Character table for point group C7v

C7v E 2C7 2(C7)2 2(C7)3 7v
linear functions,
rotations
quadratic
functions
cubic
functions
A1 +1 +1 +1 +1 +1 z x2+y2, z2 z3, z(x2+y2)
A2 +1 +1 +1 +1 -1 Rz - -
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 Cs , C7
Optical Isomerism (Chirality) no


Reduction formula for point group C7v

Type of representation

general 3N vib

E 2C7 2(C7)2 2(C7)3 7v




Multipoles

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

First nonvanishing multipole: dipole

Literature



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