Two-dimensional coronene fractals: modified reverse degree indices, comparative analysis of information entropy and predictive modeling of spectral properties.

Topological characterization through graph-theoretical methods translates chemical and structural data into quantitative values that represent the molecular system. Our research explores the use of topological indices to study fractal structures. Molecular fractals are complex geometric configurations that exhibit self-similarity at different levels and systematically formed by repeating a fundamental unit. This study focuses on coronene-based molecular fractals, where coronene, a benzenoid molecule with a symmetrical graphite-like structure, finds applications in organic semiconductors, sensors, and molecular electronics, due to its unique electronic and optical properties. Additionally, information entropy is employed to evaluate and compare the structural complexities of coronene fractals. Spectra-based energetic properties such as total $\pi$ -electron energy, HOMO-LUMO energy gaps, spectral diameter, delocalization and resonance energies are calculated to assess their kinetic and thermodynamic stability. Furthermore, predictive models are provided for estimating spectral characteristics across higher-dimensional coronene fractal structures.