Divagations about the periodic table: Boolean hypercube and quantum similarity connections |
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Authors: | Ramon Carbó-Dorca Tanmoy Chakraborty |
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Institution: | 1. Institut de Química Computacional i Catàlisi, Universitat de Girona, Girona, 17071 Catalonia, Spain;2. Department of Chemistry, Manipal University Jaipur, Dehmi Kalan, Jaipur, Rajasthan, India, 303007 |
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Abstract: | In this study, several simple aspects associated with the periodic table (PT) of the elements are commented. First, the connection of the PT with the structure of a seven-dimensional Boolean hypercube leads afterward to discuss the nature of those PT elements bearing prime atomic numbers. Second, the use of quantum similarity (QS) to obtain an alternative insight on the PT element relations will be also developed. The foundation of the second part starts admitting that any element of the PT can be attached to a schematic electronic density function, constructed with a single Gaussian function: a Gaussian atomic density function, allowing to consider the PT elements as a set of quantum objects, and permits a straightforward construction of a QS matrix. Such QS scheme can be applied to the whole PT or to any subset of it. Manipulation of the QS matrices attached to any quantum object set allows the evaluation of statistical-like values, acting as coordinates to numerically or graphically represent the chosen PT atomic element sets. © 2019 Wiley Periodicals, Inc. |
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Keywords: | periodic table (PT) of the elements PT as a seven-dimensional hypercube prime atomic numbers quantum similarity (QS) Gaussian atomic density functions simplified atomic QS atomic QS matrix atomic QS statistical-like parameters graphical representation of PT atomic sets |
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