Chemistry Reference
In-Depth Information
(C
xyz
3
(C
2
)
I
(
D
2
basis, Fig.
D.2
)
D
(C
5
)
D
)
D
⎛
⎞
⎛
⎞
⎛
⎞
φφ
−
1
φφ
−
1
1
−
001
100
010
−
100
0
⎝
⎠
⎝
⎠
⎝
⎠
1
2
|
T
1
x
,
|
T
1
y
,
|
T
1
z
−
1
10
001
−
φ
−
1
1
φ
⎛
⎞
⎛
⎞
⎛
⎞
φ
−
1
1
−
φ
001
100
010
−
100
0
⎝
⎠
⎝
⎠
⎝
⎠
1
2
φ
−
1
|
T
2
x
,
|
T
2
y
,
|
T
2
z
−
−
φ
−
1
10
001
−
φ
−
1
−
φ
1
−
√
5
√
5
√
5
⎛
⎝
⎞
⎠
⎛
⎝
⎞
⎠
⎛
⎝
⎞
⎠
−
1
−
1000
0001
0100
0001
10 00
0
√
5
−
−
−
−
3
1
1
100
00
1
4
√
51
|
G
a
,
|
G
x
,
|
G
y
,
10
00 01
−
−
13
|
G
z
−
√
5
−
1
−
31
I
|
Hθ
,
|
H
,
|
Hξ
,
|
Hη
,
|
Hζ
D
(C
xyz
3
D
(C
2
)
D
(C
5
)
)
⎛
⎝
⎞
⎠
√
3
4
⎛
⎝
√
3
2
⎞
⎠
1
4
1
√
8
1
1
√
8
⎛
⎝
⎞
⎠
−
−
√
2
−
1
−
2
−
000
10 0
0 0
√
3
4
√
3
√
8
√
3
√
8
√
3
2
1
4
−
−
0
−
01 0
0 0
1
2
000
00001
00100
00010
−
√
3
00
100
00 0
−
1
1
2
1
2
−
0
√
8
√
8
−
10
1
√
2
1
2
1
2
0
−
0
√
3
√
8
00 0
0 1
1
√
8
1
2
1
2
0
−
|
H
components do not denote components that transform like the functions
d
z
2
and
d
x
2
It is important to note that in the Boyle and Parker basis the
|
Hθ
and
y
2
, but refer to linear combinations of these:
−
3
8
d
z
2
5
8
d
x
2
|
Hθ
=
+
y
2
−
5
8
d
z
2
3
8
d
x
2
|
H
=−
+
y
2
−
states to point-group
canonical bases for the case of the octahedral group. Similar tables for subduc-
tion to the icosahedral canonical basis have been published by Qiu and Ceulemans
[
8
]. Extensive tables of bases in terms of spherical harmonics for several branching
schemes are also provided by Butler [
9
].
Griffith has presented the subduction of spherical
|
JM
