Character table for point group D∞h

D∞h E 2C ... ∞σv i 2S ... ∞C'2
linear functions,
rotations
quadratic
functions
cubic
functions
A1g+g +1 +1 ... +1 +1 +1 ... +1 - x2+y2, z2 -
A2g-g +1 +1 ... -1 +1 +1 ... -1 Rz - -
E1gg +2 +2cos(φ) ... 0 +2 -2cos(φ) ... 0 (Rx, Ry) (xz, yz) -
E2gg +2 +2cos(2φ) ... 0 +2 +2cos(2φ) ... 0 - (x2-y2, xy) -
E3gg +2 +2cos(3φ) ... 0 +2 -2cos(3φ) ... 0 - - -
Eng +2 +2cos(nφ) ... 0 +2 (-1)n2cos(nφ) ... 0 - - -
... ... ... ... ... ... ... ... ... - - -
A1u+u +1 +1 ... +1 -1 -1 ... -1 z - z3, z(x2+y2)
A2u-u +1 +1 ... -1 -1 -1 ... +1 - - -
E1uu +2 +2cos(φ) ... 0 -2 +2cos(φ) ... 0 (x, y) - (xz2, yz2) [x(x2+y2), y(x2+y2)]
E2uu +2 +2cos(2φ) ... 0 -2 -2cos(2φ) ... 0 - - [xyz, z(x2-y2)]
E3uu +2 +2cos(3φ) ... 0 -2 2cos(3φ) ... 0 - - [y(3x2-y2), x(x2-3y2)]
Enu +2 +2cos(nφ) ... 0 -2 (-1)n+12cos(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 CsCi
C2,C3,C4,C5,C6,…,C
D2,D3,D4,D5,D6,…,D
C2v,C3v,C4v,C5v,C6v,…,C∞v,
C2h,C3h,C4h,C5h,C6h,…,C∞h
D2h,D3h,D4h,D5h,D6h,…
D2d,D3d,D4d,D5d,D6d,…,D∞d
S4,S6,S8,S10,S12,…,S
Optical Isomerism (Chirality) no
Polarno


Force field analysis for point group D∞h

Force field analysis for linear molecules

Number of atoms:



Examples

Hydrogen Carbondioxide Acetylene
Carbonsuboxide Diacetylene



Multipoles

dipole (p) Σ+uu
quadrupole (d) Σ+ggg
octopole (f) Σ+uuuu
hexadecapole (g) Σ+ggggg
32-pole (h) Σ+uuuuu+Hu
64-pole (i) Σ+ggggg+Hg+Ig
128-pole (j) Σ+uuuuu+Hu+Iu+Ju
256-pole (k) Σ+ggggg+Hg+Ig+Jg+Kg
512-pole (l) Σ+uuuuu+Hu+Iu+Ju+Ku+Lu

First nonvanishing multipole: quadrupole

Literature



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

Last update Mai, 23rd 2018 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement