Reduction formula for point group Td



Characters for molecular motions
Motion E 8C3 3C2 6S4 6d
Cartesian 3N 51 0 -1 -1 5
Translation 3 0 -1 -1 1
Rotation 3 0 -1 1 -1
Vibration 45 0 1 -1 5



Decomposition into Irreducible representations
Motion A1 A2 E T1 T2 Total
Cartesian 3N 3 1 4 5 8 21
Translation 0 0 0 0 1 1
Rotation 0 0 0 1 0 1
Vibration 3 1 4 4 7 19



Molecule Parameter
Number of Atoms (N) 17
Number of internal coordinates 45
Number of independant internal coordinates 3
Number of vibrational modes 19





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E T1 T2 Total
Linear (IR) 3 1 4 4 7 7 / 12
Quadratic (Raman) 3 1 4 4 7 14 / 5
IR + Raman - 1 - 4 7 7 / 5



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 8C3 3C2 6S4 6d
linear 1 45 0 1 -1 5
quadratic 2 1.035 0 23 1 35
cubic 3 16.215 15 23 -1 135
quartic 4 194.580 0 276 12 580
quintic 5 1.906.884 0 276 -12 1.876
sextic 6 15.890.700 120 2.300 12 6.300


Decomposition into Irreducible representations
Force field Tensor
Order
A1 A2 E T1 T2
linear 1 3 1 4 4 7
quadratic 2 55 37 92 118 135
cubic 3 717 650 1.352 1.990 2.058
quartic 4 8.290 7.994 16.284 24.146 24.430
quintic 5 79.954 79.022 158.976 237.854 238.798
sextic 6 664.018 660.862 1.324.760 1.984.478 1.987.622


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