The Metallic Valence From Chemistry to a Solid State Case

The Metallic Valence From Chemistry to a Solid State Case 

The concept of valence developed in the preceding section is the basis of the first correlations aiming at a global theory of the actinide metallic bond. These correlations were established between the atomic volumes of actinide elemental metals, and the electronic configuration of the actinide atoms Their aim was to provide a general theory of actinides (i.e. to give an answer to the questions i. and ii. of Sect. A.I.l.) within the framework of a simple model of the metallic bond. 

It is known that the cohesion of a metal is ensured by the electrons partially filling a conduction (or valence) band. The wave functions of these conduction electrons are Bloch functions, i.e. amplitude modulated plane waves. Even though these wave functions are linear combinations of the electronic wave functions in the isolated atoms, reminiscence of the atomic orbitals is lost (or is eventually contained in the amplitude factor). The conduction electrons are, of course, originally, the outer or valence electrons of the atoms but in a metal, to describe them as s, p, d or f, i.e. with the quantum number proper to the atomic case, has little meaning. They may be considered to many purposes to be free electrons . 

The simplest model of a metal is therefore the one in which the metal is depicted as an array of ions glued together by conduction (quasi-free) electrons. If this is the case, one may define a metallic valence as being, essentially, the charge left in the ion cores when outer electrons have been stripped off. Conversely, the metallic valence can be defined as the contribution of outer electrons each atom gives to the sea of bonding conduction electrons. 

The loss of outer electrons from the atoms to a conduction band, in such a simple picture, bears a similarity to the redox process which is supposed to occur in molecular bonds, and which is at the basis of the oxidation state or formal valence concept. If this is the case, the metallic valence should coincide with one of the valences that one encounters in compounds, possibly with the most stable one. 

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