Reduction formula for point group Td



Characters of input representation
E 8C3 3C2 6S4 6d
6 0 2 0 2



Decomposition into Irreducible representations
A1 A2 E T1 T2 Total
1 0 1 0 1 3





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E T1 T2 Total
Linear (IR) 1 0 1 0 1 1 / 2
Quadratic (Raman) 1 0 1 0 1 3 / 0
IR + Raman - 0 - 0 1 1 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 8C3 3C2 6S4 6d
linear 1 6 0 2 0 2
quadratic 2 21 0 5 1 5
cubic 3 56 2 8 0 8
quartic 4 126 0 14 2 14
quintic 5 252 0 20 0 20
sextic 6 462 3 30 2 30


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 E T1 T2
linear 1 1 0 1 0 1
quadratic 2 3 0 3 1 3
cubic 3 6 2 6 4 8
quartic 4 11 3 14 11 17
quintic 5 18 8 26 24 34
sextic 6 32 16 45 47 61


Literature




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

Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement