Orbital-Free Surrogate Functionals Yield Transferable Interatomic Potentials and Electron Densities

Abstract

Orbital-free density functional theory seeks to compute the energy of an electronic system directly from its electron density, avoiding one-electron wave functions and thereby offering a route to scalable electronic structure calculations. Machine-learned orbital-free density functionals have recently achieved promising results on small organic molecules, predicting energies with sub-millihartree accuracy. However, their convergence in density optimization remains sensitive to hyperparameter tuning and architectural choices. Here, we extend the recently introduced (weak) surrogate functional framework - designed to predict ground-state electron densities only - to also yield their energy, resulting in"strong"surrogate functionals. We find that these learned functionals enable stable convergence across all tested neural network backbones, reducing electron density errors relative to the Kohn-Sham reference by an order of magnitude compared to previous OF-DFT methods. More importantly, the predicted energies are competitive with state-of-the-art machine-learned interatomic potentials (MLIPs) trained only on energies, while exhibiting superior generalization to larger, unseen systems.