Comparison of Hybrid Functionals HSE and PBE0 in Calculating the Defect Properties of CsPbI₃

Density functional theory calculations play an important role in the study of defects in halide perovskites.Although the traditional semi-local functionals (such as PBE) can obtain the band gaps close to the experiments, they fail to accurately describe the positions of the band edges.Utilizing more accurate hybrid functionals combined with the spin-orbit coupling (SOC) effect with full structure relaxation is considered to be necessary for the prediction of defect properties.There are two types of hybrid functionals in the literature, namely the screened HSE and the unscreened PBE0.In this study, taking the orthorhombic phase CsPbI 3 as an example, these methods were compared for the calculation of defect properties.The results show that there is no obvious difference between two methods for bulk properties, but qualitative differences appear for the defect properties.Most of the shallow-level defects predicted in the HSE calculations become deep-level defects in the PBE0 calculations.Meanwhile, there are qualitative differences between the defect transition levels and the Kohn-Sham levels.The origin of above differences lies in the fact that the Hartree-Fock exchange potential has long-range interaction.Therefore, in unscreened hybrid functionals, such as PBE0, it is more difficult to obtain convergent results with a manageable supercell size.In contrast, HSE exhibits a screening effect on the Hartree-Fock exchange potential and can obtain accurate defect energy levels using relatively small supercell sizes.Therefore, all results here demonstrate that the HSE hybrid functional owns a significant advantage in dealing with this problem even though a large Hartree-Fock mixing parameter (about 0.43) is needed.