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Enhancing the Scalability and Applicability of Kohn-Sham Hamiltonians for Molecular Systems

ICLR 2025 · Probabilistic and scientific modeling › Molecules and proteins · approach: Machine-learned interatomic potentials · 0 citations (OpenAlex)

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Introduces PubChemQH, a larger Kohn-Sham Hamiltonian dataset of 40-100 atom molecules, a wavefunction alignment loss (WALoss) and the WANet architecture to make learned Hamiltonians physically applicable for SCF and total energy prediction.

Problem

Learned Kohn-Sham Hamiltonian predictors trained with elementwise MAE/MSE losses give small Hamiltonian errors but large total-energy errors on large molecules, limiting scalability and applicability of DFT acceleration.

Approach

A physics-motivated loss that projects the predicted Hamiltonian onto the ground-truth eigenvectors (after simultaneous reduction of the H/S pair) and penalizes deviation from orbital energies, with increased weight on occupied orbitals plus LUMO; combined with WANet (eSCN convolution, sparse long-short-range MoE pair head, many-body MACE-style diagonal head).

Key results

• On PubChemQH, WANet w/ WALoss reduces system energy MAE from 63579.233 kcal/mol (WANet) to 47.193 kcal/mol, and relative SCF iterations to 82% versus 334% for WANet without WALoss.
• WALoss lowers HOMO MAE from 60.14 to 0.7122 for WANet, while Hamiltonian MAE rises slightly on QH9 (0.0502 to 0.0914 for WANet w/ WALoss).
• Compared with property-regression baselines, WANet w/ WALoss achieves 88.88% lower LUMO MAE and 58.81% lower gap MAE than Equiformer V2 regression.

Measured effects reported in the paper

Surprising findings

• Lower elementwise Hamiltonian MAE does not translate into lower total energy error: the initial guess (Hamiltonian MAE 0.5512) yields much lower system energy error (374 kcal/mol) than the trained WANet (63579 kcal/mol at MAE 0.6274).
• WALoss increases Hamiltonian MAE on QH9 while improving occupied orbital energy and eigenvector similarity.

Limitations

• Generating the large training set is computationally costly (about one month on 128 V100 GPUs).
• Hamiltonian MAE is worse than some baselines with WALoss, so the trade-off between elementwise accuracy and physical utility is not fully resolved.
• Evaluation is limited to molecular systems with a single DFT functional/basis set (B3LYP/def2-TZVP) and the PubChemQH dataset does not appear to be released.

Experimental setup

Datasets: PubChemQH QH9 PubChemQC

Benchmarks: PubChemQH QH9 stable QH9 dynamic elongated alkanes scalability test

Metrics: Hamiltonian MAE HOMO MAE LUMO MAE HOMO-LUMO gap MAE occupied orbital energy MAE orbital energy MAE eigenvector cosine similarity system energy MAE relative SCF iterations dipole moment MAE

Baselines: QHNet PhisNet Equiformer V2 UniMol+ UniMol 2 minao initial guess

Builds on: QHNet PhisNet eSCN MACE Gumbel-softmax mixture of experts

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