Reduction formula for point group Td



Characters for molecular motions
Motion E 8C3 3C2 6S4 6d
Cartesian 3N 78 0 -2 0 8
Translation 3 0 -1 -1 1
Rotation 3 0 -1 1 -1
Vibration 72 0 0 0 8



Decomposition into Irreducible representations
Motion A1 A2 E T1 T2 Total
Cartesian 3N 5 1 6 8 12 32
Translation 0 0 0 0 1 1
Rotation 0 0 0 1 0 1
Vibration 5 1 6 7 11 30



Molecule Parameter
Number of Atoms (N) 26
Number of internal coordinates 72
Number of independant internal coordinates 5
Number of vibrational modes 30





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E T1 T2 Total
Linear (IR) 5 1 6 7 11 11 / 19
Quadratic (Raman) 5 1 6 7 11 22 / 8
IR + Raman - 1 - 7 11 11 / 8



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 8C3 3C2 6S4 6d
linear 1 72 0 0 0 8
quadratic 2 2.628 0 36 0 68
cubic 3 64.824 24 0 0 376
quartic 4 1.215.450 0 666 18 2.010
quintic 5 18.474.840 0 0 0 8.856
sextic 6 237.093.780 300 8.436 0 37.268


Decomposition into Irreducible representations
Force field Tensor
Order
A1 A2 E T1 T2
linear 1 5 1 6 7 11
quadratic 2 131 97 228 307 341
cubic 3 2.803 2.615 5.394 8.009 8.197
quartic 4 51.234 50.220 101.454 151.350 152.346
quintic 5 771.999 767.571 1.539.570 2.307.141 2.311.569
sextic 6 9.889.379 9.870.745 19.759.824 29.626.351 29.644.985


Literature




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

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