Reduction formula for point group S6



Characters for molecular motions
Motion E C3(z) (C3)2 i (S6)5 S6
Cartesian 3N 54 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 48 0 0 0 0 0



Decomposition into Irreducible representations
Motion Ag Eg Au Eu Total
Cartesian 3N 9 9 9 9 36
Translation (x,y,z) 0 0 1 1 2
Rotation (Rx,Ry,Rz) 1 1 0 0 2
Vibration 8 8 8 8 32



Molecule Parameter
Number of Atoms (N) 18
Number of internal coordinates 48
Number of independant internal coordinates 8
Number of vibrational modes 32





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Eg Au Eu Total
Linear (IR) 8 8 8 8 16 / 16
Quadratic (Raman) 8 8 8 8 16 / 16
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 48 0 0 0 0 0
quadratic 2 1.176 0 0 24 0 0
cubic 3 19.600 16 16 0 0 0
quartic 4 249.900 0 0 300 0 0
quintic 5 2.598.960 0 0 0 0 0
sextic 6 22.957.480 136 136 2.600 8 8


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag Eg Au Eu
linear 1 8 8 8 8
quadratic 2 200 200 192 192
cubic 3 3.272 3.264 3.272 3.264
quartic 4 41.700 41.700 41.600 41.600
quintic 5 433.160 433.160 433.160 433.160
sextic 6 3.826.728 3.826.656 3.825.856 3.825.792


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