{
  "abstract": "The recently proposed partial-active-space (PAS) multi-state second-order perturbation theory (PASPT2) [Precis. Chem. 4, 997 (2026)] features connected amplitudes and a connected, closed intermediate Hamiltonian. Despite these hallmarks, PASPT2 (denoted as PASPT2H from now on) is not strictly size-extensive, as originally thought (and numerically confirmed), albeit strictly size-consistent. Nevertheless, PASPT2 is near-extensive for the states with major projections on the chosen PAS $\\mathcal{M}_0$. This becomes more transparent upon introducing PASPT2X, a strictly size-extensive variant. Compared with the intruder-prone PASPT2X, the intruder-free PASPT2H merely neglects the second-order corrections that are important only for those states with major projections on the orthogonal complement $\\mathcal{R}_X$ of $\\mathcal{M}_0$ within the closed space $\\mathcal{M}_X$ ($=\\mathcal{M}_0\\oplus\\mathcal{R}_X$); however, such states are not supported by the chosen finite one-particle basis set. The weak violation of size-extensivity is therefore numerically insignificant for the target states supported by $\\mathcal{M}_0$, reinforcing the theoretical basis of PASPT2H.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.22152",
  "author_total": 3,
  "authors": [
    {
      "name": "Chunzhang Liu"
    },
    {
      "name": "Ning Zhang"
    },
    {
      "name": "Wenjian Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/axqff6pvtnb4h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.22152",
  "fulltext_url": null,
  "id": "axqff6pvtnb4h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.22152",
  "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",
      "physics.chem-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2607.22152",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/axqff6pvtnb4h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:54Z",
      "native_id": "2607.22152",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.22152"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    }
  ],
  "title": "Putting PASPT2 on a Firmer Basis",
  "title_text": "Putting PASPT2 on a Firmer Basis",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:50Z",
  "url": "https://research.draconitic.com/paper/axqff6pvtnb4h",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1021/prechem.6c00106",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}