PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Atomic, Molecular & Optical Physics · Molecular structure and spectra
Deriving the Spectrum, Ch Polyatomic molecules: normal modes and symmetry
Problem
Carbon disulfide, S=C=S, is a linear centrosymmetric triatomic molecule (bond length RCS=1.554A˚), point group D∞h. It has three fundamental vibrations: a symmetric stretch in which the carbon atom stays still while the two sulfur atoms move outward and inward together in phase; an antisymmetric stretch in which the carbon moves opposite to the two sulfur atoms; and a doubly degenerate bend perpendicular to the molecular axis. The measured wavenumbers are 658cm−1 (symmetric stretch), 1535cm−1 (antisymmetric stretch) and 397cm−1 (bend).
((a)) Classify the three vibrations by symmetry species, using the inspection method used for carbon dioxide (the group D∞h has no finite reduction formula).
((b)) State which fundamentals are active in the infrared, which in the Raman spectrum, and whether any single fundamental is active in both.
((c)) For each infrared-active fundamental, predict whether its rotational fine structure is a parallel band or a perpendicular band.
((d)) State whether CS2 has an allowed pure rotational (microwave) spectrum, and give the reason.