Reduction formula for point group C6



Characters for molecular motions
Motion E C6 C3 C2 (C3)2 (C6)5
Cartesian 3N 18 12 0 -6 0 12
Translation (x,y,z) 3 2 0 -1 0 2
Rotation (Rx,Ry)* 2 1 -1 -2 -1 1
Vibration 13 9 1 -3 1 9
* Linear molecule


Decomposition into Irreducible representations
Motion A B E1 E2 Total
Cartesian 3N 6 0 6 0 12
Translation (x,y,z) 1 0 1 0 2
Rotation (Rx,Ry)* 0 0 1 0 1
Vibration 5 0 4 0 9
* Linear molecule


Molecule Parameter
Number of Atoms (N) 6
Number of internal coordinates 13
Number of independant internal coordinates 5
Number of vibrational modes 9





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B E1 E2 Total
Linear (IR) 5 0 4 0 9 / 0
Quadratic (Raman) 5 0 4 0 9 / 0
IR + Raman 5 0 4 - 9 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C6 C3 C2 (C3)2 (C6)5
linear 1 13 9 1 -3 1 9
quadratic 2 91 41 1 11 1 41
cubic 3 455 125 5 -25 5 125
quartic 4 1.820 285 5 60 5 285
quintic 5 6.188 517 5 -116 5 517
sextic 6 18.564 783 15 228 15 783


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A B E1 E2
linear 1 5 0 4 0
quadratic 2 31 0 20 10
cubic 3 115 40 100 50
quartic 4 410 200 340 265
quintic 5 1.186 880 1.136 925
sextic 6 3.398 2.800 3.184 2.999


Literature




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

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