Reduction formula for point group S6



Characters for molecular motions
Motion E C3(z) (C3)2 i (S6)5 S6
Cartesian 3N 48 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 42 0 0 0 0 0



Decomposition into Irreducible representations
Motion Ag Eg Au Eu Total
Cartesian 3N 8 8 8 8 32
Translation (x,y,z) 0 0 1 1 2
Rotation (Rx,Ry,Rz) 1 1 0 0 2
Vibration 7 7 7 7 28



Molecule Parameter
Number of Atoms (N) 16
Number of internal coordinates 42
Number of independant internal coordinates 7
Number of vibrational modes 28





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Eg Au Eu Total
Linear (IR) 7 7 7 7 14 / 14
Quadratic (Raman) 7 7 7 7 14 / 14
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 42 0 0 0 0 0
quadratic 2 903 0 0 21 0 0
cubic 3 13.244 14 14 0 0 0
quartic 4 148.995 0 0 231 0 0
quintic 5 1.370.754 0 0 0 0 0
sextic 6 10.737.573 105 105 1.771 7 7


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag Eg Au Eu
linear 1 7 7 7 7
quadratic 2 154 154 147 147
cubic 3 2.212 2.205 2.212 2.205
quartic 4 24.871 24.871 24.794 24.794
quintic 5 228.459 228.459 228.459 228.459
sextic 6 1.789.928 1.789.872 1.789.333 1.789.284


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