Reduction formula for point group S4



Characters for molecular motions
Motion E S4 C2 (S4)3
Cartesian 3N 66 0 -2 0
Translation (x,y,z) 3 -1 -1 -1
Rotation (Rx,Ry,Rz) 3 1 -1 1
Vibration 60 0 0 0



Decomposition into Irreducible representations
Motion A B E Total
Cartesian 3N 16 16 17 49
Translation (x,y,z) 0 1 1 2
Rotation (Rx,Ry,Rz) 1 0 1 2
Vibration 15 15 15 45



Molecule Parameter
Number of Atoms (N) 22
Number of internal coordinates 60
Number of independant internal coordinates 15
Number of vibrational modes 45





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B E Total
Linear (IR) 15 15 15 30 / 15
Quadratic (Raman) 15 15 15 45 / 0
IR + Raman - 15 15 30 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E S4 C2 (S4)3
linear 1 60 0 0 0
quadratic 2 1.830 0 30 0
cubic 3 37.820 0 0 0
quartic 4 595.665 15 465 15
quintic 5 7.624.512 0 0 0
sextic 6 82.598.880 0 4.960 0


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A B E
linear 1 15 15 15
quadratic 2 465 465 450
cubic 3 9.455 9.455 9.455
quartic 4 149.040 149.025 148.800
quintic 5 1.906.128 1.906.128 1.906.128
sextic 6 20.650.960 20.650.960 20.648.480


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