Skip to main content
SpringerLink
Log in

Fractal dimension of the interatomic distance histogram: New 3D descriptor of molecular structure

  • Published:
Russian Journal of General Chemistry Aims and scope Submit manuscript

Abstract

A method is developed for the calculation of a new 3D descriptor of molecular structure, which is the fractal dimension of the histogram of interatomic distances serving as a measure of the structure complexity in the geometric aspect. The new descriptor was found to depend mainly on three factors: the number of atoms in a molecule, the number of bars in the histogram, and the point symmetry group. The fractal dimension of the histogram of interatomic distances was found to be of a very specific character.

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

References

  1. Mandelbrot, B., The Fractal Geometry of Nature, Moscow: Institute of Computer Sciences, 2002.

    Google Scholar 

  2. Feder, E., Fractals, Moscow: Mir, 1991.

    Google Scholar 

  3. Risovic, D., Mahovic Poljacek, S., and Gojo, M., Applied Surface Science, 2009, vol. 255, no. 7, pp. 4283–4288.

    Article  CAS  Google Scholar 

  4. Eftekhari, A., Physica, B: Condensed Matter, 2007, vol. 387, nos. 1–2, pp. 92–97.

    Article  CAS  Google Scholar 

  5. Ghanbari, Kh., Mousavi, M.F., Shamsipur, M., Rahmanifar, M.S., and Heli, H., Synthetic Metals, 2006, vol. 156, nos. 14–15, pp. 911–916.

    Article  CAS  Google Scholar 

  6. Koňas, P., Buchar, J., and Severa, L., European Journal of Mechanics, A, Solids, 2009, vol. 28, no. 3, pp. 545–550.

    Article  Google Scholar 

  7. Chang-Yong, Lee, Physical Review, E, 2006, vol. 73, p. 042901.

    Article  Google Scholar 

  8. Mihranyan, A. and Strømme, M., Surface Science, 2007, vol. 601, pp. 315–319.

    Article  CAS  Google Scholar 

  9. Ono, Y., Mayama, H., Furó, I., Sagidullin, A.I., Matsushima, K., Ura, H., Uchiyama, T., and Tsujii, K., J. Colloid and Interface Science, 2009, vol. 336, no. 1, pp. 215–225.

    Article  CAS  Google Scholar 

  10. Artemenko, A.G., Kovdienko, N.A., Kuz’min, V.E., Kamalov, G.L., Lozitskaya, R.N., Fedchuk, A.S., Lozitsky, V.P., Dyachenko, N.S., and Nosach, L.N., Experimental Oncology, 2002, vol. 24, pp. 123–127.

    CAS  Google Scholar 

  11. http://www.hyper.com/.

  12. http://www.knowitall.com/.

  13. http://www.talete.mi.it/.

  14. Svoistva organicheskikh soedinenii. Spravochnik (Properties of Organic Compounds. Handbook), Potekhin, A.A., Ed., Leningrad: Khimiya, 1984.

    Google Scholar 

  15. Kronover, R.M., Fraktaly i khaos v dinamicheskikh sistemakh. Osnovy teorii (Fractals and Chaos in Dynamic Systems. Theoretical Fundamentals), Moscow: Postmarket, 2000, p. 137.

    Google Scholar 

  16. Blatov, V.A., Shevchenko, A.P., and Peresypkina, E.V., Poluempiricheskie raschetnye metody kvantovoi khimii: Uchebnoe posobie (Semiempirocal Calculation Methods of Quantum Chemistry. A Tutorial), Samara: Univers-Grupp, 2005.

    Google Scholar 

  17. Forsythe, G.E., Malcolm, M.A., and Moler, C.B., Computer Methods for Mathematical Computations, Moscow: Mir, 1980.

    Google Scholar 

  18. Dimov, N., Osman, A., Mekenyan, O., and Papazova, D., Analytica Chimica Acta, 1994, vol. 298, no. 3, pp. 303–317.

    Article  CAS  Google Scholar 

  19. http://www.moleculardescriptors.eu/.

Download references

Author information

Authors and Affiliations

  1. Institute of Physiologically Active Substances, Russian Academy of Sciences, Severnyi pr. 1, Chernogolovka, Moscow Oblast, 142432, Russia

    V. A. Grigor’ev & O. A. Raevskii

Authors
  1. V. A. Grigor’ev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. A. Raevskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. A. Grigor’ev.

Additional information

Original Russian Text © V.A. Grigor’ev, O.A. Raevskii, 2011, published in Zhurnal Obshchei Khimii, 2011, Vol. 81, No. 3, pp. 353–359.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grigor’ev, V.A., Raevskii, O.A. Fractal dimension of the interatomic distance histogram: New 3D descriptor of molecular structure. Russ J Gen Chem 81, 449–455 (2011). https://doi.org/10.1134/S1070363211030017

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1070363211030017

Keywords

Search

Navigation