Enumeration of periodic tetrahedral frameworks

Michael Treacy, K. H. Randall, S. Rao, J. A. Perry, D. J. Chadi

Research output: Contribution to journalArticle

142 Citations (Scopus)

Abstract

We describe a computer method for generating periodic 4-connected frameworks. Given the number of unique tetrahedral atoms and the crystallographic space group type, the algorithm systematically explores all combinations 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-dimensional 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 choice of asymmetric unit. About 3% of the 4-connected graphs refine to reasonable 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 consideration of small numbers of unique atoms.

Original languageEnglish (US)
Pages (from-to)768-791
Number of pages24
JournalZeitschrift fur Kristallographie
Volume212
Issue number11
StatePublished - 1997
Externally publishedYes

Fingerprint

enumeration
Atoms
atoms
simulated annealing
Simulated annealing
Explosions
Conformations
explosions
apexes
topology
Topology
computer programs
symmetry

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

Treacy, M., Randall, K. H., Rao, S., Perry, J. A., & Chadi, D. J. (1997). Enumeration of periodic tetrahedral frameworks. Zeitschrift fur Kristallographie, 212(11), 768-791.

Enumeration of periodic tetrahedral frameworks. / Treacy, Michael; Randall, K. H.; Rao, S.; Perry, J. A.; Chadi, D. J.

In: Zeitschrift fur Kristallographie, Vol. 212, No. 11, 1997, p. 768-791.

Research output: Contribution to journalArticle

Treacy, M, Randall, KH, Rao, S, Perry, JA & Chadi, DJ 1997, 'Enumeration of periodic tetrahedral frameworks', Zeitschrift fur Kristallographie, vol. 212, no. 11, pp. 768-791.
Treacy M, Randall KH, Rao S, Perry JA, Chadi DJ. Enumeration of periodic tetrahedral frameworks. Zeitschrift fur Kristallographie. 1997;212(11):768-791.
Treacy, Michael ; Randall, K. H. ; Rao, S. ; Perry, J. A. ; Chadi, D. J. / Enumeration of periodic tetrahedral frameworks. In: Zeitschrift fur Kristallographie. 1997 ; Vol. 212, No. 11. pp. 768-791.
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