{
  "abstract": "Density fitting (DF) reduces the computational cost of correlated electronic-structure methods but can become unstable when the fitting metric contains small eigenvalues or near-linear dependencies. We introduce a set of protocols based on Tikhonov regularization (TR) combined with the Discrete Picard Condition (DPC) to adaptively determine an effective truncation of the auxiliary space in DF-MP2. Truncation indices are selected using either a two-line L-curve fit or local sharp-corner protocols. The TR-DPC approaches are evaluated against conventional DF-MP2 and Cholesky decomposition (CD) across the S22 benchmark set and an AlkB hydrogen-atom-transfer reaction. The three-point sharp-corner methods provide the best overall accuracy among the TR-DPC protocols, while the two-line method is less accurate but more robust for reduced or poorly matched auxiliary spaces. CD provides the closest agreement with conventional DF-MP2; however, for the systems examined here, it generates more Cholesky vectors than the number of functions in the corresponding DF auxiliary basis and is accompanied by greater computational cost. TR-DPC provides a useful alternative by reducing the effective auxiliary representation while maintaining small, often sub-kcal mol⁻¹, errors, providing a balance between accuracy, representation size, and computational cost.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Chemistry and Biochemistry",
    "The University of Texas at Dallas",
    "Department of Physics"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0,
        1
      ],
      "name": "Jose P. Madriaga",
      "orcid": "0000-0002-4478-2126"
    },
    {
      "affs": [
        0,
        1,
        2
      ],
      "name": "G. Andrés Cisneros",
      "orcid": "0000-0001-6629-3430"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/65c7jb3mj8db7.bib",
  "cited_by": 0,
  "doi": "10.26434/chemrxiv.15007787/v2",
  "fulltext_url": null,
  "id": "65c7jb3mj8db7",
  "issns": [],
  "landing_url": "https://chemrxiv.org/doi/full/10.26434/chemrxiv.15007787/v2",
  "language": null,
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "3107|Advanced Chemical Physics Studies"
    ]
  ],
  "openalex": "W7213559634",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": "American Chemical Society (ACS)",
  "ris": "https://research.draconitic.com/paper/65c7jb3mj8db7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:19Z",
      "native_id": "10.26434/chemrxiv.15007787",
      "source": "chemrxiv",
      "url": "https://chemrxiv.org/doi/full/10.26434/chemrxiv.15007787/v2"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3107|Advanced Chemical Physics Studies",
      "subfield": "amo"
    }
  ],
  "title": "Regularized Alternatives to Conventional Density Fitting: Tikhonov Regularization with Discrete Picard Condition",
  "title_text": "Regularized Alternatives to Conventional Density Fitting: Tikhonov Regularization with Discrete Picard Condition",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:19Z",
  "url": "https://research.draconitic.com/paper/65c7jb3mj8db7",
  "venue": "ChemRxiv",
  "versions": []
}