Formal structure of periodic system of elements

Abstract

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 generalised periodic system allows envisioning periodic systems in other disciplines of science and humanities.

Challenges for the Periodic Systems of Elements: Chemical, Historical and Mathematical Perspectives

“…The ordered hypergraph structure is general enough to allow also changing objects, that is, it is not only restricted to chemical elements. The hypergraph structure is therefore the most general structure encompassing all possible periodic systems, not only of chemical objects, but of any other nature, even outside the chemistry realm . One could even envision periodic systems in other disciplines, where the only requirement is to have orderable and classifiable objects.…”

“…Hence, at the level of possible structures there are many, depending on the properties used to order and classify the elements. The several possibilities for classifying and ordering bring up different periodic systems and their relationships form a super structure . All possible periodic systems lie in that super structure and their relationships are worth exploring .…”

“…Contemporary mathematics is equipped with hypergraphs and simplices, which are formal devices to treat n ‐ary relations, which are the relations we are referring to . An initial step in that direction was using the hypergraph structure of the systems to address order relationships among classes of similar single‐covalent bonds …”

Divagations about the periodic table: Boolean hypercube and quantum similarity connections

“…Such possibility provided several colorful diagrams, where atomic numbers were represented along a pair of additional atomic properties, constructing in this way every atom in the PT as a point of a 3D graph. j) No wonder about the latent usefulness of such possible kind of PT representation possibilities, which the present author does not know if have been applied and how, apart from a recent study of Scerri . No doubt they can be used to understand a bit more than the PT and the relationships between the atomic properties. k) Actual attempts of describing the PT, which have not been included in the initial version of this manuscript, like the extensive study of Leal and Restrepo will be now considered.…”

“…Thus, apparently and according to the referee, the use of partially ordered set techniques promoted by Ref. , could shed light into the PT conundrum.…”