Transformer-inspired architectures make machine-learned electron densities accurate and transferable enough to bypass self-consistency

Pretraining has shown strong potential for learning transferable representations, yet it remains underexplored for electron-density-based molecular learning. Electron density provides a continuous three-dimensional description of molecular electronic structure, capturing both local spatial patterns and global physical quantities. This raises a key question: can electron-density fields be used for self-supervised pretraining to learn a shared representation that transfers across diverse electronic-structure-related tasks? We propose ED-DiT, a physics-guided Diffusion Transformer for self-supervised pretraining on electron-density point clouds. ED-DiT learns reusable representations by reconstructing corrupted and partially masked log-density fields across diffusion noise levels. An electron-number consistency constraint is further introduced to preserve the total electronic mass. The pretrained encoder can be adapted to property prediction, open-/closed-shell classification, molecule-electron-density retrieval, and molecule-conditioned electron-density prediction. Experiments on six EDBench tasks show that ED-DiT consistently outperforms the same architecture trained from scratch, especially under limited supervision. For molecule-conditioned electron-density prediction, it reduces RMSE from 2.2474 to 1.3753 and surpasses the available baseline. With only 10% labels, it improves orbital energy prediction RMSE from 0.0293 to 0.0138. These results demonstrate the effectiveness of physics-guided electron-density pretraining for learning transferable molecular representations.

Machine-learning interatomic potentials (MLIPs) have enabled molecular dynamics at near ab initio accuracy, yet remain limited to energies and forces by construction, leaving electronic observables such as dipole moments and polarizabilities inaccessible. We introduce DenSNet, a density-first approach to machine-learned electronic structure that learns the Hohenberg--Kohn map from nuclear configurations to the ground-state electron density. Our approach employs an SE(3)-equivariant neural network to predict density coefficients of a flexible atom-centered Gaussian basis, combined with a $Δ$-learning strategy that uses superposed atomic densities as a prior to accelerate training. A second equivariant network then maps the predicted density to the total energy, providing a unified framework for molecular dynamics and electronic structure. We validate DenSNet on ethanol, ethanethiol, and resorcinol, where infrared spectra from machine-learned trajectories show excellent agreement with experimental gas-phase measurements. To test scalability, we train on polythiophene oligomers with 1--6 monomers and extrapolate to chains of up to 12 monomers, generating stable long-time trajectories whose infrared spectra agree with reference density functional theory calculations. Here, we show that reinstating the electron density as the central learned quantity opens a practical route to transferable prediction of spectroscopic and electronic observables in large-scale molecular simulations.

Machine learning surrogates for density functional theory (DFT) have been increasingly used to reduce the cost of first-principles calculations. In this arena, predicting real-space electron densities offers a scalable and transferable initialization for self-consistent field (SCF) procedures. However, current methods face a clear dilemma. That is, grid-based architectures incur a high computational cost, while basis-set methods fail to capture the structural correlations inherent in the coefficient space. Here, we develop OrbFlow, an $\mathrm{SE}(3)$-equivariant generative model that predicts Gaussian-type orbital (GTO) coefficients via flow matching. OrbFlow retains the efficiency of a compact atom-centered basis while replacing pointwise regression with a learned probability path over the full coefficient space. It is trained through a two-phase trajectory curriculum that mitigates discretization drift during numerical integration. OrbFlow achieves state-of-the-art accuracy on QM9, reducing density error by 13.6% relative to the previous best model, and reduces error by 51% to 63% on every molecule of the MD benchmark relative to the strongest prior method sharing its basis. The predicted density also cuts SCF iterations by up to 68% with zero-shot transfer to unseen exchange-correlation functionals and recovers dipole and quadrupole moments to within a few percent of DFT references without any SCF calculation.