Hubbard Interactions From Density-Functional Perturbation Theory

DFT+U is a simple and powerful tool to model systems containing partially-filled manifolds of localized states. However, the Hubbard parameters are often treated semi-empirically, which is a somewhat unsatisfactory approach. Conceptual methods to determine U from first principles have nevertheless been introduced long ago, based either on the constrained random-phase approximation or linear-response theory. These approaches make DFT+U a fully self-contained method but are often overlooked due to their cost or complexity. We introduce a computationally inexpensive and straightforward approach to determine the linear-response U, hitherto obtained from the difference between bare and self-consistent inverse electronic susceptibilities evaluated from supercell calculations. By recasting these calculations in the language of density-functional perturbation theory we remove the need of supercells, and allow for a fully automated determination of susceptibilities and Hubbard parameters. Such developments open the way for deployment in high-throughput studies, can be extended to intersite couplings V, while providing the community with a simple tool to calculate consistent values of U for any system at hand. Last, the approach is showcased with applications to transition-metal compounds.