Reduction formula for point group D3h



Characters for molecular motions
Motion E 2C3 (z) 3C'2 h (xy) 2S3 3v
Cartesian 3N 33 0 -3 7 -2 7
Translation (x,y,z) 3 0 -1 1 -2 1
Rotation (Rx,Ry,Rz) 3 0 -1 -1 2 -1
Vibration 27 0 -1 7 -2 7



Decomposition into Irreducible representations
Motion A'1 A'2 E' A''1 A''2 E'' Total
Cartesian 3N 4 2 7 0 5 4 22
Translation (x,y,z) 0 0 1 0 1 0 2
Rotation (Rx,Ry,Rz) 0 1 0 0 0 1 2
Vibration 4 1 6 0 4 3 18



Molecule Parameter
Number of Atoms (N) 11
Number of internal coordinates 27
Number of independant internal coordinates 4
Number of vibrational modes 18





Force field analysis


Allowed / forbidden vibronational transitions
Operator A'1 A'2 E' A''1 A''2 E'' Total
Linear (IR) 4 1 6 0 4 3 10 / 8
Quadratic (Raman) 4 1 6 0 4 3 13 / 5
IR + Raman - 1 6 0 - - 6 / 1



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2C3 (z) 3C'2 h (xy) 2S3 3v
linear 1 27 0 -1 7 -2 7
quadratic 2 378 0 14 38 2 38
cubic 3 3.654 9 -14 154 1 154
quartic 4 27.405 0 105 545 -4 545
quintic 5 169.911 0 -105 1.687 4 1.687
sextic 6 906.192 45 560 4.784 5 4.784


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 4 1 6 0 4 3
quadratic 2 48 22 69 22 34 57
cubic 3 354 284 633 251 335 582
quartic 4 2.491 2.166 4.659 2.129 2.349 4.476
quintic 5 14.696 13.905 28.599 13.570 14.466 28.038
sextic 6 77.259 74.587 151.821 74.068 76.180 150.228


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