Chapter 12 - Topic 12E - Vibrational spectroscopy of polyatomic molecules - Exercises - Page 529: 12E.8(a)

--All nine vibration modes are Raman active. --All nine vibration modes except the one with A2 symmetry species are IR active. (If necessary, please right click the document attached below couples of times to download it to magnify it).

Step 1: If the symmetry species for particular vibration mode(s) of CH2Cl2 molecule has the same symmetry species as x, y and z at the right two columns of the C2v character table, the mode(s) is/are IR active. If the symmetry species for particular vibration mode(s)has the same symmetry species as xy, yz, xz, x2 ,y2, z2 ,x2-y2 , x2+y2 or x2+y2+z2, the mode(s) is/are Raman active. Step 2: Now at exercise 12E.7 (a) we find the symmetry species of the 9 vibration modes of CH2Cl2 are 4A1 + 1A2 + 2B1 + 2B2. According to the symmetry species for these 9 vibration modes, let’s also draw a diagram about the vibration motions for them shown in the answer part. Notice for a symmetry species, the motion remains unchanged under a symmetry operator giving character 1; the motion is reversed under a symmetry operator giving character -1. Step 3: According to the C2v character table shown below: the four vibration modes with A1 symmetry species, the two vibration modes with B1 symmetry species and the two vibration modes with B2 symmetry species are all IR active as they have the same symmetry species as x, y & z. All 9 vibration modes are Raman active because they all have the same symmetry species as xy, yz, xz, x2 ,y2 & z2 .