Comparing Hubbard parameters from linear-response theory and a Hartree-Fock-based approach

Density-functional theory with on-site U and inter-site V Hubbard corrections (DFT+U+V) is widely used to predict properties of transition-metal and rare-earth compounds, but its accuracy depends critically on how these parameters are obtained. While they can be determined empirically, first-principles approaches offer better consistency, though their results can differ and a systematic comparison is lacking. Here, we compare two widely used approaches, linear-response theory (LRT) and the Hartree-Fock-based pseudohybrid functional formalism, applied to representative oxides (MnO, NiO, CoO, FeO, BaTiO₃, ZnO, and ZrO₂). For partially occupied transition-metal d states, both methods yield comparable U values, but they differ significantly for nearly empty or fully filled d shells. For O-2p states, LRT systematically predicts large U values (~ 10eV), whereas the pseudohybrid approach gives system-dependent values. Even larger differences appear for the inter-site V: the former yields small values (< 1eV), while the latter gives larger values (~ 3eV) due to its dependence on charge redistribution. We further show that the pseudopotential choice, which defines Hubbard projectors, affects the parameters and their agreement. Overall, while parallels between these two methods exist, they rely on different assumptions, leading to variations in predictions of material properties.