Character table for point group C3v

C3v E 2C3 (z) 3v
linear functions,
rotations
quadratic
functions
cubic
functions
A1 +1 +1 +1 z x2+y2, z2 z3, x(x2-3y2), z(x2+y2)
A2 +1 +1 -1 Rz - y(3x2-y2)
E +2 -1 0 (x, y) (Rx, Ry) (x2-y2, xy) (xz, yz) (xz2, yz2) [xyz, z(x2-y2)] [x(x2+y2), y(x2+y2)]


Additional information

Number of symmetry elements h = 6
Number of irreducible representations n = 3
Abelian group no
Number of subgroups2
Subgroups Cs , C3
Optical Isomerism (Chirality) no
Polar yes


Reduction formula for point group C3v

Type of representation

general 3N vib

E 2C3 (z) 3v




Examples

Ammonia Chloroform Acetonitrile
Xenonhexafluoride 1,1,1-Trichloroethane Trioxane
Triquinacene 1-Azabicyclo[2.2.2]octane Sumanene



Multipoles

dipole (p) A1+E
quadrupole (d) A1+2E
octopole (f) 2A1+A2+2E
hexadecapole (g) 2A1+A2+3E
32-pole (h) 2A1+A2+4E
64-pole (i) 3A1+2A2+4E
128-pole (j) 3A1+2A2+5E
256-pole(k) 3A1+2A2+6E
512-pole (l) 4A1+3A2+6E

First nonvanishing multipole: dipole

Literature



Character tables for chemically important point groups Computational Laboratory for Analysis, Modeling and Visualization Constructor University Bremen

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