Valence, nonintegral

A condition where metal ions within a coordination complex or cluster are present in more than one oxidation state. In such systems, there is often complete delocalization of the valence electrons over the entire complex or cluster, and this is thought to facilitate electron-transfer reactions. Mixed valency has been observed in iron-sulfur proteins. Other terms for this behavior include mixed oxidation state and nonintegral oxidation state. 

Nonstoichiometric compounds are mixed-valence compounds with nonintegral electron/atom ratios. Electronic properties of these compounds depend crucially on the nature and magnitude of nonstoichiometry. Electronic conduction in many such compounds occurs by hopping between the cations of different valencies (e.g. Pr " " and Pr" " in Pri2022)- Nonstoichiometry with a wide range of compositions is more common in oxides, sulphides, and related materials where the bonding is not completely ionic. In ionic nonstoichiometric compounds, structural rearrangements... 

There are several interesting families of inorganic mixed-valence compounds that we have not discussed here (see Yvon, 1979 McCarley, 1982). For example, there are metal-cluster compounds such as the Chevrel phases, M,jMo6X8(X = S or Se) and condensed metal-cluster chain compounds such as TlMojScj, TijTe, NaMo O and M PtjO. TTF halides and TTF-TCNQ complexes (Section 1.9) constitute molecular mixed-valent systems in which the mixed valency is associated with an entire molecule the charge on TTF in such compounds is nonintegral. The structure of TTF-Br(, 79 and... 

Conversely, the presence of some metal ions of lower oxidation state in the metal ion sublattice requires vacant anion sites to balance the charge. In some cases, the charge imbalance is caused by ions of some other element or, rarely, by multiple valence of the anions. In any event, the empirical formula of a recognizable solid transition metal compound may be variable over a certain range, with nonintegral atomic proportions. Such non-stoichiometric compounds may be regarded as providing extreme examples of impurity defects. 

The groups of Kobayashi and Underhill have focused their attention on partially oxidized Ni and Pt mnt complex anions with nonstoichiometric proportions of different cations. Such nonintegral valence salts have the general structure (cation), M(mnt)" (H2 0)x (x = 0-2), in which n can be anywhere between 0.5 and 0.82. 

Even if we do accept the simple Bohr theory of valence, there is still the difficulty of how to handle chemical valence when the aufbau principle breaks down for free atoms, or when the n and l of individual electrons are poorly defined. In some cases, instabilities of valence can be expected. Nonintegral valences are indeed observed for many elements of the long periods in the condensed phase. This aspect of chemical valence will be further discussed in chapter 11, where it will also be related to properties of the radial equation. 

Instabilities of valence (viz. atoms flipping from one state of valence to another as a function of changes in the environment) and mixed valence (an atom exhibits simultaneously two valences, or two valence states coexist on the same site) are both related to intermediate valence (the atom in the condensed phase exhibits some mean, nonintegral valence). The effects are usually encountered when dealing with 4/ and 5/ electrons, and it is therefore very relevant to determine the / count, or effective number of / electrons on a given site. Various core-level spectroscopies have been used to probe / electron occupancies, and there is a vast literature on this field (see the review by Fuggle [615]). 

In recent years there has been increased interest in mixed valent homonu-clear complexes which exhibit unusual electronic properties arising from the rapid electron transfer between the metal sites, such that the metal atoms are in the equivalent nonintegral oxidation state. These complexes may have interesting electrical and magnetic properties via a valence interchange mechanism if interaction occurs between isolated clusters or within an infinite polymer. To date only small isolated oligomers have been characterized. General reviews of the mixed valent complexes are available for the interested reader (198, 355, 455, 468, 534). 

It is also appropriate to mention recent experimental work on concentrated metallic lanthanide alloys and compounds which exhibit Kondo-like anomalies in their physical properties. This work indicates that lanthanide ions which behave nonmagnetically below a characteristic temperature To (as evidenced by a magnetic susceptibility which, below To, approaches a finite value as T 0) can be quite generally pictured to have a time-averaged 4f shell occupation which is nonintegral. The nonintegral 4f shell occupation (or nonintegral valence) can actually be observed by means of measurements of the lattice constant, Moss-bauer isomer shift, soft X-ray absorption and X-ray photoemission spectroscopy (XPS). 

Fig. 11.20. Magnetic susceptibility vs temperature for several nonmagnetic Yb compounds with nonintegral valence. The rapid increase below 50 K is attributed to less than 1% of Yb20j impurity. For comparison, the magnetic susceptibility of YbjOj (Yb ) and YbAlj (Yb ) are also shown [after Sales (1974) Maple and Wohlleben (1974)].

Studies on concentrated lanthanide metallic systems have also made it possible to establish a correlation between nonintegral valence (observable in concentrated lanthanide systems through lattice constant, Mdssbauer isomer shift, soft X-ray absorption and X-ray photoemission spectroscopy measurements) and nonmagnetic behavior of a lanthanide ion below the characteristic temperature. This has led to the concept of valence fluctuations (or interconfiguration fluctuations) which has stimulated the current intense activity among theorists and experimentalists alike. 

The chapter by Wachter (132), which is one of the most extensive and comprehensive ones in the entire Handbook series, reviews intermediate valence and heavy fermions in a wide variety of lanthanide and actinide compounds, ranging from metallic to insulating materials. The behaviors of these materials are discussed from the basic idea that a gap exists between two narrow f-like subbands, i.e. the hybridization gap model, which can account for the observed physical and electronic properties. As pointed out by Wachter, heavy fermions are intermediate valence materials by virtue of the fact that they have nonintegral f occupation values. The main difference between normal intermediate valence materials is that their Fermi energies are in the hybridization gap, while for the heavy fermion materials the Fermi energy is not in the gap. 

Among cerium compounds CeAb, CeB4, CeN and a few intermetallic compounds (see table 20.1) are believed to exhibit nonintegral valence state... 

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