Predictive potential of eigenvalues-based graphical indices for determining thermodynamic properties of polycyclic aromatic hydrocarbons with applications to polyacenes

For the structure-property modeling of thermodynamic properties of polycyclic aromatic hydrocarbons (PAHs), this paper explores the effectiveness of a specific class of graphical indices defined based on eigenvalues, also known as valency-spectral graphical indices. The 30 lower PAHs have been selected as test molecules. The heat capacity (Cp) and entropy (So) are the standard choices for characterizing thermodynamic properties due to their close correlation with the thermodynamic properties of a similar nature. A computer -dependent method is proposed to calculate valency-spectral indices of chemical graphs, and it is employed to compute the indices for our test molecules. The statistical inferences reveal an unexpected finding for the Estrada harmonic energy, a less familiarized spectral descriptor within the research community, outperforming all the existing descriptors, followed by the positive & negative inertia indices. The Estrada harmonic energy achieved the highest mean correlation coefficient of rho> 0.99. On the other hand, well-studied descriptors such as Laplacian energy and adjacency energy still maintained their effectiveness in correlating the thermodynamic properties of PAHs; however, they were significantly outperformed by the Estrada harmonic energy. The three best valency-spectral indices are employed in the structure-property modeling of thermodynamic properties of linear polyacenes.