Crystal structure modeling

The crystal structure model of heat-treated Li OH - Mn02 is considered to be as shown in Fig. 40. It is composed of y // -Mn02 which includes some Li, and Li2Mn03. y //9-Mn02 has onedimensional channels, whereas Li2Mn03 has a structure in which Li atoms reside as layers, which accounts for its being named... 

Before the elucidation of the CAR X-ray crystal structure, modeling studies mainly focused on the constitutive activity of the receptor. For example, homology modeling along with molecular dynamics simulations was combined to identify critical amino acid residues responsible for the constitutive activation [43]. Especially, the role of Tyr326 as a molecular mimicry of a bound ligand in the interaction with the AF-2 helix was underscored. Mutational analyses and the later elucidation of the human CAR X-ray crystal structure confirmed an important role of this amino acid for the receptor s constitutive activity [41,44]. 

Figure 9. The crystal structure model for calcium gellan viewed along the c-axis. The calcium ions are shown by filled circles and water molecules by open circles. (Reproduced with permission from Ref. 14. Copyright 1989 Elsevier.)...

Fig. 4. Computer-generated crystal structure models nop row. left to right) Cuprite, zinc-blende, rutile, perovskite. iridymite (second row) Cristobalite. potassium dihydrogen phosphate, diamond, pyrites, arsenic (third rowt Cesium chloride, sodium chloride, wurtzite. copper, niccolite (fourth row) Spinel, graphite, beryllium, carbon dioxide, alpha i uanz. [AT T Bel Laboratories ...

Figure 6. Application of packing energy minimization method to poly(ethylene oxide) (16). (a) Starting model of uniform helix (b) stable crystal structure model obtained by energy minimization calculations and (c) the structure determined by x-ray analysis.

In 1995, an elaborated method was developed for accurate structure analysis using X-ray powder diffraction data, that is, the MEM/Rietveld method [1,9]. The method enables us to construct the fine structural model up to charge density level, and is a self-consistent analysis with MEM charge density reconstruction of powder diffraction data. It also includes the Rietveld powder pattern fitting based on the model derived from the MEM charge density. To start the methods, it is necessary to have a primitive (or preliminary) structural model. The Rietveld method using this primitive structural model is called the pre-Rietveld analysis. It is well known that the MEM can provide useful information purely from observed structure factor data beyond a presumed crystal structure model used in the pre-Rietveld analysis. The flow chart of the method is shown in Fig. 2. 

A perfect crystal structure model is very helpful for theoretical calculations, reaction mechanism analysis, and some physical property analysis such as conductivity, magnetic susceptibility, chemical potential, etc. Powder XRD (or neutron diffraction) Rietveld refinement is one of the most popular methods used to characterize crystal structure. 

The introduction and implementation of heteronuclear-based multidimensional techniques have revolutionized the protein NMR field. Large proteins (> 100 residues) are now amenable to detailed NMR studies and structure determination. These techniques, however, necessarily require a scheme by which and isotopes can be incorporated into the protein to yield a uniformly labeled sample. Additional complications, such as extensive covalent post-translational modifications, can seriously limit the ability to efficiently and cost effectively express a protein in isotope enriched media - the c-type cytochromes are an example of such a limitation. In the absence of an effective labeling protocol, one must therefore rely on more traditional proton homonuclear NMR methods. These include two-dimensional (1) and, more recently, three-dimensional H experiments (2,3). Cytochrome c has become a paradigm for protein folding and electron transfer studies because of its stability, solubility and ease of preparation. As a result, several high-resolution X-ray crystal structure models for c-type cytochromes, in both redox states, have emerged. Although only subtle structural differences between redox states have been observed in these... 

FIGURE 23.3 Crystal structure models of YBa CujOy, TlBa2Ca2Cu309, Bi2Sr2CaCu208, Bi2Sr2Ca2Cu30io, Tl2Ba2CaCu20g, and Tl2Ba2Ca2Cu30io, which are representative HTSCs with a greater than 77 K. 

OL-Tungsten is the only stable modification. It has a body-centered cubic lattice of space group - Im3m (No. 229). A diffraction pattern is shown in Fig. 1.7, together with a crystal structure model. 

FIGURE 1 A one-dimensional crystal structure model for a tiny perfect crystallite, illustrating, on the left, the scattering density function for the crystal, the shape function, the infinite structure model, the lattice, and the contents of a single unit cell the Fourier transforms of these functions are given on the right. 

Figure 19.14 shows the projections of the molecular chains to the a-c plane in the crystal structure models previously proposed [35, 36]. In both models, oxygen atoms, which are drawn as larger circles, are placed randomly in either site of the two possible positions. However, there are significant differences in relative positions of the respective atoms, and in hydrogen bonds depicted by broken lines between these two models. Because of the... 

Fig. 19.14. Crystal structure models of PVA (a) Bunn s model [36] and (b) Sakurada s model [35] projection of the chains to the a-c plane.

Ohoyama, K., et al.. Revised crystal structure model of Li2NH by neutron powder diffraction. Journal of the Physical Society of Japan, 2005. 74(1) p. 483 87. 

In powder X-ray diffraction, the three-dimensional information of a single-crystal diffraction-data set is compressed into one dimension, immensely complicating the structure determination, but it remains the most important tool for structure and identification. A powder pattern provides a unique fingerprint of a crystalline substance, and therefore also of the polymorphs of a compound. The simplest application is to reveal or to confirm the existence of distinct polymorphs. In some cases it is possible to determine crystal-structure models of a specific polymorph from powder patterns, which can then be refined with Rietveld s technique. 

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