Representation of 3D Structures

Spanned by tbc atoms 4, 2, and 1, and 2, 1, and 3 (tlic ry-planc), Except of the first three atoms, each atom is described by a set of three internal coordinates a distance from a previously defined atom, the bond angle formed by the atom with two previous atoms, and the torsion angle of the atom with three previous atoms. A total of 3/V - 6 internal coordinates, where N is the number of atoms in the molecule, is required to represent a chemical structure properly in 3D space. The number (,3N - 6) of internal coordinates also corresponds to the number of degrees of freedom of the molecule. 

Z-matriccs arc commonly used as input to quantum mechanical ab initio and serai-empirical) calculations as they properly describe the spatial arrangement of the atoms of a molecule. Note that there is no explicit information on the connectivity present in the Z-matrix, as there is, c.g., in a connection table, but quantum mechanics derives the bonding and non-bonding intramolecular interactions from the molecular electronic wavefunction, starting from atomic wavefiinctions and a crude 3D structure. In contrast to that, most of the molecular mechanics packages require the initial molecular geometry as 3D Cartesian coordinates plus the connection table, as they have to assign appropriate force constants and potentials to each atom and each bond in order to relax and optimi-/e the molecular structure. Furthermore, Cartesian coordinates are preferable to internal coordinates if the spatial situations of ensembles of different molecules have to be compared. Of course, both representations are interconvertible. 

Tabic 2-6 gives an overview on the most common file formats for chemical structure information and their respective possibilities of representing or coding the constitution, the configuration, i.c., the stereochemistry, and the 3D structure or conformation (see also Sections 2..3 and 2.4). Except for the Z-matrix, all the other file formats in Table 2-6 which are able to code 3D structure information arc using Cartesian coordinates to represent a compound in 3D space. 

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Figure 13 Ribbon representation of 3D structures of (a) monomericform of NpPAL from Nostocpuncf/fomie (PDB ID 2NYF), (b) monomeric form of HAL from Pseudomonas putida (PDB ID 1B8F), (c) homotetrameric form of PAL from Rhodosporidium toruloides (PDB ID 1T6P), and (d) homotetrameric form of TALfrom Rhodobacter sphaeroides (PDB ID 206Y).

As was said in the introduction (Section 2.1), chemical structures are the universal and the most natural language of chemists, but not for computers. Computers woi k with bits packed into words or bytes, and they perceive neither atoms noi bonds. On the other hand, human beings do not cope with bits very well. Instead of thinking in terms of 0 and 1, chemists try to build models of the world of molecules. The models ai e conceptually quite simple 2D plots of molecular sti uctures or projections of 3D structures onto a plane. The problem is how to transfer these models to computers and how to make computers understand them. This communication must somehow be handled by widely understood input and output processes. The chemists way of thinking about structures must be translated into computers internal, machine representation through one or more intermediate steps or representations (sec figure 2-23, The input/output processes defined... 

Quantitative Structure-Activity Relationship studies search for a relationship between the activity/toxicity of chemicals and the numerical representation of their structure and/or features. The overall task is not easy. For instance, several environmental properties are relatively easy to model, but some toxicity endpoints are quite difficult, because the toxicity is the result of many processes, involving different mechanisms. Toxicity data are also affected by experimental errors and their availability is limited because experiments are expensive. A 3D-QSAR model reflects the characteristics of... 

In order to calculate a physicochemical property, the structure of a molecule must be entered in some manner into an algorithm. Chemical structure notations for input of molecules into calculation software are described in Chapter 2, Section VII and may be considered as either being a 2D string, a 2D representation of the structure, or (very occasionally) a 3D representation of the structure. Of this variety of methods, the simplicity and elegance of the 2D linear molecular representation known as the Simplified Molecular Line Entry System (SMILES) stands out. Many of the packages that calculate physicochemical descriptors use the SMILES chemical notation system, or some variant of it, as the means of structure input. The use of SMILES is well described in Chapter 2, Section VII.B, and by Weininger (1988). There is also an excellent tutorial on the use of SMILES at www.daylight.com/dayhtml/smiles/smiles-intro.html. 

The complexity order of Archimedean solids in terms of the solid angle of their vertices is280 TT < CO < TC < TO < RCO < ID < TCO < TD < TCO < RID < TID. The two chiral Archimedean solids (snub octahedron, snub icosidodecahedron) were not considered. This order disagree with all four complexity given above, except in the case of the truncated tetrahedron which is predicted to be the least complex of all Archimedean solids. This discrepancy is perhaps due to different bases of the compared complexity orders the above orders being the result of 2D representation and the Balaban-Bonchev order of 3D structure of Archimedean solids. 

Novic, M. and Vracko, M. (2001) Comparison of spectrum-like representation of 3D chemical structure with other representations when used for modelling biological activity. Chemom. Intcll. Lab. Syst., 59, 33-44. 

Figure 3. Representations of the structure of (5), (a) ball and stick view of the molecular anion, (b) view of the 3D-arrangement, potassium cations are black grey polyhedra.

In these considerations on STL structure, one important aspect was not taken into account so far, namely, that of explicit stereochemistry. The STL database consists, as mentioned above, of 2D representations in the form of the SMILES string. It is at present not possible to include structural features based on molecular geometry, such as shape, charge distribution, etc. in our investigation on the molecular properties of STLs as a whole, since this would necessitate the generation of 3D structures with the correct stereochemistry for each of the 4861 molecules, which would only be possible by... 

Figure 12. Polyhedral representation of the structure of (NH4)(V0)(P04) viewed parallel to the c axis and showing the location of NH4 cation in the cavities formed by the 3D V/P/O connect.

Figure 19 Typical representations of 3D interpenetrated structures involving (a) the (3.5) net, (b) the a-Po net, (c) diamondoid nets, and (d) rutile nets. (Redrawn by Dr. S. Batten from Ref. 44.)...

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