{
  "abstract": "Hubbard-corrected density-functional theory (DFT+$U$) is a popular tool for first-principles modeling of materials with localized $d$ or $f$ electrons, but its on-site corrections tend to over-localize charge and break covalent bonds. Inter-site $+V$ corrections were introduced to counter this and are now widely used, but a formal justification has been lacking. Here we show that -- to first order in $V/U$ -- inter-site corrections are exactly equivalent to on-site DFT+$U$ evaluated on a density-matrix-dependent redefinition of the Hubbard projectors, hybridized with those of neighboring sites, providing insight into the explicit mechanism by which $V$ affects covalency. If the projectors are held frozen, as is common practice, the equivalence partially breaks down. Beyond reinterpreting the formalism, these results sharpen the questions of how $V$ should be computed and what the Hubbard subspaces fundamentally are.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.18071",
  "author_total": 3,
  "authors": [
    {
      "name": "Edward Linscott"
    },
    {
      "name": "Alberto Carta"
    },
    {
      "name": "Nicola Marzari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4af5q9fjc66kx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.18071",
  "fulltext_url": null,
  "id": "4af5q9fjc66kx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.18071",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.mtrl-sci"
    ],
    [
      "arxiv",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "physics.chem-ph"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "openalex",
      "3107|Advanced Chemical Physics Studies"
    ]
  ],
  "openalex": "W7169863602",
  "pdf_url": "https://arxiv.org/pdf/2607.18071",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4af5q9fjc66kx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2607.18071",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.18071"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mtrl-sci",
      "subfield": "condensed-matter"
    }
  ],
  "title": "DFT+U+V is equivalent to DFT+U with density-dependent hybridized projectors",
  "title_text": "DFT+U+V is equivalent to DFT+U with density-dependent hybridized projectors",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:50Z",
  "url": "https://research.draconitic.com/paper/4af5q9fjc66kx",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1103/qghb-78nd",
      "pid": "2hy87rj94sb7s",
      "relation": "published-as",
      "title": "$\\mathrm{DFT}+U+V$ is equivalent to $\\mathrm{DFT}+U$ with density-dependent hybridized projectors",
      "venue": "Physical Review Research"
    }
  ]
}