We have performed a systematic study resulting in detailed information on the structural, electronic and optical properties of the cubic (Pm$\overline{3}$m) and tetragonal (P4mm) phases of PbTiO₃ applying the GGA/PBE approximation with and without the Hubbard U potential correction. Through the variation in Hubbard potential values, we establish band gap predictions for the tetragonal phase of PbTiO₃ that are in rather good agreement with experimental data. Furthermore, the bond lengths for both phases of PbTiO₃ were assessed with experimental measurements, confirming the validity of our model, while chemical bond analysis highlights the covalent nature of the Ti–O and Pb–O bonds. In addition, the study of the optical properties of the two phases of PbTiO₃, by applying Hubbard’ U potential, corrects the systematic inaccuracy of the GGA approximation, as well as validating the electronic analysis and offering excellent concordance with the experimental results. Therefore, our results underline that the GGA/PBE approximation with the Hubbard U potential correction could be an effective method for obtaining reliable band gap predictions with moderate computational cost. Therefore, these findings will enable theorists to make use of the precise values of these two phases’ gap energies to enhance PbTiO₃’s performance for new applications.

By using DFT simulations employing the GGA/PBE and LDA/CA-PZ approximations, the effects of the Hubbard U correction on the crystal structure, electronic properties, and chemical bands of the cubic phase (Pm$\overline{3}$m) of STO were investigated. Our findings showed that the cubic phase (Pm$\overline{3}$m) STO’s band gaps and lattice parameters/volume are in reasonably good accordance with the experimental data, supporting the accuracy of our model. By applying the DFT + U method, we were able to obtain band gaps that were in reasonably good agreement with the most widely used experimental band gaps of the cubic (Pm$\overline{3}$m) phase of STO, which are 3.20 eV, 3.24 eV, and 3.25 eV. This proves that the Hubbard U correction can overcome the underestimation of the band gaps induced by both GGA/PBE and LDA/CA-PZ approximations. On the other hand, the Sr-O and Ti-O bindings appear predominantly ionic and covalent, respectively, based on the effective valence charges, electron density distribution, and partial density of states analyses. In an attempt to enhance the performance of STO for new applications, these results might also be utilized as theoretical guidance, benefitting from our precise predicted values of the gap energies of the cubic phase (Pm$\overline{3}$m).