Character table for point group C2v

C2v E C2 (z) v(xz) v(yz)
linear functions,
rotations
quadratic
functions
cubic
functions
A1 +1 +1 +1 +1 z x2, y2, z2 z3, x2z, y2z
A2 +1 +1 -1 -1 Rz xy xyz
B1 +1 -1 +1 -1 x, Ry xz xz2, x3, xy2
B2 +1 -1 -1 +1 y, Rx yz yz2, y3, x2y


Additional information

Number of symmetry elements h = 4
Number of irreducible representations n = 4
Abelian group yes
Subgroups Cs , C2
Optical Isomerism (Chirality) no


Reduction formula for point group C2v

Type of representation

general 3N vib

E C2 (z) v(xz) v(yz)




Multipoles

dipole (p) A1+B1+B2
quadrupole (d) 2A1+A2+B1+B2
octopole (f) 2A1+A2+2B1+2B2
hexadecapole (g) 3A1+2A2+2B1+2B2
32-pole (h) 3A1+2A2+3B1+3B2
64-pole (i) 4A1+3A2+3B1+3B2
128-pole (j) 4A1+3A2+4B1+4B2
256-pole(k) 5A1+4A2+4B1+4B2
512-pole (l) 5A1+4A2+5B1+5B2

First nonvanishing multipole: dipole

Literature



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