{
  "abstract": "We reformulate the overlap of wave-function derivatives that defines the atomic axial tensors (AATs) and velocity-gauge atomic polar tensors (VG-APTs) used to compute vibrational circular dichroism (VCD) rotatory strengths. In place of our earlier determinant-level derivatives, the new approach expresses these tensors as contractions involving molecular-orbital derivative integrals, perturbed and unperturbed one- and two-electron density matrices, and dot products of the perturbed correlated wave-function amplitudes. Following the elegant treatment of the diagonal Born-Oppenheimer correction by Gauss and co-workers, the formulation holds for any real, normalized CI-like wave function. The two-electron density contribution vanishes exactly, because one perturbation is real (nuclear) and the other imaginary (magnetic field or momentum); this removes multiple terms from our earlier AAT and VG-APT expressions for second-order Møller-Plesset perturbation theory (MP2) and configuration interaction singles and doubles (CISD). We also present a simplified form of the origin-independent length-gauge [LG(OI)] rotatory strength that avoids the singular-value decomposition of the outer product of the length-gauge APT and VG-APT vectors for each mode, and that clarifies how the LG(OI) and velocity-gauge rotatory strengths are related. Applying the density-based AATs and VG-APTs to ($P$)-hydrogen peroxide, (\\textit{S})-methyloxirane, and (\\textit{S})-3-chloro-1-butyne, we find that discrepancies among the gauges arise chiefly from basis-set incompleteness in the VG-APT. The charge-sum rule serves as a useful measure of that incompleteness, independent of the correlation method.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35392",
  "author_total": 3,
  "authors": [
    {
      "name": "Aparna Krishnan"
    },
    {
      "name": "Brendan M. Shumberger"
    },
    {
      "name": "T. Daniel Crawford"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ba93asxwxn820.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35392",
  "fulltext_url": null,
  "id": "ba93asxwxn820",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35392",
  "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/2610.35392",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ba93asxwxn820.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.35392",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35392"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    }
  ],
  "title": "A Density-Matrix Formulation of Vibrational Circular Dichroism Spectra for Møller-Plesset and Configuration Interaction Methods",
  "title_text": "A Density-Matrix Formulation of Vibrational Circular Dichroism Spectra for Møller-Plesset and Configuration Interaction Methods",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:35Z",
  "url": "https://research.draconitic.com/paper/ba93asxwxn820",
  "venue": "arXiv",
  "versions": []
}