A graph theoretic representation and analysis of zeolite frameworks

Zeolites are microporous materials with periodic framework structures. Efficient representation of crystal frameworks is important for the design and discovery new zeolites. We explore a graph-theoretic representation, namely Single Repeating Unit (SRU), which utilizes fewest tetrahedral atoms (T-nodes) their connectivity graph to describe zeolite framework. SRUs use topologically distinctive T-nodes, thereby significantly reducing description space. also propose several approaches identify large crystallographic frameworks. In optimization-based approach, SRU identification formulated as special instance traveling salesman problem (TSP). analyze 159 existing over 10,000 hypothetical zeolites that all observed be Hamiltonian cycle networks. Considerable reduction in T-nodes possible using SRUs. For example, Chabazite represented only 12 representation. Additionally, provide systematic approach generate Aluminum substituted different Si/Al ratios.