Reduction formula for point group Td



Characters for molecular motions
Motion E 8C3 3C2 6S4 6d
Cartesian 3N 24 0 0 0 4
Translation 3 0 -1 -1 1
Rotation 3 0 -1 1 -1
Vibration 18 0 2 0 4



Decomposition into Irreducible representations
Motion A1 A2 E T1 T2 Total
Cartesian 3N 2 0 2 2 4 10
Translation 0 0 0 0 1 1
Rotation 0 0 0 1 0 1
Vibration 2 0 2 1 3 8



Molecule Parameter
Number of Atoms (N) 8
Number of internal coordinates 18
Number of independant internal coordinates 2
Number of vibrational modes 8





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E T1 T2 Total
Linear (IR) 2 0 2 1 3 3 / 5
Quadratic (Raman) 2 0 2 1 3 7 / 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 18 0 2 0 4
quadratic 2 171 0 11 1 17
cubic 3 1.140 6 20 0 48
quartic 4 5.985 0 65 5 133
quintic 5 26.334 0 110 0 308
sextic 6 100.947 21 275 5 693


Decomposition into Irreducible representations
Force field Tensor
Order
A1 A2 E T1 T2
linear 1 2 0 2 1 3
quadratic 2 13 4 17 16 24
cubic 3 64 40 98 128 152
quartic 4 292 223 515 708 772
quintic 5 1.188 1.034 2.222 3.201 3.355
sextic 6 4.422 4.073 8.474 12.412 12.756


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