In the particular case of C 2 rotation, the matrix becomes
À1
0 0
0 À1 0
0
0 1
2
4
3
5
The multiplication of two symmetry operations can be associated to the multiplication of the corresponding matrices
r xz  r xz ¼ E
1
0 0
0 À1 0
0
0 1
2
4
3
5
1
0 0
0 À1 0
0
0 1
2
4
3
5 ¼
1 0 0
0 1 0
0 0 1
2
4
3
5
1.6 Irreducible Representations
Let us consider a molecule belonging to C 2v symmetry group (e.g., H 2 O) and the
matrices representing the group operations based on the three Cartesian coordinates
E C 2 r xz r yz
σ xz
σ yz
C 2
E
Local Cartesian coordinates in H 2 O
16
1 The Electronic Structure Determination
À1
0 0
0 À1 0
0
0 1
2
4
3
5
The multiplication of two symmetry operations can be associated to the multiplication of the corresponding matrices
r xz  r xz ¼ E
1
0 0
0 À1 0
0
0 1
2
4
3
5
1
0 0
0 À1 0
0
0 1
2
4
3
5 ¼
1 0 0
0 1 0
0 0 1
2
4
3
5
1.6 Irreducible Representations
Let us consider a molecule belonging to C 2v symmetry group (e.g., H 2 O) and the
matrices representing the group operations based on the three Cartesian coordinates
E C 2 r xz r yz
σ xz
σ yz
C 2
E
Local Cartesian coordinates in H 2 O
16
1 The Electronic Structure Determination