(582d) Smallest Repeating Units: A New Descriptor for Representing Zeolites and Periodic Frameworks

Zeolites and metal-organic frameworks (MOFs) have numerous applications in chemical separations, catalysis and gas storage. These are ultra-large crystalline frameworks with hundreds of atoms that form closed three-dimensional topologies with complex internal pore structures that include portals, channels, and cages [1]. Correct and succinct description of these frameworks is fundamental and important for generating deeper understanding that can be applied to property prediction, materials screening, and inverse design towards driving new discoveries. Several methods and topological descriptors, such as the unit cells, secondary building units (SBU), composite building units (CBU), the simplified molecular-input line-entry system (SMILES), and the smooth overlap of atomic positions (SOAP), are available. While these are useful, the inherent complexity and the combinatorially-large design space for porous frameworks require computationally efficient representations. We introduce the smallest repeating unit (SRU) which is a new descriptor that represents a periodic framework using fewest tetrahedral nodes (T-atoms) based on graph-theory.[2] This descriptor is defined by a subset of T-atoms with respect of the total number of T-atoms in the unit cell and a connectivity matrix that features both the connectivity within the SRU and between SRUs, thus fully describing a zeolite framework structure. An SRU is unique for each zeolite and thus captures the essence of the framework and connectivity within it.

Given the crystallographic description or atomic coordinates of a zeolite framework, we first identify the connectivity matrix describing the selection and the connectivity of T-atoms in the SRU. After this, we identify the SRU structure. Specifically, we develop three approaches for SRU structure identification. The first is an optimization-based approach where the structure identification is formulated as a special instance of traveling salesman problem [3]. The second approach employs a depth-first algorithmic search combined with back-tracking. The third combines the strengths of the optimization and algorithmic approaches to enhance the computational efficiency.

The Hamiltonian graph-based SRU representation is both invertible and scalable in a sense that it only uses the topologically distinctive T-atoms that must be used to construct a zeolite framework. For example, the structure of Chabazite can be represented using only 12 nodes and their connectivity matrix as a Hamiltonian graph. Our results for 158 existing zeolites suggest that the SRUs require up to four times fewer T-atoms compared to unit cells. We also find the SRUs for over 10,000 hypothetical frameworks taken from the Atlas of Prospective Zeolite Structures [4]. Interestingly, most of these frameworks have SRUs with 40 or less number of T-atoms. This is promising for future inverse design and computational discovery of novel zeolites via designing SRUs. Furthermore, SRUs allow an efficient way of systematically enumerating all plausible framework modifications via Al substitutions following the Loewenstein’s rule. As a future work, these Al-substituted frameworks can be used to quantify the variability of gas adsorption, storage and catalytic performances for different Sil/Al ratios.

References:

[1] First, E. L.; Gounaris, C. E.; Wei, J.; Floudas, C. A. Computational characterization of zeolite porous networks: an automated approach. Physical Chemistry Chemical Physics 2011, 13, 17339-17358.

[2] Gandhi, A.; Hasan, M. M. F. Smaller than the Unit Cell: Smallest Repeating Units of Zeolite Frameworks. Under Review.

[3] Applegate, D. L.; Bixby, R. E.; Chvatal, V.; & Cook, W. J. (2006). The traveling salesman problem: a computational study. Princeton university press

[4] Atlas of prospective zeolite structures http://www.hypotheticalzeolites.net, (accessed Jan 9, 2021).