Tuesday, February 23, 2010

Are you local or non-local?

I wrote in a previous post about the importance of listening to referees. I recently got back a referee report for this review on oxygen vacancies in cerium oxides (written with Elvis Shoko and Michael Smith). The report ended:

Finally, I cannot avoid suggesting the authors to have a look at: “A Conversation on VB vs MO Theory: A Never-Ending Rivalry? Roald Hoffmann, Sason Shaik, Philippe C. Hiberty. Accounts of Chemical Research 2003 36 (10), 750-756”. Perhaps, they will hear some familiar tones.

I read and enjoyed the paper [inspiring the post Marriage Counseling for Chemists] and am now trying to make concrete the connection with our work.

By a bond valence sum analysis of the structure around oxygen vacancies we consider the charge distribution arising from the two electrons left behind by removing an oxygen atom. We find rather subtle charge distributions; the two electrons do not simply localise on the two Ce ions next to the vacancy [the standard picture which is either assumed or claimed ot be supported by density functional theory based calculations]. Instead the two electrons can delocalise over the next nearest neighbours, but do not delocalise into the whole crystal.

At first the connection with the VB vs. MO debate was not clear but on reflection there may be some profound ones such as:

  • Valence Bond (VB) theory tends to localise electrons too much. Molecular Orbital (MO) theory tends delocalise electrons too much.
  • Our empirical valence bond sum approach is a very local picture and somehow capturing the same physics/chemistry as VB theory.
  • LDA is close to MO theory (it is a band theory, i.e., a non-local picture) and tends to delocalise electrons too much. Many of the LDA, and LDA+U calculations on cerium oxides artificially force electrons to localise on cerium ions.

Can we make any more connection than the above?

1 comment:

  1. I'd suggest you (and anyone else interested in this) also go back and read Mott's original paper on the Mott insulator - which makes essentially this points 1 and 3. Basically he points out that an MO wavefunction is like a metal and the VBS wavefunction describes a (Mott) insulator. So there is a phase transition (the Mott transition) separating them in the infinite xtal. This is in marked contrast to, say, H2, where both a approximations to the same (exact) wavefunction.