Towards a Physical Explanation of the Periodic Table (PT) of Chemical Elements

Abstract

A significant body of physical, mathematical and chemical knowledge has been accumulated in the past decades that forms the starting point for our task. The ap propriate questions are here formulated. If one wants to explain the Periodic Table (PT) of chemical elements with physical theory, i.e. quantum chemically, one should at first elucidate the basic principles of the PT. It is based on 3 concepts, i) the linear arrangement of elements according to the nuclear charge number, ii) the partitioning of this array in order to create a two-dimensional map, and iii) the organization of this map so that chemically similar elements appear in neighbor hoods, in particular in vertical columns. The PT has physical, mathematical and chemical aspects. From the chemical point of view, a two-sided criterion seems particularly relevant for the structure of the PT. On the empirical stoichiometric side, there are the same ‘highest chemical valence numbers’ within many of the groups of the PT. On the quantum theoretical side, there are the same ‘numbers of valence electrons’ (defined as separated from the ‘atomic cores’ on a chemically relevant energy scale), which are housed in similar sets of near-degenerate shells of ‘valence atomic orbitals (AO)’. Therefore it is quantum chemically most essential to understand i) the emergence of a comparatively large gap between the highest ns2np6 core shell and the near-degenerate (n+l)s and/or (n+l)p,nd,(n-l)f valence sub-shells, and ii) the numbers and types of orbitals above the cores available for valence activity. The specific energetic order of the optically active valence and Rydberg states, or the consequences of angular momentum couplings in unper turbed atoms, seem chemically less important. Authors of chemical textbooks and scholars interested in physical and philosophical aspects of the PT have often dis cussed chemically less relevant topics. In particular the (n+l,n) or ‘Madelung’ rule postulating e.g. 3p>4s>3d as the energetic order of valence orbitals is chemically misleading. Valence (n+1)s AOs need not be considered at the qualitative level to explain most chemical transition metal phenomena or the alkali and alkaline earth cation compounds.