Understanding Periodic and Non-periodic Chemistry in Periodic Tables

The chemical elements are the "conserved principles" or "kernels" of chemistry that are retained when substances are altered. Comprehensive overviews of the chemistry of the elements and their compounds are needed in chemical science. To this end, a graphical display of the chemical properties of the elements, in the form of a Periodic Table, is the helpful tool. Such tables have been designed with the aim of either classifying real chemical substances or emphasizing formal and aesthetic concepts. Simplified, artistic, or economic tables are relevant to educational and cultural fields, while practicing chemists profit more from "chemical tables of chemical elements." Such tables should incorporate four aspects: (i) typical valence electron configurations of bonded atoms in chemical compounds (instead of the common but chemically atypical ground states of free atoms in physical vacuum); (ii) at least three basic chemical properties (valence number, size, and energy of the valence shells), their joint variation across the elements showing principal and secondary periodicity; (iii) elements in which the (sp)8, (d)10, and (f)14 valence shells become closed and inert under ambient chemical conditions, thereby determining the "fix-points" of chemical periodicity; (iv) peculiar elements at the top and at the bottom of the Periodic Table. While it is essential that Periodic Tables display important trends in element chemistry we need to keep our eyes open for unexpected chemical behavior in ambient, near ambient, or unusual conditions. The combination of experimental data and theoretical insight supports a more nuanced understanding of complex periodic trends and non-periodic phenomena.

Understanding the Uniqueness of 2p Elements in Periodic Tables

The Periodic Table, and the unique chemical behavior of the first element in a column (group), were discovered simultaneously one and a half centuries ago. Half a century ago, this unique chemistry of the light homologs was correlated to the then available atomic orbital (AO) radii. The radially nodeless 1s, 2p, 3d, 4f valence AOs are particularly compact. The similarity of r(2s)≈r(2p) leads to pronounced sp-hybrid bonding of the light p-block elements, whereas the heavier p elements with n≥3 exhibit r(ns) ≪ r(np) of approximately -20 to -30 %. Herein, a comprehensive physical explanation is presented in terms of kinetic radial and angular, as well as potential nuclear-attraction and electron-screening effects. For hydrogen-like atoms and all inner shells of the heavy atoms, r(2s) ≫ r(2p) by +20 to +30 %, whereas r(3s)≳r(3p)≳r(3d), since in Coulomb potentials radial motion is more radial orbital expanding than angular motion. However, the screening of nuclear attraction by inner core shells is more efficient for s than for p valence shells. The uniqueness of the 2p AO is explained by this differential shielding. Thereby, the present work paves the way for future physical explanations of the 3d, 4f, and 5g cases.

Recent attempts to change the periodic table

The article concerns various proposals that have been made with the aim of improving the currently standard 18-column periodic table. We begin with a review of 8-, 18- and 32-column formats of the periodic table. This is followed by an examination of a possible, although rather impractical, 50-column table and how it could be used to consider the changes to the periodic table that have been predicted by Pyykkö in the domain of superheavy elements. Other topics reviewed include attempts to derive the Madelung rule as well as an analysis of what this rule actually provides. Finally, the notion of an 'optimal' periodic table is discussed in the context of recent work by philosophers of science who have examined the nature of classifications in general, as well as the notion of natural kinds. The article takes an unapologetically philosophical approach rather than focusing on specific data concerning the elements. Nevertheless, some pragmatic issues and educational aspects of the periodic table are also examined. This article is part of the theme issue 'Mendeleev and the periodic table'.

The periodic table and the physics that drives it

Mendeleev's introduction of the periodic table of elements is one of the most important milestones in the history of chemistry, as it brought order into the known chemical and physical behaviour of the elements. The periodic table can be seen as parallel to the Standard Model in particle physics, in which the elementary particles known today can be ordered according to their intrinsic properties. The underlying fundamental theory to describe the interactions between particles comes from quantum theory or, more specifically, from quantum field theory and its inherent symmetries. In the periodic table, the elements are placed into a certain period and group based on electronic configurations that originate from the Pauli and Aufbau principles for the electrons surrounding a positively charged nucleus. This order enables us to approximately predict the chemical and physical properties of elements. Apparent anomalies can arise from relativistic effects, partial-screening phenomena (of type lanthanide contraction) and the compact size of the first shell of every l-value. Further, ambiguities in electron configurations and the breakdown of assigning a dominant configuration, owing to configuration mixing and dense spectra for the heaviest elements in the periodic table. For the short-lived transactinides, the nuclear stability becomes an important factor in chemical studies. Nuclear stability, decay rates, spectra and reaction cross sections are also important for predicting the astrophysical origin of the elements, including the production of the heavy elements beyond iron in supernova explosions or neutron-star mergers. In this Perspective, we critically analyse the periodic table of elements and the current status of theoretical predictions and origins for the heaviest elements, which combine both quantum chemistry and physics.

Physical origin of chemical periodicities in the system of elements

The Periodic Law, one of the great discoveries in human history, is magnificent in the art of chemistry. Different arrangements of chemical elements in differently shaped Periodic Tables serve for different purposes. “Can this Periodic Table be derived from quantum chemistry or physics?” can only be answered positively, if the internal structure of the Periodic Table is explicitly connected to facts and data from chemistry. Quantum chemical rationalization of such a Periodic Tables is achieved by explaining the details of energies and radii of atomic core and valence orbitals in the leading electron configurations of chemically bonded atoms. The coarse horizontal pseudo-periodicity in seven rows of 2, 8, 8, 18, 18, 32, 32 members is triggered by the low energy of and large gap above the 1s and nsp valence shells (2 ≤ n ≤ 6 !). The pseudo-periodicity, in particular the wavy variation of the elemental properties in the four longer rows, is due to the different behaviors of the s and p vs. d and f pairs of atomic valence shells along the ordered array of elements. The so-called secondary or vertical periodicity is related to pseudo-periodic changes of the atomic core shells. The Periodic Law of the naturally given System of Elements describes the trends of the many chemical properties displayed inside the Chemical Periodic Tables. While the general physical laws of quantum mechanics form a simple network, their application to the unlimited field of chemical materials under ambient ‘human’ conditions results in a complex and somewhat accidental structure inside the Table that fits to some more or less symmetric outer shape. Periodic Tables designed after some creative concept for the overall appearance are of interest in non-chemical fields of wisdom and art.