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 180 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 174 0 0 2 0 0 0 4



Decomposition into Irreducible representations
Motion Ag Eg Tg Au Eu Tu Total
Cartesian 3N 8 8 22 7 7 23 75
Translation 0 0 0 0 0 1 1
Rotation 0 0 1 0 0 0 1
Vibration 8 8 21 7 7 22 73



Molecule Parameter
Number of Atoms (N) 60
Number of internal coordinates 174
Number of independant internal coordinates 8
Number of vibrational modes 73





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Eg Tg Au Eu Tu Total
Linear (IR) 8 8 21 7 7 22 22 / 51
Quadratic (Raman) 8 8 21 7 7 22 37 / 36
IR + Raman - - - 7 7 - 0* / 14
* 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 1 174 0 0 2 0 0 0 4
quadratic 2 15.225 0 0 89 87 0 0 95
cubic 3 893.200 58 58 176 0 0 0 360
quartic 4 39.524.100 0 0 4.004 3.828 0 0 4.540
quintic 5 1.407.057.960 0 0 7.832 0 0 0 16.376
sextic 6 41.977.229.140 1.711 1.711 121.396 113.564 29 29 145.604


Decomposition into Irreducible representations
Force field Tensor
Order
Ag Eg Tg Au Eu Tu
linear 1 8 8 21 7 7 22
quadratic 2 661 661 1.891 630 630 1.893
cubic 3 37.303 37.274 111.583 37.213 37.184 111.673
quartic 4 1.648.065 1.648.065 4.939.923 1.646.611 1.646.611 4.940.101
quintic 5 58.630.441 58.630.441 175.879.219 58.626.347 58.626.347 175.883.313
sextic 6 1.749.089.901 1.749.089.031 5.247.134.463 1.749.044.017 1.749.043.176 5.247.142.473


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