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 252 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 246 0 0 2 0 0 0 4



Decomposition into Irreducible representations
Motion Ag Eg Tg Au Eu Tu Total
Cartesian 3N 11 11 31 10 10 32 105
Translation 0 0 0 0 0 1 1
Rotation 0 0 1 0 0 0 1
Vibration 11 11 30 10 10 31 103



Molecule Parameter
Number of Atoms (N) 84
Number of internal coordinates 246
Number of independant internal coordinates 11
Number of vibrational modes 103





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Eg Tg Au Eu Tu Total
Linear (IR) 11 11 30 10 10 31 31 / 72
Quadratic (Raman) 11 11 30 10 10 31 52 / 51
IR + Raman - - - 10 10 - 0* / 20
* 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 1 246 0 0 2 0 0 0 4
quadratic 2 30.381 0 0 125 123 0 0 131
cubic 3 2.511.496 82 82 248 0 0 0 504
quartic 4 156.340.626 0 0 7.874 7.626 0 0 8.626
quintic 5 7.817.031.300 0 0 15.500 0 0 0 32.000
sextic 6 327.012.476.050 3.403 3.403 333.250 317.750 41 41 380.750


Decomposition into Irreducible representations
Force field Tensor
Order
Ag Eg Tg Au Eu Tu
linear 1 11 11 30 10 10 31
quadratic 2 1.303 1.303 3.781 1.260 1.260 3.783
cubic 3 104.767 104.726 313.843 104.641 104.600 313.969
quartic 4 6.516.573 6.516.573 19.541.469 6.513.781 6.513.781 19.541.719
quintic 5 325.715.575 325.715.575 977.122.975 325.707.575 325.707.575 977.130.975
sextic 6 13.625.623.473 13.625.621.751 40.876.509.975 13.625.501.779 13.625.500.098 40.876.525.725


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