The chemical concept of valence is of great utility. The valence of an atom, M, determines the number of neighbouring atoms with which M can form chemical bonds. For most metal ions, the valence, V, is equal to the oxidation number, O. Deviations from this equality occur when delocalization of electrons occurs. The simplest case is where V and O differ by one because one electron from each of the M atoms is completely delocalized in the conduction band. Mixed valency of transition metal and rare-earth ions in solids and compounds is a question of fundamental interest in materials physics, chemistry, and molecular biophysics.
In 1967, Robin and Day (chemists) published a classification scheme for mixed-valence that is still widely used today. Class 1 describes systems with two crystallographic sites that are clearly distinct and and the two sites have integral but unequal valence. There is a large energy associated with transfer of electrons between sites. At the other extreme is Class 3 for which there are two sites which are not distinguishable, and one assigns a non-integral valence to both sites. The classic case of this is the Creutz-Taube ion. The valence electrons are delocalised between the two sites. Class 2 is the intermediate case where the environments of the two sites are distinguishable but not very different. The energy associated with electron transfer is sufficiently small that it can be thermally activated and be associated with significant optical absorption in the visible range. On the time scale of the vibrations of the atoms the electrons may appear to be delocalised.
Classes 1 and 2 correspond to what Varma (a physicist) termed inhomogeneous mixed valence, although, perhaps, inhomogeneous integral valence may be more appropriate. Class 3 corresponds to homogeneous mixed valence.
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