A Fixed-Point Neural Operator for Size- and Functional-Transferable Hamiltonian Prediction

• URL: http://arxiv.org/abs/2606.14498v1
• Date: Fri, 12 Jun 2026 14:31:28 GMT
• Title: A Fixed-Point Neural Operator for Size- and Functional-Transferable Hamiltonian Prediction
• Abstract summary: HamEvo is a neural operator that learns the single-step self-consistent update and returns the converged Hamiltonian as its fixed point.<n>Inference is up to 242 times faster than conventional DFT.
• Score: 42.288858735711905
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Predicting the Kohn-Sham Hamiltonian with machine learning can accelerate density functional theory while retaining access to molecular orbitals, energy levels, and electronic-structure observables that energy-only surrogates cannot resolve. Yet element-wise agreement with the converged Hamiltonian, an implicit fixed point of the self-consistent field iteration, does not determine the occupied subspace that governs orbital energies and densities. Here we present HamEvo, a neural operator that learns the single-step self-consistent update and returns the converged Hamiltonian as its fixed point. HamEvo is pre-trained on intermediate self-consistent trajectories and calibrated at equilibrium with density-matrix supervision. Across benchmarks from MD17 to drug-like QMugs, HamEvo lowers Hamiltonian errors by 35-49% over direct-regression and deep-equilibrium baselines, and predicts QMugs HOMO and LUMO energies with mean absolute errors of 0.036 and 0.053 eV, near the 1 kcal/mol chemical-accuracy scale. Few-shot fine-tuning with only 20 reference conformations extends HamEvo to molecules of up to 122 atoms, well beyond the size range covered by pre-training. With thermal molecular-dynamics sampling, HamEvo captures temperature-dependent HOMO-LUMO gap renormalization beyond the harmonic approximation. Inference is up to 242 times faster than conventional DFT.

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