{
  "id": 16002032,
  "title": "Stationarity Constraints Improve Both Energies and Densities of Machine-Learned Exchange-Correlation Functionals",
  "url": "https://urgent.news/2026/10/21/stationarity-constraints-improve-both-energies-and-densities-of",
  "topic": "ai",
  "section": "AI",
  "published": "2026-10-21T16:49:03.000Z",
  "source": {
    "name": "arXiv cs.AI",
    "slug": "arxiv-cs-ai",
    "url": "https://arxiv.org/abs/2610.30022v1"
  },
  "original_language": "en",
  "account": null,
  "summary": "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…",
  "key_points": [],
  "editors_take": null,
  "illustration": null,
  "coverage": {
    "outlets": 1,
    "also_reported_by": []
  },
  "ai_generated": true,
  "disclaimer": "Summaries, key points and the editor’s take are written by software from other outlets’ reporting and may contain errors — always check the linked original."
}