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PreprintarXiv licencearXiv

Stationarity Constraints Improve Both Energies and Densities of Machine-Learned Exchange-Correlation Functionals

  • Yuhao Chen
  • Donald G. Truhlar
  • Xiao He
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Abstract

Empirical exchange-correlation functionals are fitted on fixed orbitals but used self-consistently, so better energies often come with worse densities. We show that the Brillouin residual of a trained functional on the Kohn-Sham orbitals of an accurate density controls, to first order, both the self-consistent density shift and the gap between fitted and self-consistent energies. Penalizing it requires no self-consistent-field solution during training. Trained on 6 energies and 11 CCSD densities, a neural meta-GGA surpasses SCAN in both atomization energies and densities of unseen molecules.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026stationarity,
  title = {{Stationarity Constraints Improve Both Energies and Densities of Machine-Learned Exchange-Correlation Functionals}},
  author = {Yuhao Chen and Donald G. Truhlar and Xiao He},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.30022},
  eprint = {2610.30022},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.30022},
}
RIS
TY  - UNPB
TI  - Stationarity Constraints Improve Both Energies and Densities of Machine-Learned Exchange-Correlation Functionals
AU  - Yuhao Chen
AU  - Donald G. Truhlar
AU  - Xiao He
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.30022
UR  - https://arxiv.org/abs/2610.30022
AB  - Empirical exchange-correlation functionals are fitted on fixed orbitals but used self-consistently, so better energies often come with worse densities. We show that the Brillouin residual of a trained functional on the Kohn-Sham orbitals of an accurate density controls, to first order, both the self-consistent density shift and the gap between fitted and self-consistent energies. Penalizing it requires no self-consistent-field solution during training. Trained on 6 energies and 11 CCSD densities, a neural meta-GGA surpasses SCAN in both atomization energies and densities of unseen molecules.
ER  -