Reduction formula for point group Td



Characters for molecular motions
Motion E 8C3 3C2 6S4 6d
Cartesian 3N 48 0 0 0 8
Translation 3 0 -1 -1 1
Rotation 3 0 -1 1 -1
Vibration 42 0 2 0 8



Decomposition into Irreducible representations
Motion A1 A2 E T1 T2 Total
Cartesian 3N 4 0 4 4 8 20
Translation 0 0 0 0 1 1
Rotation 0 0 0 1 0 1
Vibration 4 0 4 3 7 18



Molecule Parameter
Number of Atoms (N) 16
Number of internal coordinates 42
Number of independant internal coordinates 4
Number of vibrational modes 18





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E T1 T2 Total
Linear (IR) 4 0 4 3 7 7 / 11
Quadratic (Raman) 4 0 4 3 7 15 / 3
IR + Raman - 0 - 3 7 7 / 3



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 8C3 3C2 6S4 6d
linear 1 42 0 2 0 8
quadratic 2 903 0 23 1 53
cubic 3 13.244 14 44 0 256
quartic 4 148.995 0 275 11 1.095
quintic 5 1.370.754 0 506 0 4.056
sextic 6 10.737.573 105 2.277 11 13.803


Decomposition into Irreducible representations
Force field Tensor
Order
A1 A2 E T1 T2
linear 1 4 0 4 3 7
quadratic 2 54 27 81 97 123
cubic 3 626 498 1.110 1.586 1.714
quartic 4 6.519 5.966 12.485 18.319 18.861
quintic 5 58.192 56.164 114.356 170.267 172.295
sextic 6 451.172 444.265 895.332 1.338.464 1.345.360


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