Structural Disorder by Octahedral Tilting in Inorganic Halide Perovskites: New Insight with Bayesian Optimization

Structural disorder is common in metal-halide perovskites and important for understanding the functional properties of these materials. First-principles methods can address structure variation on the atomistic scale, but they are often limited by the lack of structure-sampling schemes required to characterize the disorder. Herein, structural disorder in the benchmark inorganic halide perovskites CsPbI₃ and CsPbBr₃ is computationally studied in terms of the three octahedral-tilting angles. The subsequent variations in energetics and properties are described by 3D potential-energy surfaces (PESs) and property landscapes, delivered by Bayesian optimization as implemented in the Bayesian optimization structure search code sampling density functional theory (DFT) calculations. The rapid convergence of the PES with about 200 DFT data points in 3D searches demonstrates the power of active learning and strategic sampling with Bayesian optimization. Further analysis indicates that disorder grows with increasing temperature and reveals that the material bandgap at finite temperatures is a statistical mean over disordered structures.