Enumeration of periodic tetrahedral frameworks
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.
© 2015 Oldenbourg Wissenschaftsverlag GmbH, Rosenheimer Str. 145, 81671 München
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- Enumeration of periodic tetrahedral frameworks
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- Rietveld refinement of the as synthesized and partially calcined forms of the molecular sieve GaPO4-ZON
- The crystal structure of dibenzoylmethane, C15H12O2 (enol form)
- The crystal and molecular structures of [Te(S2COR)2], R = nPr and CH2CH2CMe3
- Crystal structure of bis(diphenylglyoximato)nickel(II), Ni(pdg)2
- Unusual conformations adopted by standard amino acids in Aib-containing oligopeptides
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- Books Received
Articles in the same Issue
- Generalized Fibonacci numbers and coordination sequences for decorated Bethe lattices
- An improved method for analysing single crystal diffuse scattering using the Reverse Monte Carlo technique
- Enumeration of periodic tetrahedral frameworks
- Revised crystal structure of molybdenum hydroxymonophosphate, MoO2 · H2O · P(O3OH)
- The crystal structure of lithiumpentamolybdate Li4Mo5O17
- Rietveld refinement of the as synthesized and partially calcined forms of the molecular sieve GaPO4-ZON
- The crystal structure of dibenzoylmethane, C15H12O2 (enol form)
- The crystal and molecular structures of [Te(S2COR)2], R = nPr and CH2CH2CMe3
- Crystal structure of bis(diphenylglyoximato)nickel(II), Ni(pdg)2
- Unusual conformations adopted by standard amino acids in Aib-containing oligopeptides
- Physical properties and phase transitions of bis(guanidinium)zirconium bis(nitrilotriacetate)hydrate, [C(NH2)3]2Zr[N(CH2COO)3]2 · H2O
- Books Received
