Reduction formula for point group D3



Characters for molecular motions
Motion E 2C3 (z) 3C'2
Cartesian 3N 18 0 0
Translation 3 0 -1
Rotation 3 0 -1
Vibration 12 0 2



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



Molecule Parameter
Number of Atoms (N) 6
Number of internal coordinates 12
Number of independant internal coordinates 3
Number of vibrational modes 8





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E Total
Linear (IR) 3 1 4 5 / 3
Quadratic (Raman) 3 1 4 7 / 1
IR + Raman - - 4 4 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2C3 (z) 3C'2
linear 1 12 0 2
quadratic 2 78 0 8
cubic 3 364 4 14
quartic 4 1.365 0 35
quintic 5 4.368 0 56
sextic 6 12.376 10 112


Decomposition into Irreducible representations
Force field Tensor
Order
A1 A2 E
linear 1 3 1 4
quadratic 2 17 9 26
cubic 3 69 55 120
quartic 4 245 210 455
quintic 5 756 700 1.456
sextic 6 2.122 2.010 4.122


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