Skip to main content
SpringerLink
Log in

Non-periodic table of periodicities and periodic table with additional periodicities: tetrad periodicity

  • Published:
Foundations of Chemistry Aims and scope Submit manuscript

Abstract

This manuscript aims to systematically consider the main periodicity and additional (secondary, internal, and tetrad) periodicities using a uniform approach. The main features are summarized in table form. The history of the origin and development of these concepts is discussed. It is described how these periodicities manifest themselves and how they are determined at the experimental and theoretical levels. Areas of manifestation of these periodicities are outlined. As the general approach to explaining internal periodicity, attention is drawn to the symmetry of the quantum number S of atoms and the principle of equivalence of electrons and holes. Arguments are presented in favor of a more correct classification of the tetrad effect as tetrad periodicity, and an overview of this regularity is provided. A small modification of the conventional Periodic table is proposed, which reflects all the mentioned periodicities.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Notes

  1. Where n is the principal quantum number, and l is the orbital quantum number.

  2. In modern variants (Table 1), there are no subgroups in periodic tables, subgroups correspond to groups.

  3. Therefore, sometimes absence of "primogenic repulsion" is mentioned instead of the term "kainosymmetry" (Pyykkö 1988,2001, p. 567). The emphasis on the absence of a radial nodes is made in some publications (Shchukarev 1977; Kaupp 2007).

  4. According to modern terminology, "secondary periodicity is observed in all groups".

  5. This version has been criticized (Fidelis 1976).

  6. See “internal periodicity” above for single repetition.

  7. In this area, unusual designations are adopted: 1 and 3 for E are not degrees, but ordinal numbers.

References

  • Aravena, D., Atanasov, M., Neese, F.: Periodic trends in lanthanide compounds through the eyes of multireference ab initio theory. Inorg. Chem. 55, 4457–4469 (2016)

    Article  Google Scholar 

  • Basolo, F., Pearson, R.G.: Mechanisms of Inorganic Reactions: A Study of Metal Complexes in Solution, 2nd edn. Wiley, New York (1967)

    Google Scholar 

  • Biltz, W., Klemm, W.: Die Unterteilung der Reichen der Übergangselemente. Ztsch. Elektrochem. 39, 597–598 (1933)

    Google Scholar 

  • Biron, E.V.: Phenomena of secondary periodicity. Zh. Russ. Fiz.-Khim. Obshch. Ch. Khim. 47, 964–988 (1915). (in Russian)

    Google Scholar 

  • Brauner, B.: Über die Stellung der Elemente der seltenen Erden im periodischen System. Z. Elektrochem. 14, 525–527 (1908)

    Article  Google Scholar 

  • Chistyakov, V.M.: “Secondary Periodicity of Biron” in secondary d-subgroups of the short periodic table. Zh. Obshch. Khim. 38, 209–210 (1968). (in Russian)

    Google Scholar 

  • Drits M.E. (edn): Properties of Elements, Handbook, 3rd edn., vol 1, pp. 21, 23. Ruda i Metally, Moscow (2003). (in Russian)

  • Drozdov, A.A., Zlomanov, V.P., Mazo, G.N., Spiridonov, F.M.: Inorganic Chemistry. Edn. Yu. D. Tret'yakov, Vol. 3: Chemistry of transition elements, Book 2. Akademiya, Moscow. 400 pp. (2007). (in Russian)

  • Dunn, T. M.: Modern Coordination Chemistry. In: Lewis J., Wilkins R. G., Interscience Publ., Inc., New York, p. 286 (1960)

  • Fidelis, I., Siekierski, S.: The regularities in stability constants of some rare earth complexes. J. Inorg. Nucl. Chem. 28, 185–188 (1966)

    Article  Google Scholar 

  • Fidelis, I.: Double-double effect of the inner transition elements. Bull. Acad. Polon Ser. Sci. Chim. 18, 681–683 (1970)

    Google Scholar 

  • Fidelis, I., Siekierski, S.: On the regularities or tetrad effect in complex formation by ƒ-electron elements. A double-double effect. J. Inorg. Nucl. Chem. 33, 3191–3194 (1971)

    Article  Google Scholar 

  • Fidelis, I.: Why the idea of “inclined W” plots of Sinha cannot be correct The correlation between the double-double effect and the sequence of the L-quantum numbers. Inorg. Nucl. Chem. Lett. 12, 475–483 (1976)

    Article  Google Scholar 

  • Fidelis, I.K., Mioduski, T.J.: Double-double effect of the inner transition elements. In: Ferrites. Transitions Elements Luminescence. Structure and Bonding. vol. 47, pp. 27–51 (1981)

  • Filippov, G.G., Gorbunov, A.I.: On the formulation of the Periodic law of D I. Mendeleev. Zh. Fiz. Khim. 72, 1334–1336 (1998). (in Russian)

    Google Scholar 

  • Frackiewicz, K., Czerwinski, M., Siekierski, S.: Secondary periodicity in the tetrahalogeno complexes of the group 13 elements. Eur. J. Inorg. Chem. 19, 3850–3856 (2005)

    Article  Google Scholar 

  • Friedman, H.G., Jr., Choppin, G.R., Feuerbacher, D.G.: The shapes of the f orbitals. J. Chem. Educ. 41, 354–358 (1964)

    Article  Google Scholar 

  • Fuks, L., Majdan, M.: Features of solvent extraction of lanthanides and actinides. Min. Process. Extr Metullargy Rev. 21, 25–48 (2000)

    Article  Google Scholar 

  • Gurin, V.E.: Element property diagrams of a new form and the phenomenon of secondary periodicity. Zh. Obshch. Khim. 64, 367–370 (1994). (in Russian)

    Google Scholar 

  • Gusev A.I.: Petrology of adakite granitoid. Chapter 6. Lantanide Tetrad Effect (2014). Accessed 21 August 2021 (in Russian) https://monographies.ru/ru/book/view?id=242

  • Habashi, F: The Periodic Table & Mendeleev. Laval University. Quebéc City, Canada. p. 218 (2017)

  • Imyanitov, N.S.: New basis for describing periodicity. Zh. Obshch. Khim. 80, 69–72 (2010a). (in Russian)

    Google Scholar 

  • Imyanitov, N.S.: New basis for describing periodicity. Russ. J. Gen. Chem. 80, 65–68 (2010b)

    Article  Google Scholar 

  • Imyanitov, N.S.: Application of a new formulation of the periodic law to predicting the proton affinity of elements. Russ. J. Inorg. Chem. 56, 745–748 (2011a)

    Article  Google Scholar 

  • Imyanitov, N.S.: Application of a new formulation of the periodic law to predicting the proton affinity of elements. Zh. Neorg. Khim. 56, 795–798 (2011b). (in Russian)

    Google Scholar 

  • Imyanitov, N.S.: The periodic law. Formulations, equations, graphic representations. Russ. J. Inorg. Chem. 56, 2183–2200 (2011c)

    Article  Google Scholar 

  • Imyanitov, N.S.: Adequacy of the new formulation of the Periodic Law when fundamental variations occur in blocks and periods. Found. Chem. 16, 235–247 (2014)

    Article  Google Scholar 

  • Imyanitov, N.S.: Spiral as the fundamental graphic representation of the Periodic Law. Blocks of elements as the autonomic parts of the Periodic System. Found. Chem. 18, 153–173 (2016)

    Article  Google Scholar 

  • Imyanitov, N.S.: Does the period table appear doubled? Two variants of division of elements into two subsets. Intern. Second. Period. Found. Chem. 21, 255–284 (2019a)

    Article  Google Scholar 

  • Imyanitov, N.S.: Periodic law: new formulation and equation description. Pure Appl. Chem. 91, 2007–2021 (2019b)

    Article  Google Scholar 

  • Imyanitov, N.S.: Periodic Tables for cations +1, +2, +3 and anions -1. Quantitative characteristics for manifestations of internal periodicity and kainosymmetry. Found. Chem. 24, 189–219 (2022)

  • Ionova, G.V., Pershina, V.G., Spitsin, V.I.: Electronic Structure of Actinides, p. 232. Nauka, Moscow (1986). (in Russian)

    Google Scholar 

  • Ionova, G.V., Vokhmin, V.G., Spitsin, V.I.: Regularities of Changes in the Properties of Lanthanides and Actinides, p. 240. Nauka, Moscow (1990). (in Russian)

    Google Scholar 

  • Ivanova V.A.: Geochemical features of rare earth element spectra in sediments … Dissertation. VNII Oceanology, Sankt-Petersburg (2019). (in Russian). Accessed 28 August 2021 http://www.igc.irk.ru/images/Dissovet/Doctoral_dissertation/Ivanova_V.V/ivanova_diss.pdf

  • Janes, R., Moore, E.A.: Metal-Ligand Bonding. Roy. Soc. Chem. Bath Press, Glasgow (2004)

    Google Scholar 

  • Jerabek, P., Schuetrumpf, B., Schwerdtfeger, P., Nazarewicz, W.: Electron and nucleon localization functions of oganesson: approaching the thomas-fermi limit. Phys. Rev. Lett. 120, 053001 (2018)

    Article  Google Scholar 

  • Johnson, D.A.: Inter-electron repulsion and irregularities in the chemistry of transition series. In: Meyer, G., Naumann, D., Wesemann, L. (eds.) Inorganic Chemistry in Focus III, pp. 1–13. Wiley-VCH Verlag GmbH & Co., Weinheim (2006)

    Google Scholar 

  • Jørgensen, C.K.: The “Tetrad effect” of Peppard is a variation of the nephelauxetic ratio in the third decimal. J. Inorg. Nucl. Chem. 32, 3127–3128 (1970)

    Article  Google Scholar 

  • Kaupp, M.: The role of radial nodes of atomic orbitals for chemical bonding and the periodic table. J. Comput. Chem. 28, 320–325 (2007)

    Article  Google Scholar 

  • Kiselev, Y.M.: On regularities in the rare earth series. Zh. Neorg. Khim. 39, 1266–1276 (1994). (in Russian)

    Google Scholar 

  • Kiselev, Y.M.: Chemistry of Coordination Compounds, 2nd edn., pp. 263–268. MGU, Moscow (2021). (in Russian)

    Google Scholar 

  • Klemm, V.: Hundred Year System of Periods of Chemical Elements. In: Semenov, N. N. (eds) Sto Let Period. Zakona Khim. Elem., Dokl. S’ezda., Yubileinyi Mendeleev. S’ezd, 10th. pp. 57–70. Nauka, Moscow (1969). (in Russian)

  • Korableva, T.P., Korol’kov, D.V.: Theory of the periodic system, p. 176. Izd-vo SPbU, St. Petersburg (2005). (in Russian)

    Google Scholar 

  • Korol’kov, D.V., Skorobogatov, G.A.: Theoretical Chemistry, 2nd edn., p. 84. Izd-vo SPbU, St. Petersburg (2005). (in Russian)

    Google Scholar 

  • Kramida, A., Ralchenko, Y., Reader, J., NIST ASD Team.: NIST Atomic Spectra Database (ver. 5.2), Ground States and Ionization Energies (Online). National Institute of Standards and Technology, Gaithersburg, MD. http://physics.nist.gov/PhysRefData/ASD/ionEnergy.html (2014). Accessed 22 March 2017

  • Leach, M.R. (Curator): The Chemogenesis web book, The INTERNET Database of Periodic Tables (1951). http://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=24. Accessed 22 Sept 2021

  • Lima-De-Faria, A.: Periodic Tables Unifying Living Organisms at the Molecular Level: The Predictive Power of the Law of Periodicity, p. 311. World Scientific, New Jersey (2017)

    Google Scholar 

  • Magomedov, M.N.: The correlation of the parameters of interatomic interaction in crystals with the position of atom in the periodic table. High Temp. 46, 484–494 (2008)

    Article  Google Scholar 

  • Melnikov, V.P., Dmitriev, I.S.: Additional Types of Periodicity in the D. I. Mendeleev’s Periodic System, p. 95. Nauka, Moscow (1988). (in Russian)

    Google Scholar 

  • Meyer, R.J., Hauser, O.: Die Analyse der seltenen Erden und der Erdsäuren. Enke, F., Stutgart 320 S (1912)

  • Meyer, R.J.: Die Stellung der Elemente der seltenen Erden im periodischen System. Naturwissenschaften 2, 781–787 (1914)

    Article  Google Scholar 

  • Mioduski, T.: The “Regular” and “Inverse” Tetrad Effect. Comments Inorg. Chem. 19, 93–119 (1997)

    Article  Google Scholar 

  • Morozova, M.P., Li, M.-S., Golomolzina, M.V.: The enthalpy of formation of strontium compounds with elements of the main subgroup of the IV group. Vestn. Leningr. Gos. Un-Ta 10–2, 83–86 (1959). (in Russian)

    Google Scholar 

  • Nefedov, V.I., Trzhaskovskaya, M.B., Yarzhemskii, V.G.: Electronic configurations and the periodic table for superheavy elements. Dokl. Phys. Chem. 408, 149–151 (2006)

    Article  Google Scholar 

  • Neubert, D.: double shell structure of the periodic system of the elements. Z. Naturforsch. 25a, 210–217 (1970)

    Article  Google Scholar 

  • Nugent, L.J.: Theory of the tetrad effect in the lanthanide(III) and actinide(III) series. J. Inorg. Nucl. Chem. 32, 3485–3491 (1970)

    Article  Google Scholar 

  • Odabasi, H.: Some evidence about the dynamical group SO (4, 2) symmetries of the periodic table of elements. Int. J. Quantum Chem. Symp. 7, 23–33 (1973)

    Article  Google Scholar 

  • Ostrovsky, V.N.: Dynamic symmetry of atomic potential. J. Phys. B 14, 4425–4439 (1981)

    Article  Google Scholar 

  • Peppard, D.F., Mason, G.W., Lewey, S.: Di n-octyl phosphinic acid as a selective extractant for metallic cations Selected M(III) and M(VI) tracer studies. J. Inorg. Nucl. Chem. 27, 2065–2073 (1965)

    Article  Google Scholar 

  • Peppard, D.F., Mason, G.W., Lewey, S.: A tetrad effect in the liquid-liquid extraction ordering of lanthanides (III). J. Inorg. Nucl. Chem. 31, 2271–2272 (1969)

    Article  Google Scholar 

  • Pyykkö, P., Desclaux, J.P.: Relativity and the periodic system of elements. Acc. Chem. Res. 12, 276–281 (1979)

    Article  Google Scholar 

  • Pyykkö, P.: Relativistic effects in structural chemistry. Chem. Rev. 88, 563–594 (1988)

    Article  Google Scholar 

  • Pyykkö, P., Zhao, Y.-F.: The elements of Flatland: Hartree-Fock atomic ground states in two dimensions for Z = 1–24. Int. J. Quantum Chem 40, 527–544 (1991)

    Article  Google Scholar 

  • Pyykkö, P.: A note on nodal structures, partial screening, and periodic trends among alkali metals and alkaline earths. Int. J. Quantum Chem. 85, 18–21 (2001)

    Article  Google Scholar 

  • Pyykkö, P.: A suggested periodic table up to Z ≤ 172, based on Dirac–Fock calculations on atoms and ions. Phys. Chem. Chem. Phys. 13(1), 161–168 (2011)

    Article  Google Scholar 

  • Pyykkö, P.: An essay on periodic tables. Pure Appl. Chem. 91, 1959–1967 (2019)

    Article  Google Scholar 

  • Restrepo, G.: Challenges for the periodic systems of elements: chemical, historical and mathematical perspectives. Chem. Eur. J. 25, 15430–15440 (2019)

    Article  Google Scholar 

  • Scerri, E.: Books on the Elements and the Periodic Table. Accessed 9 Febr. 2022. Archived from the original on 11 August 2020. Retrieved 9 July 2018. web.archive.org/web/20200811052254/ http://www.ericscerri.com/books_elements.pdf

  • Scerri, E.R.: The Periodic Table: Its Story and its Significance, 2nd edn. Oxford University Press, New York, N.Y (2019)

    Book  Google Scholar 

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

    Article  Google Scholar 

  • Shchukarev, S.A.: D I Mendeleev’s periodic law as a basic principle of modern chemistry. Zh. Obshch. Khim. 24, 581–592 (1954). (in Russian)

    Google Scholar 

  • Shchukarev, S.A.: Modern significance of D. I. Mendeleev’s periodic law and prospects for development. In: Semenov, N. N. (edn) Sto Let Period. Zakona Khim. Elem., Dokl. na Plenarnykh Zased., Yubileinyi Mendeleev. S’ezd, 10th. pp. 40–53. Nauka, Moscow (1971). (in Russian)

  • Shchukarev, S.A.: New views of D.I. Mendeleev’s system. I. Periodicity of the stratigraphy of atomic electronic shells in the system, and the concept of kainosymmetry. Zh. Obshch. Khim. 47, 246–259 (1977)

    Google Scholar 

  • Shchukarev, S.A., Vasil’kova, I.V.: The phenomenon of secondary periodicity on the example of magnesium compounds with elements of the main subgroup of the IV group in the D.I. Mendeleev system. Vestn. Leningr. Gos. Un-Ta. 2–1, 115–120 (1953)

    Google Scholar 

  • Shchukarev, S.A., Morozova, M.P., Prokof’eva, E.A.: Higher barium phosphides. Zh. Obshch. Khim. 24, 1261–1262 (1954a)

    Google Scholar 

  • Shchukarev, S.A., Morozova, M.P., Prokof’eva, E.A.: Higher barium phosphides. Zh. Obshch. Khim. 24, 1277–1278 (1945b). (in Russian)

    Google Scholar 

  • Shchukarev, S.A., Grossman, G., Morozova, M.P.: The enthalpy of formation of zinc phosphide, Zn3P2. Zh. Obshch. Khim. 25, 607–608 (1955a)

    Google Scholar 

  • Shchukarev, S.A., Grossman, G., Morozova, M.P.: The enthalpy of formation of zinc phosphide, Zn3P2. Zh. Obshch. Khim. 25, 633–634 (1955b). (in Russian)

    Google Scholar 

  • Shriver, D.F., Atkins, P.W.: Inorganic Chemistry, 5th edn., p. 851. Oxford University Press, Oxford (2010)

    Google Scholar 

  • Siekierski, S.: Ionic Radii: effect of shell radius, cation charge and lone electron pair. Commun. Inorg. Chem. 19, 121–131 (1997)

    Article  Google Scholar 

  • Sinha, S.P.: Gadolinium Break, tetrad and double-double effects were here, what next?? Helv. Chim. Acta 58, 1978–1983 (1975)

    Article  Google Scholar 

  • Sinha, S.P.: Inclined W Systematics of the Lanthanides. In: Sinha, S.P. (ed.) Systematics and the properties of the lanthanides, pp. 71–123. Reidel, Dordrecht (1983)

    Chapter  Google Scholar 

  • Spitsyn, V.L., Vohmin, V.G., Ionova, G.V.: Regularities in f-element properties. Intern. Rev. Phys. Chem. 4, 57–80 (1985)

    Article  Google Scholar 

  • Thomsen, J.: Systematishe Durchtfuhrung thermochemischer Untersuchunden. S. 152. 160, 171. F. Enke, Stuttgart (1906)

  • Trifonov, D.N.: Afterword of the editor. In: Mel’nikov, V.P., Dmitriev, I.S.: Additional types of periodicity in the D. I. Mendeleev’s periodic system. pp. 83–93. Nauka, Moscow (1988). (in Russian)

  • Vassiliev, V.P., Lysenko, V.A., Gaune-Escard, M.: Relationship of thermodynamic data with Periodic Law. Pure Appl. Chem. 91, 879–893 (2019)

    Article  Google Scholar 

  • Vodyanitskii, Y.N.: Geochemical fractionation of lanthanides in soils and rocks: a review of publications. Eurasian Soil Sci. 45(1), 56–67 (2012)

    Article  Google Scholar 

  • Wang, S.-G., Schwarz, W.H.E.: Icon of chemistry: the periodic system of chemical elements in the new century. Angew. Chem. Int. Ed. 48, 3404–3415 (2009)

    Article  Google Scholar 

Download references

Acknowledgements

The author is very grateful to Yu.V. Gankin and E.N. Imyanitov for the editing of the English text of the article. I also gratefully acknowledge discussions with W. H. Eugen Schwarz.

Author information

Authors and Affiliations

  1. All-Russian Research Institute of Petrochemical Processes, Ul. Bryantseva, 18, kv. 155, St. Petersburg, 195269, Russia

    Naum S. Imyanitov

Authors
  1. Naum S. Imyanitov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Naum S. Imyanitov.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Imyanitov, N.S. Non-periodic table of periodicities and periodic table with additional periodicities: tetrad periodicity. Found Chem 24, 331–358 (2022). https://doi.org/10.1007/s10698-022-09437-8

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10698-022-09437-8

Keywords

Search

Navigation