Character table for point group D8

D8 E 2C8 2C4 2(C8)3 C2 4C'2 4C''2
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 z, Rz - z3, z(x2+y2)
B1 +1 -1 +1 -1 +1 +1 -1 - - -
B2 +1 -1 +1 -1 +1 -1 +1 - - -
E1 +2 +(2)½ 0 -(2)½ -2 0 0 (x, y) (Rx, Ry) (xz, yz) (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 - - [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 subgroups5
Subgroups
(Number of different orientations)
C2 (3) , C4 , C8 , D2 (2) , D4 (2)
Optical Isomerism (Chirality) yes


Reduction formula for point group D8

Type of representation

general 3N vib

E 2C8 2C4 2(C8)3 C2 4C'2 4C''2




Multipoles

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