Character table for point group C2h

C2h E C2 (z) i h
linear functions,
rotations
quadratic
functions
cubic
functions
Ag +1 +1 +1 +1 Rz x2, y2, z2, xy -
Bg +1 -1 +1 -1 Rx, Ry xz, yz -
Au +1 +1 -1 -1 z - z3, xyz, x2z, y2z
Bu +1 -1 -1 +1 x, y - xz2, yz2, x2y, xy2, x3, y3


Additional information

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


Reduction formula for point group C2h

Type of representation

general 3N vib

E C2 (z) i h




Multipoles

dipole (p) Au+2Bu
quadrupole (d) 3Ag+2Bg
octopole (f) 3Au+4Bu
hexadecapole (g) 5Ag+4Bg
32-pole (h) 5Au+6Bu
64-pole (i) 7Ag+6Bg
128-pole (j) 7Au+8Bu
256-pole(k) 9Ag+8Bg
512-pole (l) 9Au+10Bu

First nonvanishing multipole: quadrupole

Literature



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