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Calculation of Fullerene Parameters by the Implemented One-Dimensional Method for Determination of Eigenvalues and Eigenfunctions in One-Dimensional Clusters of Planar, Cylindrical, and Spherical Geometry

  • Theoretical Inorganic Chemistry
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Abstract

The eigenvalues and eigenfunctions for clusters with planar, cylindrical, and spherical geometry with arbitrary potential energy profiles were calculated by means of an implemented algorithm. The results of numerical and analytical solutions for clusters of various geometry were compared. The proposed algorithm for determination of cluster eigenvalues and eigenfunctions shows a power law rate of convergence of the solution towards the target eigenfunction coinciding with the rate of convergence in the modified Wielandt method. This algorithm was used to calculate the geometrical potential of giant fullerene as a function of radius for the state with l = 0. The numerical results are in good agreement with the theoretical results.

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References

  1. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).

    Google Scholar 

  2. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic Press, New York, 1974).

    Google Scholar 

  3. A. A. Lucas, L. Henrard, and Ph. Lambin, Phys. Rev. 49, 2888 (1994).

    Article  Google Scholar 

  4. L. Henrard, A. A. Lucas, and Ph. Lambin, Astrophys. J. 406, 92 (1993).

    Article  Google Scholar 

  5. J. C. Slater, Phys. Rev. 51, 846 (1937).

    Article  Google Scholar 

  6. P. N. D’yachkov, Electronic Properties and Application of Nanotubes (BINOM. Laboratoriya znanii, Moscow, 2011) [in Russian].

    Google Scholar 

  7. G. Ya. Slepyan, M. V. Shuba, S. A. Maksimenko, and A. Lakhtakia, Phys. Rev. B 73, 195416 (2006).

    Article  CAS  Google Scholar 

  8. S. P. Gurdzhi and V. B. Katok, Radiotekhnika, No. 3, 64 (1989).

    Google Scholar 

  9. D. Marcuse, J. Opt. Soc. Am. 68, 103 (1978).

    Article  Google Scholar 

  10. Kh. D. Ikramov, Asymmetric Eigenvalue Problem (Nauka, Moscow, 1991) [in Russian].

    Google Scholar 

  11. B. N. Parlett, The Symmetric Eigenvalue Problems (Prentice-Hall, Ehglewood Cliffs, 1980; Mir, Moscow, 1983).

    Google Scholar 

  12. L. I. Ardasheva, N. R. Sadykov, and V. E. Chernyakov, Kvant. Elektron. 19, 903 (1992).

    CAS  Google Scholar 

  13. A. N. Afanas’ev, L. A. Myalitsin, N. R. Sadykov, and M. O. Sadykova, Izv. Vyssh. Uchebn. Zaved., Fiz. 48, 11 (2005).

    Google Scholar 

  14. N. V. Yudina and N. R. Sadykov, Vestn. Nats. Issled. Yadern. Univ. “MIFI” 6, 519 (2017).

    Google Scholar 

  15. V. V. Ilyin and L. B. Piotrovskii, Rev. Clinical Pharmacol. Drug Ther. 15, 17816 (2017).

    Google Scholar 

  16. Yu. L. Voitekhovskii and D. G. Stepenshchikov, Vestn. MGTU 18, 228 (2015).

    Google Scholar 

  17. A. V. Nikolaev and B. N. Plakhutin, Usp. Khim. 79, 803 (2010).

    Google Scholar 

  18. P. N. D’yachkov and B. S. Kuznetsov, Dokl. Akad. Nauk 395, 59 (2004).

    Google Scholar 

  19. L. Henrard and Ph. Lambin, J. Phys. B: At., Mol. Opt. Phys. 29, 5127 (1996).

    Article  Google Scholar 

  20. W. A. De Heer, A. Chatelain, and D. Ugarte, Science 270, 1179 (1995).

    Article  Google Scholar 

  21. N. Hamada, S. Sawada, and S. Oshiyama, Phys. Rev. 68, 1579 (1992).

    Google Scholar 

  22. A. I. Grigor’ev, S. O. Shiryaeva, and A. N. Zharov, Nonlinear Charged Drop Oscillations (YarGU, Yaroslavl, 2006) [in Russian].

    Google Scholar 

  23. A. I. Grigor’ev, N. Yu. Kolbneva, and S. O. Shiryaeva, Zh. Tekh. Fiz. 86, 68 (2016).

    Google Scholar 

  24. A. I. Grigor’ev, N. Yu. Kolbneva, and S. O. Shiryaeva, Izv. Akad. Nauk, Ser. Mekh. Zhidk. Gaza, No. 3, 158 (2016).

    Google Scholar 

  25. A. I. Grigor’ev, N. Yu. Kolbneva, and S. O. Shiryaeva, Zh. Tekh. Fiz. 87, 914 (2017).

    Google Scholar 

  26. Ya. I. Frenkel’, Kinetic Theory of Liquids (Nauka, Moscow, 1975) [in Russian].

    Google Scholar 

  27. B. M. Smirnov, Usp. Fiz. Nauk 162, 119 (1992).

    Google Scholar 

  28. G. I. Marchuk, Mathematical Simulation for Environmental Problems (Nauka, Moscow, 1982) [in Russian].

    Google Scholar 

  29. F. V. Chaplik, Pis’ma Zh. Eksp. Teor. Fiz. 80, 140 (2004).

    Google Scholar 

  30. H. Jensen and H. Koppe, Ann. Phys. (New York) 63, 586 (1971).

    Article  Google Scholar 

  31. R. C. T. da Costa, Phys. Rev. 23, 586 (1981).

    Google Scholar 

  32. V. V. Entin and L. I. Magaril, Phys. Rev. 66, 205308 (2002).

    Article  CAS  Google Scholar 

  33. L. I. Magaril and V. V. Entin, Zh. Eksp. Teor. Fiz. 123, 867 (2003).

    Google Scholar 

  34. L. D. Landau and E. M. Lifshitz, Theoretical Physics (Moscow, Fizmatlit, 2004), vol. 3 [in Russian].

  35. V. V. Dremov and N. R. Sadykov, Opt. Spektrosk. 80, 814 (1996).

    Google Scholar 

  36. H. Wielandt, Math. Z. 50, 93 (1944).

    Article  Google Scholar 

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Yudina, N.V., Sadykov, N.R. Calculation of Fullerene Parameters by the Implemented One-Dimensional Method for Determination of Eigenvalues and Eigenfunctions in One-Dimensional Clusters of Planar, Cylindrical, and Spherical Geometry. Russ. J. Inorg. Chem. 64, 98–107 (2019). https://doi.org/10.1134/S0036023619010212

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  • DOI: https://doi.org/10.1134/S0036023619010212

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