Agreement between Mulliken populations in theory and experiment?

[Quantamania]

Fellows,
      I am here with a question about the method of Mulliken populations for atoms in a system.  I am asking it because calculations using LDA-PZ methods on hexagonal boron nitride leads to a Mulliken population of about 3.5 electrons for boron atoms and 4.5 electrons for nitrogen atoms.  This makes boron anionic and nitrogen cationic in these layers. However, in Journal of Physical Chemistry of Solids by Yamamura et al. (1997, volume 58, number 2, pages 177-183), the study of hexagonal BN with X-ray diffraction reveals a charge transfer FROM boron to nitrogen.  In the LDA-PZ results, the charge transfer is in the opposite direction, from nitrogen to boron.

How can we explain the discrepancy in the direction of charge transfer for hexagonal BN in these situations?

The LDA-PZ results correspond closely to what one would expect from a Lewis structure drawing of a h-BN layer, as double bond resonance would be needed to keep the layer planar and properly describe the bond length in this layer.  The bond length of B-N in the default model of h-BN is about 1.446 angstroms long.  Compare this with the typical B-N bond in borazine (1.436 angstroms), which is also described in the same way as h-BN layers.

Are there articles that describe agreement between Mulliken population calculations for materials and the experimental results obtained from them?

This is related to my current dissertation research, as the experimental results are not presenting the same picture of charge density in h-BN as our calculations.  I need to find out how to resolve this problem.

[Anders Blom]

Basically, the Mulliken populations are related to the basis set, while the analysis in the paper goes more to the real-space density. Although there is naturally a correlation, precisely which charge you choose to assign to an atomic site is always a bit arbitrary (and, if you wish, not even physical, just numerical). In the paper they have a particular way of saying how much charge belongs to each atom (they take as the separation point the minimum of the charge on the bond-line), which certainly is not how the Mulliken populations are defined. So some difference should be expected.

Thus the Mulliken populations are a rather blunt instrument. If you really want to compare to the experimental results, I suggest you try to make similar contour plots as in Figs 2 and 3 in the article, of the electron density. Although VNL will not give you exactly such contour, but rather a bit more colorful ones, one should be able to compare the pictures, and hopefully find some agreement. In principle you could also try to reproduce Fig 4 but it's a bit trickier.

[Quantamania]

Thanks, Dr. Blom.

I already have a similar figure in my dissertation that employs the electron density contour methods of VNL for the hexagonal BN bond, along with a C-C bond in the same unit cell for comparison.  We were able to infer how the density looks like, along with the electrostatic contours, in this structure.  Both helped us determine how the atoms were charged, as the electrostatic image gives us basins of attraction for a cationic probe.  The contours also gave us a way to begin our perturbation theory analysis of the C...X interactions, using the basins to define the energy shift directions for each interaction according to first-order and second-order perturbations.

Now I see about the arbitrary aspect...so it is based on particular definitions.  In that situation, we are seeing different definitions of the same quantity yielding different directions.  The positive thing about this is the magnitude...it is almost the same in both situations for us.  It shows that we got the ionicity of the B-N bond and potentially the atom sizes with a good estimate.

I'll take a look at the figures and see what I can do with the h-BN layer calculations.