Point Group





Additional information

Number of symmetry elements h = 0
Number of classes, irreps n = 0
Abelian group yes
Optical Isomerism (Chirality) no
Polar no
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 [Γl(xyz)]
s (l=0) 1 Monopole 1
p (l=1) 3 Dipole 3
d (l=2) 5 Quadrupole 6
f (l=3) 7 Octupole 10
g (l=4) 9 Hexadecapole 15
h (l=5) 11 Dotricontapole 21
i (l=6) 13 Tetrahexacontapole 28
j (l=7) 15 Octacosahectapole 36
k (l=8) 17 256-pole 45
l (l=9) 19 512-pole 55
m (l=10) 21 1024-pole 66
n (l=11) 23 2048-pole 78
o (l=12) 25 4096-pole 91
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
L 2L+1 Term Splitting
S (L=0) 1
P (L=1) 3
D (L=2) 5
F (L=3) 7
G (L=4) 9
H (L=5) 11
I (L=6) 13

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