DFT + U accurate for strain effect and overall properties of perovskite oxide ferroelectrics and polaron

We find that the unit cell volume (V), which affects many properties, decreases too rapidly with strain when calculated with standard density functional theories (DFTs) such as local density approximation (LDA). We find that this demerit is moderated with the use of the Hubbard potential U for local electron correlation (DFT + U). However, the introduction of U to standard DFTs, e.g., LDA and Perdew–Burke–Ernzerhof functional (PBE) optimized for solids (PBEsol), leads to the excessive underestimation of the spontaneous polarization (PS) and frequently extinguishes PS. Therefore, we attempt to improve the overall accuracy of DFTs for ferroelectrics by using U in several DFT methods including PBE that overestimates PS and lattice constants. We demonstrate that PBE with U (PBE + U) is in excellent agreement with the experimental properties of BaTiO3 and SrTiO3, with improvements in the estimates of lattice constants, PS, the phonon frequency, the antiferrodistortive angle of 105 K-phase SrTiO3, the bandgap, the strain dependence of V, and hole polarons. When the lattice parameters and PS moderately agree with the experimental data, PBE + U with a single U set can produce both electron and hole polarons. Hence, PBE + U can be a practical substitute of hybrid functionals for perovskite oxide ferroelectrics, except for the estimation of the bandgap. Furthermore, we propose an approach to construct a functional accurately depicting the incipient ferroelectric state of SrTiO3. Additionally, these results suggest that conventional DFT underestimates PS under compressive in-plane strain and predicts the unrealistic deformation of ferroelectrics and that in-plane-strained lattices can mitigate the problems associated with U.