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.
Besides showing the molecule-solid connection this can illustrate a few useful things including:
- 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?
Some of the above parallels are explored in more detail in a beautiful article How Chemistry and Physics meet in the Solid State by Roald Hoffmann, and in a forthcoming book chapter by Ben Powell.
Nice!
ReplyDeleteThis approach gives me a lucid way to connect physicists and chemists and then lead them both into quantum approaches to understanding biochemistry and biology.
Dudley Herschbach wrote an illuminating column about physics-versus-chemistry for Physics Today's April 1997 issue entitled "Chemistry: Blithe Sibling of Physics"—Charles Day
ReplyDeleteI think one of the more important connections to make using Huckel/TB theory is influence of symmetry and bond connectivity on the band-structure (and correspondingly the molecular orbitals).
ReplyDeleteA habitual homework problem of mine to give to my Intro to Cond Mat Students is an involved treatment of the tight-binding model for a 6 site ring e.g. benzene. They get a little dizzy at first when I present the problem in terms of chemistr/LCAO language, but then they thank me (and hopefully understand it better), by the time they are through!
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