Character table for point group C∞v

C∞v E 2C∞ ... ∞ σv
linear functions,
rotations
quadratic
functions
cubic
functions
A1=Σ+ +1 +1 ... +1 z x2+y2, z2 z3, z(x2+y2)
A2=Σ- +1 +1 ... -1 Rz - -
E1=Π +2 +2cos(φ) ... 0 (x, y) (Rx, Ry) (xz, yz) (xz2, yz2) [x(x2+y2), y(x2+y2)]
E2=Δ +2 +2cos(2φ) ... 0 - (x2-y2, xy) [xyz, z(x2-y2)]
E3=Φ +2 +2cos(3φ) ... 0 - - [y(3x2-y2), x(x2-3y2)]
... ... ... ... ... - - -
En +2 +2cos(nφ) ... 0 - - -




Additional information

Number of symmetry elements h = ∞
Number of irreducible representations n = ∞
Abelian group no
Number of subgroups ∞
Number of distinct subgroups ∞
Subgroups Cs
C2,C3,C4,C5,C6,…,C∞
C2v,C3v,C4v,C5v,C6v,…
Optical Isomerism (Chirality) no
Polaryes


Force field analysis for point group C∞v

Force field analysis for linear molecules

Number of atoms:


Examples

Hydrogen Chloride Hydrogen Cyanide Fluoroacetylene
Cyanoacetylene Fluorodiacetylene


Multipoles

dipole (p) Σ++Π
quadrupole (d) Σ++Π+Δ
octopole (f) Σ++Π+Δ+Φ
hexadecapole (g) Σ++Π+Δ+Φ+Γ
32-pole (h) Σ++Π+Δ+Φ+Γ+H
64-pole (i) Σ++Π+Δ+Φ+Γ+H+I
128-pole (j) Σ++Π+Δ+Φ+Γ+H+I+J
256-pole (k) Σ++Π+Δ+Φ+Γ+H+I+J+K
512-pole (l) Σ++Π+Δ+Φ+Γ+H+I+J+K+L

First nonvanishing multipole: dipole

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