Topological relations between three-periodic nets. II. Binodal nets.

The TOPOS program package was used to generate all subnets of 3- to 12-coordinated binodal nets taken from the Reticular Chemistry Structure Resource database. 38,304 binodal nets with novel topologies were revealed and stored in the TTD collection. A new invariant, the adjacency matrix of the shell graph of a node, is proposed to distinguish the node local topology. With this invariant, the first six examples of binodal-quasi-uninodal nets were discovered. 4604 organic and metal-organic frameworks were analyzed to find examples of the topologies generated. It was shown that many edge-transitive nets as well as unknown topologies occur in crystal structures.