Structural Descriptors to Correlate Pb Ion Displacement and Broadband Emission in 2D Halide Perovskites

2D hybrid lead halide perovskites exhibit versatile photoluminescent behaviors for narrowband to broadband emissions (BBEs) and have become attractive candidates for potential applications such as solid-state lighting. Establishing the relationship between the perovskite structural distortion and BBE is key but challenging in designing and optimizing the perovskite luminophores. Conventional attention is given to analyzing the intra-octahedron distortion of the [PbX₆]^4- (X = halide) unit that has not yet provided a clear structure-luminescence relationship. Herein, we introduce a descriptor, Pb displacement, to describe the inter-octahedron distortion to clarify the structure-emission relationship. The displacement of adjacent Pb centers represents the lattice distortion, which determines the broadband/narrowband emission instead of the octahedron distortion itself. We find a kite-type quadrilateral rule in (001) type 2D perovskites, that is, the degree to which the four octahedral central ions deviate from a square relates to the BBE. The kite-type arrangement of the Pb ions usually corresponds to the BBEs due to the large structure distortions. In contrast, the square-type arrangement of the Pb ions corresponds to the narrowband emissions because of the small distortions. The distortion descriptor magnifies the distortion scale, making it larger than the conventional one for the intra-octahedron distortion, which matches the general concept of excitons based on the scale of the crystal lattice. Therefore, the set of structural descriptors is better to correlate the perovskite structures and emission properties.