Question

By considering the effect of each symmetry operation
of the D3h point group on the symmetric deformation
mode shown in Fig. 3.14, confirm that this mode has
A2’’ symmetry.

Symmetric stretch 4.7 IR inactive Symmetric deformation IR active (49cm ) Asymmetric stretch IR active 19cm Doubly degenerate mode Asymmetric deformation (E) IR active (Mem') Doubly degenerate mode Fig. 3.14 The vibrational moxdes of SO, D k only three are IR active. The + and holation is used to show the up and down motion of the atoms during the mode of vibration. Two of the modes are doubly degenerate, giving a total of six nomal modes of vibration

Answer 1

The molecule So, ('heavy water') belongs to the D, point group. The character table for the Da point group is as given below. Ds. | E | 20 | 3C | o | 25s | E |2 | -1 | |2 | -1 To | | T | TIT | | || 1 10 | 1|1|

The symmetric deformation mode is as shown below In the above figure, the plus and minus signs shows the 'up' and 'down' motion of the atoms during the symmetric deformation mode.

Consider the symmetric deformation mode in the SO molecule. Perform the symmetry operations on the molecule and determine the effect of the symmetry operations on the symmetric deformation mode. List the observations as summarized in the following characters row. E 2C, 3C, 25, 30, -1 -1 -1 1 The above characters row is same as the characters row for A," in the character table for the D point group as shown below. Therefore, the symmetric deformation mode has A," symmetry.