A generalized method for constructing hypothetical nanoporous materials of any net topology from graph theory

Here we present a method for constructing hypothetical crystalline nanoporous materials, such as metalorganic frameworks (MOFs), using a graph theoretical approach. The method takes as input the discrete secondary (or structural) building units (SBUs) with defined connection points, and a desired 3-dimensional net topology in the form of a labelled quotient graph. The hypothetical materials are constructed based on the principle that using a labelled quotient graph obtained, for example from the reticular chemistry structure resource (RCSR), one can construct a net embedding in 3-D Euclidean space with an infinite number of different representations. Thus, crystalline structures can be realized by manipulating a net's embedding such that vertices of the net match the geometries of the desired SBUs. To demonstrate the methodology, 46 different network topologies (i.e. tbo, pcu), are used to build MOFs from the same pair of 4-coordinate and 3-coordinate SBUs. We further show that the method can be used to generate hypothetical MOFs where the most common realization of a net, called the barycentric representation, will not produce a viable structure. When combined with a robust force field based geometry optimizer, the method can be used to generate large and structurally diverse hypothetical databases for virtual screening purposes.