Topological Codes

Figure C3.6.10 Defect-mediated turbulence in tire complex Ginzburg-Landau equation, (a) The phase, arg( ), as grey shades, (b) The amplitude [A], witli a similar color coding. In tire left panel topological defects can be identified as points around which one finds all shades of grey. Note tire apparently random spatial pattern of amplitudes.

To code the configuration of a molecule various methods are described in Section 2.8. In particular, the use of wedge symbols clearly demonstrates the value added if stereodescriptors are included in the chemical structure information. The inclusion of stereochemical information gives a more realistic view of the actual spatial arrangement of the atoms of the molecule imder consideration, and can therefore be regarded as between the 2D (topological) and the 3D representation of a chemical structure. 

The problem of perception complete structures is related to the problem of their representation, for which the basic requirements are to represent as much as possible the functionality of the structure, to be unique, and to allow the restoration of the structure. Various approaches have been devised to this end. They comprise the use of molecular formulas, molecular weights, trade and/or trivial names, various line notations, registry numbers, constitutional diagrams 2D representations), atom coordinates (2D or 3D representations), topological indices, hash codes, and others (see Chapter 2). 

One of the most widely used - and successful representations of the constitution, the topology, of a molecule is the HOSE code (Hierarchical Ordered description of the Substructure Environment) [9]. It is an atom-centered code taking into account... 

Fig. 8.24 Evolution of a 35 x 35 lattice whose sites are initially randomly seeded with O = 1 with probability p = 1/2. The development proceeds according to T value and OT topology rules defined by code C = (84,36864,2048). The constraints are = 0, A = 10]. The appearance of localized substructures is evidence of a geometrical self-organization.

Topological indices are used to describe some components of connectivity. A more complete description is afforded by unidimensional codes (linear line notations) such as SMILES. Connectivity plus explicit attention to valence electrons is afforded by the electrotopological indices... 

However, we should emphasize that the NBO/NRT concepts of hybridization, Lewis structure, and resonance differ in important respects from previous empirical usage of these terms. In earlier phases of valence theory it was seldom possible to determine, e.g., the atomic hybridization by independent theoretical or experimental procedures, and instead this term became a loosely coded synonym for the molecular topology. For example, a trigonally coordinated atom might be categorized as sp2-hybridized or an octahedrally coordinated atom as d2sp3-hybridized, with no supporting evidence for the accuracy of these labels as descriptors of actual... 

The connectivity (topology) of the zeolite framework is characteristic for a given zeolite type, whereas the composition of the framework and the type of extra-framework species can vary. Each zeolite structure type is denoted by a three-letter code [4], As an example, Faujasite-type zeolites have the structure type FAU. The pores and cages of the different zeolites are thus formed by modifications of the TO4 connectivity of the zeolite framework. 

In the following, a brief description of the main topological indices and of related indicators for molecular constitution (such as polynomials, number sequences, codes, etc.) will be presented. 

The concept of structure comparability is of practical use in the search of correlations between topological indices and molecular properties. It does not directly contain a numerical comparability index (through the authors23) use this term for what we called above comparability code). Two such indices proposed here, as a modification of the M, index, and are denoted as 3 and 3 ... 

The above codes can be converted into topological indices 59) as ... 

From their definitions, one may admit that topological indices may code two structural factors, namely, the size and the shape of the molecule. This assumption is proved by calculating 94) the schemes (B) in Figure 2 for the 36 polyalkylcyclohexanes with 6-10 carbon atoms, and for a subseries of 22 polyalkylcyclohexanes with 10 carbon atoms (resulting in scheme (C)). The schemes (A)-(C) corroborated with the... 

---