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
arXiv:2606. 14498v1 Announce Type: cross Abstract: Predicting the Kohn-Sham Hamiltonian with machine learning can accelerate density functional theory while retaining access to molecular orbitals, energy levels, and electronic-structure observables that energy-only surrogates cannot resolve.
By Yunhong Lou, Xihang Yue, Xinran Wei, Tianqi Deng, Linchao Zhu
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
The study compares two machine‑learning approaches for predicting molecular absorption spectra: one that uses the ground‑state electron density as input and another that uses molecular geometry. Using a dataset of 6,874 molecules from QM7, the density‑based convolutional neural network achieved a higher validation correlation (0.9926) than the best geometry‑based graph model (0.9795), reducing residual decorrelation by about 64%. The authors argue that the density, which encodes bonding, charge localisation, and electronic delocalisation, provides a more informative starting point for ML models despite the modest cost of an additional DFT calculation.
whyItMatters":"The results suggest that incorporating ground‑state electron density into ML models can significantly improve the accuracy of predicted absorption spectra, potentially enabling faster and more reliable spectroscopic analysis of large molecular libraries."
By Siddharth Dhanpal, Peter Elliott, Paolo Emilio Trevisanutto, Alin M. Elena, Gilberto Teobaldi
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
The paper presents a multitask learning approach that incorporates orbitally resolved semiempirical charges into machine learning interatomic potentials (MLIPs). By training with inexpensive GFN1‑xTB orbital charges, the model reduces energy mean absolute error by 58% compared to energy‑only baselines and needs five times less data to achieve similar performance. The method also outperforms or matches models using costly DFT charges and preserves inference efficiency, offering a scalable way to build accurate, data‑efficient foundation models for complex chemical systems.
By Ihor Neporozhnii, Sjoerd Hoogland, Oleksandr Voznyy