Predicting Reactivity and Stability of Polycyclic Conjugated Hydrocarbons Using Composite Wiener and Harary Product Indices: A Bifurcation Analysis Approach

Abstract

The Wiener–Harary product index, defined as the product of the Wiener index W and the Harary index H offers a composite topological descriptor that integrates both the global distance distribution and the degree of molecular compactness. In this study, the Wiener–Harary product index W(G) × H(G) is applied to a series of representative polycyclic conjugated hydrocarbons—benzene, naphthalene, and anthracene to investigate its potential in predictng chemical reactivity and stability. The composite index is incorporated into the molecular descriptor function  C(G) = W(G) + H(G) + [W(G) × H(G)] + MDP(x = 2) where mdp represents the metric degree polynomial. The computed W, H, and W(G) × H(G) values  how a monotonic increase with molecular size and ring fusion, reflectng enhanced π-electron delocalization. Aromatic stabilization energy (ASE) measurements correlate positively with the composite index, indicating that higher W(G) × H(G) values correspond to increased thermodynamic stability. The bifurcation analysis framework reveals structural thresholds where incremental changes in ring fusion result in significant shifts in stability indices, suggesting potential “reactivity transition points” within larger polycyclic systems. These findings support the Wiener–Harary product index, in combination with the C(G) descriptor as an effective predictive tool for assessing the stability and reactivity trends in polycyclic conjugated hydrocarbons, with potential applications in QSPR/QSAR modeling and rational design of aromatic compounds.