Character table for point group D2d

(x axis coincident with C'2 axis)
D2d E 2S4 C2 (z) 2C'2 2d
linear functions,
rotations
quadratic
functions
cubic
functions
A1 +1 +1 +1 +1 +1 - x2+y2, z2 xyz
A2 +1 +1 +1 -1 -1 Rz - z(x2-y2)
B1 +1 -1 +1 +1 -1 - x2-y2 -
B2 +1 -1 +1 -1 +1 z xy z3, 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 subgroups5
Subgroups
(Number of different orientations)
Cs , C2 (2) , D2 , C2v , S4
Optical Isomerism (Chirality) no


Reduction formula for point group D2d

Type of representation

general 3N vib

E 2S4 C2 (z) 2C'2 2d




Examples

Allene Cyclobutane



Multipoles

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

First nonvanishing multipole: quadrupole

Literature



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