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 120 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 114 0 0 2 0 0 0 8



Decomposition into Irreducible representations
Motion Ag Eg Tg Au Eu Tu Total
Cartesian 3N 6 6 14 4 4 16 50
Translation 0 0 0 0 0 1 1
Rotation 0 0 1 0 0 0 1
Vibration 6 6 13 4 4 15 48



Molecule Parameter
Number of Atoms (N) 40
Number of internal coordinates 114
Number of independant internal coordinates 6
Number of vibrational modes 48





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Eg Tg Au Eu Tu Total
Linear (IR) 6 6 13 4 4 15 15 / 33
Quadratic (Raman) 6 6 13 4 4 15 25 / 23
IR + Raman - - - 4 4 - 0* / 8
* 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 1 114 0 0 2 0 0 0 8
quadratic 2 6.555 0 0 59 57 0 0 89
cubic 3 253.460 38 38 116 0 0 0 544
quartic 4 7.413.705 0 0 1.769 1.653 0 0 3.669
quintic 5 174.963.438 0 0 3.422 0 0 0 18.600
sextic 6 3.470.108.187 741 741 35.931 32.509 19 19 96.957


Decomposition into Irreducible representations
Force field Tensor
Order
Ag Eg Tg Au Eu Tu
linear 1 6 6 13 4 4 15
quadratic 2 294 294 808 267 267 816
cubic 3 10.656 10.637 31.600 10.520 10.501 31.736
quartic 4 309.653 309.653 926.240 308.598 308.598 926.744
quintic 5 7.292.896 7.292.896 21.867.677 7.288.246 7.288.246 21.872.327
sextic 6 144.606.060 144.605.680 433.750.976 144.579.099 144.578.738 433.767.088


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