Hubbard interactions from density-functional perturbation theory

DFT+U+V is a novel and powerful tool to model systems containing partially-filled manifolds of localized states. However, there is a history of treating Hubbard parameters semi-empirically, which is unsatisfactory. Conceptual methods to determine e.g. Hubbard U from first principles have nevertheless been introduced long ago, based either on the constrained random-phase approximation or on linear response theory. Still, these approaches are often overlooked due to their cost or complexity. Here, we introduce a computationally inexpensive and straightforward approach [1] to determine on-site U and inter-site V Hubbard parameters, bypassing the need to use supercells. By recasting linear-response susceptibilities in the language of density-functional perturbation theory we substitute monochromatic pertubations to supercells, and allow for a fully automated determination of Hubbard parameters in primitive cell calculations. Such developments provide the community with a robust and reliable tool to calculate consistent values of U and V for any system at hand, while opening the way for deployment in high-throughput studies. The approach is showcased with applications to the vibrational spectra of selected transition-metal compounds.
[1] I. Timrov et al., PRB 98, 085127 (2018).