Reduction formula for point group C3h



Characters for molecular motions
Motion E C3(z) (C3)2 h S3 (S3)5
Cartesian 3N 27 0 0 3 0 0
Translation (x,y,z) 3 0 0 1 -2 -2
Rotation (Rx,Ry,Rz) 3 0 0 -1 2 2
Vibration 21 0 0 3 0 0



Decomposition into Irreducible representations
Motion A' E' A'' E'' Total
Cartesian 3N 5 5 4 4 18
Translation (x,y,z) 0 1 1 0 2
Rotation (Rx,Ry,Rz) 1 0 0 1 2
Vibration 4 4 3 3 14



Molecule Parameter
Number of Atoms (N) 9
Number of internal coordinates 21
Number of independant internal coordinates 4
Number of vibrational modes 14





Force field analysis


Allowed / forbidden vibronational transitions
Operator A' E' A'' E'' Total
Linear (IR) 4 4 3 3 7 / 7
Quadratic (Raman) 4 4 3 3 11 / 3
IR + Raman - 4 - - 4 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C3(z) (C3)2 h S3 (S3)5
linear 1 21 0 0 3 0 0
quadratic 2 231 0 0 15 0 0
cubic 3 1.771 7 7 37 1 1
quartic 4 10.626 0 0 114 0 0
quintic 5 53.130 0 0 246 0 0
sextic 6 230.230 28 28 598 4 4


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A' E' A'' E''
linear 1 4 4 3 3
quadratic 2 41 41 36 36
cubic 3 304 300 291 288
quartic 4 1.790 1.790 1.752 1.752
quintic 5 8.896 8.896 8.814 8.814
sextic 6 38.482 38.466 38.280 38.268


Literature




Character tables for chemically important point groups Character table for point group C3h Constructor University Bremen

Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement