Reduction formula for point group C3



Characters for molecular motions
Motion E C3 (C3)2
Cartesian 3N 33 0 0
Translation (x,y,z) 3 0 0
Rotation (Rx,Ry,Rz) 3 0 0
Vibration 27 0 0



Decomposition into Irreducible representations
Motion A E Total
Cartesian 3N 11 11 22
Translation (x,y,z) 1 1 2
Rotation (Rx,Ry,Rz) 1 1 2
Vibration 9 9 18



Molecule Parameter
Number of Atoms (N) 11
Number of internal coordinates 27
Number of independant internal coordinates 9
Number of vibrational modes 18





Force field analysis


Allowed / forbidden vibronational transitions
Operator A E Total
Linear (IR) 9 9 18 / 0
Quadratic (Raman) 9 9 18 / 0
IR + Raman 9 9 18 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C3 (C3)2
linear 1 27 0 0
quadratic 2 378 0 0
cubic 3 3.654 9 9
quartic 4 27.405 0 0
quintic 5 169.911 0 0
sextic 6 906.192 45 45


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A E
linear 1 9 9
quadratic 2 126 126
cubic 3 1.224 1.215
quartic 4 9.135 9.135
quintic 5 56.637 56.637
sextic 6 302.094 302.049


Literature




Character tables for chemically important point groups Character table for point group C3 Constructor University Bremen

Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement