Reduction formula for point group Td



Characters for molecular motions
Motion E 8C3 3C2 6S4 6d
Cartesian 3N 12 0 0 0 2
Translation (x,y,z) 3 0 -1 -1 1
Rotation (Rx,Ry,Rz) 3 0 -1 1 -1
Vibration 6 0 2 0 2



Decomposition into Irreducible representations
Motion A1 A2 E T1 T2 Total
Cartesian 3N 1 0 1 1 2 5
Translation (x,y,z) 0 0 0 0 1 1
Rotation (Rx,Ry,Rz) 0 0 0 1 0 1
Vibration 1 0 1 0 1 3



Molecule Parameter
Number of Atoms (N) 4
Number of internal coordinates 6
Number of independant internal coordinates 1
Number of vibrational modes 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 Jacobs University Bremen

Last update Mai, 23rd 2018 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement