Coordinates, crystal structure

The empirical pseiidopotential method can be illustrated by considering a specific semiconductor such as silicon. The crystal structure of Si is diamond. The structure is shown in figure Al.3.4. The lattice vectors and basis for a primitive cell have been defined in the section on crystal structures (ATS.4.1). In Cartesian coordinates, one can write G for the diamond structure as... 

The melting and boiling points of the aluminium halides, in contrast to the boron compounds, are irregular. It might reasonably be expected that aluminium, being a more metallic element than boron, would form an ionic fluoride and indeed the fact that it remains solid until 1564 K. when it sublimes, would tend to confirm this, although it should not be concluded that the fluoride is, therefore, wholly ionic. The crystal structure is such that each aluminium has a coordination number of six, being surrounded by six fluoride ions. 

The PDB contains 20 254 experimentally determined 3D structures (November, 2002) of macromolecules (nucleic adds, proteins, and viruses). In addition, it contains data on complexes of proteins with small-molecule ligands. Besides information on the structure, e.g., sequence details (primary and secondary structure information, etc.), atomic coordinates, crystallization conditions, structure factors. 

Traditionally, least-squares methods have been used to refine protein crystal structures. In this method, a set of simultaneous equations is set up whose solutions correspond to a minimum of the R factor with respect to each of the atomic coordinates. Least-squares refinement requires an N x N matrix to be inverted, where N is the number of parameters. It is usually necessary to examine an evolving model visually every few cycles of the refinement to check that the structure looks reasonable. During visual examination it may be necessary to alter a model to give a better fit to the electron density and prevent the refinement falling into an incorrect local minimum. X-ray refinement is time consuming, requires substantial human involvement and is a skill which usually takes several years to acquire. 

Page 1171 (Figure 28 7) is adapted from crystallograpliic coordinates deposited with The Protein Data Bank PDB ID lAOl Luger A Mader W Richmond R K Sargent D F Richmond T J Crystal Structure of the Nucleosome Core Particle at 2 8 A Resolution Nature 1997 V 389 251... 

Page 1176 (Figure 28 11) is adapted from crystallographic coordinates deposited with the Protein Data Bank PDB ID 6TNA Sussman J L Holbrook S R Warrant R W Church G M Kim S H Crystal Structure of Yeast Phenylalanine tRNA I Crystallographic Refinement / Mol Biol 1978 126 607 (1978)... 

Crystal structure of solids. The a-crystal form of TiCla is an excellent catalyst and has been investigated extensively. In this particular crystal form of TiCla, the titanium ions are located in an octahedral environment of chloride ions. It is believed that the stereoactive titanium ions in this crystal are located at the edges of the crystal, where chloride ion vacancies in the coordination sphere allow coordination with the monomer molecules. 

Crystal Structure and Ionic Radii. Crystal stmcture data have provided the basis for the ionic radii (coordination number = CN = 6), which are summarized in Table 9 (13,14,17). For both and ions there is an actinide contraction, analogous to the lanthanide contraction, with increasing positive charge on the nucleus. 

The crystal structure of the adduct of titanium tetrachloride and the ester formed from ethyl 2-hydroxypropanoate (ethyl lactate) and acrylic acid has been solved. It is a chelated structure with the oxygen donor atoms being incorporated into the titanium coordination sphere along with the four chloride anions. 

Crystal structure determination has also been done with -butyllithium. A 4 1 n-BuLi TMEDA complex is a tetramer accommodating two TMEDA molecules, which, rather than chelating a lithium, link the tetrameric units. The 2 2 -BuLi TMEDA complex has a structure similar to that of [PhLi]2 [TMEDA]2. Both 1 1 -BuLi THF and 1 1 -BuLi DME complexes are tetrameric with ether molecules coordinated at each lithium (Fig. 7.2). These and many other organolithium structures have been compared in a review of this topic. ... 

The X-ray crystal structures of many of these complexes have now been determined representative examples are. shown in Fig. 4.11 from which it is clear that, at least for the larger cations, coordinative saturation and bond rhrectionality are far less significant factors than in many transition element complexes. Further interest in these ligands stems from their use in biochemical modelling since they sometimes mimic the behaviour of naturally occurring, neutral, macrocydic antibiotics such as valinomycin, monactin, nonactin, nigericin... 

Figure 6.1 The icosahedron and some of its symmetry elements, (a) An icosahedron has 12 vertices and 20 triangular faces defined by 30 edges, (b) The preferred pentagonal pyramidal coordination polyhedron for 6-coordinate boron in icosahedral structures as it is not possible to generate an infinite three-dimensional lattice on the basis of fivefold symmetry, various distortions, translations and voids occur in the actual crystal structures, (c) The distortion angle 0, which varies from 0° to 25°, for various boron atoms in crystalline boron and metal borides.

The binary oxides and hydroxides of Ga, In and T1 have been much less extensively studied. The Ga system is somewhat similar to the Al system and a diagram summarizing the transformations in the systems is in Fig. 7.13. In general the a- and y-series have the same structure as their Al counterparts. )3-Ga203 is the most stable crystalline modification (mp 1740°) it has a unique crystal structure with the oxide ions in distorted ccp and Ga " in distorted tetrahedral and octahedral sites. The structure appears to owe its stability to these distortions and, because of the lower coordination of half the Ga ", the density is 10% less than for the a-(corundum-type) form. This preference of Ga "... 

An X-ray crystal structure of the Pr N-derivative shows the presence of a bent, 2-coordinate P atom, equal P- N distances, and accurately planar 3-coordinaie N atoms as in (c) above.In liquid ammonia ammonolysis also occurs ... 

Figure 29.1 Crystal structures of ZnS. (a) Zinc blende, consisting of two, interpenetrating, cep lattices of Zn and S atoms displaced with respect to each other so that the atoms of each achieve 4-coordination (Zn-S = 235 pm) by occupying tetrahedral sites of the other lattice. The face-centred cube, characteristic of the cep lattice, can be seen — in this case composed of S atoms, but an extended diagram would reveal the same arrangement of Zn atoms. Note that if all the atoms of this structure were C, the structure would be that of diamond (p. 275). (b) Wurtzite. As with zinc blende, tetrahedral coordination of both Zn and S is achieved (Zn-S = 236 pm) but this time the interpenetrating lattices are hexagonal, rather than cubic, close-packed.

In contras t with dially lamines and their sulfonyl derivatives, IV-acy Idially lamines react with tellurium tetrahalides to give zwitterionic oxazolines 29 containing five-coordinated tellurium (85T1607). Molecular and crystal structures of one of this type of compound (29, R = Me, X = Cl) were studied by X-rays (85T1607). 

Molecular and crystal structures of the macroheterocycle 102 were studied by X-ray [96JCS(D)1203]. As for bis-imines of di(o-formylphenyl) telluride 106, [89MI1 91JOM(402)331] only one of two potentially possible intramolecular coordination N Te bonds exists in a molecule of the macrocycle 102, which, in... 

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