How Can We Explain the Stability of Conjugated Hydrocarbon- and Heterosubstituted Networks by Topological Descriptors?

Haruo      Hosoya

Abstract

Correlation between the π-electronic stability (Huckels Eπ) and several topological descriptors, including Hosoyas Z, Wieners W, and Randics 1χ , was compared for the isomeric acyclic conjugated hydrocarbon molecules from hexatriene to decapentaene. From the analysis of the best descriptor Z and mean length of conjugated paths L, the origin of π-electronic stability was logically explained. The effect of heteroatom substitution to polyenes was studied and analyzed by graph-theoretical techniques. The difference in the stability and electron flow for this heteroatom substitution was also quantitatively and easily explained. Discussion was given for the difference in the topological dependency of HOMO level of these networks with even and odd number of skeletal carbon atoms. An efficient determinantal method for calculating the Z-index for tree graphs is introduced.

Keywords: Topological index, molecular descriptor, π-electronic stability, conjugated hydrocarbon, graph-theory, aromatic stability, acyclic systems, heterosubstituted systems, Wiener's index, Randic's connectivity, Hückel molecular orbital, HOMO energy, heteroatomic substitution, heteroatomic systems, organic electron, Hydrogen-deleted molecular, non-adjacent number, structural isomers, saturated hydrocarbon molecules, acyclic alkane molecules, polycyclic graphs, boiling point, off-diagonal elements, distance matrix, QSAR, QSPR studies, combinatorial explosion, algorithm, conjugated paths, isomers, octatetraene, linear octatetraene, cross-conjugated, algebraic object, symmetrical, adjacency matrix, polynomial, orbitals, linear polyene, linear structure, decapentaene, mean length, resonance stabilization of polyenes, organic chemistry, Kekulé structure, biradical structures, Longuet-Higgins, perturbation theory, topological bond order, organic electron theory, structural formula, polarizability, heteroatom, Coulomb parameter, parametrization, tetravalency, lone pair lobe, cumbersome parametrization, heterosubsitituted, violation, horizontal lines, magnitudes, comb polyene, theorem, Rushbrooke, non-bonding, hepatrienyl, non-atrienyl, physico-chemical, pruning technique, asymmetrical adjacency