Crystallographic point coordinates

The first and very fundamental question we had to address was how many solvent molecules coordinate to a metal ion. In the case of the Be2"1" cation, the coordination of four water molecules to form [Be(H20)4]2+ (at pH<3) is corroborated based on NMR (62-68), X-ray (69-74), or even neutron diffraction data (75). In parallel, these observations are also made by different types of computer-based simulations (76-79). In the case of Li+ one can find different values in the literature. While most X-ray structures demonstrate the existence of [Li(H20)4] + (80-82), [Li(H20)5]+ (83), and [Li(H20)6]+ (84) are also found. Even if one is doubtful and sceptical from a modern crystallographic point of view, e.g., [Li(H20)5]+ and [Li(H20)6]+ were studied at room temperature, we need to clarify the coordination number before the water exchange mechanism can be investigated. 

Crystal family Symbol Crystal system Crystallographic point groups (crystal classes) Number of space groups Conventional coordinate system Bravais lattices... 

The thirty-two crystal classes (crystallographic point groups) described in Section 9.1.4 can also be classified into the same seven crystal systems, depending on the most convenient coordinate system used to indicate the location and orientation of their characteristic symmetry elements, as shown in Table 9.2.1. 

The number of reports of new compounds has increased to the point that it is no longer possible to provide exhaustive coverage of them within the confines of a reasonably sized work. As one example, there were as of the end of the year 2000 over 1,100 crystallographically characterized coordination compounds containing an 5-block element and one or more coordinated water molecules fewer than 150 of these structures were reported before 1985. 

Tablel.3-b Crystal families, crystal systems, crystallographic point groups, conventional coordinate systems, and Bravais lattices in three dimensions. Lattice point symmetries (holohedries) are given in bold...

Point Coordinates Crystallographic points, directions, and planes are specified in terms of indexing schemes. The basis for the determination of each index is a coordinate axis system defined by the unit cell for the particular crystal structure. 

Carbon diffuses in iron via an interstitial mechanism—for PCC iron from one octahedral site to an adjacent one. In Section 4.3 (Pigure 4.3a), we note that two general sets of point coordinates for this site are 0 j 1 and. Specify the family of crystallographic directions in which this diffusion of carbon in PCC iron takes place. 

Many of the nitrosyls studied are 5-coordinate, and analysis of crystallographic results indicates that, in general, in the trigonal bipyramid structures NO is found in the equatorial position in a linear geometry whereas in a square pyramidal structure, there is a bent M—N—O linkage in an apical position. A further point of interest is that in compounds like Ir(NO)Cl2(PPh3)2, the nitrosyl group bends in the more hindered (P—Ir—P) plane. 

A (crystallographic) orbit is the set of all points that are symmetry equivalent to a point. An orbit can be designated by the coordinate triplet of any of its points. If the coordinates of a point are fixed by symmetry, for example 0, q, then the orbit and the Wyckoff position are identical. However, if there is a free variable, for example z in 0, , z, the Wyckoff position comprises an infinity of orbits. Take the points 0, 0.2478... 

It is now believed that the MoFe-protein s P-cluster contains a [4Fe-3S] cuboid joined to a [4Fe-4S] cuboid, although, as discussed below, it was first reported crystallographically as two [4Fe-4S] clusters.8 Uncertainty existed for sometime as to exact nature of bridging disulfide or sulfide ligand joining the two Fe S clusters but it is now known that the P-cluster does NOT contain a disulfide bond. This is important because the all-ferrous structure [4Fe-4S]° proposed from Mossbauer studies then becomes more possible for the P-cluster s [4Fe-4S] cube. In 1993 Bolin et al.1 proposed a six-coordinate S for the P-cluster s center as in Figure la,b of Thorneley s article.8 This is now believed to be the correct conformation. A central six-coordinate S makes this cluster much harder to synthesize in the laboratory, and this feat has not been accomplished as of the date of this text s publication. Whatever its oxidation state or structure, the P-cluster mediates electron transfer from Fe-protein to the M center of MoFe-protein, and it must be reduced at some point to allow transfer of its electron(s). 

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