Composite Topological Indices and Bifurcation Trends in Polycyclic Aromatic Hydrocarbons

Abstract

Polycyclic aromatic hydrocarbons (PAHs) represent a crucial class of conjugated systems in which stability and reactivity are strongly governed by molecular topology. This study develops a composite topological descriptor C_G = log₁₀W(G) + log₁₀H(G) + log₁₀R(G) + log₁₀MDP(G,2) that integrates distance-based, degree-based, and connectivity indices—namely the Wiener, Harary, Randic, and Metric Degree Polynomial (MDP) indices. Nine representative PAHs, ranging from naphthalene to coronene, were analyzed using computational graph-theoretical methods.
The calculated C_G values were correlated with stability data derived from total and per-atom energies. The single-descriptor regression model (R² = 0.245) confirmed that topological complexity contributes meaningfully to stability prediction. When energy per atom and fusion type were incorporated into a multiple-regression framework, the predictive accuracy improved markedly (R² = 0.729). Distinct bifurcation transitions—particularly Phenanthrene → Pyrene (−46.7 %) and Tetracene → Pentacene (−38.9 %) — reflect nonlinear structural reorganizations between angular, compact, and linear systems.
The proposed descriptor and regression approach provide a practical, computationally efficient route to estimate aromatic stability and structural behavior within extended PAH families.