A Universal Deep-Learning Electron Force Field for Molecular, Electronic, and Solid-State Dynamics

Machine-learned force fields are transforming atomistic simulation by extending ab initio accuracy to larger systems and longer timescales. Yet, most machine-learned interatomic potentials treat electronic effects only implicitly and lack explicit electronic degrees of freedom. We introduce a deep-learning Electron Force Field (EFF) in which electrons are modeled as spherical Gaussian electron balls with variable positions and widths, enabling a unified treatment of electronic and nuclear motion. Nuclei and electrons interact through charge- and spin-dependent potentials, parameterized by neural networks that use local environment descriptors to capture many-body correlations. Trained on molecular and solid-state data, the deep-learning EFF captures many-body interactions among electrons and nuclei across diverse environments, enabling efficient simulations of reactive and excited-state dynamics.