Machine Learnable Language\nfor the Chemical Space\nof Nanopores Enables Structure–Property Relationships in Nanoporous\n2D Materials

The synthesis of nanoporous two-dimensional (2D) materials\nhas\nrevolutionized fields such as membrane separations, DNA sequencing,\nand osmotic power harvesting. Nanopores in 2D materials significantly\nmodulate their optoelectronic, magnetic, and barrier properties. However,\nthe large number of possible nanopore isomers makes their study onerous,\nwhile the lack of machine-learnable representations stymies progress\ntoward structure–property relationships. Here, we develop a\nlanguage for nanopores in 2D materials, called STring Representation\nOf Nanopore Geometry (STRONG), that opens the field of 2D nanopore\ninformatics. We show that STRONGs are naturally suited for machine\nlearning via recurrent neural networks, predicting formation energies/times\nof arbitrary nanopores and transport barriers for CO<sub>2</sub>,\nN<sub>2</sub>, and O<sub>2</sub> gas molecules, enabling structure–property\nrelationships. The machine learning models enable the discovery of\nspecific nanopore topologies to separate CO<sub>2</sub>/N<sub>2</sub>, O<sub>2</sub>/CO<sub>2</sub>, and O<sub>2</sub>/N<sub>2</sub> gas\nmixtures with high selectivity ratios. We also enable the rapid enumeration\nof unique configurations of stable, functionalized nanopores in 2D\nmaterials via STRONGs, allowing systematic searching of the vast chemical\nspace of nanopores. Using the STRONGs approach, we find that a mix\nof hydrogen and quinone functionalization results in the most stable\nfunctionalized nanopore configuration in graphene, a discovery made\nfeasible by expedited chemical space exploration. Additionally, we\nalso unravel the STRONGs approach as ∼1000 times faster than\ngraph theory algorithms to distinguish nanopore shapes. These advances\nin the language-based representation of 2D nanopores will accelerate\nthe tailored design of nanoporous materials.