Reduction formula for point group Cs



Characters for molecular motions
Motion E h
Cartesian 3N 18 6
Translation (x,y,z) 3 1
Rotation (Rx,Ry)* 2 0
Vibration 13 5
* Linear molecule


Decomposition into Irreducible representations
Motion A' A'' Total
Cartesian 3N 12 6 18
Translation (x,y,z) 2 1 3
Rotation (Rx,Ry)* 1 1 2
Vibration 9 4 13
* Linear molecule


Molecule Parameter
Number of Atoms (N) 6
Number of internal coordinates 13
Number of independant internal coordinates 9
Number of vibrational modes 13





Force field analysis


Allowed / forbidden vibronational transitions
Operator A' A'' Total
Linear (IR) 9 4 13 / 0
Quadratic (Raman) 9 4 13 / 0
IR + Raman 9 4 13 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E h
linear 1 13 5
quadratic 2 91 19
cubic 3 455 55
quartic 4 1.820 140
quintic 5 6.188 316
sextic 6 18.564 660


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A' A''
linear 1 9 4
quadratic 2 55 36
cubic 3 255 200
quartic 4 980 840
quintic 5 3.252 2.936
sextic 6 9.612 8.952


Literature




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

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