Sombor indices in main group metal chemistry: Computational evaluation of bismuth(iii) iodide, oxide/silicate frameworks, and dendrimers for QSAR applications

Abstract Topological indices (TIs), as numerical descriptors derived from molecular graphs, offer critical insights into structural properties of chemical compounds by quantifying atomic connectivity, independent of spatial configuration. These indices are pivotal in quantitative structure–activity relationship studies, enabling the prediction of physicochemical and biological behaviors of compounds prior to experimental analysis. In this study, we focus on the computational application of novel Sombor indices to key main group metal-based systems, including bismuth( iii ) iodide – a prominent heavy main group metal halide – as well as structurally related TOXs and silicates, which underscore the versatility of main group elements in forming diverse architectures. Additionally, we investigate nanostar dendrimers to explore topological trends in complex, hyperbranched frameworks relevant to main group metalloid-containing polymers. To validate the broader chemical utility of these indices, we analyze their degeneracy and discriminative capacity across a series of octane isomers, establishing a comparative foundation for their efficacy in distinguishing structural nuances. Our results demonstrate that these TIs exhibit strong correlations with enthalpy of vaporization, standard enthalpy of vaporization, acentric factor, and density. All evaluated indices show identical degeneracy rates of 78.67%, underscoring their consistency in structural analysis. These findings highlight the potential of Sombor indices as robust tools for modeling structure–property relationships for designing advanced materials and catalytic systems. This work bridges computational chemistry with applied main group metal research, offering predictive strategies that could streamline the development of main group derivatives for industrial applications.