Frontier-Orbital Predictions from Coarse-Grained Geometries with Physics-Constrained Neural Hamiltonians

We introduce a physics-informed machine learning framework, Orbital Electronic Coarse-Graining (Orb-ECG), for predicting frontier molecular orbital energies at coarse-grained (CG) molecular resolutions. Orb-ECG constructs a realspace overlap matrix by projecting a Gaussian orbital basis onto the CG representation and employs a neural-networkparameterized expansion of this overlap matrix to reproduce quantum-chemistry-derived eigenvalues. This model is trained end-to-end using a composite loss enforcing energy accuracy, basis localization, sparsity, and smoothness. When evaluated on bithiophene conformations, Orb-ECG demonstrates improved data efficiency and extrapolation performance relative to a physics-agnostic ML benchmark while remaining competitive in the large-data limit. In addition to orbital energies, Orb-ECG provides a CG orbital basis that enables access to 3D CG pseudo-orbitals. These CG pseudo-orbitals reliably capture average population trends, but are limited in their ability to capture conformationinduced fluctuations in the electron density, motivating future work. These method developments establish a physically grounded avenue toward efficient and generalizable electronic structure modeling at CG molecular resolutions.