Band Gap Alteration of Halide Mixing in Hybrid Perovskites: A First-Principles Study with Statistical Analysis

Despite numerous studies on the band gap of three-dimensional halide perovskites using the first-principles calculations, there are still significant discrepancies between theoretical and experimental values. Various solutions have been proposed, such as employing a system-specific hybrid functional with varying degrees of exact exchange and explicitly incorporating spin-orbit coupling effects. Our research involved a comprehensive investigation of three typical lead-containing three-dimensional perovskites MAPbI₃, MAPbBr₃, and MAPbCl₃ (MA = CH₃NH₃). Through a statistical analysis comparing mean absolute error (MAE) with experimental results, we demonstrated that the nonlocal van der Waals (vdW) density functional corrections (i.e., optB86b) yielded the most approximate lattice parameters in comparison to experimental values. Furthermore, based on these lattice parameters, the HSE06 hybrid functional is the optimal estimation of the band gap among all the options. Moreover, we investigated three sets of mixed three-dimensional halide perovskites by varying the halide component. This exploration contributes to the identification of MAPb(Br_0.333I_0.667)₃ and MAPb(Cl_0.333I_0.667)₃ as exhibiting the smallest band gap of 1.315 (1.867) eV and 1.313 (1.885) eV for PBE (HSE06), respectively. These band gaps were determined using the HSE06 method with the optimized lattice by PBE considering the optB86b corrections. The approach employed in this work produced a band gap trend closely aligned with experimental observations, underscoring the importance of adopting a reliable and material-independent computational strategy when screening new halide perovskite materials for optoelectronic applications.