DOI: https://doi.org/10.26089/NumMet.v25r109

The efficiency of regularizing algorithm for scaling quantum chemical force fields in Cartesian coordinates: applications to biologically important molecules

Authors

  • Anna V. Stepanova
  • Irina B. Davydova
  • Gulnara M. Kuramshina

Keywords:

inverse spectroscopic problem
ill-posed problems
regularized scaling factors
numerical methods
piperidine
4-piperidinemethanol

Abstract

In our study, we conducted calculations to determine scale factors in Cartesian coordinates for the inverse problem, revealing the consistency of regularized coefficients for atoms and fragments within the molecules we analyzed. Furthermore, we observed the transfer of the scale factors among similar fragments in related compounds for two molecules — piperidine and 4-piperidinemethanol. This work confirms the effectiveness of previously developed algorithms for calculating regularized scale factors for correcting the matrix of force constants (Hessian) in Cartesian coordinates.

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Published

2024-03-15

Issue

Vol. 25 (2024): Issue 1.

Section

Methods and algorithms of computational mathematics and their applications

Author Biographies

Anna V. Stepanova

Lomonosov Moscow State University
Faculty of Chemistry
• Researcher

Irina B. Davydova

Lomonosov Moscow State University
Faculty of Chemistry
• Researcher

Gulnara M. Kuramshina

Lomonosov Moscow State University
Faculty of Chemistry
• Leading Researcher

References

  1. E. B. Wilson, J. C. Decius, and P. C. Cross, Molecular Vibrations: The Theory of Infrared and Raman Vibrational Spectra (Dover, New York, 1980).
  2. M. V. Volkenstein, L. A. Gribov, M. A. El’yashevich, and B. I. Stepanov, Vibrations of Molecules (Nauka, Moscow, 1972) [in Russian].
  3. I. V. Kochikov, G. M. Kuramshina, Yu. A. Pentin, and A. G. Yagola, “A Regularizing Algorithm for Solving an Inverse Oscillation Problem,” Dokl. Akad. Nauk SSSR 261 (5), 1104-1106 (1981) [Sov. Phys. Dokl. 26 (5), 530-532 (1981)].
  4. I. V. Kochikov, G. M. Kuramshina, and A. G. Yagola, “Stable Numerical Methods of Solving Certain Inverse Problems of Vibrational Spectroscopy,” Zh. Vychisl. Mat. Mat. Fiz. 27 (11), 1651-1661 (1987) [USSR Comput. Math. Math. Phys. 27 (6), 33-40 (1987)].
    doi 10.1016/0041-5553(87)90187-X
  5. A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov, and A. G. Yagola, Numerical Methods for the Solution of Ill-Posed Problems (Springer, Dordrecht, 1995).
    doi 10.1007/978-94-015-8480-7
  6. A. N. Tikhonov, A. S. Leonov, and A. G. Yagola, Nonlinear Ill-Posed Problems (Nauka, Moscow, 1995; Chapman & Hall, London, 1998).
  7. A. G. Yagola, I. V. Kochikov, G. M. Kuramshina, and Yu. A. Pentin, Inverse Problems of Vibrational Spectroscopy (VSP, Utrecht, The Netherlands, 1999).
    doi 10.1515/9783110943269
  8. G. M. Kuramshina, F. Weinhold, I. V. Kochikov, et al., “Joint Treatment of ab initio and Experimental Data in Molecular Force Field Calculations with Tikhonov’s Method of Regularization,” J. Chem. Phys. 100 (2), 1414-1424 (1994).
    doi 10.1063/1.466619
  9. I. V. Kochikov, Yu. I. Tarasov, V. P. Spiridonov, et al., “Extension of a Regularizing Algorithm for the Determination of Equilibrium Geometry and Force Field of Free Molecules from Joint Use of Electron Diffraction, Molecular Spectroscopy and ab initio Data on Systems with Large-Amplitude Oscillatory Motion,” J. Mol. Struct. 485-486, 421-443 (1999).
    doi 10.1016/S0022-2860(99)00185-4
  10. I. V. Kochikov, Yu. I. Tarasov, V. P. Spiridonov, et al., “The Use of ab initio Anharmonic Force Fields in Experimental Studies of Equilibrium Molecular Geometry,” J. Mol. Struct. 550-551, 429-438 (2000).
    doi 10.1016/S0022-2860(00)00504-4
  11. I. V. Kochikov, Yu. I. Tarasov, V. P. Spiridonov, et al., “The Equilibrium Structure of Thiophene by the Combined Use of Electron Diffraction, Vibrational Spectroscopy and Microwave Spectroscopy Guided by Theoretical Calculations,” J. Mol. Struct. 567-568, 29-40 (2001).
    doi 10.1016/S0022-2860(01)00539-7
  12. G. M. Kuramshina and A. G. Yagola, “Regularizing Algorithms for Solving Nonlinear Ill-Posed Problems of Vibrational Spectroscopy,” Eurasian J. Math. Comput. Appl. 4 (4), 14-36 (2016).
    doi 10.32523/2306-6172-2016-4-4-14-36
  13. G. M. Kuramshina and A. G. Yagola, “Applications of Regularizing Algorithms in Structural Chemistry,” Eurasian J. Math. Comput. Appl. 5 (3), 53-72 (2017).
    doi 10.32523/2306-6172-2017-5-3-53-72
  14. I. V. Kochikov, G. M. Kuramshina, and A. V. Stepanova, “New Approach for the Correction of ab initio Molecular Force Fields in Cartesian Coordinates,” Int. J. Quantum Chem. 109 (1), 28-33 (2009).
    doi 10.1002/qua.21728
  15. I. V. Kochikov, A. V. Stepanova, and G. M. Kuramshina, “Ab initio Molecular Force Fields Fitted in Cartesian Coordinates to Experimental Frequencies of Isotopic Species Using Symmetry Constraints: Application to Indole and Pyrrole Molecules,” Struct. Chem. 30 (2), 605-614 (2019).
    doi 10.1007/s11224-018-1262-6
  16. D. Vedal, O. H. Ellestad, P. Klaboe, and G. Hagen, “The Vibrational Spectra of Piperidine and Morpholine and Their N-Deuterated Analogs,” Spectrochim. Acta A: Mol. Spectrosc. 32 (4), 877-890 (1976).
    doi 10.1016/0584-8539(76)80159-6
  17. A. Ya. Korneichuk, V. M. Senyavin, and G. M. Kuramshina, “The Molecular Structure of 4-Piperidinemethanol in Gas, Solutions, and Solid State: Spectral and Theoretical Investigations,” Struct. Chem. 30 (2), 567-582 (2019).
    doi 10.1007/s11224-019-01296-y
  18. Chemcraft -- Graphical program for visualization of quantum chemistry computations. Version 1.8.
    https://www.chemcraftprog.com . Cited February 26, 2024.
  19. M. J. Frisch, G. W. Trucks, H. B. Schlegel, et al., “Gaussian 09, Version D1,” This software product is developed by Gaussian, Inc., Wallingford, USA.
    https://gaussian.com/g09citation/. Cited February 26, 2024.

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Copyright (c) 2024 А. В. Степанова, И. Б. Давыдова, Г. М. Курамшина

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