Bispectral Analysis of Local Atomic Environments

In this talk, we explore the use of bispectra as a tool to analyze and cluster local atomic environments, enabling the identification of geometric trends across different material classes. The local environments in a material play a significant role in determining its overall properties. Understanding the complex interplay between local environment geometries and material properties is crucial to designing next-generation materials with desired properties. Bispectra are well-suited to characterizing local environments due to being a rotationally invariant, smooth, invertible (modulo a global rotation), and fixed-length descriptor. We define the bispectrum in this context as the scalars and pseudoscalars resulting from the triple tensor product of a local environment's spherical harmonic expansion with itself.

We apply the bispectra to compare the local environments of a new class of hybrid inorganic-organic materials called MOChAs with those found in other transition-metal and chalcogen-containing materials from the Materials Project and Cambridge Structural Database. MOChAs, or Metal-Organic Chalcogenides Assemblies, are self-assembled hybrid crystals in which low-dimensional transition metal chalcogenide structures are scaffolded by organic ligands. The structural diversity of organic ligands leads to a wide range of possible local environments in MOChAs, which are effectively captured by bispectra. These bispectra can be visualized and clustered, ultimately guiding the design and discovery of new MOChAs.