Reduction formula for point group T



Characters for molecular motions
Motion E 4C3 4(C3)2 3C2
Cartesian 3N 12 0 0 0
Translation 3 0 0 -1
Rotation 3 0 0 -1
Vibration 6 0 0 2



Decomposition into Irreducible representations
Motion A E T Total
Cartesian 3N 1 1 3 5
Translation 0 0 1 1
Rotation 0 0 1 1
Vibration 1 1 1 3



Molecule Parameter
Number of Atoms (N) 4
Number of internal coordinates 6
Number of independant internal coordinates 1
Number of vibrational modes 3





Force field analysis


Allowed / forbidden vibronational transitions
Operator A E T Total
Linear (IR) 1 1 1 1 / 2
Quadratic (Raman) 1 1 1 3 / 0
IR + Raman - - 1 1 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 4C3 4(C3)2 3C2
linear 1 6 0 0 2
quadratic 2 21 0 0 5
cubic 3 56 2 2 8
quartic 4 126 0 0 14
quintic 5 252 0 0 20
sextic 6 462 3 3 30


Decomposition into Irreducible representations
Force field Tensor
Order
A E T
linear 1 1 1 1
quadratic 2 3 3 4
cubic 3 8 6 12
quartic 4 14 14 28
quintic 5 26 26 58
sextic 6 48 45 108


Literature




Character tables for chemically important point groups Character table for point group T Jacobs University Bremen

Last update Mai, 23rd 2018 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement