A Fixed-Point Neural Operator for Size- and Functional-Transferable Hamiltonian Prediction
For computational chemists and materials scientists, HamEvo enables accurate and fast prediction of electronic structure properties, including orbital energies, with size transferability and thermal sampling capabilities.
HamEvo, a fixed-point neural operator, learns the self-consistent update for Hamiltonian prediction, achieving 35-49% lower errors than baselines and predicting HOMO/LUMO energies near chemical accuracy (0.036/0.053 eV MAE). It generalizes to larger molecules via few-shot fine-tuning and is up to 242× faster than DFT.
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.