### 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 language | English (US) |
---|---|

Pages (from-to) | 768-791 |

Number of pages | 24 |

Journal | Zeitschrift fur Kristallographie |

Volume | 212 |

Issue number | 11 |

State | Published - 1997 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*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.

Research output: Contribution to journal › Article

*Zeitschrift fur Kristallographie*, vol. 212, no. 11, pp. 768-791.

}

TY - JOUR

T1 - Enumeration of periodic tetrahedral frameworks

AU - Treacy, Michael

AU - Randall, K. H.

AU - Rao, S.

AU - Perry, J. A.

AU - Chadi, D. J.

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=1542606668&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1542606668&partnerID=8YFLogxK

M3 - Article

VL - 212

SP - 768

EP - 791

JO - Zeitschfrift fur Kristallographie

JF - Zeitschfrift fur Kristallographie

SN - 1433-7266

IS - 11

ER -