In the present paper we assess the performance of the exact-exchange-only (EXX) Kohn-Sham method to predict band structures of transition metal oxide and metal halide perovskites with the main emphasis on band gaps. For the considered set of prototypical systems with cubic structure, the performance of the EXX method for the prediction of band gaps is comparable with other popular methods for this purpose like density-functional calculations with the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional and one-shot $GW$ ($G_0{W}_0$). Comparison with experimental values suggests that in the case of perovskites the EXX method, like HSE and $GW$ methods, should be supplemented by a treatment of electron-phonon effects. The EXX method is computationally more efficient than $G_0{W}_0$ and also provides post-self-consistent access to one-electron wave functions and band structures within the complete Brillouin zone with much lower computational effort than both $G_0{W}_0$ and hybrid DFT methods. We confirm the importance of including the higher-lying semicore shells within the explicitly treated states for halide perovskites which was already noted by earlier studies. Calculations taking into account only the valence space without the semicore states, however, remain still a reasonable option in practice. Spin-orbit coupling effects seem to be slightly underestimated in DFT calculations both with respect to $GW$ and experiment. The source of this underestimation can be of both technical and formal nature, and this point requires more critical consideration. For ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbI}}_3$, sizable Rashba spin splittings appear for the structure with the C-N bond of the methylammonium ion not lying along the long diagonal of the cubic unit cell.

• Received 20 June 2019

DOI:https://doi.org/10.1103/PhysRevB.100.075205