Reduction of lower symmetry terms to cos 3τ′ and sin 3τ′ for vibration-internal rotation-overall rotation interactions in −XY3 molecules

In the calculation of the St, StSt, dependence of the inertia tensor and the St, dependence of the Coriolis coupling for internal rotation in −XY3 molecules, terms of lower symmetry than cos 3τ and sin 3τ appear when curvilinear internal coordinates are used for the internal rotation and other vibrations. This paper shows how these lower symmetry terms are reduced to zero after transformation to symmetry coordinates for the internal rotation and other vibrations.