Topological Space of the Chemical Elements and its Properties |
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Authors: | Guillermo Restrepo Eugenio J Llanos Héber Mesa |
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Institution: | (1) Laboratorio de Química Teórica, Universidad de Pamplona, Pamplona, Colombia;(2) Observatorio Colombiano de Ciencia y Tecnología, Carrera 7 No. 39-08, Bogotá, Colombia;(3) Departamento de Matemáticas, Universidad del Valle, Edificio 320, Oficina, 3190 Cali, Colombia |
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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 |
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Keywords: | chemical elements periodic table topology cluster analysis chemotopology |
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