Diffraction data method

Stuart, D. I., and Phillips, D. C. On the derivation of dynamic information from diffraction data. Methods in Enzymology 115, 117-142 (1985). 

Because x-rays are particularly penetrating, they are very usefiil in probing solids, but are not as well suited for the analysis of surfaces. X-ray diffraction (XRD) methods are nevertheless used routinely in the characterization of powders and of supported catalysts to extract infomration about the degree of crystallinity and the nature and crystallographic phases of oxides, nitrides and carbides [, ]. Particle size and dispersion data are often acquired with XRD as well. 

The normal mode refinement method is based on the idea of the normal mode important subspace. That is, there exists a subspace of considerably lower dimension than 3N, within which most of the fluctuation of the molecule undergoing the experiment occurs, and a number of the low frequency normal mode eigenvectors span this same subspace. In its application to X-ray diffraction data, it was developed by Kidera et al. [33] and Kidera and Go [47,48] and independently by Diamond [49]. Brueschweiler and Case [50] applied it to NMR data. 

We have developed a new method of interpretation of the photographs which does not suffer from this disadvantage. This radial distribution method, which is closely related to the method of interpretation of x-ray diffraction data developed by Zemike and Prins3 for the study of the structure of liquids and applied by Warren and Gingrich4 to crystals, consists in the calculation (from... 

Multiple isomorphous replacement allows the ab initio determination of the phases for a new protein structure. Diffraction data are collected for crystals soaked with different heavy atoms. The scattering from these atoms dominates the diffraction pattern, and a direct calculation of the relative position of the heavy atoms is possible by a direct method known as the Patterson synthesis. If a number of heavy atom derivatives are available, and... 

Otwinowski Z, Minor W. Processing of X-ray diffraction data collected in oscillation mode. Methods Enzymol 1997 276 307-26. 

Sakata, M., Uno, T., Takata, M. and Howard, C. (1993) Maximum-entropy-method analysis of neutron diffraction data, J. Appl. Cryst., 26, 159-165. 

The chemical bonding and the possible existence of non-nuclear maxima (NNM) in the EDDs of simple metals has recently been much debated [13,27-31]. The question of NNM in simple metals is a diverse topic, and the research on the topic has basically addressed three issues. First, what are the topological features of simple metals This question is interesting from a purely mathematical point of view because the number and types of critical points in the EDD have to satisfy the constraints of the crystal symmetry [32], In the case of the hexagonal-close-packed (hep) structure, a critical point network has not yet been theoretically established [28]. The second topic of interest is that if NNM exist in metals what do they mean, and are they important for the physical properties of the material The third and most heavily debated issue is about numerical methods used in the experimental determination of EDDs from Bragg X-ray diffraction data. It is in this respect that the presence of NNM in metals has been intimately tied to the reliability of MEM densities. 

An alternative method, which uses the concept of maximum entropy (MaxEnt), appeared to be a formidable improvement in the treatment of diffraction data. This method is based on a Bayesian approach among all the maps compatible with the experimental data, it selects that one which has the highest prior (intrinsic) probability. Considering that all the points of the map are equally probable, this probability (flat prior) is expressed via the Boltzman entropy of the distribution, with the entropy defined as... 

Scolecite gave the opportunity to relate the electron density features of Si-O-Si and Si-O-AI bonds to the atomic environment and to the bonding geometry. After the multipolar density refinement against Ag Ka high resolution X-ray diffraction data, a kappa refinement was carried out to derive the atomic net charges in this compound. Several least-squares fit have been tested. The hat matrix method which is presented in this paper, has been particularly efficient in the estimation of reliable atomic net charges in scolecite. 

During the last decades, a large body of structural information has been derived from gas-electron diffraction studies. The corresponding results are nearly exclusively reported in the literature in terms of r distances, or the equivalent thermal average intemuclear distances, which are denoted r. The r distances are defined by the relation, r = r — If. Alternative methods for interpreting gas-electron diffraction data are possible, for example, in terms of -geometries5, but they are currently too complex to apply in routine stmctural analyses, because they require detailed information on the molecular potential energy surface which is not usually available. 

Thioamides and their use in the preparation of the heterocyclic compounds are widely reported in the literature. Also they attract considerable interests in peptide chemistry. Molecular and crystal structures of some thioamide derivatives have been confirmed by X-ray diffraction data.8 10 Lawesson s reagent or phosphorus pentasulfide (P4S10) is actively used for the synthesis of thio-carbonyl compounds. Their preparation methods, reactions, applications in the synthesis of heterocycles and biological effects are mainly described in this section. 

Nitronates have not been adequately studied by X-ray diffraction and calculation methods. Characteristic X-ray diffraction data for different types of nitronates are given in Table 3.14. 

Once a suitable crystal is obtained and the X-ray diffraction data are collected, the calculation of the electron density map from the data has to overcome a hurdle inherent to X-ray analysis. The X-rays scattered by the electrons in the protein crystal are defined by their amplitudes and phases, but only the amplitude can be calculated from the intensity of the diffraction spot. Different methods have been developed in order to obtain the phase information. Two approaches, commonly applied in protein crystallography, should be mentioned here. In case the structure of a homologous protein or of a major component in a protein complex is already known, the phases can be obtained by molecular replacement. The other possibility requires further experimentation, since crystals and diffraction data of heavy atom derivatives of the native crystals are also needed. Heavy atoms may be introduced by covalent attachment to cystein residues of the protein prior to crystallization, by soaking of heavy metal salts into the crystal, or by incorporation of heavy atoms in amino acids (e.g., Se-methionine) prior to bacterial synthesis of the recombinant protein. Determination of the phases corresponding to the strongly scattering heavy atoms allows successive determination of all phases. This method is called isomorphous replacement. 

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