Reduction formula for point group C4



Characters for molecular motions
Motion E C4 C2 (C4)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 -2 2 -2



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



Molecule Parameter
Number of Atoms (N) 24
Number of internal coordinates 66
Number of independant internal coordinates 16
Number of vibrational modes 50





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B E Total
Linear (IR) 16 18 16 32 / 18
Quadratic (Raman) 16 18 16 50 / 0
IR + Raman 16 - 16 32 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C4 C2 (C4)3
linear 1 66 -2 2 -2
quadratic 2 2.211 3 35 3
cubic 3 50.116 -4 68 -4
quartic 4 864.501 21 629 21
quintic 5 12.103.014 -38 1.190 -38
sextic 6 143.218.999 55 7.735 55


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A B E
linear 1 16 18 16
quadratic 2 563 560 544
cubic 3 12.544 12.548 12.512
quartic 4 216.293 216.272 215.968
quintic 5 3.026.032 3.026.070 3.025.456
sextic 6 35.806.711 35.806.656 35.802.816


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