Point Group C
i
C
i
E
i
A
g
1
1
A
u
1
-1
Additional information
Number of symmetry elements
h = 2
Number of classes, irreps
n = 2
Abelian group
yes
Optical Isomerism (Chirality)
no
Polar
no
Parity
yes
Reduce representation to irreducible representations
E
i
Genrate representation from irreducible representations
A
g
A
u
Examples
1,2-Dibromo-1,2-dichloroethane (staggered)
Tartaric Acid (meso)
Direct products of irreducible representations
Binary products
⊙
A
g
A
u
A
g
A
g
A
u
A
u
A
g
Ternary Products
Quaternary Products
Spherical harmonics and Multipoles
Symmetric Powers of Γ
xyz
Spherical Harmonics Y
l
/ Multipole
Symmetric Power [Γ
l
(xyz)]
l
2l+1
Multipole
Symmetry
Rank
[Γ
l
(xyz)]
s (l=0)
1
Monopole
A
g
1
A
g
p (l=1)
3
Dipole
3A
u
3
3A
u
d (l=2)
5
Quadrupole
5A
g
6
6A
g
f (l=3)
7
Octupole
7A
u
10
10A
u
g (l=4)
9
Hexadecapole
9A
g
15
15A
g
h (l=5)
11
Dotricontapole
11A
u
21
21A
u
i (l=6)
13
Tetrahexacontapole
13A
g
28
28A
g
j (l=7)
15
Octacosahectapole
15A
u
36
36A
u
k (l=8)
17
256-pole
17A
g
45
45A
g
l (l=9)
19
512-pole
19A
u
55
55A
u
m (l=10)
21
1024-pole
21A
g
66
66A
g
n (l=11)
23
2048-pole
23A
u
78
78A
u
o (l=12)
25
4096-pole
25A
g
91
91A
g
More
First nonvanshing multipole:
Quadrupole
Further Reading
A. Gelessus, W. Thiel, W. Weber. J. Chem. Educ.
72
505 (1995)
Multipoles and symmetry
Ligand Field, d
n
term splitting
Term symbols for electronic configurations d
n
d
n
Term Symbols
d
1
= d
9
2
D
d
2
= d
8
1
S,
1
D,
1
G,
3
P,
3
F
d
3
= d
7
2
P,
2
D (2),
2
F,
2
G,
2
H,
4
P,
4
F
d
4
= d
6
1
S (2),
1
D (2),
1
F,
1
G (2),
1
I,
3
P (2),
3
D,
3
F (2),
3
G,
3
H,
5
D
d
5
2
S,
2
P,
2
D (3),
2
F (2),
2
G (2),
2
H,
2
I,
4
P,
4
D,
4
F,
4
G,
6
S
Term splitting in point group C
i
L
2L+1
Term Splitting
S (L=0)
1
A
g
P (L=1)
3
3A
g
D (L=2)
5
5A
g
F (L=3)
7
7A
g
G (L=4)
9
9A
g
H (L=5)
11
11A
g
I (L=6)
13
13A
g
Last update November, 13
th
2023 by A. Gelessus,
Impressum
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