Electronic Structures of Mesoscopic Systems: Unlocking Opportunities with Machine Learning and Orbital-Free Embedding*

The pursuit of accurately predicting equilibrium and out-of-equilibrium electronic structures in mesoscopic materials is a persistent challenge. We present a paradigm that leverages density embedding to rigorously represent the electronic structure as an assembly of interacting subsystems. The subsystems are individually addressed using electronic structure solvers tailored to each subsystem. We demonstrate that state-of-the art orbital-free DFT and time-dependent DFT effectively capture the dynamical interactions between subsystems and serve as efficient electronic structure solvers for metallic and semiconducting surfaces as well as nanoparticles. Machine learning-based solvers prove highly efficient in handling subsystems of small size, significantly reducing computational complexity. We showcase specific applications of this approach in molecular liquids, materials interfaces, and solvated metal complexes.