Chemistry Reference
In-Depth Information
4.4 The tangential
π
-orbitals transform as
Γ
π
in the
C
5
v
site group of
I
h
. Accord-
ing to Sect.
C.2
, one has:
H
u
4.5 When the projector that generated the component is characterized as
P
Γ
i
Γ
π
C
5
v
↑
I
h
=
T
1
g
+
T
1
u
+
G
g
+
G
u
+
H
g
+
kl
,the
other components may be found by varying the
k
index.
4.6 Act with an operator
S
on the projector and carry out the substitution
R
=
S
−
1
T
:
R
R
11
=
S
1
S P
Γ
0
|
G
|
R
S R
1
1
=
P
Γ
0
11
T
=
=
|
G
|
|
G
|
T
4.7 Applying the inverse transformation to the SALCs of the hydrogens in ammo-
nia yields
⎛
⎝
⎞
⎠
1
√
3
1
√
3
1
√
3
|
sp
C
=
|
2
p
y
2
√
6
1
√
6
1
√
6
sp
A
|
sp
B
|
−
−
2
s
|
2
p
x
|
1
√
2
1
√
2
0
−
4.8 This mode transforms as
E
y
. It can be written as a linear combination of a
radial and a tangent mode:
Q
=
−
1
√
2
Q
ra
y
+
1
√
2
Q
tan
y
with
1
√
2
(R
B
−
R
C
)
Q
ra
y
=
1
√
6
R(
2
φ
A
−
Q
ta
y
=
φ
B
−
φ
C
)
This mode preserves the center of mass and is a genuine normal mode.
