Reduction formula for point group D3h



Characters for molecular motions
Motion E 2C3 (z) 3C'2 h (xy) 2S3 3v
Cartesian 3N 216 0 0 72 0 0
Translation (x,y,z) 3 0 -1 1 -2 1
Rotation (Rx,Ry,Rz) 3 0 -1 -1 2 -1
Vibration 210 0 2 72 0 0



Decomposition into Irreducible representations
Motion A'1 A'2 E' A''1 A''2 E'' Total
Cartesian 3N 24 24 48 12 12 24 144
Translation (x,y,z) 0 0 1 0 1 0 2
Rotation (Rx,Ry,Rz) 0 1 0 0 0 1 2
Vibration 24 23 47 12 11 23 140



Molecule Parameter
Number of Atoms (N) 72
Number of internal coordinates 210
Number of independant internal coordinates 24
Number of vibrational modes 140





Force field analysis


Allowed / forbidden vibronational transitions
Operator A'1 A'2 E' A''1 A''2 E'' Total
Linear (IR) 24 23 47 12 11 23 58 / 82
Quadratic (Raman) 24 23 47 12 11 23 94 / 46
IR + Raman - 23 47 12 - - 47 / 35



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2C3 (z) 3C'2 h (xy) 2S3 3v
linear 1 210 0 2 72 0 0
quadratic 2 22.155 0 107 2.697 0 105
cubic 3 1.565.620 70 212 69.792 24 0
quartic 4 83.369.265 0 5.777 1.399.197 0 5.565
quintic 5 3.568.204.542 0 11.342 23.121.576 0 0
sextic 6 127.860.662.755 2.485 209.827 327.363.605 323 198.485


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A'1 A'2 E' A''1 A''2 E''
linear 1 24 23 47 12 11 23
quadratic 2 2.124 2.018 4.142 1.622 1.621 3.243
cubic 3 136.353 136.247 272.553 124.713 124.607 249.297
quartic 4 7.066.874 7.061.203 14.128.077 6.830.892 6.830.786 13.661.678
quintic 5 299.280.012 299.274.341 598.554.353 295.426.416 295.420.745 590.847.161
sextic 6 10.682.438.076 10.682.233.920 21.364.670.592 10.627.778.125 10.627.772.454 21.255.549.498


Literature




Character tables for chemically important point groups Character table for point group D3h Constructor University Bremen

Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement