Topo-Reactive QSAR

1 A Historical Perspective on Topology and Link to Chemical Graphs 

FIGURE 3.11 Konigsberg bridges in 1736 (left), the associated multi-graph (middle), and its eulerian version (right) adapted from Refs. (Atanasiu, 1971 Putz et al., 2008b). 

However, the graphs were rediscovered with other several occasions in physics by Kirchhoif s (1842) studies on electrical networks and, in chemistry, by the seminal works of Couper, Butlerov, and Kekule when founding the modem stmcture theory of chemical compounds. 

Basically, the use of graph theory in chemistry may be seen as another representation of quantum chemistry, as a simplification version of it. As most of molecular stmctures may be seen as having two main electronic components one is giving the o-electron framework that creates the effective field in which the n-electrons - the other component - move, the simplification may be achieved since these two components may be seen as independents. Although having no rigorous justification such context enables the path descriptions of atoms-in-molecule and, nevertheless, was recorded with an impressing success in chemical bond description. 

Practically, the correspondence of quantum and chemical terms with those used in graph theory, see Table 3.6, make possible the developing of the mathematical chemistry still preserving its observable interpretation. 

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Principle 2 an unambiguous algorithm the Spectral-, Diagonal-, Projective-, Quantum Amplitude-, Residual-, Alert-, Catastrophe-, SMILES- and topo-reactive QSAR variants ... 

Nevertheless the whole plethora of finite difference schemes of Table 3.5 may be used for electronegativity and chemical hardness while employing a different kind of QSAR, in a topo-reactive fashion as is in the next described. 

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