Distance-based topological descriptors for measuring the π-electronic energy of benzenoid hydrocarbons with applications to carbon nanotubes

In this paper, we provide efficient regression models for correlating the π-electronic energies of carbon nanotubes and nanocones. First, a computational technique for determining distance-based, eccentricity-based, degree-distance-based, and degree-based molecular descriptors is proposed. Then, the application of our technique has been explained for the family of fibonacenes. Importantly, we use the proposed computational technique to determine commonly occurring distance-based molecular descriptors and generate regression models to determine their correlation with the π-electronic energies of lower polycyclic aromatic hydrocarbons (PAHs). Unlike its reputation among chemical graph theorists and reticular chemists, the fourth version of the geometric–arithmetic index outperforms all the distance-based descriptors having the correlation coefficient 0.999. This warrants further usage of the fourth geometric–arithmetic index in quantitative structure-activity relationship models. To ensure the applicability of our proposed study, we use the proposed computational technique to compute analytically explicit expressions for certain distance-based molecular descriptors for certain infinite families of carbon nanotubes and carbon nanocones. Our results assist in correlating the π-electronic energies of underlying chemical structures of these nanotubes and nanocones.