Character table for point group D7d

D7d E 2C7 2(C7)2 2(C7)3 7C'2 i 2(S14)5 2(S14)3 2S14 7d
linear functions,
rotations
quadratic
functions
cubic
functions
A1g +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 - x2+y2, z2 -
A2g +1 +1 +1 +1 -1 +1 +1 +1 +1 -1 Rz - -
E1g +2 +2cos(2/7) +2cos(4/7) +2cos(6/7) 0 +2 +2cos(2/7) +2cos(4/7) +2cos(6/7) 0 (Rx, Ry) (xz, yz) -
E2g +2 +2cos(4/7) +2cos(6/7) +2cos(2/7) 0 +2 +2cos(4/7) +2cos(6/7) +2cos(2/7) 0 - (x2-y2, xy) -
E3g +2 +2cos(6/7) +2cos(2/7) +2cos(4/7) 0 +2 +2cos(6/7) +2cos(2/7) +2cos(4/7) 0 - - -
A1u +1 +1 +1 +1 +1 -1 -1 -1 -1 -1 - - -
A2u +1 +1 +1 +1 -1 -1 -1 -1 -1 +1 z - z3, z(x2+y2)
E1u +2 +2cos(2/7) +2cos(4/7) +2cos(6/7) 0 -2 -2cos(2/7) -2cos(4/7) -2cos(6/7) 0 (x, y) - (xz2, yz2) [x(x2+y2), y(x2+y2)]
E2u +2 +2cos(4/7) +2cos(6/7) +2cos(2/7) 0 -2 -2cos(4/7) -2cos(6/7) -2cos(2/7) 0 - - [xyz, z(x2-y2)]
E3u +2 +2cos(6/7) +2cos(2/7) +2cos(4/7) 0 -2 -2cos(6/7) -2cos(2/7) -2cos(4/7) 0 - - [y(3x2-y2), x(x2-3y2)]


Additional information

Number of symmetry elements h = 28
Number of irreducible representations n = 10
Abelian group no
Subgroups Cs , Ci , C2 , C7 , D7 , C7v , S14
Optical Isomerism (Chirality) no


Reduction formula for point group D7d

Type of representation

general 3N vib

E 2C7 2(C7)2 2(C7)3 7C'2 i 2(S14)5 2(S14)3 2S14 7d




Multipoles

dipole (p) A2u+E1u
quadrupole (d) A1g+E1g+E2g
octopole (f) A2u+E1u+E2u+E3u
hexadecapole (g) A1g+E1g+E2g+2E3g
32-pole (h) A2u+E1u+2E2u+2E3u
64-pole (i) A1g+2E1g+2E2g+2E3g
128-pole (j) A1u+2A2u+2E1u+2E2u+2E3u
256-pole(k) 2A1g+A2g+3E1g+2E2g+2E3g
512-pole (l) A1u+2A2u+3E1u+3E2u+2E3u

First nonvanishing multipole: quadrupole

Literature



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