Reduction formula for point group D6



Characters for molecular motions
Motion E 2C6 (z) 2C3 (z) C2 (z) 3C'2 3C''2
Cartesian 3N 324 0 0 0 0 0
Translation 3 2 0 -1 -1 -1
Rotation 3 2 0 -1 -1 -1
Vibration 318 -4 0 2 2 2



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 E1 E2 Total
Cartesian 3N 27 27 27 27 54 54 216
Translation 0 1 0 0 1 0 2
Rotation 0 1 0 0 1 0 2
Vibration 27 25 27 27 52 54 212



Molecule Parameter
Number of Atoms (N) 108
Number of internal coordinates 318
Number of independant internal coordinates 27
Number of vibrational modes 212





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 E1 E2 Total
Linear (IR) 27 25 27 27 52 54 77 / 135
Quadratic (Raman) 27 25 27 27 52 54 133 / 79
IR + Raman - - 27 27 52 - 52 / 54



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2C6 (z) 2C3 (z) C2 (z) 3C'2 3C''2
linear 1 318 -4 0 2 2 2
quadratic 2 50.721 8 0 161 161 161
cubic 3 5.410.240 -10 106 320 320 320
quartic 4 434.171.760 8 0 13.040 13.040 13.040
quintic 5 27.960.661.344 -4 0 25.760 25.760 25.760
sextic 6 1.505.215.602.352 55 5.671 708.400 708.400 708.400


Decomposition into Irreducible representations
Force field Tensor
Order
A1 A2 B1 B2 E1 E2
linear 1 27 25 27 27 52 54
quadratic 2 4.322 4.161 4.212 4.212 8.428 8.479
cubic 3 451.056 450.736 450.846 450.846 901.634 901.744
quartic 4 36.188.588 36.175.548 36.179.892 36.179.892 72.359.788 72.364.132
quintic 5 2.330.070.138 2.330.044.378 2.330.052.966 2.330.052.966 4.660.105.930 4.660.114.518
sextic 6 125.435.047.717 125.434.339.317 125.434.575.432 125.434.575.432 250.869.148.056 250.869.384.171


Literature




Character tables for chemically important point groups Character table for point group D6 Jacobs University Bremen

Last update Mai, 23rd 2018 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement