Reduction formula for point group C6



Characters for molecular motions
Motion E C6 C3 C2 (C3)2 (C6)5
Cartesian 3N 75 2 0 -1 0 2
Translation (x,y,z) 3 2 0 -1 0 2
Rotation (Rx,Ry,Rz) 3 2 0 -1 0 2
Vibration 69 -2 0 1 0 -2



Decomposition into Irreducible representations
Motion A B E1 E2 Total
Cartesian 3N 13 12 13 12 50
Translation (x,y,z) 1 0 1 0 2
Rotation (Rx,Ry,Rz) 1 0 1 0 2
Vibration 11 12 11 12 46



Molecule Parameter
Number of Atoms (N) 25
Number of internal coordinates 69
Number of independant internal coordinates 11
Number of vibrational modes 46





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B E1 E2 Total
Linear (IR) 11 12 11 12 22 / 24
Quadratic (Raman) 11 12 11 12 34 / 12
IR + Raman 11 12 11 - 22 / 12



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C6 C3 C2 (C3)2 (C6)5
linear 1 69 -2 0 1 0 -2
quadratic 2 2.415 2 0 35 0 2
cubic 3 57.155 -1 23 35 23 -1
quartic 4 1.028.790 0 0 630 0 0
quintic 5 15.020.334 0 0 630 0 0
sextic 6 185.250.786 12 276 7.770 276 12


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A B E1 E2
linear 1 11 12 11 12
quadratic 2 409 396 397 408
cubic 3 9.539 9.528 9.516 9.528
quartic 4 171.570 171.360 171.360 171.570
quintic 5 2.503.494 2.503.284 2.503.284 2.503.494
sextic 6 30.876.522 30.873.924 30.873.792 30.876.378


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