Reduction formula for point group Cs



Characters for molecular motions
Motion E h
Cartesian 3N 216 72
Translation (x,y,z) 3 1
Rotation (Rx,Ry,Rz) 3 -1
Vibration 210 72



Decomposition into Irreducible representations
Motion A' A'' Total
Cartesian 3N 144 72 216
Translation (x,y,z) 2 1 3
Rotation (Rx,Ry,Rz) 1 2 3
Vibration 141 69 210



Molecule Parameter
Number of Atoms (N) 72
Number of internal coordinates 210
Number of independant internal coordinates 141
Number of vibrational modes 210





Force field analysis


Allowed / forbidden vibronational transitions
Operator A' A'' Total
Linear (IR) 141 69 210 / 0
Quadratic (Raman) 141 69 210 / 0
IR + Raman 141 69 210 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E h
linear 1 210 72
quadratic 2 22.155 2.697
cubic 3 1.565.620 69.792
quartic 4 83.369.265 1.399.197
quintic 5 3.568.204.542 23.121.576
sextic 6 127.860.662.755 327.363.605


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A' A''
linear 1 141 69
quadratic 2 12.426 9.729
cubic 3 817.706 747.914
quartic 4 42.384.231 40.985.034
quintic 5 1.795.663.059 1.772.541.483
sextic 6 64.094.013.180 63.766.649.575


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