Distance-based graphical indices for predicting thermodynamic properties of benzenoid hydrocarbons with applications

This paper considers all the commonly occurring distance-related graphical indices and investigates their potential to predict thermodynamic properties of benzenoid hydrocarbons (BHs). Customarily, the entropy S o and the heat capacity C p have been chosen to be the representatives of thermodynamic characteristics. For test molecules, the lower 30 BHs have been opted and it is justified because the experimental data of both C p and S o is publicly available and the number 30 is sufficiently large enough to validate statistical inferences. In this paper, firstly, we propose a computer-dependent computational method to compute all distance-related (including eccentricity-related as well as valency-distance-related indices) of chemical graphs. The computational technique is employed further to evaluate the distance-related topological indices available in the literature. The statistical inferences suggested certain unexpected results as the less-studied distance descriptors such as the second atom-bond connectivity ( A B C 2 ) index, the total eccentricity ( ζ ) index, and the eccentric-connectivity ( ξ ) index outperform the well-researched descriptors such as the Szeged ( S z ), the Wiener W , the Padmakar-Ivan ( P I ) indices generate poor correlation power. Among the best descriptors for correlating thermodynamic characteristics of BHs, only the A B C 2 index showcases the mean correlation coefficient ρ > 0 . 95 which is the minimum threshold for application of a descriptor in structure–property as well as structure–activity (QSPR/QSAR) modeling. The five best distance descriptors are then employed in detailed statistical analysis and most appropriate regression models suggested by the data are non-linear. The applications of the analysis are presented in correlation of the entropy S o and the heat capacity C p of linear polyacenes.