Reduction formula for point group Td



Characters for molecular motions
Motion E 8C3 3C2 6S4 6d
Cartesian 3N 21 0 -3 -1 3
Translation 3 0 -1 -1 1
Rotation 3 0 -1 1 -1
Vibration 15 0 -1 -1 3



Decomposition into Irreducible representations
Motion A1 A2 E T1 T2 Total
Cartesian 3N 1 0 1 2 4 8
Translation 0 0 0 0 1 1
Rotation 0 0 0 1 0 1
Vibration 1 0 1 1 3 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 A1 A2 E T1 T2 Total
Linear (IR) 1 0 1 1 3 3 / 3
Quadratic (Raman) 1 0 1 1 3 5 / 1
IR + Raman - 0 - 1 3 3 / 1



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 8C3 3C2 6S4 6d
linear 1 15 0 -1 -1 3
quadratic 2 120 0 8 0 12
cubic 3 680 5 -8 0 28
quartic 4 3.060 0 36 4 72
quintic 5 11.628 0 -36 -4 144
sextic 6 38.760 15 120 0 300


Decomposition into Irreducible representations
Force field Tensor
Order
A1 A2 E T1 T2
linear 1 1 0 1 1 3
quadratic 2 9 3 12 11 17
cubic 3 36 22 53 79 93
quartic 4 151 113 264 361 395
quintic 5 515 445 960 1.421 1.495
sextic 6 1.710 1.560 3.255 4.755 4.905


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