We have analysed structural motifs in the Deem database of hypothetical zeolites, to investigate whether the structural diversity found in this database can be well-represented by classical descriptors such as distances, angles, and ring sizes, or whether a more general representation of atomic structure, furnished by the smooth overlap of atomic positions (SOAP) method, is required to capture accurately structure-property relations. We assessed the quality of each descriptor by machine-learning the molar energy and volume for each hypothetical framework in the dataset. We have found that SOAP with a cutoff-length of 6 AA, which goes beyond near-neighbor tetrahedra, best describes the structural diversity in the Deem database by capturing relevant inter-atomic correlations. Kernel principal component analysis shows that SOAP maintains its superior performance even when reducing its dimensionality to those of the classical descriptors, and that the first three kernel principal components capture the main variability in the data set, allowing a 3D point cloud visualization of local environments in the Deem database. This ``cloud atlas of local environments was found to show good correlations with the contribution of a given motif to the density and stability of its parent framework. Local volume and energy maps constructed from the SOAP/machine-learning analyses provide new images of zeolites that reveal smooth variations of local volumes and energies across a given framework, and correlations between local volume and energy in a given framework.
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