Bond-Length-Weighted Molecular Topological Indices for QSPR Modeling of Anti-Tuberculosis Drugs

This study introduces a new family of bond-length-weighted molecular topological indices (BWMTIs) within chemical graph theory and evaluates their applicability to quantitative structure–property relationship (QSPR) modeling of selected anti-tuberculosis drugs. Unlike conventional indices derived primarily from unweighted, hydrogen-suppressed molecular graphs, the proposed framework uses dimensionless normalized bond-length information as edge weights, retains hydrogen atoms, and represents multiple bonds through edge multiplicity. Seven BWMTIs, namely BES, BHES, BSES, BRES, BSRES, BFZ, and BSZ, were evaluated against eight physicochemical properties: boiling point (BLP), melting point (MLP), flash point (FLP), enthalpy of vaporization (EOV), molar refractivity (MRF), polarizability (POL), surface tension (SFT), and molar volume (MOV). Linear, quadratic, cubic, exponential, and logarithmic single-descriptor QSPR models were compared using R2, adjusted R2, RMSE,MAE,RMSELOOCV, MAELOOCV, and RLOOCV2, together with full-selection y-scrambling permutation validation. Molecular weight (MW) and edge count (EC) were additionally included as simple reference descriptors for baseline comparison and are not members of the proposed BWMTI family. Among the proposed BWMTIs, BHES produced the best cross-validated models for most physicochemical properties. Exponential models based on BHES showed the strongest BWMTI-based cross-validated performance for the closely related MRF and POL endpoints, with RLOOCV2=0.8438 and 0.8436, respectively. The simple MW or EC reference models, however, showed higher cross-validated performance for several size-related properties, whereas the BWMTI framework showed comparatively better performance for MLP. Neither approach provided useful prediction of SFT. By combining molecular connectivity, hydrogen information, bond multiplicity, and local bond-length information, the proposed BWMTIs provide an alternative graph-theoretical framework for investigating molecular structure–property relationships. The proposed models are intended as exploratory QSPR tools rather than replacements for laboratory measurements. Their broader predictive utility requires validation using larger and more diverse datasets, independent external data, and established benchmark datasets.