Topological Indices Driven Quantitative Analysis of Physicochemical and Structural Properties of Opioid Drugs

Opioid drugs represent a critical class of therapeutic compounds with diverse structural frameworks that govern their pharmacological behavior. Understanding the relationship between their molecular architecture and physico­chemical characteristics is essential for drug design and optimization. In this study, a wide range of degree-based topological indices, including the first and second Zagreb indices ( M1 , M2 ), forgotten index ( F ), hyper Zagreb indices ( HM1 , HM2 ), and harmonic index ( Y , S ), were computed to quantify the structural complexity of selected opioid drugs. These indices were systematically correlated with physicochemical descriptors such as boiling point (Bp), molar refractivity (MR), molar volume (MV), polarizability (P), density, and surface tension (ST). A comprehensive set of statistical and multivariate analyses was performed. Descriptive statistics indicated that M1 is the most stable index, while P and G exhibited high variability. Pearson and Spearman correlations confirmed M2 and HM2 as the most informative structural descriptors. Principal Component Analysis (PCA) and Factor Analysis identified key latent factors capturing over 90% of data variance. Discriminant Analysis (DA) achieved a classification accuracy of ∼ 91 . 6%, effectively distinguishing morphinan and synthetic opioids. Canonical Correlation Analysis (CCA) revealed a strong multivariate association (canonical correlation = 0.94) between topological indices ( M1 , M2 , S , HM2 ) and physicochemical properties (Bp, MR, MV, P, atomic mass). MANOVA confirmed the significant influence of physicochemical descriptors on structural indices, and multiple as well as stepwise regression highlighted boiling point, molar refractivity, and molar volume as dominant predictors of M2 . These findings demonstrate that molecular topology, particularly indices M2 , HM2 , S , and M1 , is strongly interrelated with key physicochemical properties, providing valuable insights into the structural complexity, classi­fication, and pharmacological relevance of opioid drugs. The study underscores the potential of topological indices as predictive tools in drug design and molecular modeling.