Russian Chemical Bulletin

, Volume 45, Issue 8, pp 1810–1826 | Cite as

Order, disorder, and geometrical information indices of molecules

  • S. A. Dembovsky
  • P. A. Koz'min
General and Inorganic Chemistry
Received:
  • 24 Downloads

Abstract

Structural features of various molecular systems with symmetry of point groups ranging fromC1 to the icosahedral symmetry are analyzed in the framework of the model suggested previously for the evaluation of order and disorder in the arrangement of atoms in a molecule based on the equationQ = I -P/3n (whereQ is the index of order, andP is the number of independent coordinates needed to fix ann-atomic molecule in the Cartesian coordinate system). TheQ value depends on various structural parameters of the molecule: the number of atoms in it, the symmetry, the dimensionality, and the number of structural degrees of freedom. The disorder indexP/3n = 1 -Q correlates with Shannon's entropy of information, andQ correlates with negentropy or excess information; this makes it possible to useP/3n as a new geometrical information molecular index that is obtained by a nonprobabilistic method. Analysis of the relationship between order and chaos in molecular systems, as well as of the specific order indexq =Q/n, makes it possible to identify both general and specific features of molecules.

Key words

molecule order chaos disorder symmetry point group information information index information entropy degree of freedom 
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    G. Careri,Poryadok i besporyadok v strukture materii [Order and Disorder in the Structure of Matter], Mir, Moscow, 1985, 228 pp. (Russ. Transl.) [G. Careri, Ordine e disordine della materia, Laterza, Roma, 1982].Google Scholar
  2. 2.
    I. Prigozhin,Ot sushchestvuyushchego k voznikayushchemu [From the Existing to Nascent], Nauka, Moscow, 1985, 327 pp. (in Russian).Google Scholar
  3. 3.
    I. Prigozhin and I. Stengers,Vremya, khaos i kvant [Time, Chaos, and Quantum], Progress, Moscow, 1994, 272 pp. (in Russian).Google Scholar
  4. 4.
    Yu. L. Klimontovich,Turbulentnoe dvizhenie i struktura khaosa: Novyi podkhod k statisticheskoi teorii otkrytykh sistem [Turbulent Motion and the Structure of Chaos: A Novel Approach to the Statistical Theory of Open Systems], Nauka, Moscow, 1990, 317 pp. (in Russian).Google Scholar
  5. 5.
    I. M. Ziman,Models of Disorder: The Theoretical Physics of Homogeneously Disordered Systems, Cambridge University Press, London, 1979.Google Scholar
  6. 6.
    S. R. Elliott,Nature, 1991,354, 445.Google Scholar
  7. 7.
    S. R. Elliott,J. Phys., Condens. Matter, 1992,4, 7661.Google Scholar
  8. 8.
    E. A. Chechetkina,J. Phys., Condens. Matter, 1995,7, 3099.Google Scholar
  9. 9.
    A. I. Kitaigorodskii,Poryadok i besporyadok v mire atomov [Order and Disorder in the World of Atoms], Nauka, Moscow, 1984, 172 pp. (in Russian).Google Scholar
  10. 10.
    C. Shannon and W. Weaver,Mathematical Theory of Communication, Univ. Illinois, Urbana, 1949.Google Scholar
  11. 11.
    Chemical Applications of Topology and Graph Theory, Ed. R. B. King, Elsevier, Amsterdam, 1983.Google Scholar
  12. 12.
    Yu. A. Zhdanov,Entropiya informatsh v organicheskoi khimii [Entropy of Information in Organic Chemistry], Izd. RGU, Rostov, 1979, 55 pp. (in Russian).Google Scholar
  13. 13.
    D. G. Bonchev,Kharakterizatsiya khimicheskikh struktur s pomoshch yu teorii informatsii i teorii grafov [Characterization of Chemical Structures Using Information Theory and Graph Theory], Sc. D. Thesis (Chemistry), Moscow State University, Moscow, 1984, 409 pp. (in Russian).Google Scholar
  14. 14.
    D. Bonchev, D. Kamensky, and V. Kamenska,Bull. Math. Biol., 1976,38, 119.Google Scholar
  15. 15.
    D. Bonchev and G. Lickomanov,Math. Chem., 1977,3, 3.Google Scholar
  16. 16.
    D. Bonchev,Information Theoretic Indices for Characterization of Chemical Structures, Research Studies Press, Chichester, 1983, 249 pp.Google Scholar
  17. 17.
    M. I. Stankevich, I. V. Stankevich, and N. S. Zefirov,Usp. Khim., 1988,57, 337 [Russ. Chem. Rev., 1988,57 (Engl. Transl.)].Google Scholar
  18. 18.
    Yu. S. Nekrasov, E. E. Tepfer, and Yu. S. Sukharev, inPrilozhenie teorii grafov v khimii [Applications of the Graph Theory to Chemistry], Izd. IM SO RAN, Novosibirsk, 1994,151, 8 (in Russian).Google Scholar
  19. 19.
    V. A. Skorobogatov, E. V. Konstantinova, and Yu. S. Nekrasov,Math. Chem., 1991,26, 215.Google Scholar
  20. 20.
    A. N. Kolmogorov,Vest. Akad. Nauk SSSR [Commun. of the USSR Academy of Sciences], 1965,5, 94 (in Russian).Google Scholar
  21. 21.
    A. N. Kolmogorov,Probl. Peredachi Inform. [Problems of Information Transfer], 1969,5, 3 (in Russian).Google Scholar
  22. 22.
    R. S. Ingarden and K. Urbanek,Colloq. Math., 1962,9, 131.Google Scholar
  23. 23.
    P. A. Koz'min,Dokl. Akad. Nauk, 1995,343, 205 [Dokl. Chem., 1995,343 (Engl. Transl.)].Google Scholar
  24. 24.
    P. A. Koz'min,Zh. Neotg. Mater. [J. Inorg. Materials], 1995,31, 884 (in Russian).Google Scholar
  25. 25.
    S. A. Dembovsky and E. A. Chechetkina,Stekloobrazovanie [Glass Formation], Nauka, Moscow, 1990, 264 pp. (in Russian).Google Scholar
  26. 26.
    I. Hargittai and M. Hargittai,Symmetry Through the Eyes of a Chemist, Plenum, New York 1995.Google Scholar
  27. 27.
    R. Gillespie and I. Hargittai,The VSEPR Model for Molecular Geometry, Allyn and Bacon, Boston-LondonToronto-Sydney-Tokyo-Singapore, 1991.Google Scholar
  28. 28.
    D. Hohl, R. O. Jones, R. Car, and M. Parrinello,J. Chem. Phys., 1989,89, 6823.Google Scholar
  29. 29.
    R. Gillespie,Molecular Geometry, Van Nostrand Company, London, 1972.Google Scholar
  30. 30.
    W. Ashbey,An Introduction to Cybernetics, Wiley, New York, 1956.Google Scholar
  31. 31.
    V. M. Glushkov, inKibernetika, myshlenie, zhizn' [Cybernetics, Thinking, and Life], Mysl', Moscow, 1964 (in Russian).Google Scholar
  32. 32.
    L. Brillouin,Science and Information Theory, Academic Press, New York, 1966.Google Scholar
  33. 33.
    B. N. Delone, N. P. Dolbilin, M. I. Shtogrin, and R. V. Galiulin,Dokl. Akad. Nauk SSSR, 1976,227, 19 [Dokl. Mathem., 1976,227 (Engl. Transl.)].Google Scholar
  34. 34.
    R. V. Galiulin,Kristallografiya [Crystallography], 1980,25, 91 (in Russian).Google Scholar
  35. 35.
    R. V. Galiulin,Kristallografiya [Crystallography], 1994,39, 581 (in Russian).Google Scholar
  36. 36.
    G. D. Mendenhall, A. Greenberg, and I. F. Liebman,Mesomolecules: From Molecules to Materials, Chapman and Hall, New York, 1995.Google Scholar
  37. 37.
    J.-M. Lehn,Supramolecular Chemistry: Concepts and Perspectives, VCN, Weinheim, 1995.Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • S. A. Dembovsky
    • 1
  • P. A. Koz'min
    • 1
  1. 1.N. S. Kurnakov Institute of General and Inorganic ChemistryRussian Academy of SciencesMoscowRussian Federation

Personalised recommendations