## Point Group C1

C1 E
A 1

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

A

Binary products
A
A A

## Spherical harmonics and MultipolesSymmetric 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
More

First nonvanshing multipole: Dipole

• 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