On the reflection symmetries of atoms and diatomic molecules: derivation of Σ+ and Σ states in terms of the united atom and electron configuration

  • Koichiro YamakawaEmail author
  • Katsuyuki Fukutani
Regular Article


The reflection symmetries of atoms and diatomic molecules are discussed in detail. We introduce the classification of the atomic states in light of their transformational properties for reflection, and show the absence of the negative terms, namely S terms, in the one- and two-electron systems. The selection rule that no dipole transition occurs between S terms is readily derived using only the reflection symmetry. We also give an elementary proof of the rule on determining molecular Σ ± terms from atomic terms. Furthermore, based on the picture of the electron configuration in molecular orbitals, general functional forms of Σ ± states are shown. By using these forms, we derive the resultant Σ ± terms for the electron configurations that have not been treated previously, and make clear what causes the correlation between the reflection symmetry and spin multiplicity. The way shown in the present paper enables determination of Σ ± terms arising from any electron configuration.

Graphical abstract


Molecular Physics and Chemical Physics 


  1. 1.
    G. Herzberg, Molecular Spectra and Molecular Structure Vol.1: Spectra of Diatomic Molecules, 2nd edn. (Van Nostrand Reinhold Company, 1950)Google Scholar
  2. 2.
    E. Wigner, E.E. Witmer, Z. Physik 51, 859 (1928)CrossRefADSGoogle Scholar
  3. 3.
    P. Pechukas, R.N. Zare, Am. J. Phys. 40, 1687 (1972)CrossRefADSGoogle Scholar
  4. 4.
    Y.N. Chiu, J. Chem. Phys. 58, 722 (1972)CrossRefADSGoogle Scholar
  5. 5.
    V.P. Bellary, T.K. Balasubramanian, B.J. Shetty, Pramana 51, 445 (1998)CrossRefADSGoogle Scholar
  6. 6.
    K. Yamakawa, K. Fukutani, J. Phys. B 46, 085101 (2013)CrossRefADSGoogle Scholar
  7. 7.
    F. Hund, Z. Physik 63, 719 (1930)CrossRefADSGoogle Scholar
  8. 8.
    R.S. Mulliken, Rev. Mod. Phys. 4, 1 (1932)CrossRefADSGoogle Scholar
  9. 9.
    R.S. Mulliken, Phys. Rev. 32, 186 (1928)CrossRefADSGoogle Scholar
  10. 10.
    M. Kotani, Y. Mizuno, K. Kayama, J. Phys. Soc. Jpn 12, 707 (1957)CrossRefADSGoogle Scholar
  11. 11.
    B.F. Minaev, Spectrochim. Acta A 60, 1027 (2004)CrossRefADSGoogle Scholar
  12. 12.
    E.U. Condon, G. H. Shortley, The Theory of Atomic Spectra (Cambridge University Press, 1935)Google Scholar
  13. 13.
    K. Yamakawa, T. Sugimoto, K. Fukutani, Mol. Sci. 5, AC0014 (2011)Google Scholar
  14. 14.
    J. M. Hollas, Modern Spectroscopy (John Wiley and Sons, 4th ed., 2004)Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of PhysicsGakushuin UniversityTokyoJapan
  2. 2.Institute of Industrial ScienceThe University of TokyoTokyoJapan

Personalised recommendations