Learning Equivariant Non-Local Electron Density Functionals
<|reference_start|>Learning Equivariant Non-Local Electron Density Functionals: The accuracy of density functional theory hinges on the approximation of non-local contributions to the exchange-correlation (XC) functional. To date, machine-learned and human-designed approximations suffer from insufficient accuracy, limited scalability, or dependence on costly reference data. To address these issues, we introduce Equivariant Graph Exchange Correlation (EG-XC), a novel non-local XC functional based on equivariant graph neural networks. EG-XC combines semi-local functionals with a non-local feature density parametrized by an equivariant nuclei-centered point cloud representation of the electron density to capture long-range interactions. By differentiating through a self-consistent field solver, we train EG-XC requiring only energy targets. In our empirical evaluation, we find EG-XC to accurately reconstruct `gold-standard' CCSD(T) energies on MD17. On out-of-distribution conformations of 3BPA, EG-XC reduces the relative MAE by 35% to 50%. Remarkably, EG-XC excels in data efficiency and molecular size extrapolation on QM9, matching force fields trained on 5 times more and larger molecules. On identical training sets, EG-XC yields on average 51% lower MAEs.<|reference_end|>
@article{gao2024learning,
    title={Learning Equivariant Non-Local Electron Density Functionals},
    author={Nicholas Gao, Eike Eberhard, Stephan G"unnemann},
    journal={arXiv preprint arXiv:2410.07972},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.07972},
    primaryClass={cs.LG physics.chem-ph physics.comp-ph}
}