Reduction formula for point group T



Characters for molecular motions
Motion E 4C3 4(C3)2 3C2
Cartesian 3N 156 0 0 0
Translation (x,y,z) 3 0 0 -1
Rotation (Rx,Ry,Rz) 3 0 0 -1
Vibration 150 0 0 2



Decomposition into Irreducible representations
Motion A E T Total
Cartesian 3N 13 13 39 65
Translation (x,y,z) 0 0 1 1
Rotation (Rx,Ry,Rz) 0 0 1 1
Vibration 13 13 37 63



Molecule Parameter
Number of Atoms (N) 52
Number of internal coordinates 150
Number of independant internal coordinates 13
Number of vibrational modes 63





Force field analysis


Allowed / forbidden vibronational transitions
Operator A E T Total
Linear (IR) 13 13 37 37 / 26
Quadratic (Raman) 13 13 37 63 / 0
IR + Raman - - 37 37 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 4C3 4(C3)2 3C2
linear 1 150 0 0 2
quadratic 2 11.325 0 0 77
cubic 3 573.800 50 50 152
quartic 4 21.947.850 0 0 3.002
quintic 5 675.993.780 0 0 5.852
sextic 6 17.463.172.650 1.275 1.275 79.002


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A E T
linear 1 13 13 37
quadratic 2 963 963 2.812
cubic 3 47.888 47.838 143.412
quartic 4 1.829.738 1.829.738 5.486.212
quintic 5 56.334.278 56.334.278 168.996.982
sextic 6 1.455.284.988 1.455.283.713 4.365.773.412


Literature




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

Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement