The revenge of the Patterson methods. III. Ab initio phasing from powder diffraction data

In the present paper, the third and last of a series (the first two papers were dedicated to the crystal structure solution of proteins), the Patterson superposition method, based on the use of the symmetry minimum function, has been applied to powder diffraction patterns. The method has been modified to take into account the special challenges of this kind of data and to optimize the performance of the approach. The new algorithms have been implemented in a computer program and applied also to single-crystal data of small and medium-size crystal structures. The experimental results have been compared with those obtained via direct methods, so enabling the role and the perspectives of these two approaches in the global phasing problem to be established, no matter what the experimental technique (powder or single-crystal diffraction) or the size of the structures (small, medium or macro-molecules).