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Journal of Mathematical Chemistry

, Volume 57, Issue 2, pp 516–532 | Cite as

Dipole moment of polyhedral water clusters: mathematical relationships and their application

  • Mikhail V. KirovEmail author
Original Paper
  • 31 Downloads

Abstract

Polyhedral water clusters are characterized by exponential proton disorder and a complex molecular interaction. Nevertheless, a simple theory has been developed for these systems. It allows predicting classes of the most stable proton configurations that differ in the arrangement of hydrogen atoms (protons) in the hydrogen bonds. The stability for a particular configuration is evaluated on the basis of the analysis of local topological characteristics of the hydrogen bond network. However, the stability of water clusters is determined also by another, clearly non-topological global characteristic: the magnitude of the total dipole moment. In this article we show that the total dipole moment of polyhedral water clusters is proportional to the vector sum of polyhedron edges if their direction coincides with the direction of hydrogen bonds. This makes it possible not to take into account separately the contribution of free (dangling) hydrogen atoms when classifying proton configurations.

Keywords

Water clusters Hydrogen bonds Dipole moment Interaction potentials 

Mathematics Subject Classification

52C99 

Notes

Funding

The reported study was funded by RFBR according to the Research Project No. 15-03-04274.

References

  1. 1.
    V. Vaida, J. Chem. Phys. 135, 020901 (2011)CrossRefGoogle Scholar
  2. 2.
    A.A. Vostrikov, D.Y. Dubov, Tech. Phys. Lett. 34, 221–224 (2008)CrossRefGoogle Scholar
  3. 3.
    K. Liu, J.D. Cruzan, R.J. Saykally, Science 271, 929–933 (1996)CrossRefGoogle Scholar
  4. 4.
    C.J. Gruenloh, J.R. Carney, C.A. Arrington, T.S. Zwier, S.Y. Fredericks, K.D. Jordan, Science 276, 1678–1681 (1997)CrossRefGoogle Scholar
  5. 5.
    F.N. Keutsch, R.J. Saykally, Proc. Natl. Acad. Sci. 98, 10533–10540 (2001)CrossRefGoogle Scholar
  6. 6.
    S. Maheshwary, N. Patel, N. Sathyamurthy, A.D. Kulkarni, S.R. Gadre, J. Phys. Chem. A 105, 10525–10537 (2001)CrossRefGoogle Scholar
  7. 7.
    S. Yoo, S.S. Xantheas, in Handbook of Computational Chemistry, ed. by J. Leszczynski (Springer, Berlin, 2011), p. 761Google Scholar
  8. 8.
    E.D. Sloan, C.A. Koh, Clathrate Hydrates of Natural Gasses, 3rd edn. (CRC Press, Boca Raton, 2008)Google Scholar
  9. 9.
    L. Pauling, J. Am. Chem. Soc. 57, 2680–2684 (1935)CrossRefGoogle Scholar
  10. 10.
    M.V. Kirov, J. Struct. Chem. 34, 557–561 (1994)CrossRefGoogle Scholar
  11. 11.
    S.S. Xantheas, Chem. Phys. 258, 225–231 (2000)CrossRefGoogle Scholar
  12. 12.
    M.V. Kirov, J. Struct. Chem. 37, 84–91 (1996)CrossRefGoogle Scholar
  13. 13.
    D.J. Anick, J. Mol. Struct. (Theochem) 587, 97–110 (2002)CrossRefGoogle Scholar
  14. 14.
    V. Chihaia, S. Adams, W.F. Kuhs, Chem. Phys. 297, 271–287 (2004)CrossRefGoogle Scholar
  15. 15.
    S. McDonald, L. Ojamae, S.J. Singer, J. Phys. Chem. 102, 2824–2832 (1998)CrossRefGoogle Scholar
  16. 16.
    M.V. Kirov, G.S. Fanourgakis, S.S. Xantheas, Chem. Phys. Lett. 461, 180–188 (2008)CrossRefGoogle Scholar
  17. 17.
    J.-L. Kuo, J.V. Coe, S.J. Singer, J. Chem. Phys. 114, 2527–2540 (2001)CrossRefGoogle Scholar
  18. 18.
    D.J. Anick, J. Chem. Phys. 119, 12442–12456 (2003)CrossRefGoogle Scholar
  19. 19.
    J.D. Bernal, R.H. Fowler, J. Chem. Phys. 1, 515–548 (1933)CrossRefGoogle Scholar
  20. 20.
    P.W. Fowler, S. Nikolic, R. De Los Reyesa, W. Myrvold, Phys. Chem. Chem. Phys. 17, 23257–23264 (2015)CrossRefGoogle Scholar
  21. 21.
    H.J. Berendsen, J. Postma, W. Van Gunsteren, W.F. Hermans, in Intermolecular forces, ed. by B. Pullman (Springer, Dordrecht, 1981), pp. 331–342CrossRefGoogle Scholar
  22. 22.
    W.L. Jorgensen, J. Chandrasekhar, J.D. Madura, R.W. Impey, M.L. Klein, J. Chem. Phys. 79, 926–935 (1983)CrossRefGoogle Scholar
  23. 23.
    M.W. Mahoney, W.L. Jorgensen, J. Chem. Phys. 112, 8910–8922 (2000)CrossRefGoogle Scholar
  24. 24.
    L.X. Dang, B.M. Pettitt, J. Phys. Chem. 91, 3349–3354 (1987)CrossRefGoogle Scholar
  25. 25.
    P. Ren, J.W. Ponder, J. Phys. Chem. B 107, 5933–5947 (2003)CrossRefGoogle Scholar
  26. 26.
    L.D. Landau, E.M. Lifschitz, Course of Theoretical Physics: The Classical Theory of Fields (Pergamon Press, Oxford, 2009)Google Scholar
  27. 27.
    F.H. Stillinger, A. Rahman, J. Chem. Phys. 60, 1545–1557 (1974)CrossRefGoogle Scholar
  28. 28.
    E.H. Lieb, Phys. Rev. 162, 162–172 (1967)CrossRefGoogle Scholar
  29. 29.
    E.W. Weisstein, Wolfram Web Resource. http://mathworld.wolfram.com
  30. 30.
    J.W. Ponder, TINKER, Software Tools for Molecular Design, Version 6.2 (Washington University School of Medicine, Saint Louis, MO, 2012). http://dasher.wustl.edu/tinker
  31. 31.
    G.S. Fanourgakis, S.S. Xantheas, J. Phys. Chem. A 110, 4100–4106 (2006)CrossRefGoogle Scholar
  32. 32.
    M.V. Kirov, J. Struct. Chem. 47, 691–698 (2006)CrossRefGoogle Scholar
  33. 33.
    D.J. Anick, J. Chem. Phys. 132, 164311 (2010)CrossRefGoogle Scholar
  34. 34.
    M.V. Kirov, Phys. Chem. Chem. Phys. 18, 27351–27357 (2016)CrossRefGoogle Scholar
  35. 35.
    M.V. Kirov, Phys. A 388, 1431–1445 (2009)CrossRefGoogle Scholar
  36. 36.
    A. Lenz, L. Ojamäe, Phys. Chem. Chem. Phys. 7, 1905–1911 (2005)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Tyumen Scientific Centre, Siberian Branch RASTyumenRussia
  2. 2.Tyumen Industrial UniversityTyumenRussia

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