Releasing 125,999 ready-to-use molecular Hamiltonians

Today, we're releasing the BECOME Quantum Hamiltonian Catalog. It contains 125,999 active-space Hamiltonians for real molecules, each built with the same recipe and validated file by file. Every entry is an 8-electron, 8-orbital Hamiltonian in standard FCIDUMP format, paired with its 3D geometry and a SHA-256 fingerprint. It is built for developers of classical solvers, quantum algorithm researchers, and machine-learning groups who need realistic molecular Hamiltonians without building them first. The full catalog and its Data Descriptor are archived on Zenodo, the build code is on GitHub, and both are free to use.

Why we built it

Full configuration interaction programs and quantum algorithms for chemistry both take a molecular Hamiltonian as input. Preparing one is slow, specialized work. It means generating orbitals, choosing an active space, transforming integrals and checking the results, and each of those steps requires expertise and several pieces of software.

Large, standardized, open sets of ready-to-use Hamiltonians from real molecules have been hard to find. Related resources exist, but they serve different needs. HamLib provides qubit Hamiltonians across several problem classes, and QH9 provides atomic-orbital Hamiltonian matrices for QM9 geometries. Our catalog fills a different gap. It provides fermionic one- and two-electron integrals in a fixed molecular-orbital active space, all at the same size, for 125,999 molecules.

Every Hamiltonian has the same dimension: 8 spatial orbitals, 16 spin orbitals and 8 electrons. Each entry is sized so that a full-CI reference can be computed for it, so any approximate method can be benchmarked against it, across 125,999 real molecules. The catalog also gives machine-learning groups a large, uniform training set, and it gives quantum algorithm developers a realistic testbed with classically verifiable answers.

What's in the catalog

• 125,999 molecules, each identified by its PubChem compound ID (CID), with 6,642 distinct molecular formulas.
• Real, chemically diverse small molecules (1–13 heavy atoms, median 8). The molecules contain H, B, C, N, O, F, P, S, Cl and Br, range from 2 to 34 atoms in total (median 17), and have 16 to 200 basis functions (median 136).
• One consistent recipe. Each entry uses the PM6-optimized geometry from PubChemQC and a restricted Hartree–Fock (RHF) calculation in the 6-31G* basis. The active space spans HOMO−3 to LUMO+3, and all lower occupied orbitals are frozen into the core energy.
• Everything needed to use or check an entry. Each one has an FCIDUMP file, an XYZ geometry, a row in a searchable index, and a SHA-256 hash.
• Ready to solve. The index gives each entry's RHF energy and HOMO–LUMO gap (in Eh), plus the source PubChemQC B3LYP total energy (in eV), so every entry comes with its mean-field reference and a cross-check to the published B3LYP energy. Files load with standard FCIDUMP readers such as pyscf.tools.fcidump.read.

How we validated it

Every molecule passed the same gates, and no parameter was tuned for any individual molecule.

• Structure check. We recomputed each molecule's B3LYP energy and required it to match PubChemQC to within 10⁻⁴ Eh.
• Stable reference. Each RHF solution had to converge and be both internally stable and stable toward unrestricted Hartree–Fock (UHF).
• Read-back. Each file was re-read and had to reproduce its integrals and core energy to within 10⁻¹⁰ and its RHF energy to within 10⁻⁸ Eh.
• Independent checker. A separate parser that does not use PySCF checked every file for header consistency, complete and finite integrals, symmetry conflicts and the Cauchy–Schwarz inequality. All 125,999 files were accepted.
• Final verification. Every file was re-read once more against its recorded hashes and RHF energy. The largest deviation was 1.9 × 10⁻¹¹ Eh.

Design choices

Every entry follows the same choices.

• Geometries are PM6-optimized, as in PubChemQC, so every entry traces to a public source.
• The basis is 6-31G*.
• All molecules are neutral singlets with a UHF-stable RHF reference.
• Active orbitals are chosen by RHF orbital-energy order, a single rule applied identically to every molecule.
• The core energy line in each file includes the frozen-core electronic energy, not just nuclear repulsion.

Get the data

• Dataset and Data Descriptor (primary): Zenodo, doi:10.5281/zenodo.23601240 (https://doi.org/10.5281/zenodo.23601240)
• Build code (Apache 2.0): GitHub, tag catalog-1.1 (https://github.com/BelovedEcosystem/pubchemqc-fcidump-build/tree/catalog-1.1)

The catalog is released under CC BY 4.0. If you use it, please cite our Data Descriptor:

Echeruo, C. U. Ready-to-use eight-electron eight-orbital active-space Hamiltonians for 125,999 small neutral molecules. Zenodo (2026, October 23). https://doi.org/10.5281/zenodo.23601240

Acknowledgments

We thank M. Nakata, T. Maeda, T. Shimazaki and M. Hashimoto of the PubChemQC project for making their B3LYP/6-31G*//PM6 data openly available.