Bonding of sp-valent metals

The sp-valent metals such as sodium, magnesium and aluminium constitute the simplest form of condensed matter. They are archetypal of the textbook metallic bond in which the outer shell of electrons form a gas of free particles that are only very weakly perturbed by the underlying ionic lattice. The classical free-electron gas model of Drude accounted very well for the electrical and thermal conductivities of metals, linking their ratio in the very simple form of the Wiedemann-Franz law. However, we shall now see that a proper quantum mechanical treatment is required in order to explain not only the binding properties of a free-electron gas at zero temperature but also the observed linear temperature dependence of its heat capacity. According to classical mechanics the heat capacity should be temperature-independent, taking the constant value of kB per free particle. 

The above model of an sp-valent metal as a gas of free electrons would exhibit no bonding because the only contribution to the energy is the repulsive kinetic energy. It takes an average value per electron, which is given by... 

The free-electron gas model is a good starting point for the sp-valent metals where the loosely bound valence electrons are stripped off from their ion cores as the atoms are brought together to form the solid. However, bonding in the majority of elements and compounds takes place through saturated... 

Cleavage of a C(sp)-C(sp) single bond by low-valent titanocene and zirconocene has been reported [36]. Treatment of a diyne with those metallocenes in tetrahydrofuran (THF) produced the dimer of the alkynylmetallocene complex, in which the alkyne moiety was bonded to the metal center in both a-and it-fashions (Scheme 1.27). 

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