Constraint-induced direct phasing method

The best and most detailed structural information is obtained when the diffraction pattern of a single crystal a few tenths of a millimetre in each dimension is analyzed, but growing high-quality crystals of this size is often difficult, sometimes impossible. However, many crystallization experiments that do not yield single crystals do yield showers of randomly oriented microcrystals that can be exposed to X-rays simultaneously to produce a powder diffraction pattern. Although single-crystal diffraction data consist of discrete spots or X-ray reflections, the diffraction of microcrystals in a powder forms rings so that the reflections overlap. Thus, the analysis is more challenging due to unavoidable errors in the structure-factor amplitudes and the low-resolution data available for structure determination. This paper introduces a constraint-induced phasing method that (i) improves structure solutions measured by success rate, quality of solutions and various figures of merit, and (ii) extends low-resolution powder diffraction data to atomic resolution by adding unmeasured reflections. Application results have shown clearly that the constraint-induced phasing method is an effective way to produce initial structure models that are suitable for further structural refinement and completion.