Reduction formula for point group S4



Characters for molecular motions
Motion E S4 C2 (S4)3
Cartesian 3N 72 0 0 0
Translation (x,y,z) 3 -1 -1 -1
Rotation (Rx,Ry,Rz) 3 1 -1 1
Vibration 66 0 2 0



Decomposition into Irreducible representations
Motion A B E Total
Cartesian 3N 18 18 18 54
Translation (x,y,z) 0 1 1 2
Rotation (Rx,Ry,Rz) 1 0 1 2
Vibration 17 17 16 50



Molecule Parameter
Number of Atoms (N) 24
Number of internal coordinates 66
Number of independant internal coordinates 17
Number of vibrational modes 50





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B E Total
Linear (IR) 17 17 16 33 / 17
Quadratic (Raman) 17 17 16 50 / 0
IR + Raman - 17 16 33 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E S4 C2 (S4)3
linear 1 66 0 2 0
quadratic 2 2.211 1 35 1
cubic 3 50.116 0 68 0
quartic 4 864.501 17 629 17
quintic 5 12.103.014 0 1.190 0
sextic 6 143.218.999 17 7.735 17


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A B E
linear 1 17 17 16
quadratic 2 562 561 544
cubic 3 12.546 12.546 12.512
quartic 4 216.291 216.274 215.968
quintic 5 3.026.051 3.026.051 3.025.456
sextic 6 35.806.692 35.806.675 35.802.816


Literature




Character tables for chemically important point groups Character table for point group S4 Constructor University Bremen

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