<p>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<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$^2$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>2</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>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 <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\rho >0.95$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ρ</mi> <mo>></mo> <mn>0.95</mn> </mrow> </math></EquationSource> </InlineEquation>). In contrast, downstream QSAR performance is only weakly affected by the QM level. Across paired dataset<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\times$</EquationSource> <EquationSource Format="MATHML"><math> <mo>×</mo> </math></EquationSource> </InlineEquation>model blocks (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">$n=30$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>=</mo> <mn>30</mn> </mrow> </math></EquationSource> </InlineEquation>), 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 (<InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\sim$</EquationSource> <EquationSource Format="MATHML"><math> <mo>∼</mo> </math></EquationSource> </InlineEquation>0.855–0.856). A repeated-measures omnibus test indicates a statistically detectable method effect (Friedman <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$p=0.006$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>=</mo> <mn>0.006</mn> </mrow> </math></EquationSource> </InlineEquation>) but with a small effect size (Kendall’s <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$W=0.094$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>W</mi> <mo>=</mo> <mn>0.094</mn> </mrow> </math></EquationSource> </InlineEquation>), and post-hoc Wilcoxon tests with Holm correction identify only one robust pairwise difference (B3LYP/3-21 G vs. HF/STO-3 G, <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$p_{\textrm{Holm}}=0.025$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>p</mi> <mtext>Holm</mtext> </msub> <mo>=</mo> <mn>0.025</mn> </mrow> </math></EquationSource> </InlineEquation>). Thus, the observed performance shifts are marginal in magnitude (<InlineEquation ID="IEq9"> <EquationSource Format="TEX">$\le$</EquationSource> <EquationSource Format="MATHML"><math> <mo>≤</mo> </math></EquationSource> </InlineEquation>1–2%) compared with the 10–100<InlineEquation ID="IEq10"> <EquationSource Format="TEX">$\times$</EquationSource> <EquationSource Format="MATHML"><math> <mo>×</mo> </math></EquationSource> </InlineEquation> 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.</p>

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

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2026年2月19日

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Jianmin Li,
Rongling Gu,
Shijie Du,
Lu Xu

摘要

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 $^2$ $^{2}$ 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 $\rho >0.95$ $ρ > 0.95$ ). In contrast, downstream QSAR performance is only weakly affected by the QM level. Across paired dataset $\times$ $\times$ model blocks ( $n=30$ $n = 30$ ), 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 ( $\sim$ $\sim$ 0.855–0.856). A repeated-measures omnibus test indicates a statistically detectable method effect (Friedman $p=0.006$ $p = 0.006$ ) but with a small effect size (Kendall’s $W=0.094$ $W = 0.094$ ), and post-hoc Wilcoxon tests with Holm correction identify only one robust pairwise difference (B3LYP/3-21 G vs. HF/STO-3 G, $p_{\textrm{Holm}}=0.025$ $p_{Holm} = 0.025$ ). Thus, the observed performance shifts are marginal in magnitude ( $\le$ $\leq$ 1–2%) compared with the 10–100 $\times$ $\times$ 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.