Point Group C1

C1 E
A 1

Additional information

Number of symmetry elements h = 1
Number of classes, irreps n = 1
Abelian group yes
Optical Isomerism (Chirality) yes
Polar yes
Parity no

Reduce representation to irreducible representations


Genrate representation from irreducible representations


Direct products of irreducible representations

Binary products

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

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 C1
L 2L+1 Term Splitting
S (L=0) 1 A
P (L=1) 3 3A
D (L=2) 5 5A
F (L=3) 7 7A
G (L=4) 9 9A
H (L=5) 11 11A
I (L=6) 13 13A

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