Abstract
Structure solution of molecular crystals from powder diffraction data by real-space methods becomes challenging when the total number of degrees of freedom (DoF) for molecular position, orientation and intramolecular torsions exceeds a value of 20. Here we describe the structure determination from powder diffraction data of three pharmaceutical salts or cocrystals, each with four molecules per asymmetric unit on general position: Lamivudine camphorsulfonate (1, P 21, Z=4, Z′=2; 31 DoF), Theophylline benzamide (2, P 41, Z=8, Z′=2; 23 DoF) and Aminoglutethimide camphorsulfonate hemihydrate [3, P 21, Z=4, Z′=2; 31 DoF (if the H2O molecule is ignored)]. In the salts 1 and 3 the cations and anions have two intramolecular DoF each. The molecules in the cocrystal 2 are rigid. The structures of 1 and 2 could be solved without major problems by DASH using simulated annealing. For compound 3, indexing, space group determination and Pawley fit proceeded without problems, but the structure could not be solved by the real-space method, despite extensive trials. By chance, a single crystal of 3 was obtained and the structure was determined by single-crystal X-ray diffraction. A post-analysis revealed that the failure of the real-space method could neither be explained by common sources of error such as incorrect indexing, wrong space group, phase impurities, preferred orientation, spottiness or wrong assumptions on the molecular geometry or other user errors, nor by the real-space method itself. Finally, is turned out that the structure solution failed because of problems in the extraction of the integrated reflection intensities in the Pawley fit. With suitable extracted reflection intensities the structure of 3 could be determined in a routine way.
Concrete minimal 3 × 3 Hermitian matrices and some general cases