Selection Rules and Intensity Calculations for a Cs Asymmetric Top Molecule Containing a Methyl Group Internal Rotor

Abstract

A detailed discussion is presented of the relationships between four different molecular symmetry groups. i.e.. D 2, C s , C 3 v , and C ( m) 3 v commonly used to discuss energy level symmetry species and electric-dipole selection rules for internal rotor problems in molecules with a symmetric rotor top and a frame with a plane of symmetry. paying particular attention to confusion arising from the fact that the smaller groups are not always subgroups of the larger, and the groups are applied to different parts of the internal rotation problem (i.e., D 2 to pure rotation, C s to vibration-rotation, C 3 v and C ( m) 3 v to torsion-rotation). The meaning in this context of the traditional K a , K c labels for rotational energy levels in molecules with internal rotation is examined in detail. A discussion is also given of the relationship between three different schemes for defining a molecule-fixed axis system in internal rotation problems. i.e., the principal axis method, the internal axis method, and a hybrid method referred to here as the "rho axis method," paying particular attention to the meaning of a-type, b-type, and c-type transitions when using each of these axis systems. Some of the above ideas were helpful in adding intensity calculations to our earlier computer program treating internal rotation and overall rotation in acetaldehyde-like molecules, and these intensity calculations are also briefly discussed.