New Insights into Aromaticity through Novel Delta Polynomials and Delta Aromatic Indices

Abstract

We have developed novel polynomials called delta polynomials, which are, in turn, derived from the characteristic and matching polynomials of graphs associated with polycyclic aromatic compounds. Natural logarithmic aromatic indices are derived from these delta polynomials, which are shown to provide new insights into the aromaticity of polycyclic aromatic compounds, including the highly symmetric C60 buckminsterfullerene, several other fullerenes, graphene, kekulene series and other cycloarenes, such as polycyclic circumcoronaphenes and coronoids. The newly developed aromatic index yields a value of 6.77 for graphene, 6.516865 for buckminsterfullerene C60(Ih), 5.914023 for kekulene (D6h symmetry), 6.064420 for coronene (D6h), 6.137828 for circumcoronene (D6h), 6.069668 for dicronylene and so forth. Hence, the novel scaled logarithmic aromatic delta indices developed here appear to provide good quantitative measures of aromaticity, especially when they are used in conjunction with other aromatic indicators.

Topological Deformations of Manifolds by Algebraic Compositions in Polynomial Rings

“…In other words, the symmetry or asymmetry of the graph structures affects the properties of the associated characteristic polynomials. In the views of applicational aspects involving the characteristic polynomials, symmetries and graphs in the domain of chemical sciences, the molecules can be represented in numerical forms representing the underlying graph structures with varying symmetries, and the chemical properties of the molecules vary accordingly [21,22].…”