Reduction formula for point group D3



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



Decomposition into Irreducible representations
Motion A1 A2 E Total
Cartesian 3N 6 6 12 24
Translation 0 1 1 2
Rotation 0 1 1 2
Vibration 6 4 10 20



Molecule Parameter
Number of Atoms (N) 12
Number of internal coordinates 30
Number of independant internal coordinates 6
Number of vibrational modes 20





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E Total
Linear (IR) 6 4 10 14 / 6
Quadratic (Raman) 6 4 10 16 / 4
IR + Raman - - 10 10 / 0



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


Decomposition into Irreducible representations
Force field Tensor
Order
A1 A2 E
linear 1 6 4 10
quadratic 2 86 69 155
cubic 3 846 814 1.650
quartic 4 6.896 6.744 13.640
quintic 5 46.512 46.240 92.752
sextic 6 271.021 270.069 541.035


Literature




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

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