Reduction formula for point group S6



Characters for molecular motions
Motion E C3(z) (C3)2 i (S6)5 S6
Cartesian 3N 90 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 84 0 0 0 0 0



Decomposition into Irreducible representations
Motion Ag Eg Au Eu Total
Cartesian 3N 15 15 15 15 60
Translation (x,y,z) 0 0 1 1 2
Rotation (Rx,Ry,Rz) 1 1 0 0 2
Vibration 14 14 14 14 56



Molecule Parameter
Number of Atoms (N) 30
Number of internal coordinates 84
Number of independant internal coordinates 14
Number of vibrational modes 56





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Eg Au Eu Total
Linear (IR) 14 14 14 14 28 / 28
Quadratic (Raman) 14 14 14 14 28 / 28
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 84 0 0 0 0 0
quadratic 2 3.570 0 0 42 0 0
cubic 3 102.340 28 28 0 0 0
quartic 4 2.225.895 0 0 903 0 0
quintic 5 39.175.752 0 0 0 0 0
sextic 6 581.106.988 406 406 13.244 14 14


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag Eg Au Eu
linear 1 14 14 14 14
quadratic 2 602 602 588 588
cubic 3 17.066 17.052 17.066 17.052
quartic 4 371.133 371.133 370.832 370.832
quintic 5 6.529.292 6.529.292 6.529.292 6.529.292
sextic 6 96.853.512 96.853.302 96.849.088 96.848.892


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