Reduction formula for point group D3



Characters for molecular motions
Motion E 2C3 (z) 3C'2
Cartesian 3N 60 0 -2
Translation (x,y,z) 3 0 -1
Rotation (Rx,Ry,Rz) 3 0 -1
Vibration 54 0 0



Decomposition into Irreducible representations
Motion A1 A2 E Total
Cartesian 3N 9 11 20 40
Translation (x,y,z) 0 1 1 2
Rotation (Rx,Ry,Rz) 0 1 1 2
Vibration 9 9 18 36



Molecule Parameter
Number of Atoms (N) 20
Number of internal coordinates 54
Number of independant internal coordinates 9
Number of vibrational modes 36





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E Total
Linear (IR) 9 9 18 27 / 9
Quadratic (Raman) 9 9 18 27 / 9
IR + Raman - - 18 18 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2C3 (z) 3C'2
linear 1 54 0 0
quadratic 2 1.485 0 27
cubic 3 27.720 18 0
quartic 4 395.010 0 378
quintic 5 4.582.116 0 0
sextic 6 45.057.474 171 3.654


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 E
linear 1 9 9 18
quadratic 2 261 234 495
cubic 3 4.626 4.626 9.234
quartic 4 66.024 65.646 131.670
quintic 5 763.686 763.686 1.527.372
sextic 6 7.511.463 7.507.809 15.019.101


Literature




Character tables for chemically important point groups Character table for point group D3 Constructor University Bremen

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