Reduction formula for point group D3



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



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



Molecule Parameter
Number of Atoms (N) 6
Number of internal coordinates 12
Number of independant internal coordinates 2
Number of vibrational modes 8





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E Total
Linear (IR) 2 2 4 6 / 2
Quadratic (Raman) 2 2 4 6 / 2
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 0
quadratic 2 78 0 6
cubic 3 364 4 0
quartic 4 1.365 0 21
quintic 5 4.368 0 0
sextic 6 12.376 10 56


Decomposition into Irreducible representations
Force field Tensor
Order
A1 A2 E
linear 1 2 2 4
quadratic 2 16 10 26
cubic 3 62 62 120
quartic 4 238 217 455
quintic 5 728 728 1.456
sextic 6 2.094 2.038 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