Onsite and intersite electronic correlations in the Hubbard model for halide perovskites

Halide perovskites (HPs) are widely viewed as promising photovoltaic and light-emitting materials for their suitable band gaps in the visible spectrum. Density functional theory (DFT) calculations employing (semi)local exchange-correlation functionals usually underestimate the band gaps for these systems. Accurate descriptions of the electronic structures of HPs often demand higher-order levels of theory such as the Heyd-Scuseria-Ernzerhof (HSE) hybrid density functional and $GW$ approximations that are much more computationally expensive than standard DFT. Here, we investigate three representative types of HPs, $AB{X}_{3}$ halide perovskites, vacancy-ordered double perovskites, and bond disproportionated halide perovskites (BDHPs), using $\mathrm{DFT}+U+V$ with onsite $U$ and intersite $V$ Hubbard parameters computed self-consistently without a priori assumption. The inclusion of Hubbard corrections improves the band gap prediction accuracy for all three types of HPs to a similar level of advanced methods. Moreover, the self-consistent Hubbard $U$ is a meaningful indicator of the true local charge state of multivalence metal atoms in HPs. The inclusion of the intersite Hubbard $V$ is crucial to properly capture the hybridization between valence electrons on neighboring atoms in BDHPs that have breathing-mode distortions of halide octahedra. In particular, the simultaneous convergence of both Hubbard parameters and crystal geometry enables a band gap prediction accuracy superior to HSE for BDHPs but at a fraction of the cost. Our work highlights the importance of using self-consistent Hubbard parameters when dealing with HPs that often possess intricate competitions between onsite localization and intersite hybridization.