Character table for point group D3

D3 E 2C3 (z) 3C'2
linear functions,
rotations
quadratic
functions
cubic
functions
A1 +1 +1 +1 - x2+y2, z2 x(x2-3y2)
A2 +1 +1 -1 z, Rz - z3, y(3x2-y2), z(x2+y2)
E +2 -1 0 (x, y) (Rx, Ry) (x2-y2, xy) (xz, yz) (xz2, yz2) [xyz, z(x2-y2)] [x(x2+y2), y(x2+y2)]


Additional information

Number of symmetry elements h = 6
Number of irreducible representations n = 3
Abelian group no
Number of subgroups2
Subgroups C2 , C3
Optical Isomerism (Chirality) yes


Reduction formula for point group D3

Type of representation

general 3N vib

E 2C3 (z) 3C'2




Multipoles

dipole (p) A2+E
quadrupole (d) A1+2E
octopole (f) A1+2A2+2E
hexadecapole (g) 2A1+A2+3E
32-pole (h) A1+2A2+4E
64-pole (i) 3A1+2A2+4E
128-pole (j) 2A1+3A2+5E
256-pole(k) 3A1+2A2+6E
512-pole (l) 3A1+4A2+6E

First nonvanishing multipole: quadrupole

Literature



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