A COMBINATORIAL METHOD OF GENERATING PERIODIC TETRAHEDRAL FRAMEWORKS M. M. J. Treacy, K. H. Randall, S. Rao, J. A. Perry, D. J. Chadi, NEC Research Institute, Inc., 4 Independence Way, Princeton, NJ 08540

A combinatorial method for generating periodic 4-connected frameworks is described. The computer algorithm requires, as input, the number of unique tetrahedral atoms and the crystallographic space group type. The algorithm then searches systematically over all possible combinations of connected crystallographic sites that are consistent with 4-connected nets. The resulting graphs are then relaxed by simulated annealing to identify the regular tetrahedral zeolite topologies

Results are presented for one unique tetrahedral atom in each of the 230 crystallographic space group types. 5,043 unique 3-dimensional 4-connected uninodal graphs are found. About 3% of these graphs refine to reasonable tetrahedral topologies. All the known uninodal zeolites, and dense silicon dioxide phases are identified, and many (if not all) of the previously known hypothetical uninodal frameworks are found. A number of new dense and microporous frameworks are described. There is a combinatorial explosion of graphs as the number of unique vertices is increased, a result which currently restricts this method to consideration of small numbers of unique atoms.

We also highlight idiosyncrasies in the International Tables for Crystallography concerning the descriptions of the asymmetric units. Topological discrepancies arise when comparing enantiomeric pairs of space group types.