The paper introduces a machine‑learning approach that incorporates the ground‑state electron density as input while enforcing it to be the minimum of a surrogate functional derived from orbital‑free density functional theory. This method outperforms state‑of‑the‑art models on six of seven extensive properties in the QM9 dataset and shows better generalization to larger molecules in the QM40 dataset. Models that use the density without enforcing the surrogate functional constraints perform worse on all extensive properties of both datasets.
By Manuel V. Klockow, Simon Wagner, Roman Remme, Dominic Plein, Fred A. Hamprecht
The paper presents a neural operator that learns the Kohn–Sham map, directly predicting electron density from the Kohn–Sham potential without orbital diagonalization. Using a domain‑invariant SE(3)‑equivariant Fourier neural operator trained on 8,504 molecules and solids, the model achieves quasi‑linear scaling self‑consistent field (SCF) convergence across diverse systems—including organic molecules, insulators, and metals—while reproducing Kohn–Sham DFT accuracy for densities, spectra, and structural observables. This enables large‑scale simulations, such as magnesium dislocation densities with 82,500 valence electrons, on a single GPU.
By Danish Khan, Maurice D. Hanisch, Nikolai Argatoff, Evan Xie, Sandeep Sharma, Anima Anandkumar
The paper introduces MEHnet-MG, an equivariant neural network that predicts a one‑electron Hamiltonian from a single inexpensive B3LYP/def2‑SVP calculation and uses it to compute a wide range of molecular properties—energy, optical gap, dipole, quadrupole, polarizability, Mulliken charges, and Mayer bond orders—at coupled‑cluster accuracy for nine main‑group elements, including phosphorus, sulfur, and chlorine. Trained on a new CCSD(T) dataset, the model reduces property errors by factors ranging from 3.8 to 230 compared to various DFT methods while adding only ~25 ms per molecule. Importantly, by deriving properties from a predicted Hamiltonian rather than pooling atomic features, the architecture naturally incorporates correct size‑scaling, enabling accurate extrapolation to large π‑conjugated systems (up to 58 atoms) where traditional pooling‑based models fail.
By Wenhao He, Xu Chen, Noah Song, Haowei Xu, Tim S. Hindges, Bohan Li, Zihan Lin, Yu Yao, Avetik R. Harutyunyan, Fang Liu, Yao Wang, Hao Tang, Ju Li
Machine-learned interatomic potentials (MLIPs) excel at in-distribution tasks, accelerating drug and material development, yet they struggle to generalize out-of-distribution. We propose to push the c...
The paper introduces Physics‑Aligned Electronic Ground‑State Models (GSMs) that sit between machine‑learned interatomic potentials and Kohn‑Sham density functional theory in terms of computational cost and accuracy. By aligning GSM learning objectives with KS‑DFT equations and enforcing physical constraints, the authors develop new training techniques—OrthoNormal‑Loss (ON‑Loss), Grassmann Restricted Occupied‑Orbital Training (GROOT), and Residual Optimal‑gauge Conditioning‑aware KS‑Eq. Training (ROCKET)—which dramatically reduce energy and force errors in size‑extrapolation tests from QM9 to QM40. The models also achieve near‑chemical‑accuracy predictions on reactive chemistry benchmarks and demonstrate efficient label‑free self‑consistency fine‑tuning.
whyItMatters":"The work advances the cost‑accuracy frontier for electronic structure predictions, enabling more reliable out‑of‑distribution generalization in drug and material discovery."
By Eike S. Eberhard, Xaver Kainz, Viktor Kotsev, Abdulrahman Aldossary, Stephan G\"unnemann
The paper introduces OrbFlow, an SE(3)-equivariant generative model that predicts Gaussian-type orbital coefficients for electron density using flow matching. By training with a two-phase trajectory curriculum, OrbFlow improves accuracy on QM9 and MD benchmarks, reducing density errors significantly compared to previous models. The predicted densities also accelerate self-consistent field procedures, cutting iterations by up to 68% and accurately reproducing dipole and quadrupole moments without additional SCF calculations.
By Chenxing Liang, Chengdong Wang, Yuchao Lin, Xiaofeng Qian, Shuiwang Ji