Point Group Ci



Ci E i
Ag 1 1
Au 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


Ag Au




Examples

1,2-Dibromo-1,2-dichloroethane (staggered) Tartaric Acid (meso)



Direct products of irreducible representations


Binary products
Ag Au
Ag Ag
Au AuAg

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 Ag 1 Ag
p (l=1) 3 Dipole 3Au 3 3Au
d (l=2) 5 Quadrupole 5Ag 6 6Ag
f (l=3) 7 Octupole 7Au 10 10Au
g (l=4) 9 Hexadecapole 9Ag 15 15Ag
h (l=5) 11 Dotricontapole 11Au 21 21Au
i (l=6) 13 Tetrahexacontapole 13Ag 28 28Ag
j (l=7) 15 Octacosahectapole 15Au 36 36Au
k (l=8) 17 256-pole 17Ag 45 45Ag
l (l=9) 19 512-pole 19Au 55 55Au
m (l=10) 21 1024-pole 21Ag 66 66Ag
n (l=11) 23 2048-pole 23Au 78 78Au
o (l=12) 25 4096-pole 25Ag 91 91Ag
More

First nonvanshing multipole: Quadrupole

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 Ci
L 2L+1 Term Splitting
S (L=0) 1 Ag
P (L=1) 3 3Ag
D (L=2) 5 5Ag
F (L=3) 7 7Ag
G (L=4) 9 9Ag
H (L=5) 11 11Ag
I (L=6) 13 13Ag


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