Neighborhood Face Index: A New Quantitative Structure Property Relationship (QSPR) Approach for Predicting Physical Properties of Polycyclic Chemical Compounds

Topological indices (TIs) are numerical parameters that characterize the biochemical and physio-chemical properties of compounds. These graph-based descriptors are valuable tools for predicting key attributes, such as melting points, boiling points, bond energies, and bond lengths, based on the molecular structures of the compounds. A variety of TIs have been developed, including the Randić index, Zagreb index, atom-bond connectivity index, geometric index, and harmonic index. In this work, we introduce a new topological index called the neighborhood face index, which demonstrates a strong correlation with various physical properties such as bond energies and boiling points, achieving a correlation coefficient of $R\ge 0.9994$. This indicates its robust predictive capability. Furthermore, the results are thoroughly analyzed using graphical tools to provide deeper insights.