System mixed-valence

One of the Hume-Rothery rules for isomorphic systems requires the components to have the same valence. However, when the components have different valences, some interesting phase diagrams can result. A classic example of a mixed valence system occurs 

Ca-Na monotectic system. There is a solid phase transition from aCa to pCa at 447°C. The Na-aCa eutectic temperature is only 0.45°C below the melting point of Na. (Reprinted from Massalski, T.B., Handbook of Binary Alloy Phase Diagrams, ASM, 1990. Reprinted with permission of ASM International. All rights reserved.) 

In two-component systems, the Gibbs phase rule allows one degree of freedom, usually in the form of a temperature vs. composition line. If there is little or no excess heat of mixing and the components are highly compatible, i.e., nearly same atomic radius and electronegativity, same crystal structure, and same valence (Hume-Rothery rules), the system can have complete solid and liquid solubility over the entire range of composition. Such systems are said to be isomorphous. However, even isomorphic systems do not solidify 

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Hendrickson, D. N. In Mixed Valence Systems Applications in Chemistry, Physics and Biology Prassides, K., Ed. NATO ASI Series, Kluwer, Dordrecht, 1991 pp. 67-90. 

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. 

Most of the mixed-valence systems mentioned by Robin and Day and by Hush were in the solid state. The problem of creating discrete chemical systems for which experiments could be carried out either in solution or in the solid state was first attacked experimentally by Creutz and Taube (6). Their approach was to link together the two metal sites through a ligand bridge, which led to dimers and oligomers. 

DR. PAUL SCHATZ (University of Virginia) I think I know what Dr. Meyer meant in his talk, but all mixed-valence systems have stationary states. For example, consider the ammonia molecule. It tunnels back and forth between two umbrella forms, 9 10... 

DR. SCHATZ All mixed valence systems have stationary states. In any such state the probability distribution is time independent. Hence, it is incorrect to say that a mixed valence state is inherently time dependent. 

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... 

It would clearly be of great interest to have experimental transfer rates in mixed-valence systems. We note the recent use... 

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,... 

One experimental source of these essential data (for mixed-valence systems) is the intervalence transfer absorption band. The moments of the envelope (particularly the first and second moments) can be interpreted to yield values for x and (from a study of temperature dependence) for an effective coupling frequency. The study of effects of solvent variation can also lead to separation of x into intramolecular and environmental components. ... 

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... 

Larsson and co-workers have used relation (18) to calculate Tjb for organic molecules in which two centers are bridged by saturated groups [65,66], and for mixed valence systems [67]. The stationary states /i and /2 are determined by a CNDO/S method, with extensive configuration interaction and use of semi-empirical parameters. The nuclear configuration Q where relation (18) is valid is adjusted so as to satisfy the delocalization property expressed by (17). These... 

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. ... 

In a mixed-valence system, the isomer shift is able to distinguish the jump time th relative to the time t = 10 s for a MQssbauer nuclear excited state to decay to the ground state. 

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. 

Of particular interest are the photochemical investigations of the Cu(11)/ Mo(CN)g]4- mixed-valence system. Photochemical investigations have been performed by both monochromatic and polychromatic irradiations at selected energy regions. Low concentrations of octacyanomolybdatefIV) and copper(ll) have been used by reason of the low solubility of polymeric forms which are formed at higher concentrations. The analytical estimation of free cyanide has been used to monitor the photochemical reactions according to Scheme 3.. ... 

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