Topological atom bonding description

The topological or graph-theoretical approaches attempt to define the bonding and antibonding orbitals available to a cluster in terms of a sort of valence-bond description, where hybridized atomic orbitals are directed in space to form either localized or multicenter functions. (See also Hybridization) The analysis of a complex structure involving delocalized bonding may, however, require some seemingly subjective decisions about how the atomic orbitals overlap, where the multicenter bonds should be formed, and so forth. 

A tremendous number of various fragments are used in structure-property studies atoms, bonds, topological torsions , chains, cycles, atom- and bond-centered fragments, maximum common substructures, line notation (WLN and SMILES) fragments, atom pairs and topological multiplets, substituents and molecular frameworks, basic subgraphs, etc. Their detailed description is given below. 

Consequently, it must be emphasized that precautions have to be taken with the conventional rough description of molecules based on the chemical bond pattern. In a molecule that contains at least two atoms which do not belong to the first row of the periodic table, the energy and all the monoelectronic properties are literally spread out over the whole molecule. Obviously, the concept of chemical bond, based as it is on the principle of topological proximity, is inadequate on its own for a correct description of the chemical and physical behavior of such a molecule. 

A modem description of a conventional hydrogen bond as well as its older, more accurate definition are based on Bader s theory of atoms in molecules (AIM theory) [4]. Bader considers matter a distribution of charge in real space of point-like nuclei embedded in the diffuse density of electron charge, p(r). All the properties of matter are manifested in the charge distribution and the topology... 

Annelation of additional aromatic units to the basic cis-1,2-diphenylethylene system exerts strong effects on its inherent reactivity. In the usual MO description these effects can be traced to the effect of the structure of the new skeleton on the highest occupied and lowest unoccupied orbitals at the atoms forming the new bond and therefore can be properly considered as topological effects. As such effects are quite numerous we shall limit ourseivs to only a few examples. Thus o-terphenyl 103) does not give any DHP under usual conditions ... 

The mathematical theory of topology is the basis of other approaches to understanding inorganic structure. As mentioned in Section 1.4 above, a topological analysis of the electron density in a crystal allows one to define both atoms and the paths that link them, and any description of structure that links pairs of atoms by bonds or bond paths gives rise to a network which can profitably be studied using graph theory. 

In this chapter we will show that the tight binding ( ) description of the covalent bond is able to provide a simple and unifying explanation for the above structural trends and behaviour. We will see that the ideas already introduced in chapter 4 on the structures of small molecules may be taken over to these infinite bulk systems. In particular, we will find that the trends in structural stability across the periodic table or within the structure maps can be linked directly to the topology of the local atomic environment through the moments theorem of Ducastelle and Cyrot-Lackmann (1971). 

Both valence bond (VB) and molecular orbital (MO) theories have been used to explain the observed shapes of molecules. What we wish to know here is the shape of a transition state containing m atoms and n electrons. Fortunately, the preferred shapes of the simple species are known or can be guessed from the numbers and kinds of bonding and nonbonding electron pairs (Gillespie, 1967). Therefore, we must examine the preferred shape of clusters of three, four or more atoms. For, to envision the topology of a transition state is tantamount to a description of the stereochemical result of an elementary process. 

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