Topological studies of 4-coordinated framework materials

We have developed a graph-theoretic approach to generating hypothetical zeolite frameworks. Zeolites are microporous aluminosilicate materials that contain crystalline arrays of pores that are large enough to hold water and small oil molecules. The framework composition is TO2, where T is a 4-coordinated atom such as Si or Al. Some occur naturally, but many are synthesized in the laboratory. There are presently only 165 known materials with unique frameworks. The fact that there are only 165 of them has spurred many synthesis chemists to find new frameworks with different interesting pore properties.

Our database is generated by first creating all the 4-coordinated graphs that are consistent with a given space group symmetry for a fixed number of crystallographically unique 4-coordinated atoms. The method we use is called a Symmetry Constrained Intersite Bonding Search (SCIBS). We then attempt to imbed the graphs in real space, looking for those solutions that allow the TO4 tetrahedral units to conform. Not all graphs are embeddable in real space, frequently resembling tangled chickenwire. We use a combination of simulated annealing, genetic algorithms and geometric constraints to optimize the frameworks. Initially we use a simple tetrahedral cost function due to Boisen, Gibbs and Bukowisnky. Promising structures are also refined using the GULP program.

The whole procedure, SCIBS plus the embedding, is carried out on a 64-processor computer cluster that is dedicated to this project. The structures are then uploaded to a publically-accessible database at At present there are over 1.3 million hypothetical frameworks, and that number is growing steadily.

To help identify the most interesting frameworks, a computer-automated method was created to characterize the porosity. The technique uses Delaunay triangulation to identify the empty spaces within the framework. Delaunay triangulation (or strictly, tetrahedration in 3-dimensions), identifies those combinations of four atoms that define empty circumspheres. No circumsphere can contain a framework atom (by definition). The Delaunay circumspheres therefore decorate the empty spaces within the zeolite framework, and therefore reveal the channels and open pores within the zeolite. The database shows many of the structural and topological properties of each framework.

Future work will be to try to use the Delaunay triangulation to identify molecules that fit inside the hypothetical frameworks, hopefully providing clues how to synthesize them.

More details about the SCIBS method can be found at

Last updated July 5th, 2005.

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