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 57 0 0 -3 -3 0 0 9
Translation 3 0 0 -1 -3 0 0 1
Rotation 3 0 0 -1 3 0 0 -1
Vibration 51 0 0 -1 -3 0 0 9



Decomposition into Irreducible representations
Motion Ag Eg Tg Au Eu Tu Total
Cartesian 3N 3 3 6 1 1 9 23
Translation 0 0 0 0 0 1 1
Rotation 0 0 1 0 0 0 1
Vibration 3 3 5 1 1 8 21



Molecule Parameter
Number of Atoms (N) 19
Number of internal coordinates 51
Number of independant internal coordinates 3
Number of vibrational modes 21





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Eg Tg Au Eu Tu Total
Linear (IR) 3 3 5 1 1 8 8 / 13
Quadratic (Raman) 3 3 5 1 1 8 11 / 10
IR + Raman - - - 1 1 - 0* / 2
* 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 51 0 0 -1 -3 0 0 9
quadratic 2 1.326 0 0 26 30 0 0 66
cubic 3 23.426 17 17 -26 -82 -1 -1 354
quartic 4 316.251 0 0 351 459 0 0 1.671
quintic 5 3.478.761 0 0 -351 -1.161 0 0 6.831
sextic 6 32.468.436 153 153 3.276 4.788 9 9 25.564


Decomposition into Irreducible representations
Force field Tensor
Order
Ag Eg Tg Au Eu Tu
linear 1 3 3 5 1 1 8
quadratic 2 68 68 158 49 49 167
cubic 3 1.019 1.011 2.877 938 929 2.986
quartic 4 13.449 13.449 39.336 12.993 12.993 39.639
quintic 5 145.710 145.710 433.890 144.099 144.099 435.888
sextic 6 1.356.710 1.356.629 4.055.548 1.349.914 1.349.842 4.060.742


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