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.

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Fig. 1: Periodic tables.
Fig. 2: The Standard Model of fundamental particles.
Fig. 3: Electronic states and configurations.
Fig. 4: Relativistic effects.
Fig. 5: Localization functions.
Fig. 6: Nuclear stability.
Fig. 7: Abundancies of elements.


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This paper is dedicated to the memory of our friend and colleague Prof. Dr. Werner Kutzelnigg, who recently passed away. We acknowledge financial support by the Alexander von Humboldt Foundation (Bonn) and the Marsden Fund (17-MAU-021) of the Royal Society of New Zealand (Wellington). This work is part of the “Molecules in Extreme Environments” project funded by the Centre for Advanced Study at the Norwegian Academy of Science and Letters, Oslo, Norway. We thank W. Nazarewicz and B. Sherrill (Michigan State), M. Wiescher (Notre Dame), W. H. E. Schwarz (Siegen), Y. Oganessian (Dubna), G. Boeck (Rostock), R. Eichler (Bern), L. Pašteka (Bratislava) and L. v. Szentpaly (Stuttgart) for interesting and stimulating discussions. P.P. acknowledges a travel scholarship from the Magnus Ehrnrooth Foundation.

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Schwerdtfeger, P., Smits, O.R. & Pyykkö, P. The periodic table and the physics that drives it. Nat Rev Chem 4, 359–380 (2020).

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