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GeoMol: Torsional Geometric Generation of Molecular 3D Conformer Ensembles
Octavian-Eugen Ganea, Lagnajit Pattanaik, Connor W. Coley, Regina Barzilay, Klavs F. Jensen, William H. Green, Tommi S. Jaakkola
TL;DR
Molecular conformer generation requires predicting low-energy 3D ensembles from molecular graphs despite large conformational spaces and limitations in existing multi-stage and force-field-based methods. GeoMol uses an end-to-end, non-autoregressive, SE(3)-invariant model that predicts local structures and torsions for deterministic assembly and diverse generation. It predominantly outperforms open-source, commercial, and machine-learning baselines while achieving speed-ups, with limitations for disconnected graphs and long-distance interactions.
Problem
Molecular conformer generation must predict experimentally relevant low-energy 3D ensembles from molecular graphs, but conformational spaces grow exponentially and existing force-field optimization can be slow and error-prone.
Method
GeoMol is an end-to-end, non-autoregressive, SE(3)-invariant model that predicts local 3D structures and torsion angles for deterministic conformer assembly and uses an optimal-transport loss for diverse generation.
Results
GeoMol predominantly outperforms popular open-source, commercial, and machine-learning models, while generating conformers faster than the considered baselines.
Takeaways & Limitations
Explicitly modeling torsion angles and local molecular geometry supports differentiable 3D conformer generation for molecular modeling and related applications.
Takeaways & Limitations
GeoMol does not currently support disconnected molecular graphs and remains limited in explicitly modeling long-distance interactions, especially for macrocycles or large molecules.
Abstract
from arXiv · showhide
Prediction of a molecule's 3D conformer ensemble from the molecular graph holds a key role in areas of cheminformatics and drug discovery. Existing generative models have several drawbacks including lack of modeling important molecular geometry elements (e.g. torsion angles), separate optimization stages prone to error accumulation, and the need for structure fine-tuning based on approximate classical force-fields or computationally expensive methods such as metadynamics with approximate quantum mechanics calculations at each geometry. We propose GeoMol--an end-to-end, non-autoregressive and SE(3)-invariant machine learning approach to generate distributions of low-energy molecular 3D conformers. Leveraging the power of message passing neural networks (MPNNs) to capture local and global graph information, we predict local atomic 3D structures and torsion angles, avoiding unnecessary over-parameterization of the geometric degrees of freedom (e.g. one angle per non-terminal bond). Such local predictions suffice both for the training loss computation, as well as for the full deterministic conformer assembly (at test time). We devise a non-adversarial optimal transport based loss function to promote diverse conformer generation. GeoMol predominantly outperforms popular open-source, commercial, or state-of-the-art machine learning (ML) models, while achieving significant speed-ups. We expect such differentiable 3D structure generators to significantly impact molecular modeling and related applications.
1 Overview
Molecular conformer generation seeks low-energy 3D structures from molecular graphs, but the conformational space grows rapidly and existing computational methods can be expensive or accumulate errors. GeoMol addresses this with an end-to-end model that explicitly represents molecular geometry while avoiding unnecessary over-parameterization.
- Problem & importance: Molecular conformer generation predicts ensembles of low-energy 3D conformations solely from molecular graphs.Low-energy structures are the most stable configurations and are therefore expected to be observed most often experimentally.
- Motivation & challenges: The conformational space grows exponentially with graph size and rotatable bonds, while the number of plausible low-energy states can range from one to several thousand.Bond lengths, bond angles, torsion angles, bond types, and chirality constrain the possible structures.
- Motivation & challenges: Existing approaches include stochastic and systematic methods, often combined with distance geometry and subsequent force-field optimization.Force fields are crude approximations of the true molecular potential energy surface, and their optimization can be slow and increase error accumulation in multi-stage pipelines.
- Key contributions & model: GeoMol is designed to generate fast, high-quality, representative, diverse, and generalizable low-energy conformer ensembles from molecular graphs.The paper frames this as its central modeling question and proposes GeoMol as the corresponding approach.
- Key contributions & model: GeoMol is end-to-end trainable, non-autoregressive, and SE(3)-invariant, predicting angles and distances sufficient for deterministic 3D conformer reconstruction.It explicitly models torsion angles and local 3D structures, including bond distances and adjacent bond angles, without relying on distance geometry techniques.
2 Method
GEOMOL predicts local 3D structures, chirality, bond distances, and one torsion angle per relevant bond from molecular graphs, then deterministically assembles conformers at test time. Its losses compare invariant geometric quantities and use optimal transport to support diverse conformer generation.
- Local structure prediction: GEOMOL encodes molecular graphs with MPNNs and predicts local 3D structures for each non-terminal atom in a permutation-equivariant manner.Neighbor positions are predicted relative to the central atom, while transformer-style processing preserves the correspondence between input neighbors and outputs.
- Local structure prediction: It predicts bond distances with a symmetric model and uses local structures to obtain bond angles and directions consistently across adjacent atoms.The distance model shares parameters in both endpoint orders, while predicted directions are normalized using the predicted bond distance.
- Chirality: GEOMOL explicitly corrects tetrahedral chirality by checking the oriented volume of predicted neighbor coordinates against RDKit’s CW/CCW label.If the generated oriented volume has the wrong sign, the local structure is corrected to produce the required chiral center.
- Torsion-angle assembly: For each bond between non-terminal atoms, GEOMOL predicts a single canonical torsion angle because the remaining dihedral angles are determined by the two local structures.This avoids assigning separate torsion variables to geometrically dependent angles and reduces over-parameterization.
- Training and assembly: Training computes invariant distances and angles from local predictions, using a negative log-likelihood for one conformer and an optimal-transport loss for variable conformer sets.The conformer is assembled deterministically from local structures and torsions, while full conformer assembly occurs only at test time.
3 Experiments
GEOMOL is evaluated for low-energy conformer ensemble generation on GEOM-QM9 and GEOM-DRUGS using RMSD-based ensemble metrics and comparisons with established, commercial, and machine-learning baselines. It frequently outperforms the considered baselines and is the fastest method, while coverage remains reasonable as molecular flexibility increases.
- Datasets and baselines: GEOMOL is evaluated on GEOM-QM9 and GEOM-DRUGS, with molecule-level random train/validation/test splits and 1000 randomly sampled test molecules per dataset.The datasets are split 80%/10%/10% by molecule.
- Datasets and baselines: The comparison includes ETKDG/RDKit, OMEGA, GraphDG, and CGCF, spanning open-source, commercial, and recent machine-learning methods.ETKDG/RDKit and OMEGA are described as established baselines, while GraphDG and CGCF are recent ML models.
- Metrics and protocol: Evaluation uses RMSD-based ensemble metrics, including Coverage and Average Minimum RMSD, with δ=0.5Å for GEOM-QM9 and δ=1.25Å for GEOM-DRUGS.Recall measures how many ground-truth conformers are correctly predicted, while precision measures the quality of generated structures.
- Results: GEOMOL frequently outperforms OMEGA, RDKit/ETKDG, GraphDG, and CGCF, except for AMR-P on QM9 relative to the reported comparisons.OMEGA also fails to generate any conformers for 7% of the QM9 test set.
- Results: GEOMOL maintains reasonable COV Recall as the number of rotatable bonds increases, although greater flexibility makes conformer generation harder for all baselines.The results are shown with 95% confidence intervals in Figure 7.
- Runtime: GEOMOL is the fastest considered baseline and scales favorably for molecules with increasing numbers of rotatable bonds.The comparison includes conformer-generation test running times.
4 Conclusion
GEOMOL is an end-to-end generator of molecular 3D conformer ensembles that explicitly models torsion angles and chirality. The authors identify limitations involving disconnected graphs, long-distance interactions, and the absence of explicit ground-truth energy modeling.
- Conclusion: GEOMOL generates molecular 3D conformation ensembles end-to-end while explicitly modeling geometric aspects such as torsion angles and chirality.The authors expect differentiable structure generators to affect small-molecule conformer generation and related applications.
- Limitations and future work: The model does not directly support disconnected molecular graphs, although each connected component can be processed separately and then aligned in 3D.Ionic salts are given as an example of disconnected graphs.
- Limitations and future work: GEOMOL would benefit from explicit long-distance interaction modeling, especially for macrocycles or large molecules.The authors leave efficient treatment of these interactions for future work.
- Limitations and future work: Explicitly using ground-truth energy values could further improve GEOMOL, and future work includes fine-tuning it for docking poses or 4D QSAR descriptors.These applications are identified as future extensions.
A Proof of proposition 1
The proof analyzes how a random torsion rotation around a bond shifts the relevant dihedral angle. It formalizes local-structure alignment and dihedral computation while identifying collinearity as an exceptional case.
- Torsion rotation: A counter-clockwise torsion rotation of angle γ around bond XY shifts the resulting dihedral angle by exactly γ.The proof compares dihedral angles before and after rotating the bonds attached to the bond XY.
- Degenerate cases: The formulation excludes neighbor nodes collinear with X and Y from torsion computation because the corresponding dihedral angles are undefined.If all relevant neighbors are collinear, the torsion angle is undefined and the isolated case is left for future work.
- Local-structure alignment: The local structures of nodes X and Y are aligned by SE(3) transformations before combining their geometric information.The construction centers and rotates the local structures so corresponding bond points match.
- Dihedral computation: The CCW dihedral angle between two half-planes is computed with an atan2 expression using vector cross products and inner products.The vectors are defined from the four points forming the two planes.
D Details of the loss function
The loss and assembly details address local geometric prediction, symmetric-node matching, deterministic conformer construction, and cycle correction. The procedure remains bounded by limitations in symmetry handling, long-range interactions, and computationally expensive dataset generation.
- Loss function: Distances are modeled with normal distributions and angles with von Mises distributions in the negative log-likelihood loss.The corresponding concentration and inverse-standard-deviation parameters are tuned on the validation set.
- Symmetric-node matching: The matching loss searches permutations of symmetric terminal nodes attached to a common neighbor to find the ground-truth assignment with the best loss value.This addresses cases where message-passing networks cannot distinguish nearby symmetric graph nodes despite their different 3D positions.
- Symmetric-node matching: The symmetry treatment is limited to identical degree-1 nodes connected to the same common neighbor, with more general symmetries left for future work.The limitation follows from the stated scope of the proposed matching procedure.
- Full conformer assembly: At inference time, local structures are assembled atom by atom along a fixed graph traversal, producing a deterministic conformer up to an SE(3) transformation.The training stage does not require assembling the full conformer.
- Cycle correction: Ring correction constructs multiple cycle-specific coordinate lists, aligns them with the Kabsch algorithm, and averages corresponding vectors to smooth cycle coordinates.The procedure is illustrated as improving the assembled structure in Figure 9.
- Datasets: The GEOM dataset uses semi-empirical tight-binding DFT with CREST, whose calculations can be slow for larger molecules and motivate machine-learning conformer models.Dataset statistics are reported in Figure 10.
G Data preprocessing
Dataset files are converted into PyTorch Geometric objects after filtering molecules that RDKit cannot process, contain disconnected fragments, or lack dihedral angles.
- Each .pickle file represents one molecule and its conformers and is featurized as a PyTorch Geometric data object.
- Molecules are discarded when their SMILES strings fail RDKit processing.
- Disconnected fragments and molecules without dihedral angles are excluded from the datasets.
H Additional training details and hyperparameters
Models are trained with early stopping, validation-based hyperparameter selection, and noise tuning for coverage objectives; GEOMOL confidence intervals use repeated conformer generation.
- Each model is trained for up to 250 epochs with early stopping, retaining the checkpoint with the best validation performance.
- The noise standard deviation s is tuned on validation data to maximize either recall coverage or precision coverage.
- GEOMOL confidence intervals are estimated by running the same trained model three times per test molecule, generating 2K conformers per run.
J Results with force field optimization
The models are also evaluated after fine-tuning with MMFF94s force-field energy minimization, using GEOMOL models trained with s = 1.
- Results are reported after additional fine-tuning with MMFF94s Merck Molecular Force Field energy minimization.
- The best GEOMOL models in the force-field-fine-tuned evaluation use s = 1 during training rather than s = 5.
K Compute details
GEOMOL training uses one Nvidia V100 GPU and eight Intel Xeon Gold CPUs, with full 250-epoch training taking approximately 1.8 days on QM9 and 6.1 days on DRUGS.
- GEOMOL is trained using a single Nvidia Volta V100 GPU and eight Intel Xeon Gold 6248 CPUs.
- 1.8 days is the approximate full-training time for QM9, compared with 6.1 days for DRUGS.
L Additional coverage results
Additional analyses examine how recall coverage changes with RMSD thresholds and provide more generated-conformer examples. The discussion also situates these evaluations within application-specific use cases and notes that benchmark metrics may not reflect production workflows.
- Coverage across thresholds: Recall coverage varies with the RMSD threshold δ: larger thresholds tolerate small errors but penalize large errors, whereas smaller thresholds penalize both.The relationship is plotted in Figure 11.
- Generated examples: Additional generated-conformer examples are shown for both the GEOM-QM9 and GEOM-DRUGS test sets.The examples appear in Figures 12 and 13.
- Application context: Conformer-generation priorities depend on the application, including low-temperature properties, virtual screening, docked-pose discovery, 4D QSAR, and crystal structure prediction.The passage contrasts settings where high-population conformers, speed, or quality over quantity matter.
- Evaluation scope: The reported evaluation metrics benchmark ML conformer generators but may not represent production use, where pruning, ranking, and method-specific post-processing are often required.The authors leave exploration of such post-processing strategies for future work and caution against treating the evaluation as comprehensive evidence for or against the compared methods.
N.3 QM9 results
QM9 and DRUGS results expose where conventional conformer generators struggle and where GEOMOL is competitive, particularly for chiral structures, larger molecules, and runtime. GEOMOL still has important weaknesses in long-range interactions, macrocycles, sparse ring motifs, and steric clashes, while its training-data dependence offers downstream flexibility.
- QM9 results: ETKDG fails to embed some fused-ring molecules with multiple specified chiral centers, while removing chirality specifications produces incorrect chirality.GEOMOL addresses this issue by solving all specified chiral centers exactly.
- DRUGS results: For larger drug-like molecules, ETKDG has poor coverage in large distance spaces, whereas OMEGA becomes expensive and uses force-field energies that differ from xTB ground truths.OMEGA therefore requires RMSD cutoffs for many inputs to return results in reasonable time.
- Runtime comparison: GEOMOL, OMEGA, and GraphDG show comparable per-conformer runtime, while GEOMOL scales well as rotatable-bond counts increase and CGCF is orders of magnitude slower.The comparison parallelized each method over 40 CPU cores and excluded model startup time.
- Limitations: GEOMOL's main errors involve macrocycles, sparsely represented large rings, and steric clashes caused by weak long-range interaction modeling.Error accumulation can also cause the ring-smoothing algorithm to break down for large cycles.
- Downstream flexibility: GEOMOL can in principle reproduce the quality of its training conformers, allowing fine-tuning on higher-level-theory or solvent-inclusive conformer databases.The paper presents this as a route to downstream modifications in cheminformatics and drug discovery.
- Comparison with ML baselines: GraphDG and CGCF improve distance-space search and prediction diversity, but are not production-ready without force-field optimization; GraphDG is competitive with GEOMOL on QM9.GraphDG is described as a viable alternative for small molecules with few heavy atoms.