GEOM-QM9 Dataset Overview

• GEOM-QM9 is a high-coverage dataset comprising 3D conformer ensembles for 133,258 small organic molecules, offering exhaustive energy annotations and structural diversity.
• It employs an exhaustive conformer generation protocol using CREST metadynamics and GFN2-xTB optimization, yielding an average of 13.5 conformers per molecule with detailed energy rankings.
• The dataset supports applications in machine learning, property prediction, and generative chemistry by providing Boltzmann-weighted conformational data for ensemble-based modeling.

The GEOM-QM9 dataset is a high-coverage, energy-annotated resource of 3D molecular conformer ensembles for 133,258 small organic molecules, each with up to nine heavy atoms, and is constructed as a subset of the broader Geometric Ensemble Of Molecules (GEOM) collection. Derived from the original QM9 database of CHONF species, GEOM-QM9 offers approximately 1.8 million distinct low-energy minima, supporting research into property prediction, molecular generation, and conformer ensemble-based modeling using machine learning techniques. It leverages exhaustive conformer sampling protocols and state-of-the-art semi-empirical quantum-chemical methods to supply energetics and structural diversity with unparalleled scale and detail (Axelrod et al., 2020).

1. Origins and Context

GEOM-QM9 is based on the QM9 database, a widely adopted benchmark in molecular machine learning that enumerates constitutional isomers containing carbon, hydrogen, oxygen, nitrogen, and fluorine. While QM9 provides single reference conformations and quantum-chemical properties, GEOM-QM9 addresses the critical need for coverage of the ensemble of thermally accessible 3D molecular conformers, which underpin many properties and are central to ensemble-based property prediction and generative chemistry. The dataset is a major component of the GEOM project, which further includes drug-like and biophysically relevant species, with a consistent focus on comprehensively sampling conformational variability and annotating structures with meaningful energetic information (Axelrod et al., 2020).

2. Conformer Generation Protocol

Conformer generation for GEOM-QM9 involves several sequential steps designed to exhaustively recover low-energy configurations:

• SMILES Processing and Embedding: Each QM9 SMILES string is canonicalized and embedded in 3D using RDKit.
• Geometry Optimization: Initial structures are re-optimized at the GFN2-xTB level, ensuring consistent input for subsequent sampling.
• CREST-Based Metadynamics Sampling: Conformational exploration is performed via twelve independent CREST metadynamics (MTD) runs per molecule. Each run biases root-mean-square displacement (RMSD) collective variables using Gaussian hills to sample torsional degrees of freedom, while covalent bonds are preserved.
• Energy Minimization and Clustering: Every generated snapshot undergoes geometry optimization at the GFN2-xTB level. Conformers are clustered based on three thresholds: energy difference ($\Delta E < 0.1$ kcal/mol), RMSD ($< 0.125$ Å), and rotational constant difference ($\Delta B_e < 15$ MHz).
• Deduplication and Selection: Rotamers (structural minima equivalent up to atom reindexing) and duplicates are discarded. Unique minima within an energy window of $E_\mathrm{lim} = 6.0$ kcal/mol above the lowest-energy conformer are retained, establishing a “safety window” that exceeds typical 298 K thermal energies ($k_B T \approx 0.59$ kcal/mol).

This protocol yields, on average, 13.5 conformers per molecule, with a long-tailed distribution (standard deviation $\approx 42.2$; maximum observed: 1,101 conformers for a single species) (Axelrod et al., 2020).

3. Quantum-Chemical Energies and Boltzmann Weighting

Each conformer is assigned a single-point energy $E_i$ computed using the GFN2-xTB tight-binding Hamiltonian, a semi-empirical method known to approximate conformer energy rankings within $\sim$2 kcal/mol of higher-level quantum methods. No additional DFT-level re-ranking is performed for GEOM-QM9 to maintain computational tractability. The energy $E_i$ is always referenced relative to the global xTB minimum for that molecule, expressed in kcal/mol.

For ensemble analysis, each conformer $i$ (with degeneracy $< 0.125$0) is assigned a statistical weight

$< 0.125$1

with $< 0.125$2 in kcal/mol·K and $< 0.125$3 K. These weights, while only approximate due to omission of vibrational and translational contributions, capture the exponential population sensitivity to energy differences and facilitate calculation of ensemble descriptors such as conformational entropy ($< 0.125$4) and average energy ($< 0.125$5). Across the QM9 subset, mean $< 0.125$6 is 3.9 cal/(mol·K) and $< 0.125$7 kcal/mol (Axelrod et al., 2020).

4. Data Representation and Serialization

GEOM-QM9 is distributed in two complementary serialization formats, both designed for interoperability with downstream molecular modeling workflows:

1. MessagePack Archives: Keyed by canonical SMILES, each entry houses both species-level metadata and a list of conformer dictionaries. These dictionaries provide Cartesian coordinates (Å), GFN2-xTB energy ($< 0.125$8 in kcal/mol), degeneracy ($< 0.125$9), RMSD to the parent minimum, and Boltzmann weight ($\Delta B_e < 15$0).
2. Python Pickle Files: One file per molecule, in which each conformer is serialized as an RDKit Mol object with attached 3D coordinates, atomic numbers, formal charges, and bond orders. This facilitates tasks requiring both graph connectivity and spatial geometry.

All coordinates are in Cartesian Ångström units; atom types and connections are derived from RDKit, with no DFT-level orbital or partial charge information included for this subset (Axelrod et al., 2020).

5. Dataset Scale and Statistical Properties

GEOM-QM9 comprises 133,258 molecules with a cumulative total of approximately 1.8 million conformers. The mean number of conformers per molecule is 13.5 (standard deviation 42.2), with the maximal count per-molecule reaching 1,101. The energy window spans up to 6.0 kcal/mol above the minimum for each molecular species. The distribution of conformer counts is markedly long-tailed: most rigid species possess fewer than ten minima, while polyfunctional and highly branched molecules can yield hundreds or more. Conformer energies predominantly cluster close to the global minimum, reflecting the relatively rigid nature of the chemical space surveyed by QM9 (Axelrod et al., 2020).

Statistic	Value	Notes
Molecules	133,258	QM9 subset
Total conformers	$\Delta B_e < 15$11.8 million	Across all species
Conformers/molecule (mean)	13.5	σ = 42.2
Max conformers (any molecule)	1,101	Highly branched/polyfunctional structures
Energy window	$\Delta B_e < 15$2 kcal/mol	Above global minimum

6. Recommended Usage and Significance

The CREST+GFN2-xTB protocol delivers exhaustive coverage of low-lying minima with xTB geometries deviating by only $\Delta B_e < 15$3 Å RMSD from final DFT minima. GEOM-QM9 is therefore well-suited for:

• Training and validating graph-to-ensemble property predictors utilizing multiple conformers.
• Developing generative models that map 2D chemical graphs to diverse 3D conformers with Boltzmann-weighted accuracy.
• Estimating conformational free energies and ensemble-level properties using energetic and population data without the cost of explicit molecular dynamics or quantum sampling.

For applications demanding higher-precision energy ranking, users may perform further single-point DFT re-ranking or apply the CENSO workflow described in the parent GEOM study. However, for a broad class of machine learning benchmarks, the xTB energies and derived weights of GEOM-QM9 are adequate proxies. By integrating exhaustive conformational sampling and energy annotation at scale, GEOM-QM9 fills a previously unmet need in the field for ensemble-centered molecular datasets, thereby expanding the scope of model development and molecular design (Axelrod et al., 2020).