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Cutting Materials in Half: A Graph Theory Approach for Generating Crystal Surfaces and Its Prediction of 2D Zeolites

Witman, Matthew; Ling, Sanliang; Boyd, Peter; Barthel, Senja; Haranczyk, Maciej; Slater, Ben; Smit, Berend


Matthew Witman

Peter Boyd

Senja Barthel

Maciej Haranczyk

Ben Slater

Berend Smit


© 2018 American Chemical Society. Scientific interest in two-dimensional (2D) materials, ranging from graphene and other single layer materials to atomically thin crystals, is quickly increasing for a large variety of technological applications. While in silico design approaches have made a large impact in the study of 3D crystals, algorithms designed to discover atomically thin 2D materials from their parent 3D materials are by comparison more sparse. We hypothesize that determining how to cut a 3D material in half (i.e., which Miller surface is formed) by severing a minimal number of bonds or a minimal amount of total bond energy per unit area can yield insight into preferred crystal faces. We answer this question by implementing a graph theory technique to mathematically formalize the enumeration of minimum cut surfaces of crystals. While the algorithm is generally applicable to different classes of materials, we focus on zeolitic materials due to their diverse structural topology and because 2D zeolites have promising catalytic and separation performance compared to their 3D counterparts. We report here a simple descriptor based only on structural information that predicts whether a zeolite is likely to be synthesizable in the 2D form and correctly identifies the expressed surface in known layered 2D zeolites. The discovery of this descriptor allows us to highlight other zeolites that may also be synthesized in the 2D form that have not been experimentally realized yet. Finally, our method is general since the mathematical formalism can be applied to find the minimum cut surfaces of other crystallographic materials such as metal-organic frameworks, covalent-organic frameworks, zeolitic-imidazolate frameworks, metal oxides, etc.


Witman, M., Ling, S., Boyd, P., Barthel, S., Haranczyk, M., Slater, B., & Smit, B. (2018). Cutting Materials in Half: A Graph Theory Approach for Generating Crystal Surfaces and Its Prediction of 2D Zeolites. ACS Central Science, 4(2), 235-245.

Journal Article Type Article
Acceptance Date Jan 26, 2018
Online Publication Date Feb 6, 2018
Publication Date Feb 28, 2018
Deposit Date Nov 20, 2018
Publicly Available Date Nov 20, 2018
Journal ACS Central Science
Electronic ISSN 2374-7951
Publisher American Chemical Society
Peer Reviewed Peer Reviewed
Volume 4
Issue 2
Pages 235-245
Public URL
Publisher URL


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