Average-valence complex

At the end of the 1960s, the concept of mixed valence appeared. H. Taube, on the experimental side, and N.S. Hush, with the theoretical aspects, made seminal decisive contributions. Taube characterized the first mixed-valence and average-valence complexes by varying the nature of the ligand L in the series [(NH3)sRuLRu(NH3)s] +. In organometallic chemistry, the first mixed-valence complex, biferrocenium monocation was published in 1970. 

The frequency of infrared spectroscopy marks the frontier between average-valence complexes (class 3 below) and mixed valence complexes (class 2 below), and this technique is easily accessible. The unsymmetrical complexes belong to class 1 (below). 

The three hexanuclear clusters are mixed valency complexes of two M(III) and four M(IV) centers, and the average oxidation state of the metal is +3.67. The number of cluster valence electrons is 14, which agrees with seven M—M bonds. Relatively short M-M distances for the intra- and intertriangles suggest that the clusters can be viewed as dimers of triangular clusters. Extension of the triangle condensation would lead to higher polymers. 

Although first-year students can now recognize Kekule s confusion, the answer was astute at that time, since the distinction between average valence and mixed valence would only be made a century later in 1969 by Henry Taube and Carol Creutz using Ru(II)-Ru(III) complexes [14]. In the 1930 s, Mills and Nixon evaluated this possibility with small rings being attached to benzene (vide infra). 

Complex VII (137) seems quite clearly to be of the average valency type (Fig. la, curves 3,3). Again, there is a near infrared electronic absorption band, but it is narrower than that expected for an intervalence band and is not subject to solvent shifts. The conproportionation constant is large (Kcoa > 1013) and the valences are delocalized at least on the infrared time scale (kex > 1013 sec ). 

Results on a large number of linear-chain complexes of platinum are summarised in Table 11. Harmonic wavenumbers and anharmonicity constants have been determined in all cases. The normal coordinate seems to be related to the halogen movements involved in the proposed hopping process for the conductivity of these linear-chain mixed-valence complexes (95). The chain halogen atoms would need to move, on average, 0.54,0.38 and 0.22 A for chlorides, bromides and iodides, respectively, in order to reach the point midway between the two platinum atoms, i.e. to the situation of a platinum (III) chain. These values only differ by a factor of about two from the root-mean-square amplitudes of vibration of Vi in the Vj = 16 states these are calculated (91) to be 0.22 A for X = Cl (wi = 319.5 cm-i) and 0.20 A for X = Br (cji = 179.6 cm ). These distance changes are related to the shift in the equilibrium... 

The utilisation of bond valence sums is widely used in these rather complex structures for either the allocation of an ion with a known nominal valence to the correct coordination polyhedron or the allocation of a charge state to an ion in a known coordination polyhedron. Using the bond valence method, the valence states of the Mn ions in i -Mn203 were determined to be Mn in A, Mn in A and Mnj Mn in B, giving an average valence of Mn for the phase, as necessitated by the overall formula. Similarly, bond valence sums for the perovskite LaCUjFe Oj allow the charge state at room temperature to be assigned La Cu Fe Ojj rather than La CUj fFe FCj )0,2. 

Mixed-valence complexes are found when the two oxidation states of a binuclear complex are different whereas average-valence (symetrical binuclear) complexes are those giving an infrared absorption intermediate between those of the two monomers with the different oxidation states. 

Primary bond A bond with a larger than average valence, formed by an atom with one or more stereoactive lone pairs of electrons Residual valence The valence available to an atom in a complex for forming external bonds after the valences of the internal bonds have been satisfied... 

The Hume-Rothery phases constitute an interesting and ubiquitous group of binary and complex intermetallic substances it was indeed Hume-Rothery who, already in the twenties, observed that one of the relevant parameters in rationalizing compositions and structures of a number of phases is the average number of valence electrons per atom (nJnM). An illustration of this fact may be found in Table 4.6, where a number of the Hume-Rothery structure types have been collected, together with a few more major structure types relevant to transition metal alloys. For each phase the corresponding VEC has been reported as njnai ratio, both calculated on the basis of the s and p electrons and of s, p and d electrons. 

The method of averaging for all valence-bond structures, asTdescribed above for diborane, is extremely laborious for any except very simple molecules. A statistical theory of resonating valence bonds that can be easily applied to complex as well as simple molecules has been developed.87 It can be illustrated by application to B6H9. Let us begin by assigning the probability 1 to the nonbridging B—II bonds and to the other bonds in the molecule ... 

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