Enumeration of periodic tetrahedral frameworks. II. Polynodal graphs

Michael Treacy, I. Rivin, E. Balkovsky, K. H. Randall, M. D. Foster

Research output: Contribution to journalArticlepeer-review

184 Scopus citations


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 nT = 1,2. nT = 4 was achieved for some space groups that were rich in mirror symmetry. There was a combinatorial explosion of graphs with increasing nT in some space groups, which ultimately limited the method. The uninodal graphs, nT = 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 nT=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.

Original languageEnglish (US)
Pages (from-to)121-132
Number of pages12
JournalMicroporous and Mesoporous Materials
Issue number1-3
StatePublished - Sep 20 2004


  • 3-Dimensional nets
  • 4-Connected 3D nets
  • Enumeration
  • Frameworks
  • Hypothetical
  • Zeolites

ASJC Scopus subject areas

  • Chemistry(all)
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials


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