INDEX structural models

Hildebrand T., Ruegsegger P. Quantifieation of bone microarchitecture with the structure model index. CMBBE, v.l, 15-23, 1997. 

Recent developments and prospects of these methods have been discussed in a chapter by Schneider et al. (2001). It was underlined that these methods are widely applied for the characterization of crystalline materials (phase identification, quantitative analysis, determination of structure imperfections, crystal structure determination and analysis of 3D microstructural properties). Phase identification was traditionally based on a comparison of observed data with interplanar spacings and relative intensities (d and T) listed for crystalline materials. More recent search-match procedures, based on digitized patterns, and Powder Diffraction File (International Centre for Diffraction Data, USA.) containing powder data for hundreds of thousands substances may result in a fast efficient qualitative analysis. The determination of the amounts of different phases present in a multi-component sample (quantitative analysis) is based on the so-called Rietveld method. Procedures for pattern indexing, structure solution and refinement of structure model are based on the same method. 

Toraya s WPPD approach is quite similar to the Rietveld method it requires knowledge of the chemical composition of the individual phases (mass absorption coefficients of phases of the sample), and their unit cell parameters from indexing. The benefit of this method is that it does not require the structural model required by the Rietveld method. Furthermore, if the quality of the crystallographic structure is poor and contains disordered pharmaceutical or poorly refined solvent molecules, quantification by the WPPD approach will be unbiased by an inadequate structural model, in contrast to the Rietveld method. If an appropriate internal standard of known quantity is introduced to the sample, the method can be applied to determine the amorphous phase composition as well as the crystalline components.9 The Rietveld method uses structural-based parameters such as atomic coordinates and atomic site occupancies are required for the calculation of the structure factor, in addition to the parameters refined by the WPPD method of Toraya. The additional complexity of the Rietveld method affords a greater amount of information to be extracted from the data set, due to the increased number of refinable parameters. Furthermore, the method is commonly referred to as a standardless method, since the structural model serves the role of a standard crystalline phase. It is generally best to minimize the effect of preferred orientation through sample preparation. In certain instances models of its influence on the powder pattern can be used to improve the refinement.12... 

Then TREOR (4) program [18] was used to index the pattern automatically and finally all peaks were indexed by orthorhombic system, resulting in the figure of merit, M(10)=32, F(10)=21. SOS (II) program [16] was performed to refine the cell edges (a = 0.8969(7) nm, b = 0.7011(8) nm, c = 0.596(1) nm) and calculated out more indices of the reflections. The cell volume is about half of that of cubic modification. So the orthorhombic system (hereafter 5 -ZrW, 5M00 4O8) is a new crystal structure other than the pressure-induced orthorhombic y-ZrW208 structural model. 

Figure 1. The indexing of 6 -Zr W, 6M004O,. The indices were calculated from the TREOR program. The tick marks under the pattern were demonstrations of the failed index by known structural models. The tick marks were the allowed Bragg reflection positions of space groups of P(-3)c (the lowest), Pa(-3) (middle low), P2 3 (middle up) and P 2,2, 2, (top) models of ZrWjO, or ZrMo20j. The inset emphasizes that both indices 110 and 101 can not be indexed by any structure.

In Direct methods, the intensities are extracted from an indexed powder diffraction pattern by profile fitting procedures such as the Le Bail method and Pawley method. Then the integrated intensities obtained are corrected for Torentz polarization and normalized. These corrected intensity values are then subjected to routine Direct-method procedures. The structural model obtained is completed using difference Fourier maps. This method works successfully when a sufficient number of intensities could be extracted from the powder diffraction pattern. 

Measurement of the accuracy of NMR-derived structures is a much more difficult task than estimating their precision. An absolute measure of the accuracy of an NMR-derived structure is not possible in the absence of any knowledge about the true structure and therefore it has to be measured by some statistic.2 3 One advantage of iterative relaxation matrix analysis (IRMA),204 205 in which the structure is iteratively refined by comparison of the experimental NOESY spectrum with a synthetic spectrum back-calculated from the coordinates of the current structural model, is that it enables an NMR R factor to be calculated,203 205 which is analogous to the R factor (or reliability index) used in crystallography. However, IRMA is not widely used for structure calculations and hence NMR R factors are rarely reported. 

Fischer, J.R. and Rarey, M. (2007) SwiFT an index structure for reduced graph descriptors in virtual screening and clustering./. Chem. Inf. Model., 47, 1341-1353. 

Figure 9.13 Index plots of structural model parameter estimates expressed as percent change from baseline using the delete-1 jackknife. Each patient was assigned an index number ranging from 1 to 78 and then singularly removed from the data set. The delete-1 data set was then used to fit the model in Eq. (9.14) using FOCE-I.

ModBase http //alto.compbio.ucsf.edu/modbase-cgi/index.cgi Annotated comparative 3D structures/models 5... 

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