High-order Equivariant Flow Matching for Density Functional Theory Hamiltonian Prediction

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.

Flexible MOF Generation with Torsion-Aware Flow Matching

Designing metal-organic frameworks (MOFs) with novel chemistries is a long-standing challenge due to their large combinatorial space and the complex 3D arrangements of building blocks. While recent deep generative models have enabled scalable MOF generation, they assume (1) a fixed set of building blocks and (2) known ground-truth local block-wise 3D coordinates. However, this limits their ability to (1) design novel MOFs and (2) generate the structure using novel building blocks. We propose a two-stage de novo MOF generation framework that overcomes these limitations by modeling both chemical and geometric degrees of freedom. First, we train a SMILES-based autoregressive model to generate novel metal and organic building blocks, paired with cheminformatics for 3D structure initialization. Second, we introduce a flow-matching model that predicts translations, rotations, and torsional angles to assemble flexible blocks into valid 3D frameworks. Our experiments demonstrate improved reconstruction accuracy, the generation of valid, novel, and unique MOFs, and the ability of our model to create novel building blocks.

Gaussian Plane-Wave Neural Operator for Electron Density Estimation

This work studies machine learning for electron density prediction, which is fundamental for understanding chemical systems and density functional theory (DFT) simulations. To this end, we introduce the Gaussian plane-wave neural operator (GPWNO), which operates in the infinite-dimensional functional space using the plane-wave and Gaussian-type orbital bases, widely recognized in the context of DFT. In particular, both high- and low-frequency components of the density can be effectively represented due to the complementary nature of the two bases. Extensive experiments on QM9, MD, and material project datasets demonstrate GPWNO's superior performance over ten baselines.