A new kind of atlas of zeolite building blocks

Abstract

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 6Å, 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.

Learning grain boundary segregation energy spectra in polycrystals

“…For an accelerated option of the ML framework, we propose using the 10 principal components obtained from PCA as the input for the linear regression algorithm 49,50 . As the problem is now reduced to fitting P SOAP + 1 coefficients (instead of F SOAP + 1), we conservatively only need~P × 10 = 100 data-points for training; 100 molecular statics computations involving the substitution of a single solute atom at a grain boundary site in a polycrystal give insight on the entire segregation spectrum.…”

Geometric landscapes for material discovery within energy–structure–function maps

“…Applying methods such as regularized entropy match (REMatch) or even simple averaging on the local SOAP descriptor allows the comparison of structures by quantifying their structural similarity. 33,34,70 Here, in addition to the comparison with the SOAP method, we compare persistent homology with the conventional geometric descriptors, a four-dimensional vector of the crystal density, surface area, pore volume, and pore size, to further elucidate what is gained using the persistent homology approach.…”

“…The SOAP descriptors for each atomic species in the crystal structure were computed with hyperparameters similar to the previous work on zeolites, 70 i.e., using 12 radial basis functions, 9 spherical harmonics, and Gaussians with width of 0.3. To compare structures we used the distance metric induced by adopting normalized kernel, either the regularized entropy match (REMatch) 33 kernel or the average structural kernel.…”

Prediction of Thermal Properties of Zeolites through Machine Learning

“…Nevertheless, this structural database of hypothetical zeolites has been widely used in the exploration and systematic prediction of structure/property relationships. 42,52,53…”