Reduction formula for point group D6



Characters for molecular motions
Motion E 2C6 (z) 2C3 (z) C2 (z) 3C'2 3C''2
Cartesian 3N 36 0 0 0 -4 0
Translation 3 2 0 -1 -1 -1
Rotation 3 2 0 -1 -1 -1
Vibration 30 -4 0 2 -2 2



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 E1 E2 Total
Cartesian 3N 2 4 2 4 6 6 24
Translation 0 1 0 0 1 0 2
Rotation 0 1 0 0 1 0 2
Vibration 2 2 2 4 4 6 20



Molecule Parameter
Number of Atoms (N) 12
Number of internal coordinates 30
Number of independant internal coordinates 2
Number of vibrational modes 20





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 E1 E2 Total
Linear (IR) 2 2 2 4 4 6 6 / 14
Quadratic (Raman) 2 2 2 4 4 6 12 / 8
IR + Raman - - 2 4 4 - 4 / 6



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2C6 (z) 2C3 (z) C2 (z) 3C'2 3C''2
linear 1 30 -4 0 2 -2 2
quadratic 2 465 8 0 17 17 17
cubic 3 4.960 -10 10 32 -32 32
quartic 4 40.920 8 0 152 152 152
quintic 5 278.256 -4 0 272 -272 272
sextic 6 1.623.160 7 55 952 952 952


Decomposition into Irreducible representations
Force field Tensor
Order
A1 A2 B1 B2 E1 E2
linear 1 2 2 2 4 4 6
quadratic 2 50 33 36 36 76 79
cubic 3 416 416 398 430 818 832
quartic 4 3.500 3.348 3.396 3.396 6.796 6.844
quintic 5 23.210 23.210 23.030 23.302 46.330 46.422
sextic 6 135.829 134.877 135.192 135.192 270.360 270.675


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