---
title: 'GEOM: Geometric Ensemble of Molecules'
url: https://www.emergentmind.com/topics/geometric-ensemble-of-molecules-geom
type: topic
---

# GEOM: Geometric Ensemble of Molecules

Searching arXiv for the GEOM paper and recent benchmark follow-ups to ground the article in the literature.
GEOM, the **Geometric Ensemble Of Molecules**, is a large-scale dataset of molecules annotated with many energetically ranked three-dimensional conformers and associated energetic or experimental metadata, introduced to move molecular machine learning beyond the common representation of a molecule as either a **2D graph** or a **single 3D structure** [2006.05531]. Its central premise is that real molecules are flexible and, at finite temperature, occupy an **ensemble of conformers** on a potential energy surface; many properties therefore depend on that ensemble rather than on one arbitrarily chosen geometry. The dataset reports **more than 450,000 molecules/species** and about **37 million molecular conformations**, and was designed to support both **property prediction from conformer ensembles** and **generative models that sample 3D conformations** [2006.05531].

## 1. Conceptual basis

GEOM is motivated by a representational limitation in molecular machine learning. A 2D graph or SMILES string specifies connectivity, but not the three-dimensional shapes accessible to a molecule. A single optimized 3D conformer supplies one geometry, but not the full thermal ensemble. GEOM addresses this gap by providing **the entire conformational ensemble** and its associated weights and energies, with the explicit aim of supporting models that learn from conformational flexibility rather than from a single static structure [2006.05531].

The original paper frames this as especially important for properties tied to binding, reactivity, and solution-phase behavior. The figures described in the paper explicitly contrast a SMILES representation, a stereochemical graph, and an overlay of conformers, emphasizing that the 3D ensemble contains information absent from either simpler representation. This is particularly salient for flexible drug-like molecules, which in GEOM have an average of **6.5 rotatable bonds** and can therefore be conformationally rich [2006.05531].

A plausible implication is that GEOM does not merely enlarge prior molecular datasets quantitatively; it changes the target of learning from a structure to a distribution over structures. That distinction underlies its subsequent role in both conformer generation and 3D molecular generation benchmarks.

## 2. Dataset composition and scale

GEOM consists of two major subsets together with a higher-accuracy BACE refinement. The original paper reports the following composition [2006.05531]:

| Subset | Species | Notes |
|---|---:|---|
| QM9 | **133,258** | Small molecules, limited to **9 heavy atoms** |
| Experimental-data subset | **317,928** | Drawn largely from AICures drug data and MoleculeNet |
| BACE high-accuracy subset | **1,511** | Additional DFT free-energy annotations in implicit water |
| BACE DFT-optimized subset | **534** | Further refined with DFT geometry optimization |

Within the experimental-data portion, the paper states that GEOM includes **304,466 drug-like species** from AICures and **16,865 molecules** from MoleculeNet. Within MoleculeNet, it covers the physical chemistry and physiology categories in full, plus the BACE biophysics benchmark [2006.05531].

GEOM is also notable for its conformer counts per molecule. The AICures drug subset averages **102.6 conformers per species**, with some molecules having **up to 7,451** conformers, while QM9 averages **13.5 conformers per species** with a maximum of **1,101** [2006.05531]. These counts distinguish GEOM from datasets that attach one optimized geometry to each graph.

## 3. Conformer generation pipeline

The conformers in GEOM were generated with **CREST**, a conformer search package designed for efficient, thermodynamically meaningful exploration of molecular flexibility. CREST combines **meta-dynamics sampling** with the semi-empirical quantum method **GFN2-xTB**, and the paper presents this choice as a compromise between speed and accuracy: force fields are fast but often poor at ranking conformers, whereas full DFT is too expensive to run at the scale of millions of structures [2006.05531].

The dataset construction pipeline includes **SMILES normalization**, **salt stripping/protonation handling** for drug-like molecules, initial conformer seeding with **RDKit and MMFF**, **xTB pre-optimization**, CREST sampling, graph re-identification with **xyz2mol**, and higher-accuracy **DFT re-ranking/optimization** for a BACE subset [2006.05531]. CREST repeatedly runs meta-dynamics trajectories with different bias parameters, then optimizes sampled geometries with GFN2-xTB, identifies conformers, rotamers, and duplicates using thresholds on energy, RMSD, and rotational constants, and restarts from newly found low-energy structures when needed.

The default CREST filtering thresholds reported in the paper are **0.1 kcal/mol** for energy, **0.125 Å** for RMSD, and **15.0 MHz** for rotational constants, with a final energy window of **6.0 kcal/mol** [2006.05531]. The stated purpose of this window is to retain practically relevant conformers while ignoring very high-energy structures unlikely to contribute to room-temperature populations.

For the BACE subset, the original CREST ensembles were generated using an **ALPB water model**, then refined with **CENSO** using ORCA and **C-PCM water** at the DFT stage; single-point calculations were done at **r2scan-3c/mTZVPP** in water [2006.05531]. CENSO uses a staged DFT optimization strategy, discarding high-energy conformers during optimization and computing more accurate conformational thermodynamics, including entropic corrections via a **biased Hessian method**.

## 4. Energy annotation and ensemble probabilities

A defining feature of GEOM is that the conformers are **energy annotated**. CREST assigns each conformer an approximate statistical weight via a Boltzmann-like expression that includes rotamer degeneracy:
$$
p_i^{\mathrm{CREST}}=\frac{d_i\,\exp(-E_i/k_B T)}{\sum_j d_j\,\exp(-E_j/k_B T)}.
$$
Here \(d_i\) is the conformer’s degeneracy and \(E_i\) is its xTB energy [2006.05531]. The paper explicitly notes that this is only an approximation to the true equilibrium probability because it omits some free-energy terms, but it is intended as a useful initial ensemble weight.

For higher accuracy, GEOM provides more refined annotations for the BACE subset. For **1,511 BACE species**, the paper reports **single-point DFT energies** and xTB quasi-harmonic frequencies, enabling improved free-energy estimates; **534 BACE ensembles** were further optimized with DFT in a method based on **CENSO** [2006.05531]. The corresponding free energy is written as
$$
G_i = E_{\mathrm{gas}}^{(i)} + \delta G_{\mathrm{solv}}^{(i)} + G_{\mathrm{trv}}^{(i)},
$$
where \(E_{\mathrm{gas}}\) is the gas-phase electronic energy, \(\delta G_{\mathrm{solv}}\) is the solvation free energy, and \(G_{\mathrm{trv}}\) captures translation, rotation, and vibration contributions. The resulting ensemble probability is
$$
p_i^{\mathrm{CENSO}}=\frac{\exp(-G_i/k_B T)}{\sum_j \exp(-G_j/k_B T)}.
$$

The paper emphasizes the distinction between these two weighting schemes: **CREST** provides broad coverage of thermally accessible conformers, but its weights are not as reliable as **DFT-based** weights; **CENSO** uses the full free energy rather than only the electronic energy and does not include rotamer degeneracy in the probability formula [2006.05531]. This dual annotation strategy gives GEOM both scale and a smaller high-accuracy benchmark for conformational energetics.

## 5. Labels, tasks, and validation

Beyond geometry and energy, GEOM includes experimentally measured endpoints from AICures and MoleculeNet. In the AICures drug set, the paper lists properties spanning **biophysics, physiology, physical chemistry, and antiviral/antibacterial screening**, including **SARS-CoV-2 inhibition**, **SARS-CoV-2 3CL protease inhibition**, **SARS-CoV 3CL protease inhibition**, **SARS-CoV PL protease inhibition**, and growth inhibition of **E. coli** and **Pseudomonas aeruginosa** [2006.05531].

From MoleculeNet, GEOM includes **ESOL**, **FreeSolv**, **Lipophilicity** \((\log K_{\mathrm{octanol-water}})\), **BACE**, **BBBP**, **Tox21**, **ToxCast**, **SIDER**, and **ClinTox** [2006.05531]. These labels were intended to support conformer-aware property prediction. The authors explicitly suggest ensemble-level prediction tasks such as conformational entropy and free energy,
$$
S=-R\sum_i p_i\log p_i,\qquad G=-TS,
$$
the average conformer energy,
$$
\langle E\rangle = \sum_i p_i E_i,
$$
and the number of unique conformers in an ensemble.

The paper reports initial baseline results showing that **ChemProp** and a **SchNet-based model** can predict these quantities reasonably well, with the **SchNetFeatures** model slightly outperforming graph-only models on some tasks [2006.05531]. GEOM was also proposed as a benchmark for generative models that take a graph and produce a plausible set of 3D conformations.

Validation in the original work includes checks of **parsing correctness**, **graph recovery**, and **energy/geometry agreement** across xTB, DFT single points, and CENSO. The paper’s summarized validation findings are that xTB has moderate correlation with DFT for conformer energies, CENSO further improves ranking and geometry, and the CREST geometries are already close to DFT-optimized structures [2006.05531].

## 6. Later benchmark role and methodological revision

GEOM rapidly became a standard benchmark family for 3D molecular generation and conformation generation. Subsequent work uses **GEOM-QM9** and **GEOM-Drugs** to evaluate distinct generative paradigms: diffusion-based conformer generation in **GeoDiff** [2203.02923], **Bayesian Flow Networks** in **GeoBFN** [2403.15441], geometric-representation-conditioned generation in **GeoRCG** [2410.03655], rigid-motif generation in **MotiFlow** [2601.16955], vector-field representations in **VecMol** [2603.12734], flexible ensemble generation in **FlexiFlow** [2511.17249], and manifold-decomposed flow matching in **GO-Flow** [2605.25577]. This suggests that GEOM has functioned not only as a dataset but also as a common experimental substrate for comparing representational assumptions about 3D molecular structure.

The benchmark role of GEOM-Drugs has also exposed evaluation issues. **“GEOM-Drugs Revisited: Toward More Chemically Accurate Benchmarks for 3D Molecule Generation”** argues that common evaluation protocols contained incorrect valency definitions, bugs in bond order calculations, and force-field choices inconsistent with the reference data [2505.00169]. That work reports that fractured molecules produced by GFN2-xTB optimization failures affected about **0.18%** of the dataset, that corrected molecular stability typically drops by about **1–3%**, and that retraining on a fully kekulized version of GEOM-Drugs can improve validity by about **5% for 4 out of 6 models** [2505.00169].

This later critique does not negate the original rationale for GEOM. Rather, it clarifies that the scientific value of an ensemble dataset depends not only on scale and annotation depth but also on chemically faithful preprocessing and evaluation. In that sense, GEOM’s history includes both dataset construction and the subsequent refinement of how ensemble-based molecular generation should be measured [2006.05531].

Source: https://www.emergentmind.com/topics/geometric-ensemble-of-molecules-geom