QSPR modeling of physicochemical properties in atmospheric photo-oxidized indole derivatives: integrating topological indices with linear, quadratic, and logarithmic regression

Abstract This study bridges graph-theoretical methods and computational physics by evaluating degree-based topological indices for sixteen indole derivatives-indole, 2-Formylformanilide, indoxyl, isatin, anthranilic acid, isatoic anhydride, indigo dye, indirubin, tryptanthrin, indoxyl red, 1H-indole-4-amine, 2-methyl-1H-Indole, 2-phynel-1H-indole, 1H-indole-6-carbaldehydel, 1h-indole-3-carbaldehyde, and 5-chloro-1h-indole to predict their physicochemical properties. By interpreting molecular structures as quantum-mechanical graphs, we compute topological indices as descriptors of electronic and structural connectivity, which are then employed in linear, quadratic, and logarithmic regression models to estimate density, boiling point, melting point, water solubility, molecular weight, and vapor pressure. These properties are critical for understanding molecular interactions, phase transitions, and material behavior in condensed matter systems. Statistical evaluation ( r , r 2 , F-statistic, p -value) reveals robust predictive accuracy for boiling point ( r > 0.824) and molecular weight ( r > 0.99), aligning with their direct dependence on molecular topology and quantum mechanical parameters. The models for vapor pressure and solubility also demonstrate moderate success, reflecting their sensitivity to intermolecular forces and entropy-driven processes. By linking graph invariants to measurable physical properties, this work advances computational strategies for rapid material characterization, offering a scalable alternative to resource-intensive quantum simulations. The results highlight the potential of topological indices as low-cost, high-efficiency tools for designing organic semiconductors, photonic materials, and molecular sensors, with implications for condensed matter physics and nanotechnology. This approach underscores the synergy between discrete mathematics and physical chemistry, enabling predictive modeling of complex systems through a unified theoretical framework.