Local similarity in organic crystals and the non-uniqueness of X-ray powder patterns

Abstract

Two new concepts for molecular solids,`local similarity' and`boundary-preserving isometry', are de®ned mathematically and a theorem which relates these concepts is formulated.`Locally similar' solids possess an identical short-range structure and a`boundary-preserving isometry' is a new mathematical operation on a ®nite region of a solid that transforms mathematically a given solid to a locally similar one. It is shown further that the existence of such a`boundary-preserving isometry' in a given solid has in®nitely many`locally similar' solids as a consequence. Chemical implications, referring to the similarity of X-ray powder patterns and patent registration, are discussed as well. These theoretical concepts, which are ®rst introduced in a schematic manner, are proved to exist in nature by the elucidation of the crystal structure of some diketopyrrolopyrrole (DPP) derivatives with surprisingly similar powder patterns. Although the available powder patterns were not indexable, the underlying crystals could be elucidated by using the new technique of ab initio prediction of possible polymorphs and a subsequent Rietveld re®ne-ment. Further ab initio packing calculations on other molecules reveal that`local crystal similarity' is not restricted to DPP derivatives and should also be exhibited by other molecules such as quinacridones. The`boundary-preserving isometry' is presented as a predictive tool for crystal engineering purposes and attempts to detect it in crystals of the Cambridge Structural Database (CSD) are reported.

Adaptability of aripiprazole towards forming isostructural hydrogen bonding networks in multi-component salts: a rare case of strong O–H⋯O− ↔ weak C–H⋯O mimicry

“…1a The identical supramolecular blueprint in isostructural crystals may give rise to certain unique properties. Karfunkel et al 3 and Hao et al 2e noted similar colouristic properties of two isostructural crystals, one shown by DPP pigment (1,4-diketopyrrolo [3,4-c]-pyrrole) and the other a co-crystal with a different DPP derivative. In contrast, Cinc ˇic ´et al 4 showed a systematic variation in the thermal properties of several isostructural crystals by replacing structurally equivalent donors and acceptors (NH, O, S) in halogen bonded cocrystals.…”

Method for the computational comparison of crystal structures

“…RDFs are independent of cell choice, and can be physically interpreted. RDFs have been used to describe molecules with the goal of simulating IR spectra (Gasteiger et al, 1996;Hemmer et al, 1999), and have been used in the form of a radial distribution matrix for crystals (Karfunkel et al, 1999). In the latter application each row in the distribution matrix is an RDF describing the interatomic distances for one atom-type pair.…”

“…This descriptor does not suffer from the problems mentioned above and has an interpretable physical meaning. A potential disadvantage is that it is not always unique under certain conditions (Karfunkel et al, 1999).…”

Interplay of phenyl–perfluorophenyl stacking, C–H⋯F, C–F⋯π and F⋯F interactions in some crystalline aromatic azinesElectronic supplementary information (ESI) available: experimental powder X-ray diffraction spectra. See http://www.rsc.org/suppdata/cc/b2/b202181a/

“…There is excellent overlap in the experimental PXRD traces of 2 and 4 (see Supplementary data †) suggesting that there is local similarity (i.e. synthomorphism) 12 in the internal arrangement of atoms in these structures. Given these similarities, identity in the melting points of 2 and 4 (117, 118 °C) may be traced to their crystal packing.…”