Structure model optimization

The outcome of the ab-initio crystal structure solution process by Direct Methods depends on not only the quality of the extracted integrated intensities but also the experimental resolution [1]. In fact, the limited experimental resolution distorts the Fourier synthesis even at atomic resolution: when the resolution is larger than 1 Å, the electron density map is an imperfect representation of the true density. This is particularly true in case of organic compound for which, because of the low atomic scattering factors of the light atoms constituting the molecule, the experimental diffraction intensity at high diffraction angle value is very weak and unusable. In case of powder diffraction data, the resolution bias errors combine with uncertainty on moduli and/or phases of structure factors and often provide an approximate electron density map to which a structure model far from the correct one corresponds: some peaks are missed, false positions occur, some other positions are misplaced from the true ones. Such a quality of structure model requires an optimization step preliminary to the final refinement by the Rietveld method. In fact, the low convergent rate of the Rietveld method does not guarantee the attainment of the correct solution if the starting model to be refined is very rough. Therefore, the ab-initio crystal structure solution process by powder diffraction data usually includes procedures aiming at improving the model: recovering the missed atoms and locating atom peaks in better positions. Several methods have been developed for improving a structure model. They have been introduced in the software package EXPO [2], the program devoted to execute all the steps of the powder solution pathway. Herein, we quote the following procedures [3]: a. Weighted Least-Squares Fourier Recycling method (WLSQ-FR) [4]; b. Resolution Bias Modification algorithm (RBM) [5-7]; c. COVMAP approach [8]; d. Random-model-based method (RAMM) [9].