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EDBench: Large-Scale Electron Density Data for Molecular Modeling
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Introduces EDBench, a dataset of B3LYP/6-31G**/+G** electron density (CUBE files) for 3.36M PCQM4Mv2 molecules, plus six ED-centric benchmark tasks (prediction, retrieval, generation) evaluated with GeoFormer, EquiformerV2, PointVector, X-3D and HGEGNN.
Problem
Machine-learning force fields model atoms and simple quantum properties but ignore electron density, which is hard to obtain at scale because DFT is expensive; no large-scale ED dataset or ED-centric benchmark exists.
Approach
Compute electron density for 3.36M drug-like molecules with B3LYP DFT via Psi4 and define benchmark tasks (energy components, orbital energies, multipole moments, open/closed shell, MS-ED retrieval, ED generation from structure) built on scaffold splits, plus a heterogeneous-graph EGNN (HGEGNN) that generates ED from structure.
Key results
- X-3D outperforms PointVector on ED5-EC, ED5-MM and ED5-OCS (e.g., ED5-MM magnitude MAE 0.6820 vs 0.7397).
- HGEGNN generates ED at 0.013-0.024 s/mol versus 245.8 s/mol for DFT, with Pearson up to 99.2% at rho_tau=0.2.
- Replacing DFT EDs with HGEGNN-generated EDs in ED5-EC improved PointVector downstream performance (reported as relative improvements).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use X-3D instead of PointVector for ED property prediction | ED-based prediction models · ED5-EC and ED5-MM | MAE | Helped |
| Use X-3D instead of PointVector | ED5-OCS classification · ED5-OCS | Accuracy, ROC-AUC, AUPR | Helped |
| Use PointVector instead of X-3D | ED5-OE orbital energy prediction · ED5-OE | MAE×100 | Helped |
| Raise the ED threshold from ρτ=0.1 to ρτ=0.2 (ablation) | HGEGNN · ED5-EDP | MAE: 0.3362±0.2900 -> 0.0448±0.0133 | Helped |
| Raise the ED threshold from ρτ=0.1 to ρτ=0.2 (ablation) | HGEGNN · ED5-EDP | Pearson (%): 81.0±8.1 -> 99.2±0.8 | Helped |
| Raise the ED threshold from ρτ=0.1 to ρτ=0.2 (ablation) | HGEGNN · ED5-EDP | Spearman (%): 56.4±13.7 -> 91.0±9.1 | Helped |
| Use HGEGNN-predicted ED instead of DFT-generated ED | PointVector on downstream ED5-EC · ED5-EC | MAE | Helped |
| Vary the ED threshold and sampling-point count (ablation) | PointVector · ED prediction tasks | model performance | Mixed |
Surprising findings
- Model-generated electron densities gave better downstream performance than DFT-computed densities, which the authors attribute to smoother, more learnable patterns rather than higher physical fidelity.
- Orbital energy prediction was markedly more accurate than energy component prediction for both models.
Limitations
- Molecules are mostly small (under 20 heavy atoms) drug-like species, limiting coverage of larger or materials systems.
- Only B3LYP/6-31G**/+G** used; higher-level functionals and basis sets not included in the dataset.
- Benchmark tasks use subsets of at most 50,000 molecules; retrieval uses in-batch negatives that may be too easy.
Experimental setup
Datasets: PCQM4Mv2
Benchmarks: ED5-EC ED5-OE ED5-MM ED5-OCS ED5-MER ED5-EDP
Metrics: MAE accuracy ROC-AUC AUPR F1-score top-k accuracy Pearson Spearman RMSE
Baselines: GeoFormer EquiformerV2 PointVector X-3D DFT
Builds on: PCQM4Mv2 Psi4 EGNN InfoNCE Hohenberg-Kohn theorem
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