Enumeration of periodic tetrahedral frameworks. II. Polynodal graphs

In a previous study, we developed a database of periodic 4-connected graphs [Zeit. Kristallogr. 212 (1997) 768]. The database was built using a symmetry constrained intersite bonding search (SCIBS) method. This method enumerates all possible 4-connected nets within each space group type given the number of unique tetrahedral vertices, HT. Approximately 107 graphs were obtained, mostly for n_T = 1,2. n_T = 4 was achieved for some space groups that were rich in mirror symmetry. There was a combinatorial explosion of graphs with increasing n_T in some space groups, which ultimately limited the method. The uninodal graphs, n_T = 1, were refined by simulated annealing. A simple cost function was used that favoured a regular tetrahedral arrangement of neighbouring silicon atoms to emulate zeolite frameworks. Many plausible hypothetical uninodal zeolitic frameworks were reported. Since that report, we have improved the efficiency of the combinatorial search, and extended the range of our graph database to n_T=7 for some high mirror symmetry space groups. We have also implemented a more sophisticated Monte Carlo strategy for imbedding graphs in real space as an SiO₂ composition. Plausible refinements are then further optimized using the GULP program. Presently, there are almost 10¹⁰ graphs in our database, and the number of plausible regular tetrahedral SiO₂ frameworks identified now exceeds 100,000.