Journal of Mathematical Chemistry

, Volume 39, Issue 2, pp 401–416

Topological Space of the Chemical Elements and its Properties

  • Guillermo Restrepo
  • Eugenio J. Llanos
  • Héber Mesa
Article

DOI: 10.1007/s10910-005-9041-1

Cite this article as:
Restrepo, G., Llanos, E.J. & Mesa, H. J Math Chem (2006) 39: 401. doi:10.1007/s10910-005-9041-1

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

Keywords

chemical elementsperiodic tabletopologycluster analysischemotopology

AMS subject classification

54A1005C0580A50

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Guillermo Restrepo
    • 1
  • Eugenio J. Llanos
    • 2
  • Héber Mesa
    • 3
  1. 1.Laboratorio de Química TeóricaUniversidad de PamplonaPamplonaColombia
  2. 2.Observatorio Colombiano de Ciencia y TecnologíaBogotáColombia
  3. 3.Departamento de MatemáticasUniversidad del ValleCaliColombia