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Graph similarity drives zeolite diffusionless transformations and intergrowth


Predicting and directing polymorphic transformations is a critical challenge in zeolite synthesis1,2,3. Interzeolite transformations enable selective crystallization4,5,6,7, but are often too complex to be designed by comparing crystal structures. Here, computational and theoretical tools are combined to both exhaustively data mine polymorphic transformations reported in the literature and analyse and explain interzeolite relations. It was found that crystallographic building units are weak predictors of topology interconversion and insufficient to explain intergrowth. By introducing a supercell-invariant metric that compares crystal structures using graph theory, we show that diffusionless (topotactic and reconstructive) transformations occur only between graph-similar pairs. Furthermore, all the known instances of intergrowth occur between either structurally similar or graph similar frameworks. We identify promising pairs to realize diffusionless transformations and intergrowth, with hundreds of low-distance pairs identified among known zeolites, and thousands of hypothetical frameworks connected to known zeolite counterparts. The theory may enable the understanding and control of zeolite polymorphism.

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Fig. 1: Types of zeolite transformations and classical explanations.
Fig. 2: Graph and supercell matching.
Fig. 3: Structural and graph similarities in zeolites.

Data availability

The zeolite datasets analysed during the current study are available online at the IZA Database ( and at the Predicted Crystallography Open Database ( Complete references for the literature analysed in this work, pairwise distances between known zeolites and isomorphism between hypothetical and known zeolites are available in the Supplementary Information.

Code availability

The code used to download journal articles for large-scale text mining is available at The code used to variationally compare crystal structures as supercell graphs is available from the corresponding author on request.


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D.S.-K. acknowledges the MIT Nicole and Ingo Wender Fellowship, the MIT Robert Rose Presidential Fellowship and the MIT Energy Initiative (MITEI) Storage Seed Fund for financial support. R.G.-B. thanks MIT DMSE, Toyota Faculty Chair and MITEI for support. The work of E.O. and Z.J. was partially funded by National Science Foundation Award no. 1534340, DMREF, the MIT-Sensetime Alliance on Artificial Intelligence, and the Office of Naval Research (ONR) under Contract no. N00014-16-1-2432. D.S.-K. and R.G.-B. thank A. Corma, M. Moliner and Y. Román-Leshkov for fruitful discussions.

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Authors and Affiliations



R.G.-B. conceived the project. D.S.-K. and R.G.-B. formulated the hypothesis of graph-similar transformations. D.S.-K. developed the graph and supercell matching methods, wrote the computer code and performed all the calculations. Z.J. and E.O. performed the literature mining and database query. Z.J., E.O. and D.S.-K. reviewed the extracted articles. D.S.-K. and R.G.-B. wrote the first version of the manuscript and made the figures. All the authors contributed to the final version of the manuscript.

Corresponding author

Correspondence to Rafael Gómez-Bombarelli.

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The authors declare no competing interests.

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Supplementary information

Supplementary Information

Appendices A–F, Supplementary Figs. 1–11, Tables 1–3 and refs. 1–262.

Supplementary Data 1

Normalized SOAP distance and D-measure for each of the 29,890 pairs of known zeolites. The csv file is sorted alphabetically by the zeolite IZA codes. The elements mij(A,B) (equation (D10)) of the transformation matrices M(A) and M(B) that minimize the graph distance between the frameworks (equation (D14)) are also given.

Supplementary Data 2

Hypothetical zeolites from PCOD with energy above quartz and their isomorphic IZA known zeolites. Only hypothetical zeolites with at least one isomorphic counterpart are shown in the table.

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Schwalbe-Koda, D., Jensen, Z., Olivetti, E. et al. Graph similarity drives zeolite diffusionless transformations and intergrowth. Nat. Mater. 18, 1177–1181 (2019).

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