Reduction formula for point group C3



Characters for molecular motions
Motion E C3 (C3)2
Cartesian 3N 15 0 0
Translation 3 0 0
Rotation 3 0 0
Vibration 9 0 0



Decomposition into Irreducible representations
Motion A E Total
Cartesian 3N 5 5 10
Translation 1 1 2
Rotation 1 1 2
Vibration 3 3 6



Molecule Parameter
Number of Atoms (N) 5
Number of internal coordinates 9
Number of independant internal coordinates 3
Number of vibrational modes 6





Force field analysis


Allowed / forbidden vibronational transitions
Operator A E Total
Linear (IR) 3 3 6 / 0
Quadratic (Raman) 3 3 6 / 0
IR + Raman 3 3 6 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C3 (C3)2
linear 1 9 0 0
quadratic 2 45 0 0
cubic 3 165 3 3
quartic 4 495 0 0
quintic 5 1.287 0 0
sextic 6 3.003 6 6


Decomposition into Irreducible representations
Force field Tensor
Order
A E
linear 1 3 3
quadratic 2 15 15
cubic 3 57 54
quartic 4 165 165
quintic 5 429 429
sextic 6 1.005 999


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