SQMolecular: Exact FCI Correlation Energies for Delta-Learning

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 717 public-domain organic molecules across 10,038 thermal geometries, each paired in-file with its cheap MP2 baseline. 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 (Sirius Quantum). This release ships geometry and energies only.

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, on the same active space, for 14 geometries (one equilibrium plus 13 thermal distortions). The shipped label is the FCI energy; the shipped baseline is the MP2 energy; their difference is the correlation residual a cheap method misses: the natural delta-learning target.

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, matched)
delta-learning target	no	no	partial	native (FCI - MP2)
molecule diversity	134k	~10	broad	717
conformers / molecule	1	many	many	14 (diversity and conformers)
reproducible recipe	partial	partial	partial	deterministic

1. Exact correlation, not approximated. DFT labels carry functional error you cannot separate from model error. FCI solves the active-space correlation exactly, giving a clean target for measuring how well a model captures correlation.
2. Matched cheap and exact, shipped together. MP2 and FCI on the same active space make FCI - MP2 a ready-made delta-learning target (Ramakrishnan et al. 2015).
3. Diversity and conformers in one set. 717 diverse molecules and 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, flattened 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
corr_residual_hartree	float	fci - mp2, the correlation the cheap method misses
active_space	str	active-space spec, (6,6)
basis	str	orbital basis, 6-31g
level	str	label level, fci
source, source_license	str	structure provenance

717 molecules, 14 geometries each, 10,038 rows.

Result

Sample efficiency: the ReLab engine reaches chemical accuracy from ~160 training labels; the standard classical descriptor never does. Predicting the correlation residual FCI - MP2 on held-out conformers, held-out MAE averaged over 5 seeds:

training labels	ReLab engine	Coulomb-matrix descriptor
10	3.02 mHa	5.64 mHa
40	1.89	4.85
160	1.44 (crosses chemical accuracy)	4.12
320	1.32	3.82
640	1.27 (best)	3.60

The ReLab engine crosses the 1.6 mHa chemical-accuracy line (1 kcal/mol) at ~160 labels; the Coulomb-matrix descriptor (Rupp et al. 2012) never reaches it, at 3.29 mHa even at full data. A shuffled-label control sits at chance (35.7 mHa), confirming the signal is real. Reported as measured on the shipped file and reproducible; evaluation is within-molecule (held-out conformers) in the near-equilibrium regime.

Load

from datasets import load_dataset
import numpy as np

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

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

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, filtered to 2 to 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 drawn from a fixed RNG (Gaussian, sigma = 0.08 A). Electronic structure is computed with pyscf (Sun et al. 2020): 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 baseline is MP2 (Moller-Plesset 1934) 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 to 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, a smooth local neighborhood, not a bond-dissociation or strongly-correlated scan. This is the near-equilibrium dynamic-correlation regime, where mean-field is already decent.
• Labels are classically computable at this scale: a benchmark of method and data quality, not a supremacy claim.
• Evaluation is within-molecule (held-out conformers); cross-molecule transfer is characterized in a separate release.
• We lead on exact, matched, clean, not on scale. The strongly-correlated (bond-breaking) release is the planned follow-on.

References

• Moller, Plesset 1934. Phys. Rev. 46, 618. Second-order perturbation theory (MP2).
• 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.
• Chmiela, Tkatchenko, Sauceda, et al. 2017. arXiv:1611.04678. MD17.
• Smith, Nebgen, Zubatyuk, et al. 2019. arXiv:1906.06154. ANI-1ccx (CCSD(T)).
• Sun, Zhang, Banerjee, et al. 2020. arXiv:2002.12531. PySCF.

Citation and credit

Produced with the ReLab quantum data engine, Sirius Quantum. https://github.com/Sirius-Quantum, https://siriusquantum.com

License

CC-BY-4.0. Molecular structures are public-domain (PubChem-derived); the FCI/MP2 labels are standard electronic structure.