Decomposed into the irreducible ones:
3A 1 þ 2 E
In order to apply the projection operator, the following transformation table is
compiled
Transformation table of the base functions
C 3v
E
C3
C3
2
rv(H5)
rv(H6)
rv(H7)
u 1
u 1
u 1
u 1
u 1
u 1
u 1
u 2
u 2
ðÀ1=2 u 2 À
p
3=2 u 3 Þ
ð À 1=2 u 2 þ
p
3=2 u 3 Þ
u 2
ðÀ1=2 u 2 þ
p
3=2 u 3 Þ
ð À 1=2 u 2 À
p
3=2 u 3 Þ
u 3
u 3
ð
p
3=2 u 2 À 1=2 u 3 Þ
ð À
p
3=2 u 2 À 1=2 u 3 Þ
À u 3
ð
p
3=2 u 2 þ 1=2 u 3 Þ
ð À
p
3=2 u 2 þ 1=2 u 3 Þ
u 4
u 4
u 4
u 4
u 4
u 4
u 4
u 5
u 5
u 6
u 7
u 5
u 7
u 6
u 6
u 6
u 7
u 5
u 7
u 6
u 5
u 7
u 7
u 5
u 6
u 6
u 5
u 7
By using the projection operator, applied to either not degenerate or degenerate
representations (A 1 and E), the following symmetry orbitals are obtained.
2A 1 ¼ u 1 þ u 5 þ u 6 þ u 7
1E x ¼ Àu 2 À 2u 5 þ u 6 þ u 7
1E y ¼ u 3 þ u 6 À u 7
1e x
1e y
34
2 Symmetry Orbitals for Different Bis and Polyatomic Molecules