Topology Prediction of Gas-Separating Metal-Organic Frameworks with Low Symmetry Vertices

Topology serves as a blueprint for the construction of reticular structures such as metal-organic frameworks, especially for those based on building blocks with highly symmetrical shapes. However, it remains a challenge to predict the topology of the frameworks from less symmetrical units, because their corresponding vertex figures are largely deformed from the perfect geometries with no "default" net embedding. Furthermore, vertices involving flexible units may have multiple shape choices, and the competition among their designated topologies makes the structure prediction in large uncertainty. Herein, the deformation index is proposed to characterize the symmetry loss of the vertex figure by comparing it with its ideal geometry. The mathematical index is employed to predict the shapes of two in situ formed Co-based metalloligands (pseudo-tetrahedron and pseudo-square), which further dictate the framework topology (flu and scu) when they are joined with the [Zr₆O₈]-based cuboid units. The two frameworks with very similar constituents provide an ideal platform to investigate how the pore shapes and interconnectivity influence the gas separation. The net with cylindrical channels outperforms the other with discreate cages in C₃H₈/C₂H₆/CH₄ separation, benefiting from the facile accessibility of its interaction sites to the guests imposed by the specific framework topology.