A GROUP-THEORETICAL TREATMENT OF VIBRATIONAL, TORSIONAL, AND ROTATIONAL MOTIONS IN CH3—C≡C—SiH3

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Abstract
A set of coordinates is described for methylsilylacetylene which allows a separation of the molecular wave function into a vibrational part, a torsional part, and a rotational part. The transformation properties of these coordinates, and vibrational, torsional, or rotational wave functions containing them, are discussed in terms of a double group of the molecular symmetry group appropriate for the classification of the overall wave functions of the molecule. Particular attention is given to the symmetry properties of vibrational symmetry coordinates and normal modes, since these symmetry properties are rather different from those encountered in molecules without free internal rotation. An exact and an approximate rotational–torsional–vibrational kinetic-energy operator is derived. Selection rules on symmetry species and also on angular-momentum quantum numbers are presented for electric dipole transitions.

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