Chemical topology molecular graphs

Toropov AA, Toropova AP, Nesterova AI, Nabiev OM (2004b) QSPR modeling of complex stability by correlation weighing of the topological and chemical invariants of molecular graphs. Russ. J. Coord. Chem. 30 611-617. 

S. H. Bertz, "A Mathematical Model of Molecular Complexity" in Chemical Applications of Topology and Graph Theory, from a Symposium held at the University of Georgia, 18-22 April 1983, R.B. King (Editor), "Studies in... 

The study of chemical reactions requires the definition of simple concepts associated with the properties ofthe system. Topological approaches of bonding, based on the analysis of the gradient field of well-defined local functions, evaluated from any quantum mechanical method are close to chemists intuition and experience and provide method-independent techniques [4-7]. In this work, we have used the concepts developed in the Bonding Evolution Theory [8] (BET, see Appendix B), applied to the Electron Localization Function (ELF, see Appendix A) [9]. This method has been applied successfully to proton transfer mechanism [10,11] as well as isomerization reaction [12]. The latter approach focuses on the evolution of chemical properties by assuming an isomorphism between chemical structures and the molecular graph defined in Appendix C. 

Graph theory is largely applied to the characterization of chemical structures, as well as to structure-property and structure-activity correlations, by means of so-called topological indices. These are numerical quantities based on various invariants or characteristics of molecular graphs. 

We shall now apply the techniques that we described above to prove the topological chirality of some molecular knots and links. Note that if we succeed in proving that a molecular graph is topologically chiral then it will follow that the molecule that it represents is chemically chiral, since any molecular motion corresponds to a rigid or flexible deformation of the molecular graph. In particular, it is not chemically possible for one molecular bond to pass through another molecular bond. 

The derivation of the topological distance matrix from the molecular graph is followed by the assignment of PPPs to the nodes of the graph. The following list provides chemical definitions of the five PPP types that are implemented in the CATS descriptor. The upper-case letter in parentheses is the abbreviation of each PPP type. Additionally, a functional group description is paired with its corresponding SMARTS in square brackets ... 

From the PDB and topological analysis, we construct a molecular graph with untyped bonds and recognized chemical rings. For correct chemical recognition, we need to determine hybridization states, from which we then try to derive correct bond types. 

A numerical value associated with chemical constitution that can be used to correlate chemical structure with various physical properties, chemical reactivity, or biological reactivity. The numerical basis tor topological indices is provided (depending on how a molecular graph is converted into a numerical value) by either the adjacency matrix or the topological distance matrix. In the latter, the topological distance between two vertices is the number of edges in the shortest path between these. 

It is the largest eigenvalue of the matrix obtained as the sum of the adjacency matrix A and the topological distance matrix D representing a molecular graph [Schultz et al., 1990]. Its logarithm was used to model physico-chemical properties [Cash, 1995c]. 

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. 

Balaban, A.T, Bonchev, D. and Seitz, W.A. (1993a). Topological/Chemical Distances and Graph Centers in Molecular Graphs with Multiple Bonds. J.Mol.Struct. (Theochem), 280,253-260. 

Balaban, A.T. (1997a). From Chemical Graphs to 3D Molecular Modeling. In From Chemical Topology to Three-Dimensional Geometry (Balaban, A.T., ed.). Plenum Press, New York (NY), pp. 1-24. 

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