Reduction formula for point group Cs



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



Decomposition into Irreducible representations
Motion A' A'' Total
Cartesian 3N 15 12 27
Translation (x,y,z) 2 1 3
Rotation (Rx,Ry,Rz) 1 2 3
Vibration 12 9 21



Molecule Parameter
Number of Atoms (N) 9
Number of internal coordinates 21
Number of independant internal coordinates 12
Number of vibrational modes 21





Force field analysis


Allowed / forbidden vibronational transitions
Operator A' A'' Total
Linear (IR) 12 9 21 / 0
Quadratic (Raman) 12 9 21 / 0
IR + Raman 12 9 21 / 0



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


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A' A''
linear 1 12 9
quadratic 2 123 108
cubic 3 904 867
quartic 4 5.370 5.256
quintic 5 26.688 26.442
sextic 6 115.414 114.816


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