High-order Equivariant Flow Matching for Density Functional Theory Hamiltonian Prediction
Seongsu Kim, Nayoung Kim, Dongwoo Kim, Sungsoo Ahn
Density functional theory (DFT) is a fundamental method for simulating quantum chemical properties, but it remains expensive due to the iterative self-consistent field (SCF) process required to solve the Kohn–Sham equations. Recently, deep learning methods are gaining attention as a way to bypass this step by directly predicting the Hamiltonian.However, they rely on deterministic regression and do not consider the highly structured nature of Hamiltonians.In this work, we propose QHFlow, a high-order equivariant flow matching framework that generates Hamiltonian matrices conditioned on molecular geometry. Flow matching models continuous-time trajectories between simple priors and complex targets, learning the structured distributions over Hamiltonians instead of direct regression. To further incorporate symmetry, we use a neural architecture that predicts SE(3)-equivariant vector fields, improving accuracy and generalization across diverse geometries. To further enhance physical fidelity, we additionally introduce a fine-tuning scheme to align predicted orbital energies with the target. QHFlow achieves state-of-the-art performance, reducing Hamiltonian error by 71% on MD17 and 53% on QH9. Moreover, we further show that QHFlow accelerates the DFT process without trading off the solution quality when initializing SCF iterations with the predicted Hamiltonian, significantly reducing the number of iterations and runtime.