Groupe de dégénérescence de l'Hamiltonien de vibration–rotation des molécules toupies sphériques. Application à l'étude des moments de transition

Abstract

Symmetry properties, widely used for theoretical study of molecular energy levels or transition probabilities, are generally referred to the only invariance group of the molecule which is a group of isometrics in the frame of reference fixed with respect to the molecule. However, operators and wave functions of the purely rotational problem, and the transition operators have also symmetry properties related to the isometries of the laboratory frame of reference. We propose to take all those properties into account by introducing the molecular degeneracy group G × (F)O(3), where G is the invariance group of the molecular field and (F)O(3) is the group of rotations in the fixed frame of reference. In the case of spherical top molecules, the invariance group G of the molecular field can be extended, in a first approximation, to the complete rotation group (m)O(3), leading to the utilization of the chain [Formula: see text]. Using tensor techniques, we give general formulas for the calculation of transition moments for electrical dipole absorption processes (rotation–vibration and pure rotation) and Raman scattering.[Journal translation]