Reduction formula for point group C6



Characters for molecular motions
Motion E C6 C3 C2 (C3)2 (C6)5
Cartesian 3N 9 6 0 -3 0 6
Translation (x,y,z) 3 2 0 -1 0 2
Rotation (Rx,Ry)* 2 1 -1 -2 -1 1
Vibration 4 3 1 0 1 3
* Linear molecule


Decomposition into Irreducible representations
Motion A B E1 E2 Total
Cartesian 3N 3 0 3 0 6
Translation (x,y,z) 1 0 1 0 2
Rotation (Rx,Ry)* 0 0 1 0 1
Vibration 2 0 1 0 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 E1 E2 Total
Linear (IR) 2 0 1 0 3 / 0
Quadratic (Raman) 2 0 1 0 3 / 0
IR + Raman 2 0 1 - 3 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C6 C3 C2 (C3)2 (C6)5
linear 1 4 3 1 0 1 3
quadratic 2 10 5 1 2 1 5
cubic 3 20 6 2 0 2 6
quartic 4 35 6 2 3 2 6
quintic 5 56 6 2 0 2 6
sextic 6 84 7 3 4 3 7


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A B E1 E2
linear 1 2 0 1 0
quadratic 2 4 0 2 1
cubic 3 6 2 4 2
quartic 4 9 4 6 5
quintic 5 12 8 10 8
sextic 6 18 12 14 13


Literature




Character tables for chemically important point groups Character table for point group C6 Jacobs University Bremen

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