Character table for point group D2

D2 E C2 (z) C2 (y) C2 (x)
linear functions,
rotations
quadratic
functions
cubic
functions
A +1 +1 +1 +1 - x2, y2, z2 xyz
B1 +1 +1 -1 -1 z, Rz xy z3, y2z, x2z
B2 +1 -1 +1 -1 y, Ry xz yz2, x2y, y3
B3 +1 -1 -1 +1 x, Rx yz xz2, xy2, x3


Additional information

Number of symmetry elements h = 4
Number of irreducible representations n = 4
Abelian group yes
Subgroup C2
Optical Isomerism (Chirality) yes


Reduction formula for point group D2

Type of representation

general 3N vib

E C2 (z) C2 (y) C2 (x)




Multipoles

dipole (p) B1+B2+B3
quadrupole (d) 2A+B1+B2+B3
octopole (f) A+2B1+2B2+2B3
hexadecapole (g) 3A+2B1+2B2+2B3
32-pole (h) 2A+3B1+3B2+3B3
64-pole (i) 4A+3B1+3B2+3B3
128-pole (j) 3A+4B1+4B2+4B3
256-pole(k) 5A+4B1+4B2+4B3
512-pole (l) 4A+5B1+5B2+5B3

First nonvanishing multipole: quadrupole

Literature



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