Living legend of the local density approximation

February 13, 2011

The consensus from decades of condensed matter theory research, using a variety of basis sets and independent implementations, is that the local density approximation (LDA) to density functional theory (DFT) underestimates the band gaps of semiconducting or insulating materials. The reason for this is known and well documented [e.g. Sham and Schlüter, 1983].

To some, this is a conspiracy of the highest order:

Comments on "Quasiparticle self-consistent GW theory of III-V nitride semiconductors: Bands, Gap bowing, and effective masses"
Comments on "Efficient Band Gap Prediction for Solids"
Comment on "Band structures and optical spectra of InN polymorphs: Influence of quasiparticle and excitonic effects"
Comment on "Band gap bowing and electron localization of GaXIn1-XN"
Comments on "Band gap and band parameters of InN and GaN from quasiparticle energy calculations based on exact-exchange density-functional theory"

The general message from this series of comments (in high profile journals) is that the LDA is fine as it is - at least in the implementation of Bagayoko, Zhao, and Williams. An explanation for the results can be found in a reply to one of the comments from Furthmüller et al: "Bagayoko et al. used minimal basis sets of atomic-like orbitals... they were able to determine reasonable gaps of semiconductors already within DFT-LDA. We cannot deny the success of this approach; however, in our opinion this success is somehow accidental...  minimal basis sets open gaps between occupied and unoccupied states.” They were too polite to quote Einstein: “Marvelous, what ideas the young people have these days. But I don't believe a word of it.”