First-principles Hubbard parameters with automated and reproducible workflows

We introduce an automated, flexible framework (aiida-hubbard) to self-consistently calculate Hubbard $U$ and $V$ parameters from first-principles. By leveraging density-functional perturbation theory, the computation of the Hubbard parameters is efficiently parallelized using multiple concurrent and inexpensive primitive cell calculations. Furthermore, the intersite $V$ parameters are defined on-the-fly during the iterative procedure to account for atomic relaxations and diverse coordination environments. We demonstrate the scalability and reliability of the framework by computing in high-throughput fashion the self-consistent onsite $U$ and intersite $V$ parameters for 115 Li-containing bulk solids. Our analysis of the Hubbard parameters calculated reveals a significant correlation of the onsite $U$ values on the oxidation state and coordination environment of the atom on which the Hubbard manifold is centered, while intersite $V$ values exhibit a general decay with increasing interatomic distance. We find, e.g., that the numerical values of $U$ for Fe and Mn 3d orbitals can vary up to 3 eV and 6 eV, respectively; their distribution is characterized by typical shifts of about 0.5 eV and 1.0 eV upon change in oxidation state, or local coordination environment. For the intersite $V$ a narrower spread is found, with values ranging between 0.2 eV and 1.6 eV when considering transition metal and oxygen interactions. This framework paves the way for the exploration of redox materials chemistry and high-throughput screening of $d$ and $f$ compounds across diverse research areas, including the discovery and design of novel energy storage materials, as well as other technologically-relevant applications.