Eur. Phys. J. D (2015) 69: 175
https://doi.org/10.1140/epjd/e2015-60142-4

Regular Article

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

¹ Department of Physics, Gakushuin University, 1-5-1 Mejiro, Toshima-ku, 171-8588 Tokyo, Japan
² Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, 156-8505 Tokyo, Japan

^a e-mail: koichiro.yamakawa@gakushuin.ac.jp

Received: 3 March 2015
Received in final form: 23 May 2015
Published online: 19 July 2015

Abstract

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.