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 72 0 0 0 0 0 0 8
Translation 3 0 0 -1 -3 0 0 1
Rotation 3 0 0 -1 3 0 0 -1
Vibration 66 0 0 2 0 0 0 8



Decomposition into Irreducible representations
Motion Ag Eg Tg Au Eu Tu Total
Cartesian 3N 4 4 8 2 2 10 30
Translation 0 0 0 0 0 1 1
Rotation 0 0 1 0 0 0 1
Vibration 4 4 7 2 2 9 28



Molecule Parameter
Number of Atoms (N) 24
Number of internal coordinates 66
Number of independant internal coordinates 4
Number of vibrational modes 28





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Eg Tg Au Eu Tu Total
Linear (IR) 4 4 7 2 2 9 9 / 19
Quadratic (Raman) 4 4 7 2 2 9 15 / 13
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 66 0 0 2 0 0 0 8
quadratic 2 2.211 0 0 35 33 0 0 65
cubic 3 50.116 22 22 68 0 0 0 352
quartic 4 864.501 0 0 629 561 0 0 1.809
quintic 5 12.103.014 0 0 1.190 0 0 0 7.752
sextic 6 143.218.999 253 253 7.735 6.545 11 11 31.441


Decomposition into Irreducible representations
Force field Tensor
Order
Ag Eg Tg Au Eu Tu
linear 1 4 4 7 2 2 9
quadratic 2 106 106 268 87 87 276
cubic 3 2.148 2.137 6.212 2.060 2.049 6.300
quartic 4 36.349 36.349 107.828 35.850 35.850 108.140
quintic 5 505.410 505.410 1.511.759 503.472 503.472 1.513.697
sextic 6 5.972.716 5.972.584 17.898.296 5.964.303 5.964.182 17.904.520


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