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

摘要

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 informationthat predicts whether a zeolite is likely to be synthesizable in the2D form and correctly identifies the expressed surface in known layered2D zeolites. The discovery of this descriptor allows us to highlightother zeolites that may also be synthesized in the 2D form that have not been experimentally realized yet. Finally, our methodis general since the mathematical formalism can be applied to findthe minimum cut surfaces of other crystallographic materials suchas metal–organic frameworks, covalent-organic frameworks, zeolitic-imidazolateframeworks, metal oxides, etc.