Reduction formula for point group Cs



Characters for molecular motions
Motion E h
Cartesian 3N 45 15
Translation (x,y,z) 3 1
Rotation (Rx,Ry,Rz) 3 -1
Vibration 39 15



Decomposition into Irreducible representations
Motion A' A'' Total
Cartesian 3N 30 15 45
Translation (x,y,z) 2 1 3
Rotation (Rx,Ry,Rz) 1 2 3
Vibration 27 12 39



Molecule Parameter
Number of Atoms (N) 15
Number of internal coordinates 39
Number of independant internal coordinates 27
Number of vibrational modes 39





Force field analysis


Allowed / forbidden vibronational transitions
Operator A' A'' Total
Linear (IR) 27 12 39 / 0
Quadratic (Raman) 27 12 39 / 0
IR + Raman 27 12 39 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E h
linear 1 39 15
quadratic 2 780 132
cubic 3 10.660 860
quartic 4 111.930 4.578
quintic 5 962.598 20.958
sextic 6 7.059.052 85.204


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A' A''
linear 1 27 12
quadratic 2 456 324
cubic 3 5.760 4.900
quartic 4 58.254 53.676
quintic 5 491.778 470.820
sextic 6 3.572.128 3.486.924


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