Advanced computational method for studying molecular vibrations and spectra for symmetrical systems with many degrees of freedom, and its application to fullerene

  • Igor Bogush
  • Victor Ciobu
  • Florentin PaladiEmail author
Regular Article


A computational method for studying molecular vibrations and spectra for symmetrical systems with many degrees of freedom was developed. The algorithm allows overcoming difficulties on the automation of calculus related to the symmetry determination of such oscillations in complex systems with many degrees of freedom. One can find symmetrized displacements and, consequently, obtain and classify normal oscillations and their frequencies. The problem is therefore reduced to the determination of eigenvectors by common numerical methods, and the algorithm simplifies the procedure of symmetry determination for normal oscillations. The proposed method was applied to studying molecular vibrations and spectra of the fullerene molecule C60, and the comparison of theoretical results with experimental data is drawn. The computational method can be further extended to other problems of group theory in physics with applications in clusters and nanostructured materials.


Computational Methods 


  1. 1.
    S. Sternberg, Group Theory and Physics (Cambridge University Press, 1995) Google Scholar
  2. 2.
    M.I. Petrashen, E.D. Trifonov, Applications of Group Theory in Quantum Mechanics (Dover Publications, 2009) Google Scholar
  3. 3.
    N.A. Poklonski, Point Symmetry Groups (BSU, Minsk, 2003) Google Scholar
  4. 4.
    R.S. Drago, Physical Methods in Chemistry (Saunders, Philadelphia, 1977) Google Scholar
  5. 5.
    F.A. Cotton, Chemical Applications of Group Theory, 3rd edn. (Wiley-Interscience, 1990) Google Scholar
  6. 6.
    G.L. Bir, G.E. Pikus, Symmetry and Strain-Induced Effects in Semiconductors (Nauka, Moscow, 1972; English translation: Wiley, New York, 1974) Google Scholar
  7. 7.
    V. Ciobu, Ph.D. thesis, MSU, 2016, p. 172,, accessed on: 2017/23/07
  8. 8.
    D.E. Weeks, W.G. Harter, Chem. Phys. Lett. 144, 366 (1988) ADSCrossRefGoogle Scholar
  9. 9.
    J. Menéndez, J.B. Page, in Light Scattering in Solids VIII, edited by M. Cardona, G. Guntherodt (Springer-Verlag, Berlin, Heidelberg, 2000), p. 27 Google Scholar
  10. 10.
    J.G. Hou, A.D. Zhao, T. Huang, S. Lu, in Encyclopedia of Nanoscience and Nanotechnology, edited by H.S. Nalwa (American Scientific Publishers, 2004), p. 409 Google Scholar
  11. 11.
    S.F. Parker, S.M. Bennington, J.W. Taylor, H. Herman, I. Silverwood, P. Albers, K. Refson, Phys. Chem. Chem. Phys. 13, 7789 (2011) CrossRefGoogle Scholar
  12. 12.
    G.B. Adams, J.B. Page, O.F. Sankey, K. Sinha, J. Menendez, D.R. Huffmanet, Phys. Rev. B 44, 4052 (1991) ADSCrossRefGoogle Scholar
  13. 13.
    G.B. Adams, J.B. Page, O.F. Sankey, M. O’Keeffe, Phys. Rev. B 50, 17471 (1994) ADSCrossRefGoogle Scholar
  14. 14.
    P. Giannozzi, S. Baroni, J. Chem. Phys. 100, 8537 (1994) ADSCrossRefGoogle Scholar
  15. 15.
    A.A. Quong, M.R. Pederson, J.L. Feldman, Solid State Commun. 87, 535 (1993) ADSCrossRefGoogle Scholar
  16. 16.
    X.Q. Wang, C.Z. Wang, K.M. Ho, Phys. Rev. B 48, 1993 (1884) Google Scholar
  17. 17.
    J. Che, T. Çagin, W.A. Goddard III, Nanotechnology 10, 263 (1999) ADSCrossRefGoogle Scholar
  18. 18.
    V. Schettino, M. Pagliai, L. Ciabini, G. Cardini, J. Phys. Chem. A 105, 11192 (2001) CrossRefGoogle Scholar
  19. 19.
    K. Refson, P.R. Tulip, S.J. Clark, Phys. Rev. B 73, 155114 (2006) ADSCrossRefGoogle Scholar
  20. 20.
    Yu.I. Prylutskyy, S.S. Durov, L.A. Bulavin, I.I. Adamenko, K.O. Moroz, I.I. Geru, I.N. Dihor, P. Scharff, P.C. Eklund, L. Grigorian, Int. J. Thermophys. 22, 943 (2001) CrossRefGoogle Scholar
  21. 21.
    I.I. Adamenko, K.O. Moroz, Yu.I. Prylutskyy, P.C. Eklund, P. Scharff, T. Braun, Int. J. Thermophys. 26, 795 (2005) ADSCrossRefGoogle Scholar
  22. 22.
    X. Blase, C. Attaccalite, V. Olevano, Phys. Rev. B 83, 115103 (2011) ADSCrossRefGoogle Scholar
  23. 23.
    J.A. Snyman, Practical Mathematical Optimization: An Introduction to Basic Optimization Theory and Classical and New Gradient-Based Algorithms (Springer US, 2005) Google Scholar
  24. 24.
    V. Ciobu, F. Paladi, Gh. Căpăţână, Studia Universitatis Moldaviae 2, 10 (2015) Google Scholar
  25. 25.
    I. Boguş, V. Ciobu, F. Paladi, Studia Universitatis Moldaviae 7, 3 (2015) Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Theoretical PhysicsMoldova State UniversityChisinauRepublic of Moldova

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