Reduction formula for point group Cs



Characters for molecular motions
Motion E h
Cartesian 3N 24 6
Translation (x,y,z) 3 1
Rotation (Rx,Ry,Rz) 3 -1
Vibration 18 6



Decomposition into Irreducible representations
Motion A' A'' Total
Cartesian 3N 15 9 24
Translation (x,y,z) 2 1 3
Rotation (Rx,Ry,Rz) 1 2 3
Vibration 12 6 18



Molecule Parameter
Number of Atoms (N) 8
Number of internal coordinates 18
Number of independant internal coordinates 12
Number of vibrational modes 18





Force field analysis


Allowed / forbidden vibronational transitions
Operator A' A'' Total
Linear (IR) 12 6 18 / 0
Quadratic (Raman) 12 6 18 / 0
IR + Raman 12 6 18 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E h
linear 1 18 6
quadratic 2 171 27
cubic 3 1.140 92
quartic 4 5.985 273
quintic 5 26.334 714
sextic 6 100.947 1.715


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A' A''
linear 1 12 6
quadratic 2 99 72
cubic 3 616 524
quartic 4 3.129 2.856
quintic 5 13.524 12.810
sextic 6 51.331 49.616


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