Character table for point group I

I E 12C5 12(C5)2 20C3 15C2
linear functions,
rotations
quadratic
functions
cubic
functions
A +1 +1 +1 +1 +1 - x2+y2+z2 -
T1 +3 -2cos(4/5) -2cos(2/5) 0 -1 (x, y, z) (Rx, Ry, Rz) - [x(z2+y2), y(z2+x2), z(x2+y2)]
T2 +3 -2cos(2/5) -2cos(4/5) 0 -1 - - [x3, y3, z3]
G +4 -1 -1 +1 0 - - [x(z2-y2), y(z2-x2), z(x2-y2), xyz]
H +5 0 0 -1 +1 - [2z2-x2-y2, x2-y2, xy, xz, yz] -

Information for point groups with fivefold rotational axis


Additional information

Number of symmetry elements h = 60
Number of irreducible representations n = 5
Abelian group no
Number of subgroups7
Subgroups C2 , C3 , C5 , D2 , D3 , D5 , T
Optical Isomerism (Chirality) yes


Reduction formula for point group I

Type of representation

general 3N vib

E 12C5 12(C5)2 20C3 15C2




Multipoles

dipole (p) T1
quadrupole (d) H
octopole (f) T2+G
hexadecapole (g) G+H
32-pole (h) T1+T2+H
64-pole (i) A+T1+G+H
128-pole (j) T1+T2+G+H
256-pole(k) T2+G+2H
512-pole (l) T1+T2+2G+H

First nonvanishing multipole: 64-pole

Literature



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