Reduction formula for point group Cs



Characters for molecular motions
Motion E h
Cartesian 3N 15 5
Translation (x,y,z) 3 1
Rotation (Rx,Ry)* 2 0
Vibration 10 4
* Linear molecule


Decomposition into Irreducible representations
Motion A' A'' Total
Cartesian 3N 10 5 15
Translation (x,y,z) 2 1 3
Rotation (Rx,Ry)* 1 1 2
Vibration 7 3 10
* Linear molecule


Molecule Parameter
Number of Atoms (N) 5
Number of internal coordinates 10
Number of independant internal coordinates 7
Number of vibrational modes 10





Force field analysis


Allowed / forbidden vibronational transitions
Operator A' A'' Total
Linear (IR) 7 3 10 / 0
Quadratic (Raman) 7 3 10 / 0
IR + Raman 7 3 10 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E h
linear 1 10 4
quadratic 2 55 13
cubic 3 220 32
quartic 4 715 71
quintic 5 2.002 140
sextic 6 5.005 259


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A' A''
linear 1 7 3
quadratic 2 34 21
cubic 3 126 94
quartic 4 393 322
quintic 5 1.071 931
sextic 6 2.632 2.373


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