Reduction formula for point group Cs



Characters for molecular motions
Motion E h
Cartesian 3N 72 24
Translation (x,y,z) 3 1
Rotation (Rx,Ry,Rz) 3 -1
Vibration 66 24



Decomposition into Irreducible representations
Motion A' A'' Total
Cartesian 3N 48 24 72
Translation (x,y,z) 2 1 3
Rotation (Rx,Ry,Rz) 1 2 3
Vibration 45 21 66



Molecule Parameter
Number of Atoms (N) 24
Number of internal coordinates 66
Number of independant internal coordinates 45
Number of vibrational modes 66





Force field analysis


Allowed / forbidden vibronational transitions
Operator A' A'' Total
Linear (IR) 45 21 66 / 0
Quadratic (Raman) 45 21 66 / 0
IR + Raman 45 21 66 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E h
linear 1 66 24
quadratic 2 2.211 321
cubic 3 50.116 3.104
quartic 4 864.501 24.081
quintic 5 12.103.014 158.424
sextic 6 143.218.999 914.641


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A' A''
linear 1 45 21
quadratic 2 1.266 945
cubic 3 26.610 23.506
quartic 4 444.291 420.210
quintic 5 6.130.719 5.972.295
sextic 6 72.066.820 71.152.179


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