Character table for point group Dh

Dh E 2C ... v 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 - -
E1g=g +2 +2cos() ... 0 +2 -2cos() ... 0 (Rx, Ry) (xz, yz) -
E2g=g +2 +2cos(2) ... 0 +2 +2cos(2) ... 0 - (x2-y2, xy) -
E3g=g +2 +2cos(3) ... 0 +2 -2cos(3) ... 0 - - -
Eng +2 +2cos(n) ... 0 +2 (-1)n2cos(n) ... 0 - - -
... ... ... ... ... ... ... ... ... - - -
A1u=+u +1 +1 ... +1 -1 -1 ... -1 z - z3, z(x2+y2)
A2u=-u +1 +1 ... -1 -1 -1 ... +1 - - -
E1u=u +2 +2cos() ... 0 -2 +2cos() ... 0 (x, y) - (xz2, yz2) [x(x2+y2), y(x2+y2)]
E2u=u +2 +2cos(2) ... 0 -2 -2cos(2) ... 0 - - [xyz, z(x2-y2)]
E3u=u +2 +2cos(3) ... 0 -2 2cos(3) ... 0 - - [y(3x2-y2), x(x2-3y2)]
Enu +2 +2cos(n) ... 0 -2 (-1)n+12cos(n) ... 0 - - -
... ... ... ... ... ... ... ... ... - - -




Additional information

Number of symmetry elements h =
Number of irreducible representations h =
Abelian group no
Optical Isomerism (Chirality) no


Force field analysis for point group Dh

Force field analysis for linear molecules

Number of atoms:



Multipoles

dipole (p) +u+u
quadrupole (d) +g+g+g
octopole (f) +u+u+u+u
hexadecapole (g) +g+g+g+g+g
32-pole (h) +u+u+u+u+u+Hu
64-pole (i) +g+g+g+g+g+Hg+Ig
128-pole (j) +u+u+u+u+u+Hu+Iu+Ju
256-pole (k) +g+g+g+g+g+Hg+Ig+Jg+Kg
512-pole (l) +u+u+u+u+u+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