Atomic coordinates array

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. 

A comparison of the parameters of the Sn atom coordination in the dihalides (Table 94) with the structures of analogous lactamomethyl halide derivatives of five- and six-coordinate Si and Ge derivatives (Tables 33, 34 and 90) demonstrates that the spatial array of the hypervalent fragments containing six-coordinate atoms is less sensitive to the replacement of the halide ligands and the central atoms504. The covalency of the M—Hal bond increases and that of the M—O bond decreases in the series M = Si, Ge and Sn494. 

This can be accounted for qualitatively by employing a simple model which permits the prediction of H (and S and G) for the above phases. Schematically we can think of our respective solid, liquid and gas as shown in Figure 22.1. The structure of a liquid, unlike that of a solid, cannot be specified in terms of an array of identical cells in a so called crystal structure specified by atomic coordinates, it has only a limited degree of short-range order and radial distribution (probability) functions are employed in its description. In the case of an (ideal) gas the molecules are unconstrained by attractive forces between them and here the gas (as also does a liquid) assumes the shape of its containing envelope. The enthalpy term, II, is related to the degree of attraction between the molecules in the respective phases and this is indicated by the fact (as we shall see below) that enthalpy has to be expended (Frame 21, section 21.2) in order to convert one phase into another in the sequence solid —> liquid — gas. 

B, J, C, N) performs the desired calculation I and J are singly dimensional integer arrays, the contents of which point to elements of the A and B arrays respectively. For the present purpose A and B would be identical and would contain the atomic coordinates. The integer variable N determines the number of indexed subtractions performed. The overall operation performed... 

X-rays are scattered predominantly by electrons rather than atomic nuclei. To determine atomic coordinates, electron densities are therefore assumed to be concentrated spherically around individual nuclei. This assumption ignores all possible effects that chemical bonding may have on electronic density in molecules. Such a hypothetical array of spherical atoms located at the nuclear positions of an actual molecule in a crystal is known as a promolecule. Molecular structures determined by routine crystallographic methods are invariably the structures of promolecules. 

Praseodymium dioxide crystallizes in the fluorite-type structure (space group Fm3m) with four praseodymium atoms and eight oxygen atoms per unit cell. This structure may be visualized easily as an infinite array of coordination cubes (each consisting of a Pr atom at the center with eight O atoms at the corners) stacked so that all cube edges are shared. 

Now let us ask what is needed to numerically evaluate this expression for the Fourier transform. The diffraction vector s = k — ko, as well as X, are experimental variables that are chosen, and the Zj are known for each atom as well. The only remaining variables are the xj, and these can be generated from the atomic coordinates xj, yj, zj. Thus all we really need to compute the resultant waves making up the diffraction pattern, for any array of scattering points, are their relative positions in space. 

The array upper function requires two arguments the name of the array and the index for which the upper limit is requested. The function call array upper (coord, 1) would return the number of atoms. The function call array upper (coord, 2) would return 3. Even though the second index upper limit was specified as 3 in the table creation above, this was done for clarity and because the array was intended to hold 3-D coordinates. PostgreSQL does not enforce this upper limit. In fact, it would be possible to insert two-dimensional coordinates into the coordtest table. However, it is not allowed to mix two- and three-dimensional coordinates within any one array. Once the first atoms coordinates are given the insert statement, each succeeding atom must have the same dimensionality of coordinates. 

Each row in the coordtest table represents a molecule. The smiles column is a string of atom symbols and bonds and the coord column is an array of atom coordinates. How is it possible to keep the ordering of atoms in the smiles string in sync with the ordering of atom coordinates in the coord array When the coordinates are initially entered from the external source, they are likely to be in a common chemical file format. The program that converts from that file format to SMILES would have to output the atom coordinates in the same order as the atoms in the SMILES. 

In a molecular structure file, an atom record typically contains all of the information about that atom the atomic number or symbol, the charge, coordinates, etc. When such a file is parsed into a SMILES string and an array of coordinates, it is important to be able to associate the proper coordinate with the proper atom. The use of canonical SMILES ensures this. Because canonical SMILES defines a unique order of the atoms in a molecule, that order is used to store the coordinates. Later sections of this chapter will discuss ways in which atomic coordinates might be stored in columns of a table. 

The column structure.id is a unique integer relating the structure, sdf and property tables. The sdf.molfile column contains the molfile for each structure as defined by the vendor. The structure.name and structure.cansmiles columns contain the name and canonical smiles parsed and computed from the molfile. The structure.coord column will contain an array of atomic coordinates. The structure, atom column will contain an array of atom numbers from the file in canonical order to correspond to the atom order in the canonical SMILES. The OpenBabel/plpythonu extension functions molfile mol and molfile properties will be used to parse the vendor SDF molfiles and populate these tables. The molfile column of the sdf table is first populated from the SDF file, using the following perl script. 

While atomic coordinates form the fundamental structure of a molecule, many methods prefer to represent a three-dimensional structure as a surface or a shape. Of course, these are ultimately computed from the atomic coordinates and perhaps atomic partial charges. It may be possible to represent these molecular surfaces or shapes as an array of three-dimensional coordinates. These could be stored as a column in the database analogous to the array of atomic coordinates. It might be necessary to create another data type, perhaps a composite data type, to store molecular surfaces or shapes. Once these representations are stored, they can be used in new SQL functions to assist in searching based on molecular surface or shape. 

These functions are called with a string argument. This argument is an SQL statement that is expected to provide the required information. For ctable, this is an array of bonds. For symbol coords, these are an array of symbols and an array of coordinates for each atom. 

The calculated atom displacements for the predicted reaction mode are indicated in Fig. 2, which shows the a-axis array of mutually reacting S2N2 molecules and the resulting polymer chain. The chain atom positions calculated for partially polymerized S2N2 agree with the observed atom coordinates in this material, as determined by x-ray diffrac-tion(27), to within a RMS deviation of 0.148(23). This correct prediction of reaction mode, chain backbone structure, and chain coordinates in the partially polymerized phase is a major success of the least motion calculations. 

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