Reduction formula for point group C4



Characters for molecular motions
Motion E C4 C2 (C4)3
Cartesian 3N 24 0 0 0
Translation (x,y,z) 3 1 -1 1
Rotation (Rx,Ry,Rz) 3 1 -1 1
Vibration 18 -2 2 -2



Decomposition into Irreducible representations
Motion A B E Total
Cartesian 3N 6 6 6 18
Translation (x,y,z) 1 0 1 2
Rotation (Rx,Ry,Rz) 1 0 1 2
Vibration 4 6 4 14



Molecule Parameter
Number of Atoms (N) 8
Number of internal coordinates 18
Number of independant internal coordinates 4
Number of vibrational modes 14





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B E Total
Linear (IR) 4 6 4 8 / 6
Quadratic (Raman) 4 6 4 14 / 0
IR + Raman 4 - 4 8 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C4 C2 (C4)3
linear 1 18 -2 2 -2
quadratic 2 171 3 11 3
cubic 3 1.140 -4 20 -4
quartic 4 5.985 9 65 9
quintic 5 26.334 -14 110 -14
sextic 6 100.947 19 275 19


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A B E
linear 1 4 6 4
quadratic 2 47 44 40
cubic 3 288 292 280
quartic 4 1.517 1.508 1.480
quintic 5 6.604 6.618 6.556
sextic 6 25.315 25.296 25.168


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