Reduction formula for point group T



Characters for molecular motions
Motion E 4C3 4(C3)2 3C2
Cartesian 3N 24 0 0 0
Translation 3 0 0 -1
Rotation 3 0 0 -1
Vibration 18 0 0 2



Decomposition into Irreducible representations
Motion A E T Total
Cartesian 3N 2 2 6 10
Translation 0 0 1 1
Rotation 0 0 1 1
Vibration 2 2 4 8



Molecule Parameter
Number of Atoms (N) 8
Number of internal coordinates 18
Number of independant internal coordinates 2
Number of vibrational modes 8





Force field analysis


Allowed / forbidden vibronational transitions
Operator A E T Total
Linear (IR) 2 2 4 4 / 4
Quadratic (Raman) 2 2 4 8 / 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 18 0 0 2
quadratic 2 171 0 0 11
cubic 3 1.140 6 6 20
quartic 4 5.985 0 0 65
quintic 5 26.334 0 0 110
sextic 6 100.947 21 21 275


Decomposition into Irreducible representations
Force field Tensor
Order
A E T
linear 1 2 2 4
quadratic 2 17 17 40
cubic 3 104 98 280
quartic 4 515 515 1.480
quintic 5 2.222 2.222 6.556
sextic 6 8.495 8.474 25.168


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