Reduction formula for point group C4



Characters for molecular motions
Motion E C4 C2 (C4)3
Cartesian 3N 6 2 -2 2
Translation (x,y,z) 3 1 -1 1
Rotation (Rx,Ry)* 2 0 -2 0
Vibration 1 1 1 1
* Linear molecule


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


Molecule Parameter
Number of Atoms (N) 2
Number of internal coordinates 1
Number of independant internal coordinates 1
Number of vibrational modes 1





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B E Total
Linear (IR) 1 0 0 1 / 0
Quadratic (Raman) 1 0 0 1 / 0
IR + Raman 1 - 0 1 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C4 C2 (C4)3
linear 1 1 1 1 1
quadratic 2 1 1 1 1
cubic 3 1 1 1 1
quartic 4 1 1 1 1
quintic 5 1 1 1 1
sextic 6 1 1 1 1


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A B E
linear 1 1 0 0
quadratic 2 1 0 0
cubic 3 1 0 0
quartic 4 1 0 0
quintic 5 1 0 0
sextic 6 1 0 0


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