1
Improper Rotations S3 for D3h
•
S3
6=E
and thus six operations need to be examined
• The first operation
S3
1
was given to you in the lecture notes, Figure 1:
C3
σh
C3
σh
C3
σh
C3
1
σ
h
1
rotation reflection
S3
1
Figure 1 Components of
S3
1
improper rotation
• The operations up to
S3
3
were also given in the lecture notes Figure 2 and it was established that
S3
3=
σ
h
1
• from this diagram (Figure 2) it can also be seen that
S3
2=C3
2
C3
σh
S3
1
S3
3
S3
3=
σ
h
1
S3
2
σ
h
1
Figure 2
S3
3
operation of the D3h point group
• the full set of operations is shown in the diagram below, Figure 3:
C3
σh
S3
1
S3
2
S3
3
S3
5
S3
4
C3
σh
S3
6
Figure 3 The full set of operations for S3
• from this diagram it is can be seen that
S3
4=C3
1
• thus the only unique operations are
S3
1
and
S3
5
and hence there are only 2 unique S3 operations in
the D3h point group.
S3
1
S3
2=C3
2
S3
3=
σ
h
1
S3
4=C3
1
S3
5
S3
6=E
