Skip to main content
SpringerLink
Log in

Electrostatic forces and geometry of organic molecules. Part II. Unsaturated acyclic molecules with one double bond: C=C, C=O, or C=N

  • Published:
Review Journal of Chemistry Aims and scope Submit manuscript

Abstract

In the extension of the electrostatic approach developed in the previous paper on the basis of the available experimental and ab initio calculations data, the geometric structure of acyclic organic molecules containing one isolated chemical bond C=C, C=O, or C=N was analyzed. In agreement with conventional σ/π-representation for this type of bonds, the electrostatic model was suggested, comprising two kinds of local electron densities (LEDs) differing in topology and polarizability, which are in the close spin–spin interaction and show some asymmetry in behavior under the action of external perturbing electrostatic forces (ESFs). Based on the previously introduced concepts of LEDs, point positive charges (PPCs), directions of their most effective interaction (MEI) and using the procedure of fixed molecule (FM), the capabilities of the model were demonstrated on the examples of typical alkenes, carbonyl compounds, azomethines and oximes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

ED:

electron density

EN:

electronegativity

ESF:

electrostatic force

S-ESF:

short-range ESF

M-ESF:

middle-range ESF

L-ESF:

long-range ESF

FM:

fixed molecule

IM:

idealized molecule

LED:

local electron density

LP:

lone pair of electrons

MEI direction:

direction of the most effective interaction

MW:

microwave spectroscopy

PPC:

point positive charge

References

  1. Causa, M., Savin, A., and Silvi, B., Found. Chem., 2014, vol. 16, p. 3.

    Article  CAS  Google Scholar 

  2. Ayers, P.L., Boyd, R.J., Bultinck, P., Caffarel, M., Carbó-Dorca, R., Causá, M., Cioslowski, J., Contreras-Garcia, J., Cooper, D.L., Coppens, P., Gatti, C., Grabowsky, S., Lazzeretti, P., Macchi, P., Pendas, A.M., Popelier, P.L.A., Ruedenberg, K., Rzepa, H., Savin, A., Sax, A., Schwarz, W.H.E., and Shahbazian, S., Silvi, B., Sola, M., and Tsirelson, V., Comput. Theor. Chem., 2015, vol. 1053, p. 2.

    Article  CAS  Google Scholar 

  3. Boeyens, J.C.A., Found. Chem., 2015, vol. 17, p. 247.

    Article  CAS  Google Scholar 

  4. Lüchow, A., J. Comput. Chem., 2014, vol. 35, p. 854.

    Article  CAS  Google Scholar 

  5. Kirpichenok, M.A. and Zefirov, N.S., Zh. Org. Khim., 1987, vol. 23, p. 673.

    CAS  Google Scholar 

  6. Kirpichenok, M.A. and Zefirov, N.S., Zh. Org. Khim., 1987, vol. 23, p. 691.

    CAS  Google Scholar 

  7. Zefirov, N.S., Kirpichenok, M.A., Ismailov, F.F., and Trofimov, M.I., Dokl. Akad. Nauk SSSR, 1987, vol. 296, p. 883.

    CAS  Google Scholar 

  8. Kirpichenok, M.A., Trofimov, M.I., and Zefirov, N.S., Dokl. Akad. Nauk SSSR, 1989, vol. 304, p. 887.

    CAS  Google Scholar 

  9. Gillespie, R.J. and Nyholm, R.S., Q. Rev., Chem. Soc., 1957, vol. 11, p. 339.

    Article  CAS  Google Scholar 

  10. Kirpichenok, M.A., Titarenko, Z.Y., Vasilevich, N.A., and Ofitserov, E.N., Rev. J. Chem., 2017, vol. 7, no. 1, p. 23.

    Article  CAS  Google Scholar 

  11. Gillespie, R.J., Coord. Chem. Rev., 2008, vol. 252, p. 1315.

    Article  CAS  Google Scholar 

  12. Linnett, J.W., The Electronic Structure of Molecules: A New Approach, London: Methuen, 1966.

    Google Scholar 

  13. Hückel, E., Z. Phys., 1930, vol. 60, p. 423.

    Article  Google Scholar 

  14. Haddon, R.C., Acc. Chem. Res., 1988, vol. 21, p. 243.

    Article  CAS  Google Scholar 

  15. Bader, R.F.W., Slee, T.S., Cremer, D., and Kraka, E., J. Am. Chem. Soc., 1983, vol. 105, p. 5061.

    Article  CAS  Google Scholar 

  16. Dominikowska, J. and Palusiak, M., Struct. Chem., 2012, vol. 23, p. 1173.

    Article  CAS  Google Scholar 

  17. Deslongchamps, G. and Deslongchamps, P., Org. Biomol. Chem., 2011, vol. 9, p. 5321.

    Article  CAS  Google Scholar 

  18. Ogliaro, F., Cooper, D.L., and Karadakov, P.B., Int. J. Quantum Chem., 1999, vol. 74, p. 223.

    Article  CAS  Google Scholar 

  19. Rassat, A., Phys. Chem. Chem. Phys., 2004, vol. 6, p. 232.

    Article  CAS  Google Scholar 

  20. Gineityte, V., Lith. J. Phys., 2009, vol. 49, p. 389.

    Article  CAS  Google Scholar 

  21. Slater, J.C., Phys. Rev., 1931, vol. 37, p. 481.

    Article  CAS  Google Scholar 

  22. Pauling, L., The Nature of the Chemical Bond: An Introduction to Modern Structural Chemistry, Ithaka, NY: Cornell Univ. Press, 1960, 3rd ed.

    Google Scholar 

  23. Palke, W.E., J. Am. Chem. Soc., 1986, vol. 108, p. 6543.

    Article  CAS  Google Scholar 

  24. Bauschlicher, C.W. and Taylor, P.R., Phys. Rev. Lett., 1988, vol. 60, p. 859.

    Article  CAS  Google Scholar 

  25. Oña, O.B., Alcoba, D.R., Tiznado, W., Torre, A., and Lain, L., Int. J. Quantum Chem., 2013, vol. 113, p. 1401.

    Article  CAS  Google Scholar 

  26. Yang, Z.-Z., Cong, Y., Zhao, D.-X., Wang, C.-C., and Bao, X.-H., J. Chin. Chem. Soc., 2003, vol. 50, p. 785.

    Article  CAS  Google Scholar 

  27. Ding, L., Mu, J.-R., Wang, C.-H., and Yang, Z.-Z., Int. J. Quantum Chem., 2011, vol. 111, p. 2778.

    Article  CAS  Google Scholar 

  28. Freedman, T.B., Gao, X., Shih, M.-L., and Nafie, L.A., J. Phys. Chem. A, 1998, vol. 102, p. 3352.

    Article  CAS  Google Scholar 

  29. Monaco, G., Fowler, P.W., Lillington, M., and Zanasi, R., Angew. Chem., Int. Ed., 2007, vol. 46, p. 1889.

    Article  CAS  Google Scholar 

  30. Scemama, A., Caffarel, M., and Savin, A., J. Comput. Chem., 2007, vol. 28, p. 442.

    Article  CAS  Google Scholar 

  31. Lüchow, A. and Petz, R., J. Comput. Chem., 2011, vol. 32, p. 2619.

    Article  CAS  Google Scholar 

  32. Schild, A., Choudhary, D., Sambre, V.D., and Paulus, B., J. Phys. Chem. A, 2012, vol. 116, p. 11355.

    Article  CAS  Google Scholar 

  33. Heine, T., Islas, R., and Merino, G., J. Comput. Chem., 2007, vol. 28, p. 302.

    Article  CAS  Google Scholar 

  34. Kulkarni, S.A. and Gadre, S.R., J. Mol. Struct.: THEOCHEM, 1996, vol. 361, p. 83.

    Article  CAS  Google Scholar 

  35. Ligabue, A., Pincelli, U., Lazzeretti, P., and Zanasi, R., J. Am. Chem. Soc., 1999, vol. 121, p. 5513.

    Article  CAS  Google Scholar 

  36. Monaco, G., Zanasi, R., Pelloni, S., and Lazzeretti, P., J. Chem. Theory Comput., 2010, vol. 6, p. 3343.

    Article  CAS  Google Scholar 

  37. Viglione, R.G., Zanasi, R., and Lazzeretti, P., Org. Lett., 2004, vol. 6, p. 2265.

    Article  CAS  Google Scholar 

  38. Steiner, E. and Fowler, P.W., Phys. Chem. Chem. Phys., 2004, vol. 6, p. 261.

    Article  CAS  Google Scholar 

  39. Burgi, H.B., Dunitz, J.D., Lehn, J.M., and Wipff, G., Tetrahedron, 1974, vol. 30, p. 1563.

    Article  Google Scholar 

  40. Fleming, I., Molecular Orbitals and Organic Chemical Reactions: Reference Edition, Chichester: Wiley, 2010.

    Book  Google Scholar 

  41. Kulkarni, S.A. and Gadre, S.R., J. Mol. Struct.: THEOCHEM, 1996, vol. 361, p. 83.

    Article  CAS  Google Scholar 

  42. Ding, L., Mu, J.-R., Wang, C.-H., and Yang, Z.-Z., Int. J. Quantum Chem., 2011, vol. 111, p. 2778.

    Article  CAS  Google Scholar 

  43. Shaik, S. and Reddy, A.C., J. Chem. Soc., Faraday Trans., 1994, vol. 90, p. 1631.

    Article  CAS  Google Scholar 

  44. Durig, J.R., Ng, K.W., Zheng, C., and Shen, S., Struct. Chem., 2004, vol. 15, p. 149.

    Article  CAS  Google Scholar 

  45. Neugebauer, A. and Hafelinger, G.J., J. Mol. Struct.: THEOCHEM, 2002, vol. 578, p. 229.

    Article  CAS  Google Scholar 

  46. Zadeh, L.A., Information Control, 1965, vol. 8, p. 338.

    Article  Google Scholar 

  47. Duncan, J.L., Mol. Phys., 1974, vol. 28, p. 1177.

    Article  CAS  Google Scholar 

  48. Duncan, J.L., McKean, D.C., and Bruce, A.J., J. Mol. Spectrosc., 1979, vol. 74, p. 361.

    Article  CAS  Google Scholar 

  49. Pawlowski, F., Jorgensen, P., Olsen, J., Hegelund, F., Helgaker, T., Gauss, J., Bak, K.L., and Stanton, J.F., J. Chem. Phys., 2002, vol. 116, p. 6482.

    Article  CAS  Google Scholar 

  50. Mulliken, R.S., Rieke, C.A., and Brown, W.G., J. Am. Chem. Soc., 1941, vol. 63, p. 41.

    Article  CAS  Google Scholar 

  51. Demaison, J. and Rudolph, H.D., J. Mol. Spectrosc., 2008, vol. 248, p. 66.

    Article  CAS  Google Scholar 

  52. Scharpen, L.H. and Laurie, V.W., J. Chem. Phys., 1963, vol. 39, p. 1132.

    Article  Google Scholar 

  53. Tokue, I.O., Fukuyama, T., and Kuchitsu, K., J. Mol. Struct., 1974, vol. 23, p. 33.

    Article  CAS  Google Scholar 

  54. Lide, D.R. and Christensen, D., Spectrochim. Acta, 1961, vol. 17, p. 665.

    Article  CAS  Google Scholar 

  55. Hirota, E., Endo, Y., Saito, S., and Duncan, J.L., J. Mol. Spectrosc., 1981, vol. 89, p. 285.

    Article  CAS  Google Scholar 

  56. Hayashi, M. and Inagusa, T., J. Mol. Spectrosc., 1989, vol. 138, p. 135.

    Article  CAS  Google Scholar 

  57. Hayashi, M., Ikeda, C., and Inagusa, T., J. Mol. Spectrosc., 1990, vol. 139, p. 299.

    Article  CAS  Google Scholar 

  58. Hayashi, M. and Inada, N., J. Mol. Spectrosc., 1994, vol. 165, p. 195.

    Article  CAS  Google Scholar 

  59. Culot, J.P., In Fourth Austin Symposium on Gas Phase Molecular Structure, Austin, Texas, 1972.

    Google Scholar 

  60. Niide, Y. and Hayashi, M., J. Mol. Spectrosc., 2003, vol. 220, p. 65.

    Article  CAS  Google Scholar 

  61. Marstokk, K.-M., Mollendal, H., and Samdal, S., and Steinborn, D., J. Mol. Struct., 2001, vol. 567–568, p. 41.

    Article  Google Scholar 

  62. Saebø, S. and Radom, L., J. Mol. Struct.: THEOCHEM, 1982, vol. 89, p. 227.

    Article  Google Scholar 

  63. So, S.P., Chem. Phys. Lett., 1996, vol. 254, p. 302.

    Article  CAS  Google Scholar 

  64. Shiki, Y., Hasegawa, A.I., and Hayashi, M., J. Mol. Struct., 1982, vol. 78, p. 185.

    Article  CAS  Google Scholar 

  65. Pierce, L. and Kilb, R.W., J. Chem. Phys., 1957, vol. 27, p. 108.

    Article  Google Scholar 

  66. Francisco, J.S., J. Am. Chem. Soc., 1989, vol. 111, p. 7353.

    Article  CAS  Google Scholar 

  67. Oberhammer, H. and Boggs, J.E., J. Mol. Struct., 1979, vol. 57, p. 175.

    Article  CAS  Google Scholar 

  68. Jin, Y., Guirgis, G.A., and Durig, J.R., Struct. Chem., 2000, vol. 11, p. 229.

    Article  CAS  Google Scholar 

  69. Alabugin, I.V., Gilmore, K., and Manoharan, M., J. Am. Chem. Soc., 2011, vol. 133, p. 12608.

    Article  CAS  Google Scholar 

  70. Urban, J., Schreiner, P.R., Vacek, G., Schleyer, P.R., Huang, J.Q., and Leszczynski, J., Chem. Phys. Lett., 1997, vol. 264, p. 441.

    Article  CAS  Google Scholar 

  71. Chuang, C.-H. and Lien, M.-H., Eur. J. Org. Chem., 2004, vol. 2004, p. 1432.

    Article  CAS  Google Scholar 

  72. Nosberger, P., Bauder, A., and Gunthard, Hs.H., Chem. Phys., 1973, vol. 1, p. 418.

    Article  Google Scholar 

  73. George, W.O., Jones, B.F., Lewis, Rh., and Price, J.M., J. Mol. Struct., 2000, vol. 550–551, p. 281.

    Article  Google Scholar 

  74. Ha, T.-K., Nguyen, M.-T., and Vanquickenborne, L.G., J. Mol. Struct.: THEOCHEM, 1982, vol. 7, p. 107.

    CAS  Google Scholar 

  75. Nelson, R. and Pierce, L., J. Mol. Spectrosc., 1965, vol. 18, p. 344.

    Article  CAS  Google Scholar 

  76. Ozkabak, A.G., Philis, J.G., and Goodman, L., J. Am. Chem. Soc., 1990, vol. 112, p. 7854.

    Article  CAS  Google Scholar 

  77. Lovas, F.J. and Groner, P., J. Mol. Spectrosc., 2006, vol. 236, p. 173.

    Article  CAS  Google Scholar 

  78. Groner, P., Guirgis, G.A., and Durig, J.R., J. Chem. Phys., 1987, vol. 86, p. 565.

    Article  CAS  Google Scholar 

  79. Durig, J.R., Feng, F.S., Wang, A., and Phan, H.V., Can. J. Chem., 1991, vol. 69, p. 1827.

    Article  CAS  Google Scholar 

  80. Durig, J.R., Lin, J.E., Tolley, C.L., and Little, T.S., Spectrochim. Acta, Part A, 1991, vol. 47, p. 105.

    Article  Google Scholar 

  81. Durig, J.R., Hardin, J.A., Phan, H.V., and Little, T.S., Spectrochim. Acta, Part A, 1989, vol. 45a, p. 1239.

    Article  CAS  Google Scholar 

  82. Durig, J.R., Guirgis, G.A., Bell, S., and Brewer, W.E., J. Phys. Chem. A, 1997, vol. 101, p. 9240.

    Article  CAS  Google Scholar 

  83. Groner, P. and Warren, R.D., J. Mol. Struct., 2001, vol. 599, p. 323.

    Article  CAS  Google Scholar 

  84. Demaison, J., Herman, M., and Lievin, J., J. Chem. Phys., 2007, vol. 126, pp. 164305–1.

  85. Lii, J.-H., J. Phys. Chem. A, 2002, vol. 106, p. 8667.

    Article  CAS  Google Scholar 

  86. Kwei, G.H. and Curl, R.F., J. Chem. Phys., 1960, vol. 32, p. 1592.

    Article  CAS  Google Scholar 

  87. Bjarnov, E. and Hocking, W.H., Z. Naturforsch., A: Phys., Phys. Chem., Kosmophys., 1978, vol. 33, p. 610.

    Article  Google Scholar 

  88. Florian, J., Leszczynski, J., Johnson, B.G., and Goodman, L., Mol. Phys., 1997, vol. 91, p. 439.

    Article  CAS  Google Scholar 

  89. Jaman, A.I., Chakraborty, S., and Chakraborty, R., J. Mol. Struct., 2015, vol. 1079, p. 402.

    Article  CAS  Google Scholar 

  90. Van Eijck, B.P. and van Zoeren, E., J. Mol. Spectrosc., 1985, vol. 111, p. 138.

    Article  Google Scholar 

  91. Van Eijck, B.P., van Opheusden, J., van Schaik, M.M.M., and van Zoeren, E., J. Mol. Spectrosc., 1981, vol. 86, p. 465.

    Article  Google Scholar 

  92. Yadav, R.A., Kumar, M., Singh, R., Singh, P., Jaiswal, S., Srivastav, G., and Prasad, R.L., Spectrochim. Acta, Part A, 2008, vol. 71, p. 1565.

    Article  CAS  Google Scholar 

  93. Borisenko, K.B., Bock, C.W., and Hargittai, I., J. Mol. Struct.: THEOCHEM, 1995, vol. 332, p. 161.

    Article  CAS  Google Scholar 

  94. Hayashi, M., Inada, N., and Niide, Y., J. Mol. Struct., 1995, vols. 352–353, p. 325.

    Article  Google Scholar 

  95. Tam, H.S., Choe, J.I., and Harmony, M.D., J. Phys. Chem., 1991, vol. 95, p. 9267.

    Article  CAS  Google Scholar 

  96. Durig, D.T., Shen, S., Li, Y., and Durig, J.R., Spectrochim. Acta, Part A, 2004, vol. 60, p. 1481.

    Article  CAS  Google Scholar 

  97. McKean, D.C., J. Mol. Struct., 2002, vol. 642, p. 25.

    Article  CAS  Google Scholar 

  98. Slee, T.S., J. Am. Chem. Soc., 1986, vol. 108, p. 7541.

    Article  CAS  Google Scholar 

  99. Tsuboyama, A., Takeshita, K., Konaka, S., and Kimura, M., Bull. Chem. Soc. Jpn., 1984, vol. 57, p. 3589.

    Article  CAS  Google Scholar 

  100. Demaison, J., Margules, L., and Kleiner, I., and Csaszar, A.G., J. Mol. Spectrosc., 2010, vol. 259, p. 70.

    Article  CAS  Google Scholar 

  101. Demaison, J., Csaszar, A.G., Kleiner, I., and Mollendal, H., J. Phys. Chem. A, 2007, vol. 111, p. 2574.

    Article  CAS  Google Scholar 

  102. Marstokk, K.-M., Mollendal, H., and Samdal, S., J. Mol. Struct., 1996, vol. 376, p. 11.

    Article  CAS  Google Scholar 

  103. Godfrey, P.D., Brown, R.D., and Hunter, A.N., J. Mol. Struct., 1997, vol. 413, p. 405.

    Article  Google Scholar 

  104. Platts, J.A., Maarof, H., Harris, K.D.M., Lim, G.K., and Willock, D.J., Phys. Chem. Chem. Phys., 2012, vol. 14, p. 11944.

    Article  CAS  Google Scholar 

  105. Margules, L., Demaison, J., Sreeja, P.B., and Guillemin, J.-C., J. Mol. Spectrosc., 2006, vol. 238, p. 234.

    Article  CAS  Google Scholar 

  106. Pearson, R., Jr. and Lovas, F.J., J. Chem. Phys., 1977, vol. 66, p. 4149.

    Article  CAS  Google Scholar 

  107. Groner, P. Durig, J.R., and DesMarteau, D.D., J. Chem. Phys., 1996, vol. 105, p. 7263.

    Article  CAS  Google Scholar 

  108. Durig, J.R., Zheng, C., Gounev, T.K., Herrebout, W.A., and van der Veken, B.J., J. Phys. Chem. A, 2006, vol. 110, p. 5674.

    Article  CAS  Google Scholar 

  109. Kolandaivel, P. and Senthilkumar, K., J. Mol. Struct: THEOCHEM, 2001, vol. 535, p. 61.

    Article  CAS  Google Scholar 

  110. Hamada, Y., Tsuboi, M., and Umeyama, H., Bull. Chem. Soc. Jpn., 1980, vol. 53, p. 48.

    Article  CAS  Google Scholar 

  111. Hayashi, M. and Kuwada, K., J. Mol. Struct., 1975, vol. 28, p. 147.

    Article  CAS  Google Scholar 

  112. Ohta, K., and Sakai, T., Int. J. Quantum Chem., 2010, vol. 110, p. 1172.

    CAS  Google Scholar 

  113. Nakatsuji, H., Kato, H., and Yonezawa, T., Bull. Chem. Soc. Jpn., 1984, vol. 43, p. 698.

    Article  Google Scholar 

  114. Starykh, O.A., Handbook of Nanophysics: Nanotubes and Nanowires, Florida, Boca Raton: CRC Press, 2010, part.30.

    Google Scholar 

  115. Hestenes, D., Found. Phys., 1990, vol. 20, p. 1213.

    Article  Google Scholar 

  116. Linnett, J.W., J. Am. Chem. Soc., 1961, vol. 83, p. 2643.

    Article  CAS  Google Scholar 

  117. Svidzinsky, A., Chen, G., Chin, S., Kim, M., Ma, D., Murawski, R., Sergeev, A., Scully, M., and Herschbach, D., Int. Rev. Phys. Chem., 2008, vol. 27, p. 665.

    Article  CAS  Google Scholar 

  118. Hestenes D., in Clifford Algebras and Their Applications in Mathematical Physics, Chisholm, J.S.R. and Commons, A.K., Eds., Dordrecht: Reidel, 1986.

  119. Hestenes, D., AIP Conf. Proc., 2009, vol. 1193, p. 115.

    Article  CAS  Google Scholar 

  120. Bader, R.F.W., Atoms in Molecules: A Quantum Theory, Oxford: Clarendon, 1994.

    Google Scholar 

  121. Hernandez-Trujillo, J., Cortes-Guzman, F., Fang, D.-C., and Bader, R.F.W., Faraday Discuss., 2007, vol. 135, p. 79.

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of High Energy Chemistry, Mendeleev University of Chemical Technology, Moscow, 125047, Russia

    M. A. Kirpichenok & Z. Y. Titarenko

  2. ASINEX Ltd., ul. Geroev Panfilovtsev 20, Moscow, 125480, Russia

    N. A. Vasilevich

  3. Department of Chemistry and Technology of Biomedical Preparations, Mendeleev University of Chemical Technology, Moscow, 125047, Russia

    E. N. Ofitserov

  4. Department of Chemistry, Moscow State University, Moscow, 119992, Russia

    N. S. Zefirov

Authors
  1. M. A. Kirpichenok
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Z. Y. Titarenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. N. A. Vasilevich
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. E. N. Ofitserov
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. N. S. Zefirov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. A. Kirpichenok.

Additional information

The article is published in the original.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kirpichenok, M.A., Titarenko, Z.Y., Vasilevich, N.A. et al. Electrostatic forces and geometry of organic molecules. Part II. Unsaturated acyclic molecules with one double bond: C=C, C=O, or C=N. Ref. J. Chem. 7, 222–259 (2017). https://doi.org/10.1134/S2079978017020030

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S2079978017020030

Keywords

Search

Navigation