Foundations of Chemistry

, Volume 9, Issue 3, pp 221–234 | Cite as

From the Mendeleev periodic table to particle physics and back to the periodic table

  • Maurice R. KiblerEmail author


We briefly describe in this paper the passage from Mendeleev’s chemistry (1869) to atomic physics (in the 1900’s), nuclear physics (in 1932) and particle physics (from 1953 to 2006). We show how the consideration of symmetries, largely used in physics since the end of the 1920’s, gave rise to a new format of the periodic table in the 1970’s. More specifically, this paper is concerned with the application of the group SO(4,2)⊗SU(2) to the periodic table of chemical elements. It is shown how the Madelung rule of the atomic shell model can be used to set up a periodic table that can be further rationalized via the group SO(4,2)⊗SU(2) and some of its sub-groups. Qualitative results are obtained from this nonstandard table.


Atomic and sub-atomic physics Group theory Flavor group Periodic table of chemical elements 



Thanks are due to the Referee for pertinent criticism and useful suggestions.


  1. Barut, A.O.: Group structure of the periodic system. In: Wybourne, B.G. (ed.) The Structure of Matter, pp. 126–136. University of Canterbury Publications, Christchurch, New Zealand (1972)Google Scholar
  2. Barut, A.O., Kleinert, H.: Transition form factors in the H atom. Phys. Rev. 160, 1149–1151 (1967)CrossRefGoogle Scholar
  3. Kibler, M.R.: On the use of the group SO(4,2) in atomic and molecular physics. Mol. Phys. 102, 1221–1230 (2004)CrossRefGoogle Scholar
  4. Kibler, M.R.: A group-theoretical approach to the periodic table: old and new developments. In: Rouvray, D.H., King, R.B. (eds.) The Mathematics of the Periodic Table, pp. 237–263. Nova Science, NY (2006)Google Scholar
  5. Kibler, M., Négadi, T.: Connection between the hydrogen atom and the harmonic oscillator. Phys. Rev. A 29, 2891–2894 (1984)CrossRefGoogle Scholar
  6. Konopel’chenko, V.G., Rumer, Yu.B.: Atoms and hadrons (classification problems). Sov. Phys. Usp. 22, 837–840 (1979)CrossRefGoogle Scholar
  7. Laing, M.: Patterns in the periodic table – old and new. In: Rouvray, D.H., King, R.B. (eds.) The Periodic Table: Into the 21st Century, pp. 123–140. Research Studies Press, Baldock, UK (2004)Google Scholar
  8. Löwdin, P.-O.: Some comments on the periodic system of the elements. Int. J. Quantum Chem., Quantum Chem. Symp. 3, 331–334 (1969)CrossRefGoogle Scholar
  9. Malkin, I.A., Man’ko, V.I.: Symmetry of the hydrogen atom. Sov. Phys. JETP Lett. 2, 146–148 (1965)Google Scholar
  10. Ostrovsky, V.N.: What and how physics contributes to understanding the periodic law. Found. Chem. 3, 145–182 (2001)CrossRefGoogle Scholar
  11. Oudet, X.: Valency, ionicity and electronic configuration in rare earths. J. Phys. (Paris) 40(C5), 395–397 (1979)CrossRefGoogle Scholar
  12. Pascal, P.: Nouveau traité de chimie minérale. Masson, Paris (1960)Google Scholar
  13. Rayner-Canham, G.W.: The richness of periodic patterns. In: Rouvray, D.H., King, R.B. (eds.) The Periodic Table: Into the 21st Century, pp. 161–186. Research Studies Press, Baldock, UK (2004)Google Scholar
  14. Rouvray, D.H., King, R.B.: The Periodic Table: Into the 21st Century. Research Studies Press, Baldock ,UK (2004)Google Scholar
  15. Rumer, Yu.B., Fet, A.I.: The group spin(4) and the Mendeleev system. Teoret. Mat. Fiz. 9, 203–210 (1971)Google Scholar
  16. Scerri, E.: Prediction of the nature of hafnium from chemistry, Bohr’s theory and quantum theory. Ann. Sci. 51, 137–150 (1994)CrossRefGoogle Scholar
  17. Scerri, E.: Commentary on Allen & Knight’s response to the Löwdin challenge. Found. Chem. 8, 285–293 (2006)CrossRefGoogle Scholar
  18. Scerri, E.: The Periodic Table: Its Story and Its Significance. Oxford University Press, New York, NY (2007)Google Scholar
  19. van Spronsen, J.W.: The Periodic System of Chemical Elements: A History of the First Hundred Years. Elsevier, Amsterdam (1969)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Université de Lyon, Institut de Physique Nucléaire, université Lyon 1 and CNRS/IN2P3Villeurbanne CedexFrance

Personalised recommendations