Yet these important parallels seem to rarely be pointed out in textbooks. [One exception is a brief mention in Walter Harrison's Electronic Structure and the Properties of Solids].
Recently when I have taught solid state I have pointed out the connection and sometimes worked through the nice treatment of Huckel theory in chapter 8 of the classic book Coulson's Valence by Roy McWeeny.
- How Bloch's theorem works in a finite system.
- How energy bands emerge in the thermodynamic limit (see above).
- The correspondence between bonding (anti-bonding) orbitals in a molecule and valence (conduction) bands in a crystal.
- The potential importance of electron-electron interactions, which are completely neglected in both Huckel and tight-binding approximations. Valence bond theory takes these interactions into account.
Any other ideas?