Character table for point group D4

D4 E 2C4 (z) C2 (z) 2C'2 2C''2
linear functions,
rotations
quadratic
functions
cubic
functions
A1 +1 +1 +1 +1 +1 - x2+y2, z2 -
A2 +1 +1 +1 -1 -1 z, Rz - z3, z(x2+y2)
B1 +1 -1 +1 +1 -1 - x2-y2 xyz
B2 +1 -1 +1 -1 +1 - xy z(x2-y2)
E +2 0 -2 0 0 (x, y) (Rx, Ry) (xz, yz) (xz2, yz2) (xy2, x2y) (x3, y3)


Additional information

Number of symmetry elements h = 8
Number of irreducible representations n = 5
Abelian group no
Number of subgroups6
Number of distinct subgroups3
Subgroups
(Number of different orientations)
C2 (3) , C4 , D2 (2)
Optical Isomerism (Chirality) yes


Reduction formula for point group D4

Type of representation

general 3N vib

E 2C4 (z) C2 (z) 2C'2 2C''2




Multipoles

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

First nonvanishing multipole: quadrupole

Literature



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