Character table for point group D5

D5 E 2C5 (z) 2(C5)2 5C'2
linear functions,
rotations
quadratic
functions
cubic
functions
A1 +1 +1 +1 +1 - x2+y2, z2 -
A2 +1 +1 +1 -1 z, Rz - z3, z(x2+y2)
E1 +2 +2cos(2/5) +2cos(4/5) 0 (x, y) (Rx, Ry) (xz, yz) (xz2, yz2) [x(x2+y2), y(x2+y2)]
E2 +2 +2cos(4/5) +2cos(2/5) 0 - (x2-y2, xy) [xyz, z(x2-y2)] [y(3x2-y2), x(x2-3y2)]

Information for point groups with fivefold rotational axis


Additional information

Number of symmetry elements h = 10
Number of irreducible representations n = 4
Abelian group no
Subgroups C2 , C5
Optical Isomerism (Chirality) yes


Reduction formula for point group D5

Type of representation

general 3N vib

E 2C5 (z) 2(C5)2 5C'2




Multipoles

dipole (p) A2+E1
quadrupole (d) A1+E1+E2
octopole (f) A2+E1+2E2
hexadecapole (g) A1+2E1+2E2
32-pole (h) A1+2A2+2E1+2E2
64-pole (i) 2A1+A2+3E1+2E2
128-pole (j) A1+2A2+3E1+3E2
256-pole(k) 2A1+A2+3E1+4E2
512-pole (l) A1+2A2+4E1+4E2

First nonvanishing multipole: quadrupole

Literature



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