The determination of the crystal structure of anhydrous theophylline by X-ray powder diffraction with a systematic search algorithm, lattice energy calculations, and C-13 and N-15 solid-state NMR: A question of polymorphism in a given unit cell

When determining crystal structures of organic molecular materials from hig h-resolution powder diffraction data, the key step is the generation of rel iable trial structures fur final refinement. The subject of the study repor ted here is the pharmaceutical material anhydrous theophylline (3,7-dihydro -1,3-dimethyl- 1H-purine-2,6-dione), which contains both oxygen and nitroge n as possible hydrogen bond acceptor atoms. A systematic search of direct s pace was employed to assess every possible packing arrangement of the asymm etric unit within the experimentally determined unit cell. Trial structures were ranked in terms of calculated lattice energy and weighted residuals f rom a comparison of calculated and experimental X-ray diffraction profiles. The systematic search found two packing arrangements with different interm olecular hydrogen-bonding motifs within the same unit cell. In one, denoted NH. . . N, the amino hydrogen is hydrogen bonded to the aldimine nitrogen, and in the other, denoted (NHO)-O-. . ., to the carbonyl oxygen neighborin g the imidazole ring. These trial structures were "virtually indistinguisha ble" in terms of calculated lattice energy or X-ray profile fit. Solid-stat e NMR spectra of a commercial sample not only confirmed immediately that th ere was only one molecule in the crystallographic asymmetric unit but also produced distinctive C-13 and N-15 chemical shifts. The experimentally dete rmined N-15 chemical shifts showed considerably better agreement with value s from ab initio calculations for the trial crystal structure with N--H N h ydrogen bonding. In these calculations, representative chains of three hydr ogen-bonded molecules were employed as models for the (NHN)-N-. . . and (NH O)-O-. . . trial crystal structures. In addition, a more sophisticated anal ysis of the lattice energy hypersurfaccs. using a distributed multipole bas ed intermolecular potential, indicated that the N-(HN)-N-. . . trial struct ure is the more stable. It was noted that the NH N packing motif identified by our studies is observed in a single-crystal determination for theophyll ine reported independently while our investigations were ongoing. Our study shows how the potential for polymorphism in a "given unit cell'' may be as sessed successfully by combining several complementary experimental and the oretical approaches.