Thursday, March 31, 2011

Breaking down the physics-chemistry divide

Chemists and physicists tend to talk different languages, including when discussing the same thing. One important parallel is the common concept of the molecular orbitals in a molecule and the energy bands in a crystal. Specifically, the Huckel method to describe electronic properties of conjugated organic molecules is identical to the tight-binding method in solid state physics.

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.


  1. Nice!
    This approach gives me a lucid way to connect physicists and chemists and then lead them both into quantum approaches to understanding biochemistry and biology.

  2. 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

  3. I 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).

  4. A 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!