Reduction formula for point group D3



Characters for molecular motions
Motion E 2C3 (z) 3C'2
Cartesian 3N 324 0 0
Translation (x,y,z) 3 0 -1
Rotation (Rx,Ry,Rz) 3 0 -1
Vibration 318 0 2



Decomposition into Irreducible representations
Motion A1 A2 E Total
Cartesian 3N 54 54 108 216
Translation (x,y,z) 0 1 1 2
Rotation (Rx,Ry,Rz) 0 1 1 2
Vibration 54 52 106 212



Molecule Parameter
Number of Atoms (N) 108
Number of internal coordinates 318
Number of independant internal coordinates 54
Number of vibrational modes 212





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E Total
Linear (IR) 54 52 106 158 / 54
Quadratic (Raman) 54 52 106 160 / 52
IR + Raman - - 106 106 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2C3 (z) 3C'2
linear 1 318 0 2
quadratic 2 50.721 0 161
cubic 3 5.410.240 106 320
quartic 4 434.171.760 0 13.040
quintic 5 27.960.661.344 0 25.760
sextic 6 1.505.215.602.352 5.671 708.400


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 E
linear 1 54 52 106
quadratic 2 8.534 8.373 16.907
cubic 3 901.902 901.582 1.803.378
quartic 4 72.368.480 72.355.440 144.723.920
quintic 5 4.660.123.104 4.660.097.344 9.320.220.448
sextic 6 250.869.623.149 250.868.914.749 501.738.532.227


Literature




Character tables for chemically important point groups Character table for point group D3 Constructor University Bremen

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