Reduction formula for point group C4



Characters for molecular motions
Motion E C4 C2 (C4)3
Cartesian 3N 48 0 0 0
Translation (x,y,z) 3 1 -1 1
Rotation (Rx,Ry,Rz) 3 1 -1 1
Vibration 42 -2 2 -2



Decomposition into Irreducible representations
Motion A B E Total
Cartesian 3N 12 12 12 36
Translation (x,y,z) 1 0 1 2
Rotation (Rx,Ry,Rz) 1 0 1 2
Vibration 10 12 10 32



Molecule Parameter
Number of Atoms (N) 16
Number of internal coordinates 42
Number of independant internal coordinates 10
Number of vibrational modes 32





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B E Total
Linear (IR) 10 12 10 20 / 12
Quadratic (Raman) 10 12 10 32 / 0
IR + Raman 10 - 10 20 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C4 C2 (C4)3
linear 1 42 -2 2 -2
quadratic 2 903 3 23 3
cubic 3 13.244 -4 44 -4
quartic 4 148.995 15 275 15
quintic 5 1.370.754 -26 506 -26
sextic 6 10.737.573 37 2.277 37


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A B E
linear 1 10 12 10
quadratic 2 233 230 220
cubic 3 3.320 3.324 3.300
quartic 4 37.325 37.310 37.180
quintic 5 342.802 342.828 342.562
sextic 6 2.684.981 2.684.944 2.683.824


Literature




Character tables for chemically important point groups Character table for point group C4 Constructor University Bremen

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