Reduction formula for point group D3



Characters for molecular motions
Motion E 2C3 (z) 3C'2
Cartesian 3N 75 0 -1
Translation (x,y,z) 3 0 -1
Rotation (Rx,Ry,Rz) 3 0 -1
Vibration 69 0 1



Decomposition into Irreducible representations
Motion A1 A2 E Total
Cartesian 3N 12 13 25 50
Translation (x,y,z) 0 1 1 2
Rotation (Rx,Ry,Rz) 0 1 1 2
Vibration 12 11 23 46



Molecule Parameter
Number of Atoms (N) 25
Number of internal coordinates 69
Number of independant internal coordinates 12
Number of vibrational modes 46





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E Total
Linear (IR) 12 11 23 34 / 12
Quadratic (Raman) 12 11 23 35 / 11
IR + Raman - - 23 23 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2C3 (z) 3C'2
linear 1 69 0 1
quadratic 2 2.415 0 35
cubic 3 57.155 23 35
quartic 4 1.028.790 0 630
quintic 5 15.020.334 0 630
sextic 6 185.250.786 276 7.770


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 E
linear 1 12 11 23
quadratic 2 420 385 805
cubic 3 9.551 9.516 19.044
quartic 4 171.780 171.150 342.930
quintic 5 2.503.704 2.503.074 5.006.778
sextic 6 30.879.108 30.871.338 61.750.170


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