A revisit to molecular path codes: Ordering,comparability, and similarity of benzenoid,nonbenzenoid, and monoradical hydrocarbons

Molecular path codes are computed for 17 hydrocarbons, including benzenoid alternant, nonbenzenoid alternant, fully aromatic nonalternant, antiaromatic nonalternant, and monoradical hydrocarbons. Comparability conditions of Randi? and Wilkins 9–18] based on the theorems of Muirhead and Karamata are imposed on the partial sums of the codes. The distance/similarity matrix is constructed using the individual paths as projections in Euclidean space. Both resonance energies and total pi energies correlate with partial ordering predicted from both comparability and similarity schemes. The normalized codes succeed in discriminating combinatorial properties of the various topologies studied such as conjugated circuits.