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, ABX3 halide perovskites, vacancy-ordered double perovskites (VODPs), and bond disproportionated halide perovskites (BDHPs), using 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.

卤化物钙钛矿（Halide Perovskites, HPs）因其在可见光光谱范围内具备适宜的带隙，被广泛视为极具应用前景的光伏与发光材料。采用（半）局域交换关联泛函的密度泛函理论（Density Functional Theory, DFT）计算，通常会低估这类体系的带隙值。要准确描述卤化物钙钛矿的电子结构，往往需要更高阶的理论方法，比如Heyd-Scuseria-Ernzerhof（HSE）杂化密度泛函以及GW近似，但这类方法的计算成本远高于标准DFT。本研究针对三类典型卤化物钙钛矿——ABX3型卤化物钙钛矿、空位有序双钙钛矿（Vacancy-Ordered Double Perovskites, VODPs）以及键歧化卤化物钙钛矿（Bond Disproportionated Halide Perovskites, BDHPs），采用带有在位U和跨位点V哈伯德参数的DFT+U+V方法，其中哈伯德参数通过自洽计算得到，无需先验假设。引入哈伯德修正后，三类卤化物钙钛矿的带隙预测精度均提升至与高阶理论方法相当的水平。此外，自洽哈伯德U参数可作为卤化物钙钛矿中多价金属原子真实局域电荷状态的有效表征指标。对于存在卤化物八面体呼吸模式畸变的键歧化卤化物钙钛矿而言，引入跨位点哈伯德V参数对准确捕捉相邻原子价电子间的杂化效应至关重要。尤为关键的是，同时实现哈伯德参数与晶体几何结构的自洽收敛，可使键歧化卤化物钙钛矿的带隙预测精度优于HSE方法，且计算成本仅为其极小一部分。本研究凸显了在处理卤化物钙钛矿时采用自洽哈伯德参数的重要性——这类体系往往存在局域在位效应与跨位点杂化效应之间复杂的竞争关系。