Hubbard parameters from density-functional perturbation theory

We present a transparent and computationally efficient approach for the first-principles calculation of Hubbard parameters from linear-response theory. This approach is based on density-functional perturbation theory and the use of monochromatic perturbations. In addition to delivering much improved efficiency, the present approach makes it straightforward to calculate automatically these Hubbard parameters for any given system, with tight numerical control on convergence and precision. The effectiveness of the method is showcased in three case studies---${\mathrm{Cu}}_{2}\mathrm{O}$, NiO, and ${\mathrm{LiCoO}}_{2}$---and by the direct comparison with finite differences in supercell calculations.