Reduction formula for point group C3h



Characters for molecular motions
Motion E C3(z) (C3)2 h S3 (S3)5
Cartesian 3N 18 0 0 4 -2 -2
Translation (x,y,z) 3 0 0 1 -2 -2
Rotation (Rx,Ry,Rz) 3 0 0 -1 2 2
Vibration 12 0 0 4 -2 -2



Decomposition into Irreducible representations
Motion A' E' A'' E'' Total
Cartesian 3N 3 4 3 2 12
Translation (x,y,z) 0 1 1 0 2
Rotation (Rx,Ry,Rz) 1 0 0 1 2
Vibration 2 3 2 1 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 A' E' A'' E'' Total
Linear (IR) 2 3 2 1 5 / 3
Quadratic (Raman) 2 3 2 1 6 / 2
IR + Raman - 3 - - 3 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C3(z) (C3)2 h S3 (S3)5
linear 1 12 0 0 4 -2 -2
quadratic 2 78 0 0 14 2 2
cubic 3 364 4 4 36 0 0
quartic 4 1.365 0 0 85 -2 -2
quintic 5 4.368 0 0 176 2 2
sextic 6 12.376 10 10 344 2 2


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A' E' A'' E''
linear 1 2 3 2 1
quadratic 2 16 15 10 11
cubic 3 68 66 56 54
quartic 4 241 242 214 213
quintic 5 758 757 698 699
sextic 6 2.124 2.118 2.008 2.004


Literature




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

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