Reduction formula for point group D3



Characters for molecular motions
Motion E 2C3 (z) 3C'2
Cartesian 3N 21 0 -1
Translation 3 0 -1
Rotation 3 0 -1
Vibration 15 0 1



Decomposition into Irreducible representations
Motion A1 A2 E Total
Cartesian 3N 3 4 7 14
Translation 0 1 1 2
Rotation 0 1 1 2
Vibration 3 2 5 10



Molecule Parameter
Number of Atoms (N) 7
Number of internal coordinates 15
Number of independant internal coordinates 3
Number of vibrational modes 10





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E Total
Linear (IR) 3 2 5 7 / 3
Quadratic (Raman) 3 2 5 8 / 2
IR + Raman - - 5 5 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2C3 (z) 3C'2
linear 1 15 0 1
quadratic 2 120 0 8
cubic 3 680 5 8
quartic 4 3.060 0 36
quintic 5 11.628 0 36
sextic 6 38.760 15 120


Decomposition into Irreducible representations
Force field Tensor
Order
A1 A2 E
linear 1 3 2 5
quadratic 2 24 16 40
cubic 3 119 111 225
quartic 4 528 492 1.020
quintic 5 1.956 1.920 3.876
sextic 6 6.525 6.405 12.915


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