Modeling the Physicochemical Characteristics of Benzene Compounds Utilizing Zagreb Eta Indices

Abstract

This study presents the Zagreb Eta indices, a novel family of degree-based topological descriptors defined through multiplicative combinations of neighboring vertex degrees, designed to model the physicochemical properties of benzenoid hydrocarbons. Building on our prior work that proposed the additive Zagreb upsilon indices, we intentionally reused the same dataset of 24 benzenoid compounds-including boiling point, pi-electron energy, molecular weight, polarizability, molar volume, and molar refractivity-to directly compare predictive performance and structural sensitivity. We computed the first, second, and third Eta indices from hydrogen-suppressed molecular graphs and evaluated their correlations with physicochemical properties using Pearson correlation coefficients and linear regression models. Additionally, smoothness analysis based on structural sensitivity and abruptness metrics was conducted to assess model stability and discriminative power. The Eta indices achieved exceptionally high correlation coefficients, up to 0.9998 for pi-electron energy and over 0.9995 for polarizability and molar refractivity. Compared to classical indices and the previously introduced upsilon indices, the Eta indices demonstrated comparable or slightly superior predictive capacity while maintaining desirable smoothness characteristics. These results suggest that the multiplicative formulation of the Eta indices captures complementary structural information, underscoring their potential value as robust descriptors in QSPR modeling and highlighting the importance of alternative topological approaches in cheminformatics.