Reduction formula for point group D3d



Characters for molecular motions
Motion E 2C3 3C'2 i 2S6 3d
Cartesian 3N 108 0 0 0 0 4
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 4



Decomposition into Irreducible representations
Motion A1g A2g Eg A1u A2u Eu Total
Cartesian 3N 10 8 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 10 7 17 8 9 17 68



Molecule Parameter
Number of Atoms (N) 36
Number of internal coordinates 102
Number of independant internal coordinates 10
Number of vibrational modes 68





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1g A2g Eg A1u A2u Eu Total
Linear (IR) 10 7 17 8 9 17 26 / 42
Quadratic (Raman) 10 7 17 8 9 17 27 / 41
IR + Raman - 7 - 8 - - 0* / 15
* 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 4
quadratic 2 5.253 0 53 51 0 59
cubic 3 182.104 34 104 0 0 216
quartic 4 4.780.230 0 1.430 1.326 0 1.750
quintic 5 101.340.876 0 2.756 0 0 5.936
sextic 6 1.807.245.622 595 26.182 23.426 17 34.874


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1g A2g Eg A1u A2u Eu
linear 1 10 7 17 8 9 17
quadratic 2 470 414 884 432 435 867
cubic 3 15.261 15.101 30.345 15.153 15.209 30.345
quartic 4 399.258 397.668 796.926 398.162 398.322 796.484
quintic 5 8.447.246 8.442.900 16.890.146 8.444.278 8.445.868 16.890.146
sextic 6 150.621.120 150.590.592 301.211.406 150.599.773 150.604.119 301.203.603


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