Koopmans-compliant density functional framework for polaron self-trapping in titanate oxides

Abstract Polaron self-trapping in titanate oxides—TiO₂ (rutile and anatase) and perovskites (BaTiO₃, SrTiO₃, CaTiO₃)—is crucial for their ferroelectric and photocatalytic behavior. Here, we adopt two Koopmans-compliant approaches to investigate polaron self-trapping: (1) determining Hubbard- U parameters that fulfill the generalized Koopmans’ condition for electron localization on Ti-3 d and hole localization on O-2 p orbitals within PBEsol (a GGA functional), SCAN, and LAK (meta-GGAs); and (2) adjusting the mixing ( α ) and screening ( μ ) parameters of the HSE06 hybrid functional to satisfy the same conditions for electron and hole polarons. Our results show that applying these self-interaction corrections (SICs) yields polaron formation energies that are consistent across different Koopmans-compliant functionals. In BaTiO₃, while applying a Hubbard- U correction to Ti-3 d and O-2 p spuriously stabilizes the cubic phase over the rhombohedral one, an on-site SIC correction for the electron- and hole-polaron states restores the correct rhombohedral phase stability. This work systematically compares different Koopmans-compliant approaches for modeling small-polaron trapping in functional oxides and highlights the importance of enforcing the generalized Koopmans condition for obtaining consistent polaron energetics.