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 21 0 0 -3 -3 0 0 5
Translation 3 0 0 -1 -3 0 0 1
Rotation 3 0 0 -1 3 0 0 -1
Vibration 15 0 0 -1 -3 0 0 5



Decomposition into Irreducible representations
Motion Ag Eg Tg Au Eu Tu Total
Cartesian 3N 1 1 2 0 0 4 8
Translation 0 0 0 0 0 1 1
Rotation 0 0 1 0 0 0 1
Vibration 1 1 1 0 0 3 6



Molecule Parameter
Number of Atoms (N) 7
Number of internal coordinates 15
Number of independant internal coordinates 1
Number of vibrational modes 6





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Eg Tg Au Eu Tu Total
Linear (IR) 1 1 1 0 0 3 3 / 3
Quadratic (Raman) 1 1 1 0 0 3 3 / 3
IR + Raman - - - 0 0 - 0* / 0
* 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 15 0 0 -1 -3 0 0 5
quadratic 2 120 0 0 8 12 0 0 20
cubic 3 680 5 5 -8 -28 -1 -1 60
quartic 4 3.060 0 0 36 72 0 0 160
quintic 5 11.628 0 0 -36 -144 0 0 376
sextic 6 38.760 15 15 120 300 3 3 820


Decomposition into Irreducible representations
Force field Tensor
Order
Ag Eg Tg Au Eu Tu
linear 1 1 1 1 0 0 3
quadratic 2 9 9 13 3 3 15
cubic 3 35 33 75 23 20 97
quartic 4 155 155 367 109 109 389
quintic 5 521 521 1.393 439 439 1.523
sextic 6 1.751 1.742 4.765 1.519 1.513 4.895


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