{
  "abstract": "Density functional perturbation theory (DFPT) is an established framework for the computation of derivatives in plane-wave density functional theory (DFT). We present an implementation of DFPT for exchange-correlation (XC) functionals $E_\\mathrm{xc}(ρ,τ)$ that incorporate an explicit dependence on both the density $ρ$ and the kinetic energy density $τ$. This covers the popular class of semilocal meta-generalized gradient approximations (meta-GGAs) as well as broader nonlocal parametrizations. We sidestep the derivation of cumbersome XC second energy derivative expressions by recasting these derivatives as a Jacobian-vector product of the XC potentials, which we evaluate with algorithmic differentiation (AD) techniques. Integration with our previously developed AD-DFPT framework [N. F. Schmitz et al., npj Comput. Mater. 12, 6 (2026)] provides access to derivatives of arbitrary ground state quantities with respect to arbitrary perturbations. We employ AD-DFPT to compute a range of response properties for ZnO and BaTiO3, and find that the recent r2SCAN01 meta-GGA functional generally outperforms LDA and PBE. Finally, we showcase the optimization of a neural-network meta-GGA to self-consistently reproduce hybrid-DFT reference densities of bulk silicon, using AD-DFPT gradients. Overall, these results establish AD-DFPT as a versatile route for computing DFT derivatives at the meta-GGA level, be they common response properties or the unusual derivatives required for the gradient-based training of novel XC functionals.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35572",
  "author_total": 3,
  "authors": [
    {
      "name": "Bruno Ploumhans"
    },
    {
      "name": "Niklas Frederik Schmitz"
    },
    {
      "name": "Michael F. Herbst"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7m18jpka593f3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35572",
  "fulltext_url": null,
  "id": "7m18jpka593f3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35572",
  "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",
      "cond-mat.mtrl-sci"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "openalex",
      "3107|Advanced Chemical Physics Studies"
    ]
  ],
  "openalex": "W7214791230",
  "pdf_url": "https://arxiv.org/pdf/2609.35572",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7m18jpka593f3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:54Z",
      "native_id": "2609.35572",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35572"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mtrl-sci",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Density functional perturbation theory of meta-generalized gradient approximations using algorithmic differentiation",
  "title_text": "Density functional perturbation theory of meta-generalized gradient approximations using algorithmic differentiation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:54Z",
  "url": "https://research.draconitic.com/paper/7m18jpka593f3",
  "venue": "arXiv",
  "versions": []
}