Abstract
The new third Zagreb psi index achieves a correlation coefficient of 0.99948 for modeling the π-electron energy of benzenoid hydrocarbons, outperforming all previously reported degree-based topological indices. In this study, a novel vertex descriptor, referred to as the psi degree, is introduced by combining additive and multiplicative contributions of neighboring vertex degrees in a unified manner. Based on this concept, three Zagreb-type psi indices are defined and systematically analyzed within a quantitative structure–property relationship (QSPR) framework. Correlation and linear regression analyses demonstrate the strong predictive ability of the proposed indices, with particular emphasis on the third Zagreb psi index. In addition, structural sensitivity and smoothness analyses are performed to examine the behavior of the new descriptors under local structural modifications. While the present investigation is restricted to benzenoid hydrocarbons and linear modeling, the results indicate that Zagreb psi indices constitute chemically meaningful and promising tools for QSPR studies, motivating further applications to other molecular classes and physicochemical properties.