{
  "abstract": "We present a new approach to compare molecular geometries from a purely geometric perspective. The first step of our algorithm uses permutation-insensitive alignment of two molecules with a Gaussian-kernel-damped analog of the mean-squared deviation (MSD) between two structures. Using this procedure, we restore a proper atom-to-atom mapping between two structures. This circumvents the factorial growth of permutation sampling in root-MSD analysis by globally optimizing a nonlinear function to find the best overlay of the structures. Then, we use a physics-driven approach to derive a dimensionless criterion for comparing two structures. This criterion uses the idea of quantum fluctuations in atomic positions and requires computing the mass-weighted MSD as a measure of proximity between structures. We also provide an implementation of our approach in a Python software and numerical examples of its performance.",
  "abstract_shown": true,
  "affiliations": [
    "Center for Free-Electron Laser Science CFEL, Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, Hamburg, Germany, 22607",
    "Department of Physics, University of Hamburg, Notkestr. 9-11, Hamburg, Germany, 22607",
    "Summer School-Conference on Molecular Modeling and Computational Chemistry, 8 street 22 house, Dsegh, Armenia, 1718",
    "Computational Materials Science Laboratory, Yerevan State University, 1 Alex Manoogian St., Yerevan, Republic of Armenia, 0025",
    "Department of Molecular Chemistry and Materials Science, Weizmann Institute of Science, 234 Herzl Street, POB 26, Rehovoth, Israel, 7610001",
    "Yerevan State University, 1 Alex Manoogian Str., Yerevan, Republic of Armenia, 0025"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 18,
  "authors": [
    {
      "affs": [
        0,
        1,
        2
      ],
      "name": "Denis S. Tikhonov",
      "orcid": "0000-0003-3167-3104"
    },
    {
      "affs": [
        2
      ],
      "name": "Daniil Kiryak"
    },
    {
      "affs": [
        2
      ],
      "name": "Darya O. Klimchuk"
    },
    {
      "affs": [
        2
      ],
      "name": "Anastasiia Gorbunova"
    },
    {
      "affs": [
        2
      ],
      "name": "Natalia Papina"
    },
    {
      "affs": [
        2
      ],
      "name": "Sergey N. Roslyakov"
    },
    {
      "affs": [
        2
      ],
      "name": "Alexandr Fomkin"
    },
    {
      "affs": [
        2
      ],
      "name": "Aleksandr Bakulin"
    },
    {
      "affs": [
        2
      ],
      "name": "Ivan V. Shishlov"
    },
    {
      "affs": [
        2
      ],
      "name": "Sergey M. Tarkhanyan"
    },
    {
      "affs": [
        2,
        3
      ],
      "name": "Hamlet Yeganyan"
    },
    {
      "affs": [
        2
      ],
      "name": "Michael Fofonov"
    },
    {
      "affs": [
        2
      ],
      "name": "Sergei A. Nikolenko"
    },
    {
      "affs": [
        2
      ],
      "name": "Yuliia Yurchenko"
    },
    {
      "name": "Natalia D. Pazij"
    },
    {
      "affs": [
        2
      ],
      "name": "Sone Baghdasaryan"
    },
    {
      "affs": [
        2,
        4
      ],
      "name": "Alexandra Y. Freidzon"
    },
    {
      "affs": [
        2,
        5
      ],
      "name": "Olgert L. Dallakyan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b612cvgdgazd9.bib",
  "cited_by": 0,
  "doi": "10.26434/chemrxiv.15010303/v1",
  "fulltext_url": null,
  "id": "b612cvgdgazd9",
  "issns": [],
  "landing_url": "https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010303/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",
      "1703|Computational Drug Discovery Methods"
    ]
  ],
  "openalex": "W7221614317",
  "pdf_url": "https://chemrxiv.org/doi/pdf/10.26434/chemrxiv.15010303/v1",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": "American Chemical Society (ACS)",
  "ris": "https://research.draconitic.com/paper/b612cvgdgazd9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:22Z",
      "native_id": "10.26434/chemrxiv.15010303",
      "source": "chemrxiv",
      "url": "https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010303/v1"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "source:chemrxiv",
      "subfield": "general"
    }
  ],
  "title": "Permutation-inversion insensitive comparison of three-dimensional molecular structures",
  "title_text": "Permutation-inversion insensitive comparison of three-dimensional molecular structures",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:22Z",
  "url": "https://research.draconitic.com/paper/b612cvgdgazd9",
  "venue": "ChemRxiv",
  "versions": []
}