{
  "abstract": "We establish a new iterative method for computing rigorous lower bounds for the ground-state energies of all atoms and ions. The accuracy of the resulting bounds depends on two ingredients: the quality of the initial energy estimate and the quality of the used upper bound for the maximum number of bound electrons, $N_c(Z)$, as a function of the nuclear charge $Z>0$. In particular, this new method allows us to establish the explicit lower bound $E(N,Z) \\geq -0.8710\\,N^{1/3}Z^2$ for the ground-state energy $E(N,Z)$ of the atom/ion with $N \\in \\mathbb{N}$ electrons and nuclear charge $Z \\in (0,N]$, thereby considerably improving the best known constant $A=(3/2)^{1/3} \\approx 1.1447$ in the estimate $E(N,Z) \\geq -A\\,N^{1/3}Z^2$ for $0 < Z \\leq N$ and coming much closer to the best possible constant given by the Thomas-Fermi asymptotics $\\lim_{N \\to \\infty} |E(N,N)|N^{-7/3}= -E_{\\text{TF}}(1)\\approx 0.7687$ derived in Adv. Math., 23(1) by Lieb and Simon. To demonstrate the potential and the limits of our method, we also compute explicit lower bounds for the ground-state energies $E(N,N)$ of all atoms with $2 \\leq N \\leq 86$ and we compare them with the bounds obtained in J. Chem. Phys., 62(8) by Hertel, Lieb, Thirring and the bounds obtained by Seco in his dissertation. Finally, we also provide a uniqueness result for the expectation values of the kinetic, potential and interaction energies on the ground-state space.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34480",
  "author_total": 1,
  "authors": [
    {
      "name": "Michael Hofacker"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/91ywr19cx8fnr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34480",
  "fulltext_url": null,
  "id": "91ywr19cx8fnr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34480",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Atomic and Molecular Physics"
    ]
  ],
  "openalex": "W7223962697",
  "pdf_url": "https://arxiv.org/pdf/2610.34480",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/91ywr19cx8fnr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.34480",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34480"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Rigorous Lower Bounds for Atomic and Ionic Ground-State Energies",
  "title_text": "Rigorous Lower Bounds for Atomic and Ionic Ground-State Energies",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/91ywr19cx8fnr",
  "venue": "arXiv",
  "versions": []
}