How quantum-chemical geometry optimization level affects classical 3D descriptors and QSAR performance: a comparative...

Accurate representation of three-dimensional (3D) molecular structures is essential for quantitative structure-activity relationship (QSAR) modeling; however, it remains unclear whether increasing the level of theory used for quantum-chemical geometry optimization yields a practically meaningful benefit for classical conformation-dependent 3D descriptors (Dragon 3D) and the resulting QSAR performance. Here, we benchmark eight commonly used quantum-chemical (QM) geometry-optimization protocols-from minimal-basis Hartree-Fock (HF/STO-3 G) to def2-based hybrid density functional theory (DFT) and the composite method r $_{}^2$ SCAN-3c-across three anticancer activity datasets and ten machine-learning classifiers. Descriptor-level analyses (relative deviation, rank correlation, and chemical-space similarity) reveal systematic method dependence in descriptor magnitudes: high-accuracy def2-based DFT protocols produce highly consistent descriptor spaces, whereas some intermediate/low-level settings introduce larger variability, although molecular rankings remain largely robust (Spearman $\rho >0.95$ ). In contrast, downstream QSAR performance is only weakly affected by the QM level. Across paired dataset $\times$ model blocks ( $n=30$ ), mean balanced accuracies cluster tightly (0.852-0.871). B3LYP/3-21 G achieves the highest overall mean balanced accuracies (BA) (0.8709; 95% CI 0.8565-0.8840), while the lowest mean is observed for HF/STO-3 G (0.8518; 95% CI 0.8371-0.8661); def2-based B3LYP methods are numerically slightly lower ( $\sim$ 0.855-0.856). A repeated-measures omnibus test indicates a statistically detectable method effect (Friedman $p=0.006$ ) but with a small effect size (Kendall's $W=0.094$ ), and post-hoc Wilcoxon tests with Holm correction identify only one robust pairwise difference (B3LYP/3-21 G vs. HF/STO-3 G, $p_{\text{Holm}}=0.025$ ). Thus, the observed performance shifts are marginal in magnitude ( $\le$ 1-2%) compared with the 10-100 $\times$ differences in computational cost.To support pragmatic method selection, we propose a two-tier Absolute Efficiency Ratio (AER) framework integrating predictive performance with efficiency and methodological considerations. Overall, these results indicate a non-linear and practically weak relationship between QM geometry-optimization level, classical 3D descriptor fidelity, and QSAR performance, suggesting that QM-level upgrades mainly reshape descriptor values without yielding commensurate or actionable gains in predictive accuracy.