A Deep Learning Framework for the Electronic Structure of Water: Toward a Universal Model

Accurately modeling the electronic structure of water across scales, from individual molecules to bulk liquid, remains a grand challenge. Traditional computational methods face a critical trade-off between computational cost and efficiency. We present an enhanced machine-learning Deep Kohn-Sham (DeePKS) method for improved electronic structure, DeePKS-ES, that overcomes this dilemma. By incorporating the Hamiltonian matrix and its eigenvalues and eigenvectors into the loss function, we establish a universal model for water systems, which can reproduce high-level hybrid functional (HSE06) electronic properties from inexpensive generalized gradient approximation (PBE) calculations. Validated across molecular clusters and liquid-phase simulations, our approach reliably predicts key electronic structure properties such as band gaps and density of states, as well as total energy and atomic forces. This work bridges quantum-mechanical precision with scalable computation, offering transformative opportunities for modeling aqueous systems in catalysis, climate science, and energy storage.