Atomic coordinates 3-dimensional

Sadowski, J. and Gasteiger, J. (1993) From atoms and bonds to 3-dimensional atomic coordinates — Automatic model builders. Chemical Reviews, 93, 2567—2581. 

Sadowski,., Gasteiger,. From atoms and bonds to three-dimensional atomic coordinates automatic model builders. Chm. Rev. 1993, 7, 2567-2581. 

Preliminary three-dimensional atomic coordinates of atoms in crystal structures are usually derived from electron-density maps by fitting atoms to individual peaks in the map. The chemically reasonable arrangement of atoms so obtained is, however, not very precise. The observed structure amplitudes and their relative phase angles, needed to calculate the electron-density map, each contain errors and these may cause a misinterpretation of the computed electron-density map. Even with the best electron-density maps, the precisions of the atomic coordinates of a preliminary structure are likely to be no better than several hundredths of an A. In order to understand the chemistry one needs to know the atomic positions more precisely so that better values of bond lengths and bond angles will be available. The process of obtaining atomic parameters that are more precise than those obtained from an initial model, referred to as refinement of the crystal structure, is an essential part of any crystal structure analysis. 

Functions Using Three-Dimensional Atomic Coordinates... 

Corina CORINA (COoRdINAtes) is a rule and data based system that automatically generates three-dimensional atomic coordinates from the constitution of a molecule as expressed by a connection table or linear code, and can convert large databases of compounds http //zabib.chemie.uni-erlangen.de/software/corina/corina.html... 

The method of Andersen [11] ( Andersen s piston ) is to control the volume by reparamaterizing the coordinates to lie in a cubic box with unit side. Assuming the system occupies a cubic domain, say, [—Z,/2, L/2] x [-L/2, L/2] x [—L/2, L/2], whereL = we may write, for each three-dimensional atomic coordinate vector 9i... 

Dimensional Atomic Coordinates Automatic Model Builders. 

Molecular structures have been represented by "molecular transforms" which are computed from the three-dimensional atomic coordinates of the molecule using X-ray diffraction data C2781. Predictive abilities of 90 X were reported for classifiers developed with the learning machine (data set 72 sedatives, 114 tranquilizers) C276 - 2781. 

J. Sadowski and J. Gasteiger, Chem. Rev., 93,2567 (1993). From Atoms and Bonds to Three-Dimensional Atomic Coordinates. 

Molecular Design Limited has recently extended their MACCS-II chemical database system to MACCS-3D, for the storage and retrieval of three-dimensional atomic coordinates. Physical and biological data may be stored. A novel feature of MACCS-3D is the ability to recognize and remove duplicate coordinate sets. Coordinate sets can be retrieved from the database by specifying a combination of numerical and textual queries or by substructure. 

In this section, we concentrate on the relationship between diffraction pattern and surface lattice [5], In direct analogy with the tln-ee-dimensional bulk case, the surface lattice is defined by two vectors a and b parallel to the surface (defined already above), subtended by an angle y a and b together specify one unit cell, as illustrated in figure B1.21.4. Withm that unit cell atoms are arranged according to a basis, which is the list of atomic coordinates within drat unit cell we need not know these positions for the purposes of this discussion. Note that this unit cell can be viewed as being infinitely deep in the third dimension (perpendicular to the surface), so as to include all atoms below the surface to arbitrary depth. 

Often a degree of freedom moves very slowly for example, a heavy-atom coordinate. In that case, a plausible approach is to use a sudden approximation, i.e. fix that coordinate and do reduced dimensionality quantum-dynamics simulations on the remaining coordinates. A connnon application of this teclmique, in a three-dimensional case, is to fix the angle of approach to the target [120. 121] (see figure B3.4.14). 

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. 

In the following, we will discuss two-dimensional (2D)-to-3D conversion in this context. However, it should be emphasized that we do so only for the sake of brevity. In reality, none of the conversion programs uhlizes informahon of a 2D image of a chemical structure. Only the information on the atoms of a molecule and how they are cormected is used (i.e. the starhng informahon is the conshtution of the molecule). One could even refer to linear structure representations such as SMILES as one-dimensional. However this is not true since SMILES allows for branches and ring closure which makes its informahon content essentially 2D. Thus, all structure representahons which lack 3D atomic coordinates will in the following simply be referred to as 2D. 

At the end of the process, one obtains a large amount of information regarding the solid-state structure of a compound. Its three-dimensional structure and molecular conformation become known, as do the patterns of molecular packings that enable the assembly of the crystal. In addition, one obtains complete summaries of bond angles and bond lengths for the molecules in the crystal as well as detailed atomic coordinates for all of the atoms present in the solid. One generally finds... 

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