Topological representations

The constitution of molecules is given by lists of atoms and bonds (connectivity lists topological representation )6 . In addition, the number of free electrons for each atom is also carried in a separate vector. This is necessary as some reaction generators may transform free electrons into bonds, or vice versa. Thus, by working with free electrons and the electrons involved in bonds, all valence electrons of a molecule are explicitly specified. 

Fig. 3.4-12. Two derivatives of the hypothetical parent diaza-arachno-pentaborane N2B3H7 with an ar-5 and an ar-5 structure in a topological representation and in one with localized bonds.

Sequence of atoms in the constitutional unit(s) of a macromolecule, an oligomer molecule, a block, or a chain, which defines the essential topological representation. 

TOSAR Topological Representation of Synthetic and Analytical Relations of Concepts... 

Figure 7-4. Two representations of the fullerene C60. The upper representation shows the normal three-dimensional structure, whilst the lower one emphasises that this molecule is topologically planar. The fact that the various rings appear deformed is immaterial in this topological representation.

The main difference in the correlation vector representation of a 3D conformation in comparison with a topological representation of a molecule is that the distances between the atoms are no longer shortest paths. Instead, Euclidean distances between all atoms are used. Distances between atoms are not restricted to integer values, so the distances have to be partitioned into a set of... 

Carhart et al. [15] described a generalized structural descriptor called an atom pair which is defined in terms of the atomic environments of, and shortest path separation between, all pairs of atoms in the topological representation of a chemical structure. A similar descriptor has been suggested by Klopman [16]. More recently, Judson [20] described a more sophisticated approach to analyze structural feature of molecules for structure-activity studies. 

Fig. 1 depicts molecular structures and 2-dimensional topological representations of the hydrides under consideration. The molecular structure of B6H12 has not yet been positively established the 2-dimensional topological representation shown is based upon its boron-11 nmr spectrum. Octaborane(14) is not shown in Fig. 1 because of insufficient structural information. However, a possible arrangement is discussed in Section XII. 

Fig 1. (a) Molecular structures (b) Two-dimensional topological representations two resonance forms are necessary for B5H9 to preserve its molecular symmetry)... 

The boron-11 nmr spectrum consists of three resonances of equal intensity. At highest field is a doublet (B2,B5) and at lowest field is a doublet (Ba,B ) with a triplet in between (Bi,B4) 163> (see topological representation in Fig. 2). The standard heat of formation of hexabo-rane(12) has been experimentally determined to be 26.5 kcal. per mole217). 

Fig. 45a. Structure of Bi6H20 b Topological Representation of B,6H20 (terminal H s omitted)...

Fie. 14. Topological representation of the lowest framework orbital (a) in BiH>, and the doubly degenerate pair, (b) and (c). Six bonding electrons go into these three orbitals (4f)-... 

MOLECULAR BODIES, MOLECULAR SURFACES, AND THEIR TOPOLOGICAL REPRESENTATIONS... 

Based on HOC ranks, a Unique Topological Representation (UTR) was proposed in which topological equivalent vertices of the same rank in the graph are placed at the same level. 

The two-dimensional representation of a molecule considers how the atoms are connected, i.e. it defines the connectivity of atoms in the molecule in terms of the presence and nature of chemical bonds. Approaches based on the -+ molecular graph allow a two-dimensional representation of a molecule, usually known as the topological representation. Molecular descriptors derived from the algorithms applied to a topological representation are called 2D-descriptors, i.e. they are the so-called - graph invariants. 

Steric descriptors were obtained from -> experimental measurements of equilibrium and rate constants, - computational chemistry, geometrical and structural characteristics, and the - topological representation of a molecule. 

QSAR approaches based on the topological representation of the molecules are often called 2D-QSAR. The term 3D-QSAR is often, though improperly, used to denote only - grid-based QSAR techniques and receptor mapping techniques (see... 

A terminator may be an atom, a lone pair or a bond the link is derived from a topological representation of the molecules as the length of the path between the considered terminators. For each pair of terminators, different REX descriptors are defined according to each different link between them, i.e. all paths and not only the shortest path are considered. 

This kind of topological representation of crystal structures may be extended to more complex compounds if we focus our attention on the limited number of stronger bonds that hold the structure together. Nylon is formed by condensing... 

D (two-dimensional) descriptors derived from algorithms applied to a topological representation (molecular graph). 

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