Understanding the role of Hubbard corrections in the rhombohedral phase of BaTiO₃

We present a first-principles study of the low-temperature rhombohedral phase of BaTiO₃ using Hubbard-corrected density-functional theory. By employing density-functional perturbation theory, we compute the onsite Hubbard U for Ti(3d) states and the intersite Hubbard V between Ti(3d) and O(2p) states. We show that applying the onsite Hubbard U correction alone to Ti(3d) states proves detrimental, as it suppresses the Ti(3d)-O(2p) hybridization and drives the system towards a cubic phase. Conversely, when both onsite U and intersite V are considered, the localized character of the Ti(3d) states is maintained, while also preserving the Ti(3d)-O(2p) hybridization, restoring the rhombohedral phase of BaTiO₃. The generalized PBEsol+U+V functional yields good agreement with experimental results for the band gap and dielectric constant, while the optimized geometry is slightly less accurate compared to PBEsol. Zone-center phonon frequencies and Raman spectra are found to be significantly influenced by the underlying geometry. PBEsol and PBEsol+U+V provide satisfactory agreement with the experimental Raman spectrum when the PBEsol geometry is used, while PBEsol+U Raman spectrum diverges strongly from experimental data highlighting the adverse impact of the U correction alone in BaTiO₃. Our findings underscore the promise of the extended Hubbard PBEsol+U+V functional with first-principles U and V for the investigation of other ferroelectric perovskites with mixed ionic-covalent interactions.