A systematic determination of hubbard U using the GBRV ultrasoft pseudopotential set

Abstract

Density-functional theory (DFT) is an increasingly useful tool in modern materials discovery. Advancements in parallel computing allow for high-throughput studies that predict new examples of functional materials such as photovoltaics, electrocatalysts, and thermoelectrics. An impediment to the widespread adoption of DFT is that the method is known to over-delocalize electron density, specifically in d and f orbitals. Without corrections known as post-DFT methods, the over-delocalization effect manifests as inaccurate electronic structures, which leads to a systematic underestimation of electronic bandgap values, or in many cases predicts insulating materials to have fictitious metallic character. One method to fix this deficiency is to add a corrective potential barrier to delocalization, known as the Hubbard U, to delocalized d and f states of an atom to obtain a more accurate electronic band structure. There are ways to formally derive accurate Hubbard U values, but, in practice, U is often treated as a tunable parameter where U values are chosen to match experimentally determined bandgaps. This is problematic for determining U values of materials that have no measured bandgap or have yet to be synthesized. Here we address these issues by using linear response methods to derive Hubbard U values for 3d, 4d, and 5d transition metals using the GBRV set of ultrasoft pseudopotentials. We calculate U values for three distinct crystal structures of binary metal oxides with different oxidation states; NiO (M+2), corundum (M+3), and rutile (M+4) structure types. We show that U values derived from linear response methods follow periodic trends, and that in some cases the same value of U can be applied to different oxidation states and structure types. We use the trends presented here to elucidate a set of best practices which can be applied to further the emergent field of data-enabled materials discovery.