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

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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mrow></mml:mrow> <mml:mrow></mml:mrow> <mml:mn>2</mml:mn></mml:mmultiscripts> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ρ</mml:mi> <mml:mo>></mml:mo> <mml:mn>0.95</mml:mn></mml:mrow> </mml:math> ). In contrast, downstream QSAR performance is only weakly affected by the QM level. Across paired dataset <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>×</mml:mo></mml:math> model blocks ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>30</mml:mn></mml:mrow> </mml:math> ), 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 ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>∼</mml:mo></mml:math> 0.855-0.856). A repeated-measures omnibus test indicates a statistically detectable method effect (Friedman <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>p</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.006</mml:mn></mml:mrow> </mml:math> ) but with a small effect size (Kendall's <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>W</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.094</mml:mn></mml:mrow> </mml:math> ), and post-hoc Wilcoxon tests with Holm correction identify only one robust pairwise difference (B3LYP/3-21 G vs. HF/STO-3 G, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>p</mml:mi> <mml:mtext>Holm</mml:mtext></mml:msub> <mml:mo>=</mml:mo> <mml:mn>0.025</mml:mn></mml:mrow> </mml:math> ). Thus, the observed performance shifts are marginal in magnitude ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>≤</mml:mo></mml:math> 1-2%) compared with the 10-100 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>×</mml:mo></mml:math> 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.