Reduction formula for point group D3d



Characters for molecular motions
Motion E 2C3 3C'2 i 2S6 3d
Cartesian 3N 216 0 -8 0 0 0
Translation (x,y,z) 3 0 -1 -3 0 1
Rotation (Rx,Ry,Rz) 3 0 -1 3 0 -1
Vibration 210 0 -6 0 0 0



Decomposition into Irreducible representations
Motion A1g A2g Eg A1u A2u Eu Total
Cartesian 3N 16 20 36 16 20 36 144
Translation (x,y,z) 0 0 0 0 1 1 2
Rotation (Rx,Ry,Rz) 0 1 1 0 0 0 2
Vibration 16 19 35 16 19 35 140



Molecule Parameter
Number of Atoms (N) 72
Number of internal coordinates 210
Number of independant internal coordinates 16
Number of vibrational modes 140





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1g A2g Eg A1u A2u Eu Total
Linear (IR) 16 19 35 16 19 35 54 / 86
Quadratic (Raman) 16 19 35 16 19 35 51 / 89
IR + Raman - 19 - 16 - - 0* / 35
* 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 1 210 0 -6 0 0 0
quadratic 2 22.155 0 123 105 0 105
cubic 3 1.565.620 70 -668 0 0 0
quartic 4 83.369.265 0 7.521 5.565 0 5.565
quintic 5 3.568.204.542 0 -37.482 0 0 0
sextic 6 127.860.662.755 2.485 305.731 198.485 35 198.485


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1g A2g Eg A1u A2u Eu
linear 1 16 19 35 16 19 35
quadratic 2 1.912 1.798 3.710 1.842 1.833 3.675
cubic 3 130.313 130.647 260.925 130.313 130.647 260.925
quartic 4 6.951.174 6.944.631 13.895.805 6.947.464 6.946.486 13.893.950
quintic 5 297.341.008 297.359.749 594.700.757 297.341.008 297.359.749 594.700.757
sextic 6 10.655.198.244 10.654.946.136 21.310.143.120 10.655.065.909 10.655.012.286 21.310.076.970


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