Reduction formula for point group Cs



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


Decomposition into Irreducible representations
Motion A' A'' Total
Cartesian 3N 8 7 15
Translation (x,y,z) 2 1 3
Rotation (Rx,Ry)* 0 2 2
Vibration 6 4 10
* Linear molecule


Molecule Parameter
Number of Atoms (N) 5
Number of internal coordinates 10
Number of independant internal coordinates 6
Number of vibrational modes 10





Force field analysis


Allowed / forbidden vibronational transitions
Operator A' A'' Total
Linear (IR) 6 4 10 / 0
Quadratic (Raman) 6 4 10 / 0
IR + Raman 6 4 10 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E h
linear 1 10 2
quadratic 2 55 7
cubic 3 220 12
quartic 4 715 27
quintic 5 2.002 42
sextic 6 5.005 77


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A' A''
linear 1 6 4
quadratic 2 31 24
cubic 3 116 104
quartic 4 371 344
quintic 5 1.022 980
sextic 6 2.541 2.464


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