Validity of DFT+U band gaps in all its known functional forms

Abstract

The Density Functional Theory plus Hubbard U (DFT+U) technique is one of the most widely used tools by condensed matter physicists and solid state chemists for the simulation of transition-metal and lanthanide bearing crystals, and increasingly of much more diverse chemistries... Since the earliest days, the gap in the DFT+U single-particle eigenspectrum has been associated with the fundamental band gap, and the method has typically found more success for spectra than for total-energy derived properties. There has been some doubt, however, as to the conceptual validity of this association. Here, extending findings from recent years regarding local, semi-local, and hybrid functionals within the generalized Kohn-Sham framework, we prove and numerically demonstrate that the DFT+U eigenspectrum gap is conceptually valid, in the specific sense that it matches its own fundamental gap calculated using total-energy differences. We emphasize that this does not imply its agreement with experimental values, and indeed our argument is independent of the Hubbard U parameter. The result holds for pristine periodic systems with converged k-point sampling but not, however, for defective ones, isolated systems, or systems in which added charges exhibit spontaneous localization. We show that bandgap validity for pristine solids holds in the presence of pseudopotentials and PAW potentials, when using hybrid functionals, and in DFT+U(+J) irrespective of the level of subspace projection onto the band-edge states. We survey every collinear-spin DFT+U-type functional known to have been published to date, within a unified notation... Returning to the related but different question of band-gap correction efficiency, we offer fresh analysis of DFT+U bandgap projection dependence, and each functional's effect on energies and gaps for the hydrogen lattice in the Mott-Hubbard limit.