Character table for point group D4d

(x axis coincident with C'2 axis)
D4d E 2S8 2C4 2(S8)3 C2 4C'2 4d
linear functions,
rotations
quadratic
functions
cubic
functions
A1 +1 +1 +1 +1 +1 +1 +1 - x2+y2, z2 -
A2 +1 +1 +1 +1 +1 -1 -1 Rz - -
B1 +1 -1 +1 -1 +1 +1 -1 - - -
B2 +1 -1 +1 -1 +1 -1 +1 z - z3, z(x2+y2)
E1 +2 +(2)½ 0 -(2)½ -2 0 0 (x, y) - (xz2, yz2) [x(x2+y2), y(x2+y2)]
E2 +2 0 -2 0 +2 0 0 - (x2-y2, xy) [xyz, z(x2-y2)]
E3 +2 -(2)½ 0 +(2)½ -2 0 0 (Rx, Ry) (xz, yz) [y(3x2-y2), x(x2-3y2)]


Additional information

Number of symmetry elements h = 16
Number of irreducible representations n = 7
Abelian group no
Number of subgroups9
Number of distinct subgroups8
Subgroups
(Number of different orientations)
Cs , C2 (2) , C4 , D2 , D4 , C2v , C4v , S8
Optical Isomerism (Chirality) no


Reduction formula for point group D4d

Type of representation

general 3N vib

E 2S8 2C4 2(S8)3 C2 4C'2 4d




Multipoles

dipole (p) B2+E1
quadrupole (d) A1+E2+E3
octopole (f) B2+E1+E2+E3
hexadecapole (g) A1+B1+B2+E1+E2+E3
32-pole (h) A1+A2+B2+E1+E2+2E3
64-pole (i) A1+B1+B2+2E1+2E2+E3
128-pole (j) A1+A2+B2+2E1+2E2+2E3
256-pole(k) 2A1+A2+B1+B2+2E1+2E2+2E3
512-pole (l) A1+A2+B1+2B2+3E1+2E2+2E3

First nonvanishing multipole: quadrupole

Literature



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