Relationships between Distortions of Inorganic Framework and Band Gap of Layered Hybrid Halide Perovskites

The unprecedented structural flexibility and diversity of inorganic frameworks of layered hybrid halide perovskites (LHHPs) raise a wide range of useful optoelectronic properties thus predetermining the extraordinary high interest in this family of materials. Nevertheless, the influence of different types of distortions of their inorganic framework on key physical properties such as band gaps has not yet been quantitatively identified. We provided a systematic study of the relationships between LHHPs’ band gaps and six main structural descriptors of inorganic framework, including interlayer distances (dint), in-plane and out-of-plane distortion angles in layers of octahedra (θin, θout), layer shift factor (LSF), and axial and equatorial Pb–I bond distances (dax, deq). Using this set on the selected structural distortions, we realized the inverse materials design based on multistep density functional theory and a machine learning approach to search LHHPs with target values of the band gap. The analysis of calculated descriptors versus band gap dependences for the wide range of generated model structures of (100) single-layered LHHPs results in the following descending order of their importance: dint > θin > dax > LSFmin > θout> deq > LSFmax, and it also implies a strong interaction value for some pairs of structural descriptors. Moreover, we found that the structures with completely different distortions of inorganic frameworks could have similar band gaps, as illustrated by a number of both experimental and model structures.