SQMolecular95k: Exact FCI Correlation Energies for Delta-Learning

Following the shipped 10k SQMolecular release, this is the 95k iteration — nearly 10x the scale (94,376 geometries) and a harder cross-scaffold transfer benchmark that tests whether the representation carries to unseen chemistry, not just unseen conformers.

Exact correlation, not DFT. Most molecular-energy datasets ship DFT energies at a single equilibrium geometry. This ships the correlation treated exactly, using full-configuration- interaction (FCI) in a controlled active space, for 6,745 public-domain organic molecules across 94,376 thermal geometries, each paired in-file with two cheap baselines: second-order perturbation theory (MP2) and a fixed-step imaginary-time (Krylov) state. The result is a noise-free, delta-learning-native target: every bit of model error is the model's, not the label's.

Produced with the ReLab engine by Sirius Quantum Solutions. This release ships geometry and energies.

What this is

For each molecule, a frontier (6,6) active space is solved exactly (FCI) at the 6-31g level, and also at MP2 and at a fixed-step imaginary-time (m=3) approximation, all on the same active space, for up to 14 geometries (one equilibrium plus 13 thermal distortions; a small number of molecules have 12–13 where a geometry did not converge). The shipped label is the FCI energy; the shipped baselines are MP2 and ITE; their differences are the correlation residual a cheap method misses: the natural delta-learning target.

The imaginary-time baseline is the addition over the 10k release. On this near-equilibrium set it lands within chemical accuracy (≤1.6 mHa) of exact FCI on 95.3% of rows (mean |FCI−ITE| = 0.51 mHa), versus MP2's 39.1% (mean |FCI−MP2| = 5.52 mHa) — a strong cheap reference shipped alongside the harder MP2 residual.

Why this dataset

	QM9	MD17	ANI-1ccx	This dataset
label method	DFT (B3LYP)	DFT	CCSD(T)	FCI, exact in active space
cheap baseline in-file	no	no	no	yes — MP2 and imaginary-time, matched
delta-learning target	no	no	partial	native (FCI - MP2, FCI - ITE)
molecule diversity	134k	~10	broad	6,745
conformers / molecule	1	many	many	up to 14 (diversity and conformers)
reproducible recipe	partial	partial	partial	deterministic

1. Exact correlation, not approximated. FCI solves the active-space correlation exactly, giving a clean target for measuring how well a model captures correlation.
2. Two matched cheap references, shipped together. MP2 and the imaginary-time state on the same active space give two ready-made delta-learning targets — a hard one (FCI - MP2) and a small one (FCI - ITE).
3. Diversity and conformers in one set. 6,745 diverse molecules and up to 14 thermal geometries each.

Dataset structure

field	type	description
canonical_smiles	str	RDKit-canonical SMILES; connected single molecules only
symbols	list[str]	atomic element symbols, length = n_atoms
coords	list[float]	3D geometry, xyz in Angstrom (reshape to (n_atoms, 3))
geom_id	int	0 = equilibrium; 1 to 13 = thermally distorted (sigma = 0.08 A)
energy_fci_hartree	float	label: exact FCI total energy in the active space
energy_mp2_hartree	float	cheap reference: MP2 energy in the same active space
energy_ite_hartree	float	cheap reference: fixed-step imaginary-time (m=3) energy
corr_residual_hartree	float	fci - mp2, the correlation MP2 misses
corr_residual_ite_hartree	float	fci - ite, the (small) correlation ITE misses
predicted_property_hartree	float	shipped cheap prediction (= the ITE energy)
confidence, coverage_flag	float, str	label-free confidence (MP2–ITE agreement) + confident/ood flag
mint_baseline	str	cheap state used as the prediction, ite-m3
active_space, basis, level	str	(6,6), 6-31g, fci/mp2/ite-m3

6,745 molecules, up to 14 geometries each, 94,376 rows. Almost every row is flagged confident (the ITE baseline is accurate on ~95% of rows); 2 of 94,376 are ood.

Result

Sample efficiency, held-out chemistry (a harder cross-scaffold transfer test than the within-molecule regime of the 10k release). Predicting FCI - MP2 on scaffold-disjoint held-out molecules, held-out MAE averaged over 5 seeds:

training labels	ReLab engine (quantum)	Coulomb-matrix descriptor
20	2.57 mHa	5.49 mHa
40	2.02	5.32
80	1.95	5.85
160	1.79	6.15
640	1.84	7.34
2560	1.92	15.04

The quantum representation transfers to unseen chemistry — reaching ~1.8–2.0 mHa with tens of labels — where the standard classical descriptor (Rupp et al. 2012) never reaches 2.0 mHa and degrades as data grows (structure cannot transfer across scaffolds). On this transfer test neither reaches the 1.6 mHa chemical-accuracy line; within-distribution (random split), the quantum model reaches 1.59 mHa versus the classical descriptor's 4.20 mHa, with a shuffled-label control at chance (39.8 mHa). Reported as measured on the shipped file and reproducible; the strong-correlation and within-molecule sample-efficiency characterizations are separate.

Load

from datasets import load_dataset
import numpy as np

ds = load_dataset("SiriusQuantum/SQMolecular95k", split="train")

row = ds[0]
xyz    = np.array(row["coords"]).reshape(-1, 3)     # geometry the energy was computed on
y_fci  = row["energy_fci_hartree"]                  # exact FCI energy
y_mp2  = row["corr_residual_hartree"]               # delta-learning target (FCI - MP2)
y_ite  = row["corr_residual_ite_hartree"]           # small target (FCI - ITE)

A model can be trained directly on the shipped geometry and energies. The ReLab engine that produced the sample-efficiency result is not part of this release.

Methods

Structures are PubChem-derived public-domain SMILES (open HF mirrors), filtered to 2–10 heavy atoms, elements C/N/O/F/H, neutral, closed-shell, single connected molecule. Geometry is generated deterministically: RDKit ETKDGv3 embedding (fixed seed) plus MMFF optimization for the equilibrium, then 13 thermal distortions from a fixed RNG (Gaussian, sigma = 0.08 A). Electronic structure is computed with pyscf: restricted Hartree-Fock, then a frontier (6,6) CASCI active space (3 highest-occupied plus 3 lowest-virtual orbitals) at 6-31g. The label is the exact FCI energy in that active space; the baselines are MP2 and a fixed-step (m=3) imaginary-time Krylov state on the same active space. The classical comparator in the Result is kernel ridge on sorted Coulomb-matrix eigenvalues (Rupp et al. 2012).

Scope and limitations

• Small-molecule slice: 2–10 heavy atoms; C/N/O/F/H; closed-shell, neutral, single connected molecule.
• "Exact" means exact within the (6,6) active space and 6-31g basis, not the exact total molecular energy.
• Geometries are thermal distortions around one equilibrium minimum — the near-equilibrium dynamic-correlation regime, not a bond-dissociation or strongly-correlated scan.
• Labels are classically computable at this scale: a benchmark of method and data quality, not a supremacy claim. The Result compares representations at simulable scale.
• The confidence/coverage_flag reflect the near-equilibrium regime, where almost every row is confident; the flag is carried for harder future releases.
• The strongly-correlated (bond-breaking) release is the planned follow-on.

References

• Moller, Plesset 1934. Phys. Rev. 46, 618. Second-order perturbation theory (MP2).
• Lanczos 1950. J. Res. Natl. Bur. Stand. 45, 255. Krylov / imaginary-time subspace methods.
• Rupp, Tkatchenko, Muller, von Lilienfeld 2012. PRL 108, 058301. Coulomb-matrix descriptor.
• Ramakrishnan, Dral, Rupp, von Lilienfeld 2014. arXiv:1406.7144. QM9.
• Ramakrishnan, Dral, Rupp, von Lilienfeld 2015. arXiv:1503.04987. Delta machine-learning.
• Sun, Zhang, Banerjee, et al. 2020. arXiv:2002.12531. PySCF.

Citation and credit

Produced with the ReLab quantum data engine by Sirius Quantum Solutions. Attribution to Sirius Quantum Solutions is required for all use, including commercial (see License). https://github.com/Sirius-Quantum, https://siriusquantum.com

If you use this dataset, please cite the accompanying paper and the dataset:

@article{karli2026sqmolecular,
  title     = {SQMolecular95k: An Exact Active-Space FCI Benchmark for Delta-Learning Correlation Energies},
  author    = {Karli, Derya},
  year      = {2026},
  publisher = {Sirius Quantum Solutions},
  url       = {https://huggingface.co/datasets/SiriusQuantum/SQMolecular95k}
}

@dataset{sqmolecular95k_2026,
  title     = {SQMolecular95k: Exact FCI Correlation Energies for Delta-Learning},
  author    = {{Sirius Quantum Solutions}},
  year      = {2026},
  publisher = {Sirius Quantum Solutions},
  url       = {https://huggingface.co/datasets/SiriusQuantum/SQMolecular95k}
}

License

Custom — commercial use gated on attribution (sqmolecular95k-attribution-1.0; see LICENSE). Free for research, academic, and internal evaluation with attribution to Sirius Quantum Solutions. Commercial use is permitted only with attribution to Sirius Quantum Solutions and subject to the terms; commercialisation of the relabeled output without attribution is prohibited. The molecular structures are public-domain (PubChem-derived); the FCI/MP2/ITE relabeled output is the property of Sirius Quantum Solutions.