The Determination of the Crystal Structure of Anhydrous Theophylline by X-ray Powder Diffraction with a Systematic Search Algorithm, Lattice Energy Calculations, and ¹³C and ¹⁵N Solid-State NMR:  A Question of Polymorphism in a Given Unit Cell

When determining crystal structures of organic molecular materials from high-resolution powder diffraction data, the key step is the generation of reliable trial structures for final refinement. The subject of the study reported here is the pharmaceutical material anhydrous theophylline (3,7-dihydro-1,3-dimethyl-1 H -purine-2,6-dione), which contains both oxygen and nitrogen as possible hydrogen bond acceptor atoms. A systematic search of direct space was employed to assess every possible packing arrangement of the asymmetric unit within the experimentally determined unit cell. Trial structures were ranked in terms of calculated lattice energy and weighted residuals from a comparison of calculated and experimental X-ray diffraction profiles. The systematic search found two packing arrangements with different intermolecular 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 NH···O, to the carbonyl oxygen neighboring the imidazole ring. These trial structures were “virtually indistinguishable” in terms of calculated lattice energy or X-ray profile fit. Solid-state NMR spectra of a commercial sample not only confirmed immediately that there was only one molecule in the crystallographic asymmetric unit but also produced distinctive 13 C and 15 N chemical shifts. The experimentally determined 15 N chemical shifts showed considerably better agreement with values from ab initio calculations for the trial crystal structure with N−H···N hydrogen bonding. In these calculations, representative chains of three hydrogen-bonded molecules were employed as models for the NH···N and NH···O trial crystal structures. In addition, a more sophisticated analysis of the lattice energy hypersurfaces, using a distributed multipole based intermolecular potential, indicated that the N−H···N trial structure 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 theophylline reported independently while our investigations were ongoing. Our study shows how the potential for polymorphism in a “given unit cell” may be assessed successfully by combining several complementary experimental and theoretical approaches.