Electronic mixed valence systems

A recently proposed semiclassical model, in which an electronic transmission coefficient and a nuclear tunneling factor are introduced as corrections to the classical activated-complex expression, is described. The nuclear tunneling corrections are shown to be important only at low temperatures or when the electron transfer is very exothermic. By contrast, corrections for nonadiabaticity may be significant for most outer-sphere reactions of metal complexes. The rate constants for the Fe(H20)6 +-Fe(H20)6 +> Ru(NH3)62+-Ru(NH3)63+ and Ru(bpy)32+-Ru(bpy)33+ electron exchange reactions predicted by the semiclassical model are in very good agreement with the observed values. The implications of the model for optically-induced electron transfer in mixed-valence systems are noted. 

A vibronic coupling model for mixed-valence systems has been developed over the last few years (1-5). The model, which is exactly soluble, has been used to calculate intervalence band contours (1, 3, 4, 5), electron transfer rates (4, 5, 6) and Raman spectra (5, 7, 8), and the relation of the model to earlier theoretical work has been discussed in detail (3-5). As formulated to date, the model is "one dimensional (or one-mode). That is, effectively only a single vibrational coordinate is used in discussing the complete ground vibronic manifold of the system. This is a severe limitation which, among other things, prevents an explicit treatment of solvent effects which are... 

We follow closely previous expositions of the theory (4, 5) and include only the particular features needed for our present discussion. Let us imagine a mixed-valence system composed of two subunits, A and B, which are associated with formal oxidation states M and N, respectively. We designate the corresponding electronic Hamiltonian operators H and H, and if the... 

Creutz-Taube ion [bis(pentaammine-ruthenium)pyrazine]D (30) provides an example of this. There is good reason to suppose (in spite of many earlier arguments to the contrary) that this is a fully delocalized mixed-valence system (27). In symmetry, the one-electron levels separated by energy gap 2J are calculated to have b u (bonding) and b (antibonding) symmetry,... 

Does T differ significantly from unity in typical electron transfer reactions It is difficult to get direct evidence for nuclear tunnelling from rate measurements except at very low temperatures in certain systems. Nuclear tunnelling is a consequence of the quantum nature of oscillators involved in the process. For the corresponding optical transfer, it is easy to see this property when one measures the temperature dependence of the intervalence band profile in a dynamically-trapped mixed-valence system. The second moment of the band,... 

Methods discussed so far for determination of x assume that two ions are present and that electron transfer can be observed —as, e.g., in a mixed-valence system. What can be obtained for systems (e.g., Fe(III)(H20) /Fe(II)(H O) ) where this is not... 

Although Taube s pyrazine Ru"—Ru dimer was produced by the Ag oxidation of [(NHjljRu—NC4H4N—Ru(NH3)5] , attempts to prepare similar Ru"-Ru " complexes from [(NH3)5Ru(C5H4N)2Ru(NH3)5]" and [(NHjljRu—NC5H4C2H4C5H4N—Ru(NH3)5]" were unsuccessful. Cyclic voltammetric data indicated a two-electron oxidation to Ru" -Ru " dimers. In view of the identical ligands around each Ru atom, Mayoh and Day have questioned the localization of the Ru valencies in Taube s dimer into discrete Ru" and Ru " centres. However, a theoretical calculation of the conditions necessary for valence trapping in any mixed valence system, showed that the condition is indeed satisfied by the above Ru compound. Other workers have suggested that the available data on this complex could also be explained by a molecular orbital scheme in which the Ru ion and pyrazine-filled n (or k ) molecular orbitals are mixed, and the unpaired electron is mainly but un-symmetrically shared by the two cations. ... 

This review of mixed valence copper(I)/(II) systems has clearly established the predominance of the class I Robin and Day behaviour (Table 17), 360-362 but equally has shown how few copper class II or III systems have been well defined. This particularly applies to the class II systems, which can still be considered well-defined coordination complexes, with the electronic properties of these systems in the solid state and in solution. This suggests a fruitful area of research in these copper(I)/(II) mixed valence systems, especially of class II behaviour. 

The best characterized species is [Os2(N2)(NH3)10]5+ made as a bromide or as a tosylate from reaction of [0s(H20)(NH3)s]3+ with [Os(N2)(NH3)5]2+ in the presence of zinc amalgam. The stability of the mixed valence system (formally Os111 11) has been ascribed to electronic delocalization effects and an MO scheme proposed,2 0s but it is not clear why it appears to be more stable than its reduction product, [Os(N2)(NH3),0]4+. Magnetic circular dichroism spectra and cyclic voltammetry of the ion have been measured.28011 A number of other mixed homonuclear species are known, viz. [0s2(N2)(NH3)9(H20)]s+, [Os2(N2)(NH3)9C1]4+, [Os2(N2)(NH3)8C12]3+ and... 

Dinuclear ruthenium complexes form the largest group by far of any mixed-valence system and are the exclusive subject of this chapter. Ruthenium is the transition metal of choice to study electron transfer or exchange because it is relatively inexpensive and forms stable Ru(III) and Ru(II) coordination complexes. In addition, the synthetic coordination chemistry of ruthenium is well developed (1). 

The intellectual push to study mixed-valence complexes was provided by the publication in 1967 of two review articles, by Allen and Hush (2) and Robin and Day (3), on the physical properties of mixed-valence systems. These were followed by Hush s publication (4) of his theoretical model of intervalence transitions, which provided a link between the properties of mixed-valence complexes in solution and the Marcus theory of intermolecular electron transfer (5, 6). The review by Robin and Day classified mixed-valence complexes into three types class I,... 

The simplest form of this expression obtains for degenerate electron transfer (AG ) in e.g. symmetrical mixed valence systems ... 

Other biological mixed valence systems are known but an understanding of their electronic structures is even less well... 

Rg. 13.14 A comparison of photochemical and thenwl eteciron-transfer processes in mixed valence systems. The photochemical pathway (top) allows electron transfer prior to bond-length adjustment, while the ihermal route (bottom) requires adjustment prior to electron transfer. (CreuU, C. Prog, inorg. Chem. W83,30. 1-73. Used with pemission.)... 

Mixed-valence compounds continue to attract attention, not least because of their occurrence as intermediates of multistep redox systems Mixed-valence species are found in the geo- and biosphere, as evident from minerals such as Fe304 and from metalloproteins, where the Fe /Fe °/Fe, Cu /Cu and Mn / Mn Nn combinations are established Man-made mixed-valence compounds, starting from Prussian Blue in the early 18th century, have raised interest in what is now known as materials science because of their often special optical, electrical and magnetic properties These physical properties then prompted attempts at increasingly sophisticated levels to theoretically understand and computationally reproduce the experimental features of mixed-valence compounds More recent developments involve the application of mixed-valence systems as models and actual components in the areas of molecular electronics and molecular computing ... 

Weakly coupled mixed-valence systems or those with certain coordination modes such as chelation by a bis- or tris-bidentate acceptor ligand (e.g. bptz, bmtz or dqp) can show very low intensity IVCT bands in the NIR (Figure 3.1) or even escape completely their detection by electronic absorption spectro-electrochemistry... 

Molecules where identical or similar redox-active moieties are connected by conducting spacers generate mixed-valence systems upon partial oxidation or reduction. Spectroelectrochemistry here serves the purpose of evaluating the strength of the electronic coupling provided by the bridge, which is a central... 

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