Optimizing parametric temporal graphical indices for thermodynamic property prediction of benzenoid hydrocarbons with applications to structure-property modeling of monocarboxylic acids

Temperature-based molecular descriptors offer a compact mathematical representation of molecular structure with relevance to thermodynamic behavior. This work develops and optimizes two parametric temperature indices, T_1^α and T_2^α , defined on graph models of benzenoid hydrocarbons. Using closed-form expressions for hexagonal systems together with discrete optimization and regression analysis, we compute these indices for the 30 lower benzenoid hydrocarbons and determine the values of α that maximize their predictive ability. The optimized descriptors achieve correlations above 0.97 for heat capacity ( C_p ) and above 0.91 for entropy ( S^∘ ), while multivariate regression yields multiple-correlation values exceed 0.99 , demonstrating strong joint predictive capability. To assess generalizability, the optimized indices are further applied to nineteen monocarboxylic acids using ab initio thermodynamic data. The resulting regression models maintain high accuracy, confirming the robustness of the proposed framework. Overall, the study establishes efficient, physics-informed structure–property models in which thermodynamic properties are captured through a single tunable graph parameter. The findings support the broader application of temporal topological indices in computational chemistry and data-driven prediction of molecular thermodynamic behavior.