Reduction formula for point group C4



Characters for molecular motions
Motion E C4 C2 (C4)3
Cartesian 3N 9 3 -3 3
Translation (x,y,z) 3 1 -1 1
Rotation (Rx,Ry)* 2 0 -2 0
Vibration 4 2 0 2
* Linear molecule


Decomposition into Irreducible representations
Motion A B E Total
Cartesian 3N 3 0 3 6
Translation (x,y,z) 1 0 1 2
Rotation (Rx,Ry)* 0 0 1 1
Vibration 2 0 1 3
* Linear molecule


Molecule Parameter
Number of Atoms (N) 3
Number of internal coordinates 4
Number of independant internal coordinates 2
Number of vibrational modes 3





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B E Total
Linear (IR) 2 0 1 3 / 0
Quadratic (Raman) 2 0 1 3 / 0
IR + Raman 2 - 1 3 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C4 C2 (C4)3
linear 1 4 2 0 2
quadratic 2 10 2 2 2
cubic 3 20 2 0 2
quartic 4 35 3 3 3
quintic 5 56 4 0 4
sextic 6 84 4 4 4


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A B E
linear 1 2 0 1
quadratic 2 4 2 2
cubic 3 6 4 5
quartic 4 11 8 8
quintic 5 16 12 14
sextic 6 24 20 20


Literature




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

Last update Mai, 23rd 2018 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement