Skip to main content
SpringerLink
Log in

Topological Space of the Chemical Elements and its Properties

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

Abstract

We carried out a mathematical study of 72 chemical elements taking advantage of the chemotopological method. We selected 128 properties to define the elements (physico-chemical, geochemical and chemical properties). Then, we looked for correlated properties and we reduced the number of them to 90. In this way we defined each element as a 90-tuple. Afterwards, we applied principal component analysis and cluster analysis (4 similarity functions and 5 grouping methodologies). Then, we calculated a consensus tree for the 20 dendrograms generated by the CA. Afterwards, we extracted the similarity relationships from the consensus tree and built up a basis for a topology on the set of chemical elements. Finally, we calculated some topological properties (closures, derived sets, boundaries, interiors and exteriors) of several subsets of chemical elements. We found that alkali metals, alkaline earth metals and noble gases appear not related to the rest of the elements. Also, we found that the boundary of non-metals are the semimetals with a stair-shape on the periodic table

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. Mazurs E.G. (1974). Graphic Representations of the Periodic System During One Hundred Years. University Alabama Press, Alabama

    Google Scholar 

  2. Rayner-Canham G. and Oberton T. (2002). Descriptive Inorganic Chemistry. Freeman, New York

    Google Scholar 

  3. D.I. Mendeleev, Zeitschrift für Chemie 12 (1869) 405. (http://webserver.lemoyne.edu/faculty/giunta/mendeleev.html (accessed Apr. 2005)).

  4. Scerri E.R., Kreinovich V., Wojciechowski P. and Yager R.R. (1998). Int J Uncert Fuzz Know-Based Syst. 6: 387

    Article  Google Scholar 

  5. Négadi T. (2000). Int. J. Quantum Chem. 78: 206

    Article  Google Scholar 

  6. Zhou X.-Z., Wei K.-H., Chen G.-Q., Fan Z.-X. and Zhan J.-J. (2000). Jisuanji Yu Yingyong Huaxue 17: 167

    CAS  Google Scholar 

  7. Sneath P.H.A. (2000). Found Chem. 2: 237

    Article  CAS  Google Scholar 

  8. Restrepo G., Mesa H., Llanos E.J., Villaveces J.L. (2004). J. Chem. Inf. Comput. Sci. 44: 68

    Article  CAS  Google Scholar 

  9. Restrepo G., Mesa H., Llanos E.J., and Villaveces J.L., in: The Mathematics of the Periodic Table, eds. King R.B., and Rouvray D., (Nova, New York, 2005).

  10. Restrepo G., Mesa H., Llanos E.J., and Villaveces J.L., in: Proceedings of The Third Joint Sheffield Conference on Chemoinformatics, (The University of Sheffield, Sheffiield, 2004).

  11. Restrepo G., Villaveces J.L. (2005). Croat. Chem. Acta 78: 275

    CAS  Google Scholar 

  12. Restrepo G., Llanos E.J., and Mesa H., in: Proceedings of the International Conference of Computational Methods in Sciences and Engineering 2004 (Armonia, Attica, 2004).

  13. Otto M. (1999). Chemometrics: Statistics and Computer Application in Analytical Chemistry. Wiley-VCH, Weinheim

    Google Scholar 

  14. Brereton R.G. (2004). Chemometrics: Data Analysis for the Laboratory and Chemical Plant. Wiley, Chichester

    Google Scholar 

  15. Everitt B.S. (2001). Cluster Analysis. Arnold Publishers, Cornwall

    Google Scholar 

  16. Aldenderfer M.S., Blashfield R.K., Cluster Analysis (Sage University Paper series on Quantitative Applications in the Social Sciences, No. 44), (Sage Publications, Newbury Park, 1984).

  17. Restrepo G., Mesa H., and Villaveces J.L., On the Topological Sense of Chemical Sets, J. Math. Chem. In press.

  18. Hawkes S.J. (2001). J Chem Edu. 78: 1686

    CAS  Google Scholar 

  19. Firestone R.B. (1996). Table of Isotopes. 8th ed. Wiley-Interscience, New York

    Google Scholar 

  20. Rodgers G.E. (1995). Química Inorgánica. McGraw-Hill, Madrid

    Google Scholar 

  21. Sanderson R.T. (1960). Chemical Periodicity. Reinhold Publishing Corporation, New York

    Google Scholar 

  22. Lide D.R. (2002). CRC Handbook of Chemistry and Physics, 83rd ed. CRC Press, Cleveland (http://www.hbcpnetbase.com/)

    Google Scholar 

  23. http://www.chemicool.com/ (April 2, 2005).

  24. Railsback L.B. (2003). Geology 31:737

    Article  CAS  Google Scholar 

  25. Cruz-Garritz D., Chamizo J.A., Garritz A. (1991). Estructura Atómica: Un Enfoque Químico. Addison-Wesley Iberoamericana, Wilmington

    Google Scholar 

  26. University of Split, Faculty of Chemical Technology, Periodic Table. (http://www. ktf-split.hr/periodni/en/index.html (April 2, 2005))

  27. Dunteman G.H. (1989). Principal Components Analysis. (Sage University Paper series on Quantitative Applications in the Social Sciences, No. 07-069). Sage Publications, Newbury Park

    Google Scholar 

  28. Lance G.N., and Williams W.T. (1967). Computer J 9:373

    Google Scholar 

  29. Mendelson B. (1990). Introduction to Topology. Dover, New York

    Google Scholar 

  30. Willet P. (1998). J. Chem. Inf. Comput. Sci 38:983

    Google Scholar 

  31. Carbó R., Domingo L. (1987). Int. J. Quantum. Chem. 32:517

    Article  Google Scholar 

  32. Page R.D.M. (1996). Comput. Appl. Biosci 12:357

    CAS  Google Scholar 

  33. Felsenstein J. (2004). Inferring Phylogenies. Sinauer, Sunderland

    Google Scholar 

  34. R.D.M. Page, COMPONENT User’s Manual (Release 1.5) (University of Auckland, Auckland, 1989) (http://taxonomy.zoology.gla.ac.uk/rod/cpw.html.)

  35. Rayner-Canham G. (2000). J. Chem. Edu. 77:1053

    Article  CAS  Google Scholar 

  36. Greenwood N.N., and Earnshaw A. (2002). Chemistry of the Elements. Butterworth Heinemann, Oxford

    Google Scholar 

  37. Klemm W. (1950). Angew Chem 62:133

    Article  CAS  Google Scholar 

  38. King R.B., in: The Mathematics of the Periodic Table, eds. King R.B., and D. Rouvray (Nova, New York, 2005).

Download references

Author information

Authors and Affiliations

  1. Laboratorio de Química Teórica, Universidad de Pamplona, Pamplona, Colombia

    Guillermo Restrepo

  2. Observatorio Colombiano de Ciencia y Tecnología, Carrera 7 No. 39-08, Bogotá, Colombia

    Eugenio J. Llanos

  3. Departamento de Matemáticas, Universidad del Valle, Edificio 320, Oficina, 3190, Cali, Colombia

    Héber Mesa

Authors
  1. Guillermo Restrepo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Eugenio J. Llanos
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Héber Mesa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Guillermo Restrepo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Restrepo, G., Llanos, E.J. & Mesa, H. Topological Space of the Chemical Elements and its Properties. J Math Chem 39, 401–416 (2006). https://doi.org/10.1007/s10910-005-9041-1

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-005-9041-1

Keywords

AMS subject classification

Search

Navigation