Brief account of intermediate valence

Not only are Li+ intercalation and H+ intercalation in these solids closely similar processes, but topotactic Li+/H+ exchange has been observed on complex oxides [614] this is further evidence that soft chemistry is related to properties of the radial Schrodinger equation, the occupied angular wavefunctions being the same throughout the reversible redox cycle, so that bonds are not broken and bond directions, in particular, are hardly altered. In this respect, soft chemistry resembles physisorption, as opposed to chemisorption (see section 11.3). 

In section 5.18, we described how an atom with a strong centrifugal barrier might be poised with an orbital shared evenly between two wells, and the specific example of Ba+ was given. If an atom close to this condition is used to build a solid, then the questions arise how many of the electrons remain attached to the atom, and how many delocalise and join those of the conduction band  

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]). 

The most popular model to describe the situation uses a Hubbard Hamiltonian to represent the localisation-delocalisation of an / electron in the presence of the potential of a d core hole, thus  

Unfortunately, the model does not predict the magnitudes of these parameters, on which the transition depends. It is even conceivable in the presence of atomic multiplet structure, or of term-dependent localisation effects internal to the atom, etc., that the semiempirical parametrisation might absorb effects not really intended in the model, such as atomic multiplet splittings or term dependence of the orbitals. 

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