Reduction formula for point group Cs



Characters for molecular motions
Motion E h
Cartesian 3N 51 17
Translation (x,y,z) 3 1
Rotation (Rx,Ry,Rz) 3 -1
Vibration 45 17



Decomposition into Irreducible representations
Motion A' A'' Total
Cartesian 3N 34 17 51
Translation (x,y,z) 2 1 3
Rotation (Rx,Ry,Rz) 1 2 3
Vibration 31 14 45



Molecule Parameter
Number of Atoms (N) 17
Number of internal coordinates 45
Number of independant internal coordinates 31
Number of vibrational modes 45





Force field analysis


Allowed / forbidden vibronational transitions
Operator A' A'' Total
Linear (IR) 31 14 45 / 0
Quadratic (Raman) 31 14 45 / 0
IR + Raman 31 14 45 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E h
linear 1 45 17
quadratic 2 1.035 167
cubic 3 16.215 1.207
quartic 4 194.580 7.092
quintic 5 1.906.884 35.700
sextic 6 15.890.700 159.068


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A' A''
linear 1 31 14
quadratic 2 601 434
cubic 3 8.711 7.504
quartic 4 100.836 93.744
quintic 5 971.292 935.592
sextic 6 8.024.884 7.865.816


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