Reduction formula for point group D3



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



Decomposition into Irreducible representations
Motion A1 A2 E Total
Cartesian 3N 10 10 20 40
Translation 0 1 1 2
Rotation 0 1 1 2
Vibration 10 8 18 36



Molecule Parameter
Number of Atoms (N) 20
Number of internal coordinates 54
Number of independant internal coordinates 10
Number of vibrational modes 36





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E Total
Linear (IR) 10 8 18 26 / 10
Quadratic (Raman) 10 8 18 28 / 8
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 2
quadratic 2 1.485 0 29
cubic 3 27.720 18 56
quartic 4 395.010 0 434
quintic 5 4.582.116 0 812
sextic 6 45.057.474 171 4.466


Decomposition into Irreducible representations
Force field Tensor
Order
A1 A2 E
linear 1 10 8 18
quadratic 2 262 233 495
cubic 3 4.654 4.598 9.234
quartic 4 66.052 65.618 131.670
quintic 5 764.092 763.280 1.527.372
sextic 6 7.511.869 7.507.403 15.019.101


Literature




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

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