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 48 0 0 0 0 0 0 0
Translation 3 0 0 -1 -3 0 0 1
Rotation 3 0 0 -1 3 0 0 -1
Vibration 42 0 0 2 0 0 0 0



Decomposition into Irreducible representations
Motion Ag Eg Tg Au Eu Tu Total
Cartesian 3N 2 2 6 2 2 6 20
Translation 0 0 0 0 0 1 1
Rotation 0 0 1 0 0 0 1
Vibration 2 2 5 2 2 5 18



Molecule Parameter
Number of Atoms (N) 16
Number of internal coordinates 42
Number of independant internal coordinates 2
Number of vibrational modes 18





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Eg Tg Au Eu Tu Total
Linear (IR) 2 2 5 2 2 5 5 / 13
Quadratic (Raman) 2 2 5 2 2 5 9 / 9
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 42 0 0 2 0 0 0 0
quadratic 2 903 0 0 23 21 0 0 21
cubic 3 13.244 14 14 44 0 0 0 0
quartic 4 148.995 0 0 275 231 0 0 231
quintic 5 1.370.754 0 0 506 0 0 0 0
sextic 6 10.737.573 105 105 2.277 1.771 7 7 1.771


Decomposition into Irreducible representations
Force field Tensor
Order
Ag Eg Tg Au Eu Tu
linear 1 2 2 5 2 2 5
quadratic 2 44 44 110 37 37 110
cubic 3 562 555 1.650 562 555 1.650
quartic 4 6.281 6.281 18.590 6.204 6.204 18.590
quintic 5 57.178 57.178 171.281 57.178 57.178 171.281
sextic 6 448.016 447.960 1.341.912 447.421 447.372 1.341.912


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