Journal of Structural Chemistry

, Volume 47, Supplement 1, pp S119–S125 | Cite as

Spatial correlations of interatomic voids in molecular liquids studied using Delaunay simplices

  • M. G. Alinchenko
  • A. V. Anikeenko
  • V. P. Voloshin
  • N. N. Medvedev
  • D. Paschek
  • A. Appelhagen
  • A. Geiger


Pair correlation functions are calculated for interatomic voids determined using Delaunay simplices. Various modifications of these functions are suggested in relation to the problem formulated. In the simplest case, this correlator is a conventional radial distribution function g(r), but its calculation employs the centers of voids, but not the centers of atoms. For analysis of nonuniform systems, it is suggested that a “weighted” radial distribution function be used, where pair distances are taken with weights that depend on the volume of the voids. To study structural differences between molecular liquids (e.g., alkane isomers) we use the partial radial distribution functions that take into account only relatively “wide” voids. The ion-void distance distribution functions define voids in the hydration shells of ions an aqueous salts.


structure of a liquid free volume Delaunay simplices interatomic voids radial distribution function 


  1. 1.
    G. B. Bokii, Crystal Chemistry [in Russian], Moscow State University, Moscow (1960).Google Scholar
  2. 2.
    R. W. G. Wyckoff, Crystal Structures, Vol. 1, Wiley, New York (1963).Google Scholar
  3. 3.
    J. L. Finney and J. Wallace, J. Non-Cryst. Solids, 43, 165–180 (1981).CrossRefGoogle Scholar
  4. 4.
    M. Wilson and P. A. Madden, Phys. Rev. Lett., 80, 532–535 (1998).CrossRefGoogle Scholar
  5. 5.
    M. Wilson, P. A. Madden, N. N. Medvedev, et al., J. Chem. Soc., Faraday Trans., 94, No. 3, 1221 (1998).CrossRefGoogle Scholar
  6. 6.
    V. P. Voloshin, S. Beaufils, and N. N. Medvedev, J. Mol. Liq., 96/97, 101–112 (2002).CrossRefGoogle Scholar
  7. 7.
    G. F. Voronoi, Studies of Primitive Parallelohedra [in Russian], A Collection of Papers, Vol. 2, Ukrainian SSR Academy of Sciences, Kiev (1952).Google Scholar
  8. 8.
    B. N. Delaunay, Petersburg School of Number Theory [in Russian], USSR Academy of Sciences, Moscow (1947), pp. 196–316.Google Scholar
  9. 9.
    A. Okabe, B. Boots, K. Sugihara, and S. N. Chiu, Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, Wiley, Chichester (2000).Google Scholar
  10. 10.
    N. N. Medvedev, Voronoi-Delaunay Method in Structural Studies of Noncrystalline Systems [in Russian], Siberian Division, Russian Academy of Sciences, Novosibirsk (2000).Google Scholar
  11. 11.
    N. N. Medvedev, Dokl. Ross. Akad. Nauk, 337, No. 6, 767–771 (1994).Google Scholar
  12. 12.
    M. G. Alinchenko, A. V. Anikeenko, N. N. Medvedev, et al., J. Phys. Chem. B, 108, 19056–19067 (2004).CrossRefGoogle Scholar
  13. 13.
    N. N. Medvedev, Voronoi’s Impact on Modern Science, Book 2, P. Engel and H. Syta (eds.), Inst. Math., Kiev (1998), pp. 164–175.Google Scholar
  14. 14.
    A. V. Anikeenko, M. G. Alinchenko, V. P. Voloshin, et al., LNCS, 3045, 217–226 (2004).Google Scholar
  15. 15.
    V. P. Voloshin and N. N. Medvedev, Zh. Strukt. Khim., 46, No. 1, 96–100; 101–105 (2005).Google Scholar
  16. 16.
    C. Beisbart, M. Kerscher, and K. Mecke, Mark Correlation: Relating Physical Properties to Spatial Distributions, in: Morphology of Condensed Matter, K. Macke and D. Stoyan (eds.), Springer, Heidelberg (2002).Google Scholar
  17. 17.
    C. Ferradini and J.-P. Jay-Gerin (eds.), Excess Electrons in Dielectric Media, CRC Press, London (1991).Google Scholar
  18. 18.
    W. F. Schmidt, Liquid State. Electronics of Insulating Liquids, CRC Press, New York (1997).Google Scholar
  19. 19.
    M. G. Martin and J. I. Siepmann, J. Phys. Chem., B102, 2569–2575 (1998).Google Scholar
  20. 20.
    M. G. Martin and J. I. Siepmann, ibid., B103, 4508–4515 (1999).Google Scholar
  21. 21.
    D. Paschek and A. Geiger, ibid., 4139–4148.Google Scholar
  22. 22.
    A. V. Anikeenko, Yu. I. Naberukhin, N. N. Medvedev, et al., Radial Distribution of Voids around Ions in Water, 6th Liquid Matter Conference, 2–6 July, Utrecht, p. 202.Google Scholar
  23. 23.
    O. Ya. Samoilov, Structure of Aqueous Solutions of Electrolytes and Ion Hydration [in Russian], USSR Academy of Sciences, Moscow (1957).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • M. G. Alinchenko
    • 1
  • A. V. Anikeenko
    • 1
  • V. P. Voloshin
    • 1
  • N. N. Medvedev
    • 1
  • D. Paschek
    • 2
  • A. Appelhagen
    • 2
  • A. Geiger
    • 2
  1. 1.Institute of Chemical Kinetics and Combustion, Siberian DivisionRussian Academy of SciencesNovosibirsk
  2. 2.Dortmund UniversityGermany

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