{
  "abstract": "Evaluation of the fluctuation factor can become a computational bottleneck in ringpolymer instanton calculations, particularly at low temperatures where large numbers of ring-polymer beads are required. Conventional evaluation involves diagonalization of the full ring-polymer Hessian, with a computational cost that scales as O(P 3D3) for P beads and D physical dimensions. Here, we develop a matrix-free stochastic trace estimation approach that avoids full Hessian diagonalization. The log-determinant entering the fluctuation factor is evaluated using stochastic Lanczos quadrature, while a preconditioned Davidson algorithm is used to obtain the required low-lying eigenpairs. Control-variate and subspace-projection techniques are used to reduce the variance and improve the efficiency of the stochastic estimator. The approach is tested for proton transfer in malonaldehyde, the CH4 +H → CH3 +H2 hydrogen-abstraction reaction, and intramolecular proton transfer in dinitro-HBQ. For these systems, the calculated log(Finst) agrees with full diagonalization to within an absolute error of ≈ 0.1, while the variance is reduced by up to approximately two orders of magnitude. The matrixfree formulation shows O(P ) to O(P logP ) scaling with bead number, providing a practical alternative to full diagonalization when large numbers of ring-polymer beads are required and potentially facilitating applications to larger molecular systems.",
  "abstract_shown": true,
  "affiliations": [
    "Physical Science Division",
    "Pacific Northwest National Laboratory",
    "Applied Mathematics and Computational Research Division",
    "Lawrence Berkeley National Laboratory",
    "Department of Chemistry",
    "University of Washington"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0,
        1
      ],
      "name": "Chenghao Zhang",
      "orcid": "0000-0003-3989-6345"
    },
    {
      "affs": [
        2,
        3
      ],
      "name": "Chao Yang"
    },
    {
      "affs": [
        0,
        1,
        4,
        5
      ],
      "name": "Niranjan Govind"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4d76pby98pyjk.bib",
  "cited_by": 0,
  "doi": "10.26434/chemrxiv.15009258/v1",
  "fulltext_url": null,
  "id": "4d76pby98pyjk",
  "issns": [],
  "landing_url": "https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009258/v1",
  "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",
      "1606|Advanced Physical and Chemical Molecular Interactions"
    ]
  ],
  "openalex": "W7213985328",
  "pdf_url": "https://chemrxiv.org/doi/pdf/10.26434/chemrxiv.15009258/v1",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": "American Chemical Society (ACS)",
  "ris": "https://research.draconitic.com/paper/4d76pby98pyjk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:21Z",
      "native_id": "10.26434/chemrxiv.15009258",
      "source": "chemrxiv",
      "url": "https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009258/v1"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "openalex:1606|Advanced Physical and Chemical Molecular Interactions",
      "subfield": "physical"
    }
  ],
  "title": "Stochastic Trace Estimation Method for Ring-Polymer Instanton Theory",
  "title_text": "Stochastic Trace Estimation Method for Ring-Polymer Instanton Theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:21Z",
  "url": "https://research.draconitic.com/paper/4d76pby98pyjk",
  "venue": "ChemRxiv",
  "versions": []
}