Atomic coordinates table

Fortunately, the need to amass coordinates of atoms in reported crystal structures has already been appreciated, and efficient computer-based databases are now available. As a result, it is not necessary to type large sets of numbers into a computer, because they can be derived in computer-ready form from a database. In addition to the ready access to atomic coordinate tables, there are many excellent computer-graphics, geometrical, and statistical programs available for comparisons of structures. In practice, however, it is additionally advantageous to build molecular models either of the ball-and-stick variety or the space-filling variety, if chemical or biochemical insight is required from a comparison of molecular structures observed by crystal structure analyses. 

There are a number of different ways that the molecular graph can be conununicated between the computer and the end-user. One common representation is the connection table, of which there are various flavours, but most provide information about the atoms present in the molecule and their connectivity. The most basic connection tables simply indicate the atomic number of each atom and which atoms form each bond others may include information about the atom hybridisation state and the bond order. Hydrogens may be included or they may be imphed. In addition, information about the atomic coordinates (for the standard two-dimensional chemical drawing or for the three-dimensional conformation) can be included. The connection table for acetic acid in one of the most popular formats, the Molecular Design mol format [Dalby et al. 1992], is shown in Figure 12.3. 

Approximate atomic coordinates were obtained by assuming the effective metallic radius of magnesium to be about 1-60 A and the radii of aluminum and zinc to be about 1-40 A. The corresponding calculated structure factors were in fairly good agreement with those obtained from the observed intensities. The preliminary atomic coordinates are given in Table 1. 

Cartesian and cylindrical polar atomic coordinates of the structural repeating unit of 31 polysaccharide helices are provided in Tables A1 to A31. Errors, if any, in the original publications have been corrected. The coordinates of hydrogen atoms are given in a majority of structures. If missing, they are not available in the references cited in Table I. Each table caption contains the structure number and polymer name assigned in Table I. Refer to Table II for its chemical repeating unit. Cartesian (x, y, z) and cylindrical (r, , z) coordinates are related by x r cost ), y = r sin<(> and z is the same in both systems. 

When L = 4-CNC5H4N (PK3 = 1.86), 2-CIC5H4N (pK = 2.81), or 4-PhCOC5H4N (pKj = 3.35) [Hg2L2] [C10412 can be isolated as solids. However, under the same conditions the more basic unsubstituted pyridine (pK, = 5.21) leads to disproportionation, and no complex can be isolated. Complexes of Hg(I) of these more basic substituted pyridines can be prepared under a N2 atmosphere in MeOH at -70°C. Table 1 shows some Hg(I) complexes prepared with N-donor ligands. The majority contain an Hg2 ion with each atom coordinated to one or two N atoms as in I or II. 

Every space group listed in the family tree corresponds to a structure. Since the space group symbol itself states only symmetry, and gives no information about the atomic positions, additional information concerning these is necessary for every member of the family tree (Wyckoff symbol, site symmetry, atomic coordinates). The value of information of a tree is rather restricted without these data. In simple cases the data can be included in the family tree in more complicated cases an additional table is convenient. The following examples show how specifications can be made for the site occupations. Because they are more informative, it is advisable to label the space groups with their full Hermann-Mauguin symbols. 

The crystal data compared to expected values assuming no distortions are summarized in Table 18.1. Inspection of the atomic coordinates reveals that the distortions of the packing of spheres are only marginal. As expected, the greatest deviations are observed for the molecular compounds PI3 and NMe3. 

Table 2. Fractional atomic coordinates of Si in IM-5 after DLS refinement...

With this structure model, the refinement readily converged to very good discrepancy factors RF2 = 5.4%, Rwp = 7.3%, Rp = 5.3%. More details concerning data collection and refinement are given in Table 1, whereas the atomic coordinate, occupancies and displacement parameters of ECS-2 are reported in Table 2. 

Table 2. Atomic coordinates, occupancies and displacement parameters for ECS-2.

The geometry of the coordination compounds can be similarly predicted based on the coordination number of the central atom. Coordination numbers 2 and 3 are both relatively rare and give linear and planar or pyramidal geometries, respectively. The most important coordination numbers are 4, 5 and 6 with the latter being the most important one as nearly all cations form 6-coordinate complexes. Table 2.4 shows the geometries corresponding to the commonest coordination numbers in biological systems. 

Table 2. Refined atomic coordinates for the brucite structure.

The structure was refined with anisotropic non-hydrogen atoms. The final R-factorwas 0.142. The refined atomic coordinates are listed in Table. The atomic coordinates agreed with those published by [17] to within -0.03 A for the oxygen atom and -0.08 A for the hydrogen atom. The Mg atom is in a special position (0,0,0) so its position is not refined. 

Figure 1 Fourier synthesis of the projected potential map of Xi2S along the c-axis. Amplitudes and phases of the structure factors are calculated from the refined atomic coordinates of Ti2S and listed in Table 1. The space group of Xi2S is Pnnm and unit cell parameters a= 11.35, fc=14.05 and c=3.32 A.

Table 4.1 Distance least-squares optimized atomic coordinates for UZM-5.

Table 5.8 lists cell edges and fractional atomic coordinates obtained for an olivine mixture of composition Mgj 4Nio.6Si04 with 53.2% of the Ni distributed in M and 46.8% in Ml. The values obtained by calculation almost coincide with natural observation (see also figure 5.7). 

Table 2.2 summarizes basic crystallographic data for the iron oxides. Iron oxides, hydroxides and oxide hydroxides consist of arrays of Fe ions and 0 or OH ions. As the anions are much larger than the cations (the radius of the 0 ion is 0.14 nm, whereas those of Fe and Fe" are 0.065 and 0.082 nm, respectively), the arrangement of anions governs the crystal structure and the ease of topological interconversion between different iron oxides. Table 2.3 lists the atomic coordinates of the iron oxides. 

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