ChargeFlow: Flow-Matching Refinement of Charge-Conditioned Electron Densities

2026-03-25

AI Summary

This work addresses the prohibitive computational cost of high-accuracy electron density calculations within density functional theory (DFT), which hinders large-scale materials screening and defect simulations. The authors introduce, for the first time, a flow matching approach to model charge-state-dependent electron densities. By employing a 3D U-Net architecture on periodic real-space grids, they construct a charge-conditioned velocity field that enables an efficient end-to-end mapping from superimposed atomic densities to DFT-quality electron densities. The method significantly improves the accuracy of non-local charge redistribution and charge-state extrapolation, reducing deformation density error from 3.62% to 3.21% and increasing charge response cosine similarity from 0.571 to 0.655 across 1,671 external structures. Furthermore, it supports high-quality Bader charge analysis and electrostatic potential computations.

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Abstract

Accurate charge densities are central to electronic-structure theory, but computing charge-state-dependent densities with density functional theory remains too expensive for large-scale screening and defect workflows. We present ChargeFlow, a flow-matching refinement model that transforms a charge-conditioned superposition of atomic densities into the corresponding DFT electron density on the native periodic real-space grid using a 3D U-Net velocity field. Trained on 9,502 charged Materials Project-derived calculations and evaluated on an external 1,671-structure benchmark spanning perovskites, charged defects, diamond defects, metal-organic frameworks, and organic crystals, ChargeFlow is not uniformly best on every in-distribution class but is strongest on problems dominated by nonlocal charge redistribution and charge-state extrapolation, improving deformation-density error from 3.62% to 3.21% and charge- response cosine similarity from 0.571 to 0.655 relative to a ResNet baseline. The predicted densities remain chemically useful under downstream analysis, yielding successful Bader partitioning on all 1,671 benchmark structures and high-fidelity electrostatic potentials, which positions flow matching as a practical density-refinement strategy for charged materials.

Problem

• charge density
• density functional theory
• charged materials
• large-scale screening
• defect workflows

Innovation

• flow matching
• electron density refinement
• charge-conditioned modeling
• 3D U-Net
• density functional theory