{
  "abstract": "Several researchers have reported an atypical inversion of the lowest singlet ($S_{1}$) and triplet ($T_{1}$) excited states in nitrogen-substituted planar hydrocarbons. Contrary to Hund's rule of maximum multiplicity, poly-aza derivatives of phenalenyl, such as cyclazine and heptazine, have long been known to possess a negative singlet-triplet gap, $ΔE_{ST}=E(S_{1})-E(T_{1})$. Using the well-known Pariser-Parr-Pople (PPP) model, a semi-empirical, wave-function-based Hamiltonian for correlated $π$-electrons, we investigate the singlet-triplet gap in ten N-substituted phenalenyl motifs. Two schemes of long-range Coulomb interactions are considered, and key parameters, including the on-site orbital energy, Hubbard U, and hopping integrals, are systematically tuned to benchmark the model for reliably estimating negative singlet-triplet gaps. Full configuration-interaction (FCI) method is employed to incorporate electron-correlation effects. Ground-state and $T_{1}$ absorption spectra are subsequently calculated using the optimized PPP parameters that best reproduce the available experimental data. For validation, first-principles TDDFT calculations using various exchange--correlation functionals are also performed. Conventional adiabatic TDDFT fails to reproduce the inverted ($S_{1}-T_{1}$) ordering, indicating that the inclusion of the correlation driven multiconfigurational effects are essential for describing it. We find that the singlet TDDFT ground-state absorption spectra reproduce several qualitative features of the PPP-FCI spectra, although the TDDFT excitation energies are systematically higher. Detailed analysis of the ground-state and $T_{1}$ absorption spectra reveals significant configuration mixing, providing a comprehensive characterization of the optical response of the N-substituted phenalenyl derivatives studied.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31738",
  "author_total": 2,
  "authors": [
    {
      "name": "Medha Rakshit"
    },
    {
      "name": "Alok Shukla"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c9wf4k0dt1e78.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31738",
  "fulltext_url": null,
  "id": "c9wf4k0dt1e78",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31738",
  "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",
      "cond-mat.mtrl-sci"
    ],
    [
      "arxiv",
      "physics.chem-ph"
    ],
    [
      "openalex",
      "3107|Advanced Chemical Physics Studies"
    ]
  ],
  "openalex": "W7214781766",
  "pdf_url": "https://arxiv.org/pdf/2609.31738",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c9wf4k0dt1e78.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.31738",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31738"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mtrl-sci",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Correlation-Driven Singlet--Triplet Inversion and Optical Spectra of N-Substituted Phenalenyls: Insights from PPP-FCI and TDDFT",
  "title_text": "Correlation-Driven Singlet--Triplet Inversion and Optical Spectra of N-Substituted Phenalenyls: Insights from PPP-FCI and TDDFT",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:12Z",
  "url": "https://research.draconitic.com/paper/c9wf4k0dt1e78",
  "venue": "arXiv",
  "versions": []
}