To be a metal, or not to be? Distinguishing semiconductors from metals in high-throughput Kohn-Sham DFT

In non-interacting theories (e.g., Kohn-Sham DFT), the bandgap is the energy that separates valence bands from conduction bands in semiconductors and insulators. In most first-principles calculations, one computes the electronic band structure with a finite sampling in reciprocal space; thus, a finite (if small) gap always exists at zero temperature between the highest occupied state and the lowest unoccupied one. The problem is made more severe when a coarse k-point grid is used and/or when the gap is very small (a few tenths of an eV). We investigate current numerical methods to determine the bandgap and their sensitivity to k-point sampling and smearing. Furthermore, we explore alternative descriptors that separate metals from nonmetals, such as the electronic entropy.