Reduction formula for point group C4



Characters for molecular motions
Motion E C4 C2 (C4)3
Cartesian 3N 15 5 -5 5
Translation (x,y,z) 3 1 -1 1
Rotation (Rx,Ry)* 2 0 -2 0
Vibration 10 4 -2 4
* Linear molecule


Decomposition into Irreducible representations
Motion A B E Total
Cartesian 3N 5 0 5 10
Translation (x,y,z) 1 0 1 2
Rotation (Rx,Ry)* 0 0 1 1
Vibration 4 0 3 7
* Linear molecule


Molecule Parameter
Number of Atoms (N) 5
Number of internal coordinates 10
Number of independant internal coordinates 4
Number of vibrational modes 7





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B E Total
Linear (IR) 4 0 3 7 / 0
Quadratic (Raman) 4 0 3 7 / 0
IR + Raman 4 - 3 7 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C4 C2 (C4)3
linear 1 10 4 -2 4
quadratic 2 55 7 7 7
cubic 3 220 8 -12 8
quartic 4 715 11 27 11
quintic 5 2.002 20 -42 20
sextic 6 5.005 29 77 29


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A B E
linear 1 4 0 3
quadratic 2 19 12 12
cubic 3 56 48 58
quartic 4 191 180 172
quintic 5 500 480 511
sextic 6 1.285 1.256 1.232


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