Reduction formula for point group D3



Characters for molecular motions
Motion E 2C3 (z) 3C'2
Cartesian 3N 24 0 0
Translation 3 0 -1
Rotation 3 0 -1
Vibration 18 0 2



Decomposition into Irreducible representations
Motion A1 A2 E Total
Cartesian 3N 4 4 8 16
Translation 0 1 1 2
Rotation 0 1 1 2
Vibration 4 2 6 12



Molecule Parameter
Number of Atoms (N) 8
Number of internal coordinates 18
Number of independant internal coordinates 4
Number of vibrational modes 12





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E Total
Linear (IR) 4 2 6 8 / 4
Quadratic (Raman) 4 2 6 10 / 2
IR + Raman - - 6 6 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2C3 (z) 3C'2
linear 1 18 0 2
quadratic 2 171 0 11
cubic 3 1.140 6 20
quartic 4 5.985 0 65
quintic 5 26.334 0 110
sextic 6 100.947 21 275


Decomposition into Irreducible representations
Force field Tensor
Order
A1 A2 E
linear 1 4 2 6
quadratic 2 34 23 57
cubic 3 202 182 378
quartic 4 1.030 965 1.995
quintic 5 4.444 4.334 8.778
sextic 6 16.969 16.694 33.642


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