Reduction formula for point group Cs



Characters for molecular motions
Motion E h
Cartesian 3N 90 30
Translation (x,y,z) 3 1
Rotation (Rx,Ry,Rz) 3 -1
Vibration 84 30



Decomposition into Irreducible representations
Motion A' A'' Total
Cartesian 3N 60 30 90
Translation (x,y,z) 2 1 3
Rotation (Rx,Ry,Rz) 1 2 3
Vibration 57 27 84



Molecule Parameter
Number of Atoms (N) 30
Number of internal coordinates 84
Number of independant internal coordinates 57
Number of vibrational modes 84





Force field analysis


Allowed / forbidden vibronational transitions
Operator A' A'' Total
Linear (IR) 57 27 84 / 0
Quadratic (Raman) 57 27 84 / 0
IR + Raman 57 27 84 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E h
linear 1 84 30
quadratic 2 3.570 492
cubic 3 102.340 5.770
quartic 4 2.225.895 53.853
quintic 5 39.175.752 423.516
sextic 6 581.106.988 2.907.424


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A' A''
linear 1 57 27
quadratic 2 2.031 1.539
cubic 3 54.055 48.285
quartic 4 1.139.874 1.086.021
quintic 5 19.799.634 19.376.118
sextic 6 292.007.206 289.099.782


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