Reduction formula for point group C6



Characters for molecular motions
Motion E C6 C3 C2 (C3)2 (C6)5
Cartesian 3N 36 0 0 0 0 0
Translation 3 2 0 -1 0 2
Rotation 3 2 0 -1 0 2
Vibration 30 -4 0 2 0 -4



Decomposition into Irreducible representations
Motion A B E1 E2 Total
Cartesian 3N 6 6 6 6 24
Translation 1 0 1 0 2
Rotation 1 0 1 0 2
Vibration 4 6 4 6 20



Molecule Parameter
Number of Atoms (N) 12
Number of internal coordinates 30
Number of independant internal coordinates 4
Number of vibrational modes 20





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B E1 E2 Total
Linear (IR) 4 6 4 6 8 / 12
Quadratic (Raman) 4 6 4 6 14 / 6
IR + Raman 4 6 4 - 8 / 6



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


Decomposition into Irreducible representations
Force field Tensor
Order
A B E1 E2
linear 1 4 6 4 6
quadratic 2 83 72 76 79
cubic 3 832 828 818 832
quartic 4 6.848 6.792 6.796 6.844
quintic 5 46.420 46.332 46.330 46.422
sextic 6 270.706 270.384 270.360 270.675


Literature




Character tables for chemically important point groups Character table for point group C6 Jacobs University Bremen

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