Character table for point group D7

D7 E 2C7 2(C7)2 2(C7)3 7C'2
linear functions,
rotations
quadratic
functions
cubic
functions
A1 +1 +1 +1 +1 +1 - x2+y2, z2 -
A2 +1 +1 +1 +1 -1 z, Rz - z3, z(x2+y2)
E1 +2 +2cos(2/7) +2cos(4/7) +2cos(6/7) 0 (x, y) (Rx, Ry) (xz, yz) (xz2, yz2) [x(x2+y2), y(x2+y2)]
E2 +2 +2cos(4/7) +2cos(6/7) +2cos(2/7) 0 - (x2-y2, xy) [xyz, z(x2-y2)]
E3 +2 +2cos(6/7) +2cos(2/7) +2cos(4/7) 0 - - [y(3x2-y2), x(x2-3y2)]


Additional information

Number of symmetry elements h = 14
Number of irreducible representations n = 5
Abelian group no
Number of subgroups2
Subgroups C2 , C7
Optical Isomerism (Chirality) yes
Polar no


Reduction formula for point group D7

Type of representation

general 3N vib

E 2C7 2(C7)2 2(C7)3 7C'2



Multipoles

dipole (p) A2+E1
quadrupole (d) A1+E1+E2
octopole (f) A2+E1+E2+E3
hexadecapole (g) A1+E1+E2+2E3
32-pole (h) A2+E1+2E2+2E3
64-pole (i) A1+2E1+2E2+2E3
128-pole (j) A1+2A2+2E1+2E2+2E3
256-pole(k) 2A1+A2+3E1+2E2+2E3
512-pole (l) A1+2A2+3E1+3E2+2E3

First nonvanishing multipole: quadrupole

Literature


Character tables for chemically important point groups Computational Laboratory for Analysis, Modeling and Visualization Constructor University Bremen
Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement