Reduction formula for point group Td



Characters for molecular motions
Motion E 8C3 3C2 6S4 6d
Cartesian 3N 66 0 -2 0 6
Translation 3 0 -1 -1 1
Rotation 3 0 -1 1 -1
Vibration 60 0 0 0 6



Decomposition into Irreducible representations
Motion A1 A2 E T1 T2 Total
Cartesian 3N 4 1 5 7 10 27
Translation 0 0 0 0 1 1
Rotation 0 0 0 1 0 1
Vibration 4 1 5 6 9 25



Molecule Parameter
Number of Atoms (N) 22
Number of internal coordinates 60
Number of independant internal coordinates 4
Number of vibrational modes 25





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E T1 T2 Total
Linear (IR) 4 1 5 6 9 9 / 16
Quadratic (Raman) 4 1 5 6 9 18 / 7
IR + Raman - 1 - 6 9 9 / 7



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 8C3 3C2 6S4 6d
linear 1 60 0 0 0 6
quadratic 2 1.830 0 30 0 48
cubic 3 37.820 20 0 0 218
quartic 4 595.665 0 465 15 1.071
quintic 5 7.624.512 0 0 0 4.032
sextic 6 82.598.880 210 4.960 0 15.456


Decomposition into Irreducible representations
Force field Tensor
Order
A1 A2 E T1 T2
linear 1 4 1 5 6 9
quadratic 2 92 68 160 213 237
cubic 3 1.637 1.528 3.145 4.673 4.782
quartic 4 25.149 24.606 49.755 74.136 74.664
quintic 5 318.696 316.680 635.376 952.056 954.072
sextic 6 3.446.174 3.438.446 6.884.410 10.320.376 10.328.104


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