Alex-MP-20

Alex-MP-20 is the training set of MatterGen, as its authors release it: 675,204 structures of Alexandria and of MP-20 with at most 20 atoms per unit cell and at most 0.1 eV/atom above the hull, relaxed again with PBE. Structures with Tc, Pm or an element of atomic number 84 or more are excluded. Five structures of Alexandria are given as a larger cell, of 27 and 60 atoms.

This repository holds the complete, unfiltered dataset preprocessed to HDF5 with torchms, one file per split of the original release (there is no test split).

Files

File	Structures	Alexandria	Materials Project	Atoms per structure
train.hdf5	607,683	568,103	39,580	1–60
val.hdf5	67,521	63,115	4,406	1–20

Labels

Field	Source column	Meaning
energy_above_hull	energy_above_hull	energy above the convex hull in eV/atom, 0 to 0.1
band_gap	dft_band_gap	band gap in eV, known for 38,950 / 4,345 structures

Fields with no source in this dataset are filled with NaN: total_energy, formation_energy_per_atom.

Properties

Stored as named properties, NaN when the source has none:

Name	Source column	Meaning
space_group	space_group	number of the space group (the source has its symbol)
dft_bulk_modulus	dft_bulk_modulus	bulk modulus from DFT in GPa, 4,976 / 550 structures
ml_bulk_modulus	ml_bulk_modulus	bulk modulus from a machine-learned potential in GPa
dft_mag_density	dft_mag_density	magnetic density from DFT in Å⁻³, 597,339 / 66,362 structures
hhi_score	hhi_score	Herfindahl–Hirschman index of the supply of the elements

Source columns that are not stored: material_id, reduced_formula, chemical_system, num_sites. The column num_sites does not match the CIF for 334 / 43 rows; the structures are the ones of the CIF. Row i of a split file is row i of the corresponding source CSV.

Format

Each file stores flat concatenated arrays:

Dataset	Shape	Type	Content
lattice	(n_struct, 3, 3)	float32	lattice vectors as rows, in angstrom
num_atoms	(n_struct,)	int64	number of atoms of each structure
ptr	(n_struct,)	int64	index of the first atom of each structure in x and z
x	(n_atoms, 3)	float32	fractional coordinates in [0, 1)
z	(n_atoms,)	int64	atomic numbers
total_energy, formation_energy_per_atom, energy_above_hull, band_gap	(n_struct,)	float32	labels, NaN when unknown
properties/<name>	(n_struct,)	float32	named properties, NaN when unknown

The lattice is rebuilt from the cell lengths and angles of the source CIF, so it is in the standard orientation (first vector along x).

Usage

from torchms.data import load_dataset

dataset = load_dataset("alex-mp-20", "train")
structures = dataset[:32]  # batched Structures
structures.properties["space_group"]

Source and processing

• Source file: alex_mp_20.zip of data-release/alex-mp in microsoft/mattergen at commit 92423660a8bd70e83679086e88f88596d484dc16 (git LFS, SHA-256 6688e652e45fac4ac8b016dbc4a3280afde9ba687bdacfd8c676775ed19b6228).
• Built with torchms, scripts/build_alex_mp_20.py: CSV to CIF, then CIF to HDF5, with no filter, then the named properties attached.
• Checked against the source: same number of rows, every label and every property equal to its source column row by row, the number of atoms of each structure equal to its CIF, and a sample of 300 structures per split compared with pymatgen's parsing of the same CIF.
• The file ref.csv of the archive (the reference energies of the convex hull of MatterGen, without structures) is not included.

License

The structures of Alexandria are published under CC BY 4.0 by Schmidt et al.; this dataset is redistributed under the same license. The release of MatterGen is MIT. Refer to the sources for their terms of use.

References

• C. Zeni et al., A generative model for inorganic materials design, Nature (2025), doi:10.1038/s41586-025-08628-5.
• J. Schmidt et al., Large-scale machine-learning-assisted exploration of the whole materials space, Materials Cloud Archive 2022.126 (2022), doi:10.24435/materialscloud:m7-50.
• T. Xie et al., Crystal Diffusion Variational Autoencoder for Periodic Material Generation, ICLR 2022.
• A. Jain et al., Commentary: The Materials Project: A materials genome approach to accelerating materials innovation, APL Materials 1, 011002 (2013).