HYPOTHETICAL ZEOLITE FRAMEWORK STRUCTURES AND WEAVINGS
Hypothetical zeolites can be enumerated mathematically, by treating zeolite frameworks as graphs, where atoms are “vertices,” and bonds are “edges.” Omitting oxygen atoms, graphs can be described as four-valent mappings of Si-Si connections. Conversely, omitting Si atoms, graphs become six-valent (octahedral) mappings of O-O connections. Given the space group and the number of crystallographically unique vertices, zeolitic graphs can be generated by exploring all combinations of edges (bonds) keeping those graphs that are 4- or 6-connected, and then embedding the graphs in 3D by lowering the framework energy under a simple regular-tetrahedral (or, octahedral) cost function. Such mathematical procedures can generate some beautiful and surprising structures, including interlocking and woven structures.
In this talk we present some of our results for zeolitic structures and present a recent extension of our methods to enumerate 3D periodic weaves of threads and networks.