Transferable Machine Learning of Electronic Hamiltonians with Superposition-of-Atomic-Potentials Features

Abstract: Machine learning (ML) of electronic Hamiltonians offers a unified route to electronic wave functions and physical observables. We introduce a Hamiltonian learning framework built on electronic features derived from the superposition-of-atomic-potentials (SAP) approximation, an efficient self-consistent-field initial guess that captures essential electron-electron screening. SAP quantities define a symmetry-adapted intrinsic atomic orbital learning basis and provide physics-informed inputs to an orbital-based graph neural network that predicts converged Kohn-Sham Fock matrices. To extend the approach to larger basis sets, we further develop a downfolding scheme that predicts large-basis electronic structure from minimal-basis features. On the QM9 dataset, the model accurately reproduces frontier and core orbital energies, dipole moments, and the full density of states. For organic charge-transport materials, it yields accurate intermolecular transfer integrals for benzene, tetracyanoquinodimethane (TCNQ), and tetrathiafulvalene (TTF) dimers, and transfers to unseen substituted-benzene heterodimers with a mean absolute error of 4.8 meV. These results establish SAP-based ML of electronic Hamiltonians as a transferable and scalable tool for high-throughput electronic-structure prediction.