Jul 2026· Journal of Molecular Graphics and Modelling· Vol 148, pp.
109522
· 0 citations· 24 references
Medicine
TL;DR
Molecular net force provides a complementary diagnostic of force consistency but should not be interpreted as a direct measure of atomic-force accuracy, and the proposed framework is readily applicable to quality assessment of DFT datasets used for machine learning.
Abstract
The SPICE dataset is widely used to train and benchmark machine learning force fields, yet the numerical consistency of its underlying density functional theory (DFT) force calculations has received limited systematic evaluation. We present a large-scale analysis of molecular net forces in the B3LYP-D3BJ/DZVP subset of SPICE 1 OpenFF, comprising 16,560 molecules and approximately one million conformations. For isolated systems, fully converged DFT calculations are expected to satisfy translational invariance, yielding near-zero molecular net forces within numerical precision. We observed a mean molecular net force of 0.0001166 Hartree/Bohr (5.99 meV/Å), with 98% of molecules exceeding 0.000038 Hartree/Bohr (1.95 meV/Å). Molecular net force increased with molecular size (r = 0.59) and conformational energy spread (r = 0.61). Multivariable, bootstrap, and robust regression analyses consistently identified molecular size, conformational energy spread, mean atomic force norm, and molecular charge as independent predictors of net force (adjusted R2 = 0.45). Monte Carlo simulations showed that the observed size dependence is substantially more consistent with stochastic accumulation of small force imbalances than with fully systematic directional bias. Filtering molecules by net force reduced baseline prediction error primarily because smaller molecules were preferentially retained, rather than through improved force consistency after accounting for molecular size. Molecular net force therefore provides a complementary diagnostic of force consistency but should not be interpreted as a direct measure of atomic-force accuracy. The proposed framework is readily applicable to quality assessment of DFT datasets used for machine learning.
Density functional theory (DFT) serves as a reliable tool for atomistic molecular simulations, while machine learning potentials have become powerful complements to balance accuracy and efficiency. In this work, we release OpenGEM26 (Open Generated Ensemble of Molecules, 2026), a large-scale dataset comprising 200,000 unique molecules and 4.4 million conformations composed of H, C, N, O, S and Cl with up to ten heavy atoms. All calculations are carried out at the {\omega}B97X-D/Def2-SVP and Def2-TZVP levels with dispersion corrections, and complete structural optimization trajectories and abundant non-equilibrium structures are recorded. Statistical analyses confirm that this dataset covers a broader conformational space than QM9 in terms of energy, bond lengths and bond angles. A graph neural network-based potential GPTFF-mol is trained using the new dataset, achieving an energy mean absolute error of 16 meV/molecule, which is equivalent to 0.82meV/atom, and superior force prediction performance compared with ANI-2x. Validated by butane rotation and keto-enol tautomerization tests, the model accurately describes molecular dynamical behaviors and reaction barriers at distorted geometries. This work provides a high-quality resource and robust ML potential for efficient simulations of sulfur- and chlorine-containing organic molecules.
Yifan Huang, Fankai Xie, Jiangnan Zheng et al.· 0 citations
Coupled-cluster theory defines the accuracy standard for molecular electronic-structure properties but scales too steeply for routine application, whereas density-functional theory is affordable yet systematically biased. We resolve this trade-off with a single equivariant network, MEHnet-MG, that predicts an effective one-electron Hamiltonian from one inexpensive B3LYP/def2-SVP calculation and derives a broad suite of properties from it (energy, optical gap, dipole, quadrupole, polarizability, Mulliken atomic charges, and Mayer bond orders) at coupled-cluster accuracy across nine main-group elements, including the under-served phosphorus, sulfur, and chlorine chemistries. The model is trained on a new in-house dataset of multi-property labels computed at the CCSD(T) level for all nine elements. On a held-out test set, it reduces the error of every property by a factor of 3.8 to 230 relative to semi-local, hybrid, and double-hybrid DFT (referenced to composite CCSD(T)/cc-pVTZ; Methods), while adding only ~25 ms wall time per molecule, delivering coupled-cluster-quality predictions at the cost of a single DFT calculation. Critically, deriving every property from a predicted Hamiltonian rather than pooling per-atom features builds the correct size-scaling into the model architecture: on pi-conjugated oligothiophenes it matches finite-field CCSD polarizability and the EOM-CCSD optical gap to ~2% at the largest sizes where those references remain affordable (44 and 37 atoms, where a single CCSD field point already costs ~500x the model's entire inference) and extrapolates the corrected trends to 58-atom chains, a regime where pooling-based architectures fail by construction. Accurate extrapolation is therefore set by the model's inductive bias rather than by the training data.
The full elastic constant tensor and the surface energies of five low-index planes—(100), (101), (110), (111), and (001)—of β-Sn (tetragonal, I41/amd) are calculated using density functional theory (DFT) with the Perdew–Burke–Ernzerhof (PBE) functional and a universal machine-learning interatomic potential (MLIP; Preferred Potential, PFP v8), which provides both PBE and regularized-restored strongly constrained and appropriately normed (r2SCAN) calculation modes, each with and without Grimme’s D3 dispersion correction. Results are compared with three modified embedded-atom method (MEAM) potentials and experimental data. Both DFT and PFP resolve the long-standing order-of-magnitude C44 deficiency of MEAM potentials (1.5–7.9 GPa against the experimental 22.0 GPa), yielding C44 = 17.9–34.3 GPa. In contrast, C12 is systematically underestimated by all first-principles-based methods (15.2–41.5 GPa against 59.4 GPa) regardless of the choice of exchange–correlation functional, indicating a limitation of current functionals rather than an artifact of MLIP training. For surface energies, DFT/PBE predicts (100) to be the lowest-energy plane of β-Sn, and six of the seven non-DFT methods reproduce this. The equilibrium Wulff shapes of all methods except one MEAM potential retain a rounded polyhedral character qualitatively similar to that of DFT/PBE. Among the non-DFT methods, PFP/r2SCAN reproduces the DFT/PBE surface energies most closely. No single method simultaneously reproduces both the full elastic constant tensor and the surface-energy anisotropy of β-Sn, and the choice of computational method should be guided by the specific phenomenon of interest; among the methods tested, PFP/PBE + D3 offers the smallest mean absolute percentage error (MAPE) of 25.1% for the elastic constants with respect to experiment, while PFP/r2SCAN gives the smallest MAPE of 5.0% for the surface energies with respect to DFT/PBE.
H. Tatsumi, Atsushi M. Ito, Arimichi Takayama et al.· Modelling and Simulation in...· 0 citations
A machine learning approach is presented that accelerates DFTB simulations by predicting optimal initial atomic charges and demonstrates that ML-predicted initial charges consistently and significantly improve SCC convergence across diverse chemical systems including organic molecules, biomolecules, water clusters, transition metal oxides and solid electrolytes.
Maximilian L. Ach, Karsten Reuter, C. Panosetti· 0 citations
Foundation machine-learned force fields (MLFFs) are often pretrained on broad materials datasets whose electronic-structure conventions may not reproduce the phase energetics required for a specific correlated material. Using NiO as a case study, we examine whether incorrect source-level phase energetics can be corrected efficiently through target-level fine-tuning. Along a common structural interpolation, non-spin-polarized PBE and ferromagnetic PBE+U predict opposite energetic orderings of the octahedral Oct and square-planar Sqr phases. Pretrained DPA-4 models adapt rapidly to the NiO PBE+U surface, reaching energy and force root-mean-square errors (RMSEs) of approximately 0.5 meV/atom and 30 meV/{\AA}, respectively, with approximately 170 PBE+U labels. Crucially, models previously fine-tuned to the opposing no-U surface recover the qualitative PBE+U phase ordering with nearly the same target-data efficiency as models fine-tuned directly from their respective pretrained initializations. Our results show that incorrect source-level phase energetics can be reversed through target-level fine-tuning, and suggest a practical multi-fidelity strategy in which pretraining prioritizes broad, consistent, and affordable data, while compact target-level datasets impose energetics through application-specific fine-tuning.
DensIP is introduced, a physics-based model of intermolecular interactions that uses machine-learned electron densities and only four universal parameters that outperforms state-of-the-art general-purpose MLFFs for long-range interactions and can be applied to molecules as large as drug ligands.
Dahvyd Wing, Mihail Bogojeski, Szabolcs Góger et al.· 0 citations