Point Group Cs



Cs E σh
A' 1 1
A'' 1 -1


Additional information

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


Reduce representation to irreducible representations


E σh



Genrate representation from irreducible representations


A' A''




Examples

Hypochloric Acid Formylfluoride Sulfur S7
Acrolein Cyclopentane (envelope) Quinoline



Direct products of irreducible representations


Binary products
A' A''
A' A'
A'' A''A'

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 l(xyz)]
s (l=0) 1 Monopole A' 1 A'
p (l=1) 3 Dipole 2A'⊕A'' 3 2A'⊕A''
d (l=2) 5 Quadrupole 3A'⊕2A'' 6 4A'⊕2A''
f (l=3) 7 Octupole 4A'⊕3A'' 10 6A'⊕4A''
g (l=4) 9 Hexadecapole 5A'⊕4A'' 15 9A'⊕6A''
h (l=5) 11 Dotricontapole 6A'⊕5A'' 21 12A'⊕9A''
i (l=6) 13 Tetrahexacontapole 7A'⊕6A'' 28 16A'⊕12A''
j (l=7) 15 Octacosahectapole 8A'⊕7A'' 36 20A'⊕16A''
k (l=8) 17 256-pole 9A'⊕8A'' 45 25A'⊕20A''
l (l=9) 19 512-pole 10A'⊕9A'' 55 30A'⊕25A''
m (l=10) 21 1024-pole 11A'⊕10A'' 66 36A'⊕30A''
n (l=11) 23 2048-pole 12A'⊕11A'' 78 42A'⊕36A''
o (l=12) 25 4096-pole 13A'⊕12A'' 91 49A'⊕42A''
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 Cs
L 2L+1 Term Splitting
S (L=0) 1 A'
P (L=1) 3 A'⊕2A''
D (L=2) 5 3A'⊕2A''
F (L=3) 7 3A'⊕4A''
G (L=4) 9 5A'⊕4A''
H (L=5) 11 5A'⊕6A''
I (L=6) 13 7A'⊕6A''


Last update August, 12th 2020 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement