Formal structure of periodic system of elements

For more than 150 years, the structure of the periodic system of the chemical elements has intensively motivated research in different areas of chemistry and physics. However, there is still no unified picture of what a periodic system is. Herein, based on the relations of order and similarity, we report a formal mathematical structure for the periodic system, which corresponds to an ordered hypergraph. It is shown that the current periodic system of chemical elements is an instance of the general structure. The definition is used to devise a tailored periodic system of polarizability of single covalent bonds, where order relationships are quantified within subsets of similar bonds and among these classes. The generalized periodic system allows envisioning periodic systems in other disciplines of science and humanities.

[1]  N. S. Imyanitov.  The Periodic Law. Formulations, equations, graphic representations , 2011 .

[2]  G. Restrepo,et al.  A Network Study of Chemical Elements: From Binary Compounds to Chemical Trends , 2012 .

[3]  Yiqun Liu,et al.  Learning on Partial-Order Hypergraphs , 2018, WWW.

[4]  P. Pyykkö.  The physics behind chemistry and the periodic table. , 2012, Chemical reviews.

[5]  Ganapati P. Patil,et al.  Ranking and Prioritization for Multi-indicator Systems , 2011 .

[6]  Stefano Curtarolo,et al.  SISSO: A compressed-sensing method for identifying the best low-dimensional descriptor in an immensity of offered candidates , 2017, Physical Review Materials.

[7]  Pekka Pyykkö,et al.  Molecular single-bond covalent radii for elements 1-118. , 2009, Chemistry.

[8]  Juan Bautista BengoetxeaOliver.  Similarity and representation in chemical knowledge practices , 2014 .

[9]  D. Rouvray,et al.  The Mathematics Of The Periodic Table , 2005 .

[10]  Thilini P. Rupasinghe,et al.  Mechanical Properties of a Series of Macro- and Nanodimensional Organic Cocrystals Correlate with Atomic Polarizability. , 2015, Journal of the American Chemical Society.

[11]  Rainer Brüggemann,et al.  Dominance and separability in posets, their application to isoelectronic species with equal total nuclear charge , 2008 .

[12]  G. Restrepo.  Quantifying Complexity of Partially Ordered Sets , 2014 .

[13]  Guillermo Restrepo,et al.  Mendeleev to Oganesson: A Multidisciplinary Perspective on the Periodic Table , 2018 .

[14]  P. Jönsson,et al.  Are MCDF calculations 101% correct in the super-heavy elements range? , 2011 .

[15]  D. Klein,et al.  Network of secondary-substituted adamantane amines: NETWORK OF SECONDARY-SUBSTITUTED ADAMANTANE AMINES , 2013 .

[16]  N Schunck,et al.  Nuclear tetrahedral symmetry: possibly present throughout the periodic table. , 2002, Physical review letters.

[17]  Eric R. Scerri.  What is an element? What is the periodic table? And what does quantum mechanics contribute to the question? , 2012 .

[18]  Béla Bollobás,et al.  Hereditary properties of partitions, ordered graphs and ordered hypergraphs , 2006, Eur. J. Comb..

[19]  Ralf Wieland,et al.  PyHasse Software for Partial Order Analysis: Scientific Background and Description of Selected Modules , 2014 .

[20]  P. Pyykkö.  Is the Periodic Table all right ("PT OK")? , 2016 .

[21]  A. Rahimi,et al.  Some properties of ordered hypergraphs , 2007 .

[22]  W. Schwarz,et al.  Some solved problems of the periodic system of chemical elements , 2009 .

[23]  W. Schwarz,et al.  Icon of chemistry: the periodic system of chemical elements in the new century. , 2009, Angewandte Chemie.

[24]  Lyuben Zhechkov,et al.  DFTB Parameters for the Periodic Table: Part 1, Electronic Structure. , 2013, Journal of chemical theory and computation.

[25]  P. Pyykkö,et al.  Chemistry of the 5g Elements: Relativistic Calculations on Hexafluorides. , 2017, Angewandte Chemie.

[26]  G. Restrepo.  Building Classes of Similar Chemical Elements from Binary Compounds and Their Stoichiometries , 2017 .

[27]  Eric R. Scerri.  A tale of seven elements , 2013 .

[28]  W. Schwarz,et al.  Theoretical Basis and Correct Explanation of the Periodic System: : Review and Update , 2010 .

[29]  Torolf Ternstrom,et al.  A periodic table , 1964 .

[30]  J. Meister,et al.  PRINCIPAL COMPONENTS OF IONICITY , 1994 .

[31]  Rainer Brüggemann,et al.  Ranking of refrigerants. , 2008, Environmental science & technology.

[32]  Eric R. Scerri.  Chemistry goes abstract. , 2009, Nature chemistry.

[33]  Wei Huang,et al.  On the Highest Oxidation States of Metal Elements in MO4 Molecules (M = Fe, Ru, Os, Hs, Sm, and Pu). , 2016, Inorganic chemistry.

[34]  Peter F. Stadler,et al.  Forman-Ricci Curvature for Hypergraphs , 2018, Adv. Complex Syst..

[35]  H. Haba.  A new period in superheavy-element hunting , 2018, Nature Chemistry.

[36]  P. Pyykkö.  A suggested periodic table up to Z≤ 172, based on Dirac-Fock calculations on atoms and ions. , 2011, Physical chemistry chemical physics : PCCP.

[37]  A. Bonato,et al.  Graphs and Hypergraphs , 2022 .

[38]  P. Chattaraj,et al.  Electronic Structure Principles and Atomic Shell Structure , 2001 .

[39]  J. E. Huheey,et al.  Anorganische Chemie: Prinzipien von Struktur und Reaktivität , 1988 .

[40]  B. Jarosch,et al.  Anorganische Chemie I , 2019, Pocket Guide Chemie.

[41]  Joachim Schummer,et al.  The Chemical Core of Chemistry I: A Conceptual Approach , 1998 .

[42]  Steffen Klamt,et al.  Hypergraphs and Cellular Networks , 2009, PLoS Comput. Biol..

[43]  Bernard De Baets,et al.  Order-theoretical tools to support risk assessment of chemicals , 2012 .

[44]  W. Schwarz,et al.  100th anniversary of Bohr's model of the atom. , 2013, Angewandte Chemie.

[45]  Rainer Brüggemann,et al.  Influence of altitude concerning the contamination of humus soils in the German Alps: a data evaluation approach using PyHasse , 2010, Environmental science and pollution research international.

[46]  Douglas J. Klein,et al.  Similarity and dissimilarity in posets , 1995 .

[47]  Werner Kutzelnigg,et al.  The periodic table. Its story and its significance , 2009 .

[48]  D. Klein,et al.  Predicting densities of nitrocubanes using partial orders , 2011 .

[49]  Peng Zheng,et al.  Machine learning material properties from the periodic table using convolutional neural networks† †Electronic supplementary information (ESI) available: Training dataset analysis, training representations, training loss, predicted stable full-Heusler compounds and analysis. See DOI: 10.1039/c8sc0264 , 2018, Chemical science.

[50]  J. Katriel.  The splitting of atomic orbitals with a common principal quantum number revisited: np vs. ns. , 2012, The Journal of chemical physics.

[51]  Dennis H. Rouvray,et al.  Definition and role of similarity concepts in the chemical and physical sciences , 1992, J. Chem. Inf. Comput. Sci..

[52]  Adalbert Kerber,et al.  Ranking Objects Using Fuzzy Orders, with an Application to Refrigerants , 2011 .

[53]  P. Geerlings,et al.  Information carriers and (reading them through) information theory in quantum chemistry. , 2011, Physical chemistry chemical physics : PCCP.