Reduction formula for point group S6



Characters for molecular motions
Motion E C3(z) (C3)2 i (S6)5 S6
Cartesian 3N 180 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 174 0 0 0 0 0



Decomposition into Irreducible representations
Motion Ag Eg Au Eu Total
Cartesian 3N 30 30 30 30 120
Translation (x,y,z) 0 0 1 1 2
Rotation (Rx,Ry,Rz) 1 1 0 0 2
Vibration 29 29 29 29 116



Molecule Parameter
Number of Atoms (N) 60
Number of internal coordinates 174
Number of independant internal coordinates 29
Number of vibrational modes 116





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Eg Au Eu Total
Linear (IR) 29 29 29 29 58 / 58
Quadratic (Raman) 29 29 29 29 58 / 58
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 1 174 0 0 0 0 0
quadratic 2 15.225 0 0 87 0 0
cubic 3 893.200 58 58 0 0 0
quartic 4 39.524.100 0 0 3.828 0 0
quintic 5 1.407.057.960 0 0 0 0 0
sextic 6 41.977.229.140 1.711 1.711 113.564 29 29


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag Eg Au Eu
linear 1 29 29 29 29
quadratic 2 2.552 2.552 2.523 2.523
cubic 3 148.886 148.857 148.886 148.857
quartic 4 6.587.988 6.587.988 6.586.712 6.586.712
quintic 5 234.509.660 234.509.660 234.509.660 234.509.660
sextic 6 6.996.224.364 6.996.223.494 6.996.186.490 6.996.185.649


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