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 36 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 30 0 0 2 0 0 0 4



Decomposition into Irreducible representations
Motion Ag Eg Tg Au Eu Tu Total
Cartesian 3N 2 2 4 1 1 5 15
Translation 0 0 0 0 0 1 1
Rotation 0 0 1 0 0 0 1
Vibration 2 2 3 1 1 4 13



Molecule Parameter
Number of Atoms (N) 12
Number of internal coordinates 30
Number of independant internal coordinates 2
Number of vibrational modes 13





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Eg Tg Au Eu Tu Total
Linear (IR) 2 2 3 1 1 4 4 / 9
Quadratic (Raman) 2 2 3 1 1 4 7 / 6
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 30 0 0 2 0 0 0 4
quadratic 2 465 0 0 17 15 0 0 23
cubic 3 4.960 10 10 32 0 0 0 72
quartic 4 40.920 0 0 152 120 0 0 256
quintic 5 278.256 0 0 272 0 0 0 680
sextic 6 1.623.160 55 55 952 680 5 5 1.904


Decomposition into Irreducible representations
Force field Tensor
Order
Ag Eg Tg Au Eu Tu
linear 1 2 2 3 1 1 4
quadratic 2 25 25 55 18 18 57
cubic 3 223 218 607 205 200 625
quartic 4 1.761 1.761 5.079 1.687 1.687 5.113
quintic 5 11.713 11.713 34.663 11.543 11.543 34.833
sextic 6 68.037 68.007 202.623 67.501 67.476 202.929


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