Comparative Analysis of Kekulene Tessellation Patterns Using Generalized Reverse Degree-Sum Descriptors Combined With Graph Entropy and Energy Properties

Abstract

Molecular descriptors are essential tools for analyzing the structural and physicochemical properties of molecular systems. In this study, novel modified reverse degree-sum descriptors are applied to analyze kekulenes, a distinctive class of cycloarenes known for their aromaticity, superaromaticity, and exceptional electronic properties. These descriptors are further integrated with graph entropy measures to evaluate the structural complexity and energetic properties of three kekulene tessellation patterns: Zigzag, armchair, and rectangular. Energetic parameters, including total $\pi$-electron energy, HOMO-LUMO energy gaps, and resonance energy, are computed to provide a detailed understanding of the kinetic and thermodynamic stability of these tessellations. The modified reverse degree-sum-based methodology applies to all degree-sum-based descriptors. The variable parameter ‘$k$’ adjusts the molecular graph's degree-sum sequence to best fit the unique properties of each dataset. These enhancements strengthen correlations with physicochemical properties, improving the descriptor's effectiveness in structural analysis. Furthermore, regression models are developed to predict the energetic behavior of high-dimensional kekulene structures, offering a robust framework for advanced studies in molecular stability and design.