Reduction formula for point group T



Characters for molecular motions
Motion E 4C3 4(C3)2 3C2
Cartesian 3N 15 0 0 -1
Translation 3 0 0 -1
Rotation 3 0 0 -1
Vibration 9 0 0 1



Decomposition into Irreducible representations
Motion A E T Total
Cartesian 3N 1 1 4 6
Translation 0 0 1 1
Rotation 0 0 1 1
Vibration 1 1 2 4



Molecule Parameter
Number of Atoms (N) 5
Number of internal coordinates 9
Number of independant internal coordinates 1
Number of vibrational modes 4





Force field analysis


Allowed / forbidden vibronational transitions
Operator A E T Total
Linear (IR) 1 1 2 2 / 2
Quadratic (Raman) 1 1 2 4 / 0
IR + Raman - - 2 2 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 4C3 4(C3)2 3C2
linear 1 9 0 0 1
quadratic 2 45 0 0 5
cubic 3 165 3 3 5
quartic 4 495 0 0 15
quintic 5 1.287 0 0 15
sextic 6 3.003 6 6 35


Decomposition into Irreducible representations
Force field Tensor
Order
A E T
linear 1 1 1 2
quadratic 2 5 5 10
cubic 3 17 14 40
quartic 4 45 45 120
quintic 5 111 111 318
sextic 6 263 257 742


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