcus cross relationship [equation (1)], where and 22 are the self-exchange... 

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