QM9

The 133,885 organic molecules of QM9 (Ramakrishnan et al., 2014): up to nine heavy atoms among C, N, O and F, with their hydrogens, relaxed with B3LYP/6-31G(2df,p). They are molecules, not crystals: pbc is False and x holds positions in Å, see Periodicity.

Molecules	133,885
Atoms	2,407,753, 3 to 29 per molecule (18 on average)
Elements	H, C, N, O, F
Flagged uncharacterized	3,054

Labels

Energies are converted from Hartree to eV (1 Ha = 27.211386245988 eV). Everything else keeps the unit of the source.

Field	Source column	Unit
total_energy	U0, internal energy at 0 K	eV
band_gap	gap, LUMO − HOMO	eV

formation_energy_per_atom and energy_above_hull are NaN.

properties[...]	Source column	Unit
rotational_a, rotational_b, rotational_c	A, B, C	GHz
dipole_moment	mu	Debye
polarizability	alpha	bohr³
homo, lumo	HOMO, LUMO	eV
r2	electronic spatial extent	bohr²
zpve	zero point vibrational energy	eV
u, h, g	U, H, G at 298.15 K	eV
cv	heat capacity at 298.15 K	cal/(mol K)
u0_atomization, u_atomization, h_atomization, g_atomization	energy minus the ones of its atoms (atomref.txt)	eV
uncharacterized	1 if listed in uncharacterized.txt	0 or 1

Things to know

• Use the atomization energies to train. Labels are stored in 32 bits. A total energy of −19,000 eV is then known to 1 meV only, which is not far from the error of the best models. The atomization energies, at most 115 eV, were computed in 64 bits and are stored to 0.01 meV.
• Nothing is filtered. The 3,054 molecules whose geometry failed the consistency check of the source are kept, with uncharacterized set to 1. Most papers remove them: properties["uncharacterized"] == 0 selects the 130,831 others.
• No split. The source has none; papers draw their own.
• band_gap of a molecule is its HOMO-LUMO gap, which is not the band gap of a crystal: do not compare it with the one of the crystal datasets.
• Identifiers and SMILES are not in the file. all_index.parquet gives for each row the index of the molecule in QM9 and its SMILES and InChI, from GDB-9 and from the relaxed geometry.
• Licence: CC0.

Format

HDF5 files of flat concatenated arrays, the format of the other datasets of materials-toolkits:

Dataset	Shape	Type	Content
lattice	(n_struct, 3, 3)	float32	lattice vectors as rows, in Å; the identity for a molecule
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; positions in Å for a molecule
z	(n_atoms,)	int64	atomic numbers
pbc	(n_struct, 3)	bool	whether the structure is periodic along each lattice vector
total_energy, formation_energy_per_atom, energy_above_hull, band_gap	(n_struct,)	float32	labels, NaN when unknown
properties/<name>	(n_struct,)	float32	the properties listed above, NaN when unknown

The position of an atom in Å is x @ lattice. The lattice of a crystal is rebuilt from the lengths and the angles of its cell, in the standard orientation (first vector along x), and its fractional coordinates are wrapped into the cell. The batch array is an artefact of the writer and is not used when reading. Row i of an index file describes structure i.

Usage

from torchms.data import HDF5Dataset

dataset = HDF5Dataset.from_hub("materials-toolkits/qm9", "all.hdf5")
structures = dataset[:32]            # batched Structures
structures.properties                # the named properties, one value per structure

Built with torchms.

Source and checks

• Quantum chemistry structures and properties of 134 kilo molecules, figshare: dsgdb9nsd.xyz.tar.bz2, atomref.txt, uncharacterized.txt, checked with their MD5.
• Built by scripts/build_qm9.py. Every molecule was compared with its file, read a second time by other code: number of atoms, elements, positions, U0, gap, HOMO and the atomization energy.
• Repository: materials-toolkits/qm9, file all.hdf5.