Reduction formula for point group C3



Characters for molecular motions
Motion E C3 (C3)2
Cartesian 3N 9 0 0
Translation (x,y,z) 3 0 0
Rotation (Rx,Ry)* 2 -1 -1
Vibration 4 1 1
* Linear molecule


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



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C3 (C3)2
linear 1 4 1 1
quadratic 2 10 1 1
cubic 3 20 2 2
quartic 4 35 2 2
quintic 5 56 2 2
sextic 6 84 3 3


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A E
linear 1 2 1
quadratic 2 4 3
cubic 3 8 6
quartic 4 13 11
quintic 5 20 18
sextic 6 30 27


Literature




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

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