A non-mathematical introduction to the superspacedescription of modulated structures

摘要

The X-ray analysis of (6R,7aS)-6-(tert-butyl-dimethylsilanyl-oxy)-1-hydroxy-2-phenyl-5,6,7,7a-tetrahydropyrrolizin-3-one,C_(19)H_(27)NO_3Si, revealed a diffraction pattern which is typicalfor modulated structures: strong Bragg peaks surrounded byweaker reflections which cannot be indexed with the samethree reciprocal lattice vectors that are used to describe thestrong peaks. For this class of crystal structures the concept ofsuperspace has been developed which, however, for manycrystallographers still constitutes a Gordian Knot. As apossible tool to cut this knot the crystal structure of theabove-mentioned tetrahydropyrrolizinone derivative ispresented as an illustrative example for handling anddescribing the modulated structure of a typical pharmaceutical(i.e. molecular) compound. Having established a workingknowledge of the concepts and terminology of the superspaceapproach a concise and detailed description of the completeprocess of peak indexing, data processing, structure solutionand structure interpretation is presented for the incommen-surately modulated crystal structure of the above-mentionedcompound. The superspace symmetry applied is P21(a0y)0;the (incommensurate) q vector components at 100 K are a =0.1422 (2) and y = 0.3839 (8).