How are energy bands formed in compounds(solids)? Take for example Al2O3. Which orbitals of Al atom or O atom will form conduction band or valence band. Are the conduction or valence bands have s, p, d.... etc character? Is it that conduction band is formed out of atomic orbital of one type of atom and valence band is formed out of the orbitals of the other type of atom? In which band do the shared electrons reside in case of a covalently bonded compound? They are highly localized and can not conduct (i suppose). But then in silicon crystal or GaAs crystal the bonds are covenant but both of them conduct at room temperature.
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The bands are delocalized. The insulation character is caused by the valence band being completely filled, with a large band gap to the conduction band.
There are different ways to calculate this.
- One could start with for example plane waves and do a complete ab initio calculation of the electronic band structure.
- Or one can take a tight-binding approximation and start with a valence band composed of oxygen $2p$ orbitals and a conduction band of aluminium $3s,3p$ orbitals. That approximation would be crude (there are no bare Al$^{3+}$ ions in the oxide), but it may explain some of the properties of Al$_2$O$_3$.