Dependences of Space-Group Type Incidences of Organic and Metal-Organic Compounds on Reduced Unit-Cell Volumes

Abstract

The dependences of occurrences of the most frequent space-group types P, P2 ₁ , P2 ₁ /c, C2/c, P2 ₁ 2 ₁ 2 ₁ and Pbca on reduced (primitive) unit-cell volumes up to 8000 ų were investigated for organic and metal-organic compounds with different number of residues (1–3), i.e. for the compounds with different number of molecular constituents. The dependences for these space-group types are similar, single-peaked; their maxima are proportional to the number of asymmetric units (a compact symmetry-independent part of the unit cell) affected by Z′ (number of formula units per asymmetric unit) in the pertinent space-group types. The dependences of Z′ < 1, Z′ = 1, Z′ > 1 within each space group type on reduced unit-cell volumes are also similar in shape. From these dependences it can be inferred that ability for crystallization of organic and metal-organic molecules ceases for the structures with the reduced unit-cell volumes above 8000 Å ³ . This volume corresponds roughly to 450 non-hydrogen atoms.

Keywords:

• Space group types
• space group frequencies
• molecular packing

PACS numbers:

• 61.90.+d
• 61.50.Ah
• 61.68.+n

Acknowledgments

The authors express its gratitude to Petr Zuman from Clarkson University, N. Y., Miloš Kopecký from the Institute of Physics ASCR and John Walters for stimulating discussions and careful reading of the text. The support by the grant 158/2004/B-CH/PrF is gratefully acknowledged. The authors thank especially to Professor Václav Janovec not only for the stimulating discussions but also for inspiration for this work as well as for a long-term interest.

Notes

¹ Free centre of symmetry is an inversion centre that is not situated on the intersection of other symmetry elements.

∗” means that the value has not been determined reliably due to low number of incidences.

∗” means that the value has not been determined reliably due to low number of incidences.

² The authors prepared figures of dependences of incidences (hits, i.e. the found database-records) on reduced unit-cell volumes for the most frequent space-group types in organic and metal-organic compounds with 1–3 residues as well as for nineteen most frequent space-group types in inorganic compounds. All the curves are similar.

³ The distribution of the space group types of the macromolecules of the biological origin is affected by the fact that the pertinent molecules are pure enantiomers.