Reduction formula for point group Th



Characters for molecular motions
Motion E 4C3 4(C3)2 3C2 i 4(S6)5 4S6 3h
Cartesian 3N 60 0 0 0 0 0 0 4
Translation 3 0 0 -1 -3 0 0 1
Rotation 3 0 0 -1 3 0 0 -1
Vibration 54 0 0 2 0 0 0 4



Decomposition into Irreducible representations
Motion Ag Eg Tg Au Eu Tu Total
Cartesian 3N 3 3 7 2 2 8 25
Translation 0 0 0 0 0 1 1
Rotation 0 0 1 0 0 0 1
Vibration 3 3 6 2 2 7 23



Molecule Parameter
Number of Atoms (N) 20
Number of internal coordinates 54
Number of independant internal coordinates 3
Number of vibrational modes 23





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Eg Tg Au Eu Tu Total
Linear (IR) 3 3 6 2 2 7 7 / 16
Quadratic (Raman) 3 3 6 2 2 7 12 / 11
IR + Raman - - - 2 2 - 0* / 4
* Center of inversion: Mutual Exclusion Principle



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 4C3 4(C3)2 3C2 i 4(S6)5 4S6 3h
linear 1 54 0 0 2 0 0 0 4
quadratic 2 1.485 0 0 29 27 0 0 35
cubic 3 27.720 18 18 56 0 0 0 120
quartic 4 395.010 0 0 434 378 0 0 610
quintic 5 4.582.116 0 0 812 0 0 0 1.856
sextic 6 45.057.474 171 171 4.466 3.654 9 9 7.134


Decomposition into Irreducible representations
Force field Tensor
Order
Ag Eg Tg Au Eu Tu
linear 1 3 3 6 2 2 7
quadratic 2 71 71 181 60 60 183
cubic 3 1.183 1.174 3.443 1.153 1.144 3.473
quartic 4 16.605 16.605 49.293 16.421 16.421 49.351
quintic 5 191.255 191.255 572.431 190.791 190.791 572.895
sextic 6 1.879.057 1.878.967 5.631.191 1.876.963 1.876.882 5.632.061


Literature




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

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