Reduction formula for point group C6



Characters for molecular motions
Motion E C6 C3 C2 (C3)2 (C6)5
Cartesian 3N 216 0 0 0 0 0
Translation (x,y,z) 3 2 0 -1 0 2
Rotation (Rx,Ry,Rz) 3 2 0 -1 0 2
Vibration 210 -4 0 2 0 -4



Decomposition into Irreducible representations
Motion A B E1 E2 Total
Cartesian 3N 36 36 36 36 144
Translation (x,y,z) 1 0 1 0 2
Rotation (Rx,Ry,Rz) 1 0 1 0 2
Vibration 34 36 34 36 140



Molecule Parameter
Number of Atoms (N) 72
Number of internal coordinates 210
Number of independant internal coordinates 34
Number of vibrational modes 140





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B E1 E2 Total
Linear (IR) 34 36 34 36 68 / 72
Quadratic (Raman) 34 36 34 36 104 / 36
IR + Raman 34 36 34 - 68 / 36



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C6 C3 C2 (C3)2 (C6)5
linear 1 210 -4 0 2 0 -4
quadratic 2 22.155 8 0 107 0 8
cubic 3 1.565.620 -10 70 212 70 -10
quartic 4 83.369.265 8 0 5.777 0 8
quintic 5 3.568.204.542 -4 0 11.342 0 -4
sextic 6 127.860.662.755 37 2.485 209.827 2.485 37


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A B E1 E2
linear 1 34 36 34 36
quadratic 2 3.713 3.672 3.676 3.709
cubic 3 260.992 260.928 260.888 260.962
quartic 4 13.895.843 13.893.912 13.893.916 13.895.839
quintic 5 594.702.646 594.698.868 594.698.866 594.702.648
sextic 6 21.310.146.271 21.310.076.304 21.310.075.080 21.310.145.010


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