Reduction formula for point group S4



Characters for molecular motions
Motion E S4 C2 (S4)3
Cartesian 3N 135 -1 -1 -1
Translation (x,y,z) 3 -1 -1 -1
Rotation (Rx,Ry,Rz) 3 1 -1 1
Vibration 129 -1 1 -1



Decomposition into Irreducible representations
Motion A B E Total
Cartesian 3N 33 34 34 101
Translation (x,y,z) 0 1 1 2
Rotation (Rx,Ry,Rz) 1 0 1 2
Vibration 32 33 32 97



Molecule Parameter
Number of Atoms (N) 45
Number of internal coordinates 129
Number of independant internal coordinates 32
Number of vibrational modes 97





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B E Total
Linear (IR) 32 33 32 65 / 32
Quadratic (Raman) 32 33 32 97 / 0
IR + Raman - 33 32 65 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E S4 C2 (S4)3
linear 1 129 -1 1 -1
quadratic 2 8.385 1 65 1
cubic 3 366.145 -1 65 -1
quartic 4 12.082.785 33 2.145 33
quintic 5 321.402.081 -33 2.145 -33
sextic 6 7.177.979.809 33 47.905 33


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A B E
linear 1 32 33 32
quadratic 2 2.113 2.112 2.080
cubic 3 91.552 91.553 91.520
quartic 4 3.021.249 3.021.216 3.020.160
quintic 5 80.351.040 80.351.073 80.349.984
sextic 6 1.794.506.945 1.794.506.912 1.794.482.976


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