Reduction formula for point group T



Characters for molecular motions
Motion E 4C3 4(C3)2 3C2
Cartesian 3N 21 0 0 -3
Translation 3 0 0 -1
Rotation 3 0 0 -1
Vibration 15 0 0 -1



Decomposition into Irreducible representations
Motion A E T Total
Cartesian 3N 1 1 6 8
Translation 0 0 1 1
Rotation 0 0 1 1
Vibration 1 1 4 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 A E T Total
Linear (IR) 1 1 4 4 / 2
Quadratic (Raman) 1 1 4 6 / 0
IR + Raman - - 4 4 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 4C3 4(C3)2 3C2
linear 1 15 0 0 -1
quadratic 2 120 0 0 8
cubic 3 680 5 5 -8
quartic 4 3.060 0 0 36
quintic 5 11.628 0 0 -36
sextic 6 38.760 15 15 120


Decomposition into Irreducible representations
Force field Tensor
Order
A E T
linear 1 1 1 4
quadratic 2 12 12 28
cubic 3 58 53 172
quartic 4 264 264 756
quintic 5 960 960 2.916
sextic 6 3.270 3.255 9.660


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