ENUMERATION OF PERIODIC TETRAHEDRAL FRAMEWORKS

We describe a computer method for generating periodic 4-connected fram eworks. Given the number of unique tetrahedral atoms and the crystallo graphic space group type, the algorithm systematically explores all co mbinations of connected atoms and crystallographic sites, seeking the 4-connected graphs. The resulting symmetry-encoded graphs are relaxed by simulated annealing to identify the regular tetrahedral frameworks. Results are presented for one unique tetrahedral atom in each of the 230 crystallographic space group types. Over 6,400 unique 3-dimensiona l 4-connected uninodal graphs are found when we restrict our search to those topologies that connect to nearest-neighbour asymmetric units. In any given space group, the number of graphs can depend on the choic e of asymmetric unit. About 3% of the 4-connected graphs refine to rea sonable tetrahedral conformations, and many 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 considera tion of small numbers of unique atoms.