Reduction formula for point group S4



Characters for molecular motions
Motion E S4 C2 (S4)3
Cartesian 3N 51 -1 -1 -1
Translation (x,y,z) 3 -1 -1 -1
Rotation (Rx,Ry,Rz) 3 1 -1 1
Vibration 45 -1 1 -1



Decomposition into Irreducible representations
Motion A B E Total
Cartesian 3N 12 13 13 38
Translation (x,y,z) 0 1 1 2
Rotation (Rx,Ry,Rz) 1 0 1 2
Vibration 11 12 11 34



Molecule Parameter
Number of Atoms (N) 17
Number of internal coordinates 45
Number of independant internal coordinates 11
Number of vibrational modes 34





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B E Total
Linear (IR) 11 12 11 23 / 11
Quadratic (Raman) 11 12 11 34 / 0
IR + Raman - 12 11 23 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E S4 C2 (S4)3
linear 1 45 -1 1 -1
quadratic 2 1.035 1 23 1
cubic 3 16.215 -1 23 -1
quartic 4 194.580 12 276 12
quintic 5 1.906.884 -12 276 -12
sextic 6 15.890.700 12 2.300 12


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A B E
linear 1 11 12 11
quadratic 2 265 264 253
cubic 3 4.059 4.060 4.048
quartic 4 48.720 48.708 48.576
quintic 5 476.784 476.796 476.652
sextic 6 3.973.256 3.973.244 3.972.100


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