Teaching CSIR NET Mock Test Series Chemical Sciences Chemical Applications of Group Theory Character Tables & Selection Rules
Consider a matrix representation A of the water molecule in the basis {V̅1,V̅2}.where, V̅1 and V̅2, are the bond vectors along the two O-H bonds. Consider another matrix representation B of the same molecule in a new basis set {U̅1, U̅2}, such that \(\rm \bar U_1=\frac{1}{\sqrt2}(\bar V_1+\bar V_2), \bar U_2=\frac{1}{\sqrt2}(\bar V_1-\bar V_2)\) The character table for C2v point group is given below :
| E | C2 | σv(x, z) | σv (y, z) | |
| A1 | 1 | 1 | 1 | 1 |
| A2 | 1 | 1 | -1 | -1 |
| B1 | 1 | -1 | 1 | -1 |
| B2 | 1 | -1 | -1 | 1 |
The irreducible representations that contribute to B are
1
A1 and B1
2
A1 and B2
3
A2 and B1
4
A1 and A2