Reduction formula for point group D3d



Characters for molecular motions
Motion E 2C3 3C'2 i 2S6 3d
Cartesian 3N 108 0 -4 0 0 0
Translation (x,y,z) 3 0 -1 -3 0 1
Rotation (Rx,Ry,Rz) 3 0 -1 3 0 -1
Vibration 102 0 -2 0 0 0



Decomposition into Irreducible representations
Motion A1g A2g Eg A1u A2u Eu Total
Cartesian 3N 8 10 18 8 10 18 72
Translation (x,y,z) 0 0 0 0 1 1 2
Rotation (Rx,Ry,Rz) 0 1 1 0 0 0 2
Vibration 8 9 17 8 9 17 68



Molecule Parameter
Number of Atoms (N) 36
Number of internal coordinates 102
Number of independant internal coordinates 8
Number of vibrational modes 68





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1g A2g Eg A1u A2u Eu Total
Linear (IR) 8 9 17 8 9 17 26 / 42
Quadratic (Raman) 8 9 17 8 9 17 25 / 43
IR + Raman - 9 - 8 - - 0* / 17
* Center of inversion: Mutual Exclusion Principle



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2C3 3C'2 i 2S6 3d
linear 1 102 0 -2 0 0 0
quadratic 2 5.253 0 53 51 0 51
cubic 3 182.104 34 -104 0 0 0
quartic 4 4.780.230 0 1.430 1.326 0 1.326
quintic 5 101.340.876 0 -2.756 0 0 0
sextic 6 1.807.245.622 595 26.182 23.426 17 23.426


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1g A2g Eg A1u A2u Eu
linear 1 8 9 17 8 9 17
quadratic 2 468 416 884 434 433 867
cubic 3 15.155 15.207 30.345 15.155 15.207 30.345
quartic 4 399.152 397.774 796.926 398.268 398.216 796.484
quintic 5 8.444.384 8.445.762 16.890.146 8.444.384 8.445.762 16.890.146
sextic 6 150.618.258 150.593.454 301.211.406 150.602.635 150.601.257 301.203.603


Literature




Character tables for chemically important point groups Character table for point group D3d Constructor University Bremen

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