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PreprintCC BYChemRxiv

Permutation-inversion insensitive comparison of three-dimensional molecular structures

  • Denis S. Tikhonov1,2,3
  • Daniil Kiryak3
  • Darya O. Klimchuk3
  • Anastasiia Gorbunova3
  • Natalia Papina3
  • Sergey N. Roslyakov3
  • Alexandr Fomkin3
  • Aleksandr Bakulin3
  • Ivan V. Shishlov3
  • Sergey M. Tarkhanyan3
  • Hamlet Yeganyan3,4
  • Michael Fofonov3
6 more authors
  • Sergei A. Nikolenko3
  • Yuliia Yurchenko3
  • Natalia D. Pazij
  • Sone Baghdasaryan3
  • Alexandra Y. Freidzon3,5
  • Olgert L. Dallakyan3,6
6 affiliations
  1. 1Center for Free-Electron Laser Science CFEL, Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, Hamburg, Germany, 22607
  2. 2Department of Physics, University of Hamburg, Notkestr. 9-11, Hamburg, Germany, 22607
  3. 3Summer School-Conference on Molecular Modeling and Computational Chemistry, 8 street 22 house, Dsegh, Armenia, 1718
  4. 4Computational Materials Science Laboratory, Yerevan State University, 1 Alex Manoogian St., Yerevan, Republic of Armenia, 0025
  5. 5Department of Molecular Chemistry and Materials Science, Weizmann Institute of Science, 234 Herzl Street, POB 26, Rehovoth, Israel, 7610001
  6. 6Yerevan State University, 1 Alex Manoogian Str., Yerevan, Republic of Armenia, 0025
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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.

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Cite

BibTeXRIS
BibTeX
@misc{tikhonov2026permutationinversion,
  title = {{Permutation-inversion insensitive comparison of three-dimensional molecular structures}},
  author = {Denis S. Tikhonov and Daniil Kiryak and Darya O. Klimchuk and Anastasiia Gorbunova and Natalia Papina and Sergey N. Roslyakov and Alexandr Fomkin and Aleksandr Bakulin and Ivan V. Shishlov and Sergey M. Tarkhanyan and Hamlet Yeganyan and Michael Fofonov and Sergei A. Nikolenko and Yuliia Yurchenko and Natalia D. Pazij and Sone Baghdasaryan and Alexandra Y. Freidzon and Olgert L. Dallakyan},
  howpublished = {ChemRxiv},
  year = {2026},
  month = oct,
  doi = {10.26434/chemrxiv.15010303/v1},
  url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010303/v1},
  note = {CC BY},
}
RIS
TY  - UNPB
TI  - Permutation-inversion insensitive comparison of three-dimensional molecular structures
AU  - Denis S. Tikhonov
AU  - Daniil Kiryak
AU  - Darya O. Klimchuk
AU  - Anastasiia Gorbunova
AU  - Natalia Papina
AU  - Sergey N. Roslyakov
AU  - Alexandr Fomkin
AU  - Aleksandr Bakulin
AU  - Ivan V. Shishlov
AU  - Sergey M. Tarkhanyan
AU  - Hamlet Yeganyan
AU  - Michael Fofonov
AU  - Sergei A. Nikolenko
AU  - Yuliia Yurchenko
AU  - Natalia D. Pazij
AU  - Sone Baghdasaryan
AU  - Alexandra Y. Freidzon
AU  - Olgert L. Dallakyan
PY  - 2026
DA  - 2026/10/12
PB  - ChemRxiv
DO  - 10.26434/chemrxiv.15010303/v1
UR  - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010303/v1
AB  - 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.
ER  -