Point Group C2



C2 E C2
A 1 1
B 1 -1


Additional information

Number of symmetry elements h = 2
Number of classes, irreps n = 2
Abelian group yes
Optical Isomerism (Chirality) yes
Polar yes
Parity no


Reduce representation to irreducible representations


E C2



Genrate representation from irreducible representations


A B



Examples

Hydrogenperoxide 1,3-Dichloroallene Cyclopentane (half-chair)


Direct products of irreducible representations


Binary products
⊙ A B
A A
B BA

Ternary Products
Quaternary Products


Spherical harmonics and Multipoles
Symmetric Powers of Γxyz


Spherical Harmonics Yl / Multipole Symmetric Power [Γl(xyz)]
l 2l+1 Multipole Symmetry Rank [Γl(xyz)]
s (l=0) 1 Monopole A 1 A
p (l=1) 3 Dipole A⊕2B 3 A⊕2B
d (l=2) 5 Quadrupole 3A⊕2B 6 4A⊕2B
f (l=3) 7 Octupole 3A⊕4B 10 4A⊕6B
g (l=4) 9 Hexadecapole 5A⊕4B 15 9A⊕6B
h (l=5) 11 Dotricontapole 5A⊕6B 21 9A⊕12B
i (l=6) 13 Tetrahexacontapole 7A⊕6B 28 16A⊕12B
j (l=7) 15 Octacosahectapole 7A⊕8B 36 16A⊕20B
k (l=8) 17 256-pole 9A⊕8B 45 25A⊕20B
l (l=9) 19 512-pole 9A⊕10B 55 25A⊕30B
m (l=10) 21 1024-pole 11A⊕10B 66 36A⊕30B
n (l=11) 23 2048-pole 11A⊕12B 78 36A⊕42B
o (l=12) 25 4096-pole 13A⊕12B 91 49A⊕42B
More

First nonvanshing multipole: Dipole

Further Reading

  • A. Gelessus, W. Thiel, W. Weber. J. Chem. Educ. 72 505 (1995)
     Multipoles and symmetry



Ligand Field, dn term splitting


Term symbols for electronic configurations dn
dn Term Symbols
d1 = d9 2D
d2 = d8 1S, 1D, 1G, 3P, 3F
d3 = d7 2P, 2D (2), 2F, 2G, 2H, 4P, 4F
d4 = d6 1S (2), 1D (2), 1F, 1G (2), 1I, 3P (2), 3D, 3F (2), 3G, 3H, 5D
d5 2S, 2P, 2D (3), 2F (2), 2G (2), 2H, 2I, 4P, 4D, 4F, 4G, 6S


Term splitting in point group C2
L 2L+1 Term Splitting
S (L=0) 1 A
P (L=1) 3 A⊕2B
D (L=2) 5 3A⊕2B
F (L=3) 7 3A⊕4B
G (L=4) 9 5A⊕4B
H (L=5) 11 5A⊕6B
I (L=6) 13 7A⊕6B

Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement