Reduction formula for point group S6



Characters for molecular motions
Motion E C3(z) (C3)2 i (S6)5 S6
Cartesian 3N 252 0 0 0 0 0
Translation (x,y,z) 3 0 0 -3 0 0
Rotation (Rx,Ry,Rz) 3 0 0 3 0 0
Vibration 246 0 0 0 0 0



Decomposition into Irreducible representations
Motion Ag Eg Au Eu Total
Cartesian 3N 42 42 42 42 168
Translation (x,y,z) 0 0 1 1 2
Rotation (Rx,Ry,Rz) 1 1 0 0 2
Vibration 41 41 41 41 164



Molecule Parameter
Number of Atoms (N) 84
Number of internal coordinates 246
Number of independant internal coordinates 41
Number of vibrational modes 164





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Eg Au Eu Total
Linear (IR) 41 41 41 41 82 / 82
Quadratic (Raman) 41 41 41 41 82 / 82
IR + Raman - - - - 0* / 0
* Center of inversion: Mutual Exclusion Principle



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C3(z) (C3)2 i (S6)5 S6
linear 1 246 0 0 0 0 0
quadratic 2 30.381 0 0 123 0 0
cubic 3 2.511.496 82 82 0 0 0
quartic 4 156.340.626 0 0 7.626 0 0
quintic 5 7.817.031.300 0 0 0 0 0
sextic 6 327.012.476.050 3.403 3.403 317.750 41 41


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag Eg Au Eu
linear 1 41 41 41 41
quadratic 2 5.084 5.084 5.043 5.043
cubic 3 418.610 418.569 418.610 418.569
quartic 4 26.058.042 26.058.042 26.055.500 26.055.500
quintic 5 1.302.838.550 1.302.838.550 1.302.838.550 1.302.838.550
sextic 6 54.502.133.448 54.502.131.726 54.502.027.504 54.502.025.823


Literature




Character tables for chemically important point groups Character table for point group S6 Constructor University Bremen

Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement