3. (a) Using x, y, z vectors of each atom in aSO2molecule to derive the reducible representation(assuming that the principle axis is collinear with the z axis andthe molecule is lying on the xz plane).
(b) Classify the irreducible representations into translational,rotational, and vibrational modes.
(c) Which vibrational modes are infrared active.
(d) Sketch the three vibrational modes including the symmetricstretch, antisymmetric stretch, and symmetric bend.
(e) The calculated IR spectrum of SO2show three peaksat 1362 cm-1, 1151 cm-1, and 518cm-1. Provide a symmetric label for each of these threepeaks, provided that the two stretch modes occur at much higherwavenumbers than the bend mode andthat the antisymmetricstretch occurs at higher wavenumber than the symmetric stretch.
