High-throughput determination of Hubbard $U$ and Hund $J$ values for transition metal oxides via the linear response formalism

$\mathrm{DFT}+U$ provides a convenient, cost-effective correction for the self-interaction error (SIE) that arises when describing correlated electronic states using conventional approximate density functional theory (DFT). The success of a $\mathrm{DFT}+U$(+$J$) calculation hinges on the accurate determination of its Hubbard $U$ and Hund $J$ parameters, and the linear response (LR) methodology has proven to be computationally effective and accurate for calculating these parameters. This study provides a high-throughput computational analysis of the $U$ and $J$ values for transition metal $d$-electron states in a representative set of over 1000 magnetic transition metal oxides (TMOs), providing a frame of reference for researchers who use $\mathrm{DFT}+U$ to study transition metal oxides. In order to perform this high-throughput study, an atomate workflow is developed for calculating $U$ and $J$ values automatically on massively parallel supercomputing architectures. To demonstrate an application of this workflow, the spin-canting magnetic structure and unit cell parameters of the multiferroic olivine ${\mathrm{LiNiPO}}_4$ are calculated using the computed Hubbard $U$ and Hund $J$ values for $\mathrm{Ni}\text{−}d$ and $O\text{−}p$ states, and are compared with experiment. Both the $\mathrm{Ni}\text{−}dU$ and $J$ corrections have a strong effect on the Ni-moment canting angle. Additionally, including a $O\text{−}pU$ value results in a significantly improved agreement between the computed lattice parameters and experiment.