Charge flipping combined with histogram matching to solve complex crystal structures from powder diffraction data

The charge-flipping structure-solution algorithm introduced by Oszlányi and Süto in 2004 has been adapted to accommodate powder diffraction data. In particular, a routine for repartitioning the intensities of overlapping reflections has been implemented within the iterative procedure. This is done by modifiying the electron density map with a histogram-matching algorithm, and then using the Fourier coefficients obtained from this map to repartition the structure factor amplitudes within each overlap group. The effectiveness of the algorithm has been demonstrated with five test examples covering different classes of materials of varying complexity (ZSM-5 ([Si₉₆O₁₉₂]), cimetidine (C₁₀H₁₆N₆S), a polysalicylide ((C₇O₂H)₆), the low-temperature modification of 4-methylpyridine-N-oxide (C₆H₇NO) with 8 molecules in the asymmetric unit, and a zirconium phosphate phase (|(C₅H₆N)₄ (H₂O)₂| [Zr₁₂P₁₆O₆₀(OH)₄F₈])). It was also used to solve the structure of a layer silicate (|(CH₃)₄N)₈ (H₂O)₂₀| [Si₂₄ O₅₆]), whose space group was unclear. These structures, with 17–64 non-H atoms in the asymmetric unit (68–288 in the unit cell), could all be solved in a straightforward manner. Histogram matching proved to be an essential component of the algorithm for the more complex structures. The clear advantages of the charge-flipping algorithm are that (1) all calculations are performed in P1, so space group ambiguities, which are common with powder diffraction data, are irrelevant, (2) no chemical information such as bond distances, bond angles, or connectivity are required, so there is no danger of making incorrect assumptions about the structure, (3) it is equally effective for both organic and inorganic structures, and (4) it is fast, requiring only seconds to minutes per run.