{
  "abstract": "Anharmonic intensities reveal vibrational coupling that band positions alone cannot determine. We derive explicit second-order infrared transition moments in curvilinear normal coordinates, including kinetic metric derivatives and transport through variational resonance polyads. The vibrational perturbation-to-second-order-then-diagonalization (VP2TD) treatment covers fundamentals, overtones, three-quantum transitions, and hot bands. A general computational platform combines Extended Symmetry-Adapted Local Coordinates (ESALCs), using Cartesian (ESALC-C) or internal (ESALC-I) primitives, with interchangeable quantum-chemical programs and parallel finite differences. Independent oscillator matrices verify the intensity equations; a molecular water check reproduces second-order amplitudes within $8.4\\times10^{-8}$ atomic units. Comparisons with established tools reproduce a formaldehyde Fermi polyad within 0.163 cm$^{-1}$ and 0.061 km mol$^{-1}$ and water Raman activities within $10^{-7}$ Angstrom$^6$. For 29 matched formaldehyde rotational line pairs, the predicted hot-to-fundamental intensity ratio, using the measured lower-state energy, is consistent with the nuclear-spin-corrected median: the differences are 3.9% (ESALC-I) and 3.8% (ESALC-C), compared with a 15% uncertainty estimate for individual measured line intensities. Common analytic reference derivatives ensure identical harmonic observables, while internal coordinates reduce and localize intermode anharmonic couplings. Rotation-vibration constants extend the same tensor treatment. An integrated adiabatic discrete-variable representation treats large-amplitude motions, and finite-level partition functions provide anharmonic thermochemistry.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20488",
  "author_total": 1,
  "authors": [
    {
      "name": "Vincenzo Barone"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dq0mb6eykeqma.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20488",
  "fulltext_url": null,
  "id": "dq0mb6eykeqma",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20488",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.chem-ph"
    ],
    [
      "openalex",
      "3107|Spectroscopy and Quantum Chemical Studies"
    ]
  ],
  "openalex": "W7222279338",
  "pdf_url": "https://arxiv.org/pdf/2610.20488",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dq0mb6eykeqma.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:31Z",
      "native_id": "2610.20488",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20488"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    }
  ],
  "title": "Cartesian and Curvilinear Anharmonic Frequencies and Intensities: Perturb-then-Diagonalize Polyad Transport and Adiabatic Discrete-Variable Representation",
  "title_text": "Cartesian and Curvilinear Anharmonic Frequencies and Intensities: Perturb-then-Diagonalize Polyad Transport and Adiabatic Discrete-Variable Representation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:31Z",
  "url": "https://research.draconitic.com/paper/dq0mb6eykeqma",
  "venue": "arXiv",
  "versions": []
}