Square scheme mechanism

Fig. 5. Dual-pathway square scheme mechanism for electron transfer involving the Cun/I([9]aneS3)tt system. The vertical reactions involve ligand gain or loss while the horizontal reactions represent electron transfer. Reproduced from Ref. (6) by permission of the Royal Society of Chemistry.

Overall, the results are taken in support of the sequential (square-scheme) mechanism rather than the concerted alternative. Detailed analysis of the individual systems enabled the authors to distinguish which of the two possible square-scheme pathways was dominant. 

A reaction scheme frequently encountered in practice, the so-called square scheme mechanism, consists of the association of two EC reaction schemes as shown in Scheme 2.3 (which may as well be viewed as an association of two CE mechanisms). In the general case, the cyclic voltammetric response may be analyzed by adaptation and combination of the treatments given in Sections 2.2.1 and 2.2.2. A case of practical interest is when the follow-up reactions are fast and largely downhill. A and D are then stable reactants, whereas B and C are unstable intermediates. When the starting reactant is A (reduction process), the reaction follows the A-B-D pathway. The reoxidation preferred pathway is D-C-A. It is not the reverse of the forward... 

Figure 13.27 Dual-pathway square scheme mechanism that accounts for the rearrangements induced by the monoelectronic reduction of deprotonated rotaxane 92+. The species A and C represent the stable structure of the deprotonated rotaxane and its monoreduced form, respectively, whereas and D are metastable intermediates. Note that the exact position of the macrocycle along the axle in the reduced forms and C is not known. From a simple digital simulation of the cyclic voltammetric patterns, the following values have been obtained = - 0.59V, E°dc = - 0.34V, /cAD 0.15S- da<2.5s kBC > 100 s and kCB 1 s V...

Figure 4. Proposed dual-pathway square scheme mechanism for the Cu 7Cu electron transfer process. (A) and (B) represent the stable forms of Cu" and Cu complexes, respectively, while the species (C) and (D) represent metastable conformers.

A complete analysis of the square scheme is complex since disproportionation and/or other second-order cross-redox reactions have to be taken into consideration. However, the limiting cases of the square scheme are much more tractable. An interesting aspect of the square reaction scheme is that, in principle, it applies to all one-electron processes with reaction steps A+ B+ and A B coupled to the heterogeneous charge transfer. For example, the redox-induced hapticity change, which accompanies the reduction of Ru( j - CeMee), has been proposed [113] to be responsible for the apparently slow rate of electron transfer. That is, the limiting case of an apparent overall Einev process is observed for what in reality is a square scheme mechanism. 

The mechanism of electrochemical reduction of nitrosobenzene to phenylhydroxylamine in aqueous medium has been examined in the pH range from 0.4 to 13, by polaro-graphic and cyclic voltametry. The two-electron process has been explained in terms of a nine-membered square scheme involving protonations and electron transfer steps565. This process is part of the overall reduction of nitrobenzene to phenylhydroxylamine, shown in reaction 37 (Section VI.B.2). Nitrosobenzene undergoes spontaneous reaction at pH > 13, yielding azoxybenzene471. 

The square scheme discussed above already includes a further common motif in electroorganic mechanisms reaction As A forms a preequilibrium to both ETs in the scheme. The response of such a system in CV depends particularly on the equilibrium constant K = [A]/[A ] and the rate constants a A and If the... 

When both components of the redox couple adsorb on the electrode surface, the mechanism (2.172)-(2.174) transforms into the following square scheme [128] ... 

The two well-separated waves for the reduction of oxygen on mercury were reported by Heyrovsky [91]. The first wave corresponds to the 2e reduction of O2 to H2O2 in acidic or neutral solutions and to H02 in basic media, species that are reduced to water or OH at lower potentials. Jacq and Bloch have developed the square-scheme concept for the discussion of the mechanism of O2 reduction on Hg and on carbon [28]. 

Fig. 18 Square scheme reduction mechanism for loss of the V=0 group.

While the above technique can be used in many cases, it does require uncomplicated voltammetry and that significant Ey2 shifts are observed at guest concentrations >10 times the host concentration. If these conditions are not met, then an alternative strategy is needed. The most powerful is to use CV simulation software to fit the experimental CVs to the square scheme or a more complicated mechanism if necessary. This method allows determination of the thermodynamic parameters and possibly the kinetic parameters as well. 

The complete process can be interpreted on the basis of a square scheme, as shown in Fig. 2.1. Quickness of the mechanical steps (iv) and (ii) is ensured by the high flexibility of the molecular framework. 

Here, the i conformers each of the oxidized and the reduced forms are related by the 2 (i-1) equilibrium constants Kt and K, respectively, and by the i redox potentials Ef. A quantitative analysis of the redox potential in the square scheme of Eq. 11.4 requires a knowledge of all equilibrium constants. For labile systems this is only possible when theoretical methods can be applied. Molecular mechanics has been used in this context to calculate the conformational equilibria and then to predict the electrochemical behavior of [Co(sep)]3+/2+11511, [Co(dien)2]3+/2+11511 and [Co (S)-pn 3]3+/2+13451 (sep is defined in Table 11.1, dien in Table 8.1, pn in Table 8.2). 

The latter is involved, for example, in the reduction of aromatics to their dihydro derivatives, of quinones to hydroquinones, carbonyls to alcohols. A priori, there are six plausible different possibilities of transferring two electrons and two protons, depending on the exact order of the steps. These six paths involve the articipation of seven different intermediates A , A , AH", AH , AH ", AH2 ,and AH. It is thus seen that the discussion of the possible mechanism(s) may rapidly become an overwhelming task, particularly when more steps are involved, as in the 4e -f- 4H " sequence in Eq. (126). Thus in order to discuss the exact route followed, a convenient representation of the different possible schemes is highly desirable. Such a representation of all possible paths is given by square-schemes diagrams [101], such as that shown in Scheme 8 for the A/AH2 reduction. The horizontal... 

Z /5(diphenylphosphino)ethane], where the cis-form (C) on oxidation yields which isomerizes to the trans species, T . More complex reaction mechanisms result from coupling several square schemes together to form meshes (e.g., ladders ov fences) (8). 

It is beyond the scope of this work to consider the many other reaction schemes (e.g., ECE, electron-transfer catalyzed reactions, square schemes) that have been treated theoretically and applied to actual systems. Details of the appropriate equations and procedures to treat these cases, as well as references to the original literature, can be found in reviews (7-9, 14, 65-68). Many applications of electrochemical techniques to the elucidation of organic (69, 70) and inorganic (71, 72) reaction mechanisms have appeared. 

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