Character table for point group Td

Td E 8C3 3C2 6S4 6d
linear functions,
rotations
quadratic
functions
cubic
functions
A1 +1 +1 +1 +1 +1 - x2+y2+z2 xyz
A2 +1 +1 +1 -1 -1 - - -
E +2 -1 +2 0 0 - (2z2-x2-y2, x2-y2) -
T1 +3 0 -1 +1 -1 (Rx, Ry, Rz) - [x(z2-y2), y(z2-x2), z(x2-y2)]
T2 +3 0 -1 -1 +1 (x, y, z) (xy, xz, yz) (x3, y3, z3) [x(z2+y2), y(z2+x2), z(x2+y2)]


Additional information

Number of symmetry elements h = 24
Number of irreducible representations n = 5
Abelian group no
Number of subgroups9
Subgroups Cs , C2 , C3 , D2 , C2v , C3v , D2d , S4 , T
Optical Isomerism (Chirality) no


Reduction formula for point group Td

Type of representation

general 3N vib

E 8C3 3C2 6S4 6d




Examples

Phosphorus Methane Tetrahedrane
Neopentane Urotropine Adamantane



Multipoles

dipole (p) T2
quadrupole (d) E+T2
octopole (f) A1+T1+T2
hexadecapole (g) A1+E+T1+T2
32-pole (h) E+T1+2T2
64-pole (i) A1+A2+E+T1+2T2
128-pole (j) A1+E+2T1+2T2
256-pole(k) A1+2E+2T1+2T2
512-pole (l) A1+A2+E+2T1+3T2

First nonvanishing multipole: octopole

Literature



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