Accurately Generalizing Deep-Learning Hamiltonian Methods to Plane-Wave Density Functional Theory

Abstract

Deep neural networks that predict density functional theory (DFT) Hamiltonians from material structures offer a route to efficient electronic-structure calculations. However, extending localized atomic-orbital (AO) Hamiltonian learning to plane-wave (PW) calculations with hybrid functionals requires a compact AO representation that preserves the effects of nonlocal operators. Here we propose a projectability-guided construction of nonorthogonal AO Hamiltonians from a small, selected set of PW eigenstates and eigenvalues. High-projectability states are retained, and selected higher-energy states complete the AO subspace, avoiding an empirical shift and its arbitrary contribution to the learning targets. Because the construction uses PW eigenstates and eigenvalues, it incorporates nonlocal contributions present in the reference calculation without explicitly reconstructing their AO matrix elements. Benchmarks for MoS2 and sodium phases show accurate reproduction of PW bands with smaller AO bases than real-space reconstruction. The resulting PBE and HSE Hamiltonians can be learned by equivariant neural networks, connecting PW reference calculations with electronic-structure prediction. This approach broadens the range of PW DFT calculations available for AO Hamiltonian learning and enables compact, accurate training targets for developing more widely applicable electronic-structure models.