Chemistry Reference
In-Depth Information
Table 12.7
Reducible representation
G
and symmetry-adapted AOs for NH
3
C
3
C
3
C
3v
I
s
1
s
2
s
3
Symmetry
basis
1
A
1
1
1
1
1
1
1
k
;
s
;
z
;
h
z
¼
p
ð
h
1
þ
h
2
þ
h
3
Þ
A
2
1
1
1
1
1
1
<
:
1
x
;
h
x
¼
p ð
2h
1
h
2
h
3
Þ
cs
s
c
10
0
c s
sc
cs
sc
10
01
s
E
1
1
c
s
c
y
;
h
y
¼
p ð
h
1
h
2
Þ
A
1
E
x
E
y
G
8
2
2
4
4
4
G
¼
4
; G
¼
2
; G
¼
2
convenient, therefore, to use at once the full projector (12.29), as we shall
show in detail below.
A
1
A
1
A
1
P
k
¼
k P
P
A
1
:
s
¼
s
z
¼
z
1
6
ð
x
cx
sy
cx
þ
sy
þ
x
cx
sy
cx
þ
sy
Þ¼
0
A
1
P
x
¼
1
6
ð
y
þ
sx
cy
sx
cy
y
sx
þ
cy
þ
sx
þ
cy
Þ¼
0
A
1
P
y
¼
1
6
ð
2h
1
þ
2h
2
þ
2h
3
Þ¼
1
3
ð
h
1
þ
h
2
þ
h
3
Þ)
1
A
1
P
h
1
¼
p ð
h
1
þ
h
2
þ
h
3
Þ
Table 12.8
Transformation table of the AO basis for NH
3
under the operations
of C
3v
R
x
þ
3
3
I
s
1
s
2
s
3
C
C
k
k
k
k
k
k
k
s
s
s
s
s
s
s
z
z
z
z
z
z
z
x
x
cx
þ
sy
cx
þ
sy
x
cx
þ
sy
cx
þ
sy
y
y
sx
þ
cy
sx
þ
cy
y
sx
þ
cy
sx
þ
cy
h
1
h
1
h
3
h
2
h
1
h
3
h
2
h
2
h
2
h
1
h
3
h
3
h
2
h
1
h
3
h
3
h
2
h
1
h
2
h
1
h
3
