Classification of atomic states by geometrical and quantum-mechanical symmetries

Abstract

The eigenstates of nonrelativistic two-, three-, four-, and six-valence-electron atoms are classified according to their transformation properties under symmetry operations. In energy-favorable geometrical arrangements of the electrons, the spatial distribution of the wave function is constrained by the demand of invariance under rotation, inversion and permutation of particles. For a given term, the symmetry constraints may leave the energy-favorable arrangement accessible or inaccessible. In the latter case the term is not expected to belong to the low-energy part of the spectrum. Contrary, in the former case with no symmetry-induced inherent nodal surface in the multidimensional coordinate space of the multielectron wave function, the term is expected to belong to the low-energy part of the spectrum. The symmetry-based classification is confirmed by recent calculations.