Reduction formula for point group D3h



Characters for molecular motions
Motion E 2C3 (z) 3C'2 h (xy) 2S3 3v
Cartesian 3N 324 0 0 24 0 8
Translation 3 0 -1 1 -2 1
Rotation 3 0 -1 -1 2 -1
Vibration 318 0 2 24 0 8



Decomposition into Irreducible representations
Motion A'1 A'2 E' A''1 A''2 E'' Total
Cartesian 3N 31 27 58 23 27 50 216
Translation 0 0 1 0 1 0 2
Rotation 0 1 0 0 0 1 2
Vibration 31 26 57 23 26 49 212



Molecule Parameter
Number of Atoms (N) 108
Number of internal coordinates 318
Number of independant internal coordinates 31
Number of vibrational modes 212





Force field analysis


Allowed / forbidden vibronational transitions
Operator A'1 A'2 E' A''1 A''2 E'' Total
Linear (IR) 31 26 57 23 26 49 83 / 129
Quadratic (Raman) 31 26 57 23 26 49 137 / 75
IR + Raman - 26 57 23 - - 57 / 49



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2C3 (z) 3C'2 h (xy) 2S3 3v
linear 1 318 0 2 24 0 8
quadratic 2 50.721 0 161 447 0 191
cubic 3 5.410.240 106 320 6.128 8 1.360
quartic 4 434.171.760 0 13.040 72.528 0 18.000
quintic 5 27.960.661.344 0 25.760 741.552 0 116.112
sextic 6 1.505.215.602.352 5.671 708.400 6.858.544 85 1.120.816


Decomposition into Irreducible representations
Force field Tensor
Order
A'1 A'2 E' A''1 A''2 E''
linear 1 31 26 57 23 26 49
quadratic 2 4.352 4.176 8.528 4.182 4.197 8.379
cubic 3 451.803 450.963 902.709 450.099 450.619 900.669
quartic 4 36.194.784 36.179.264 72.374.048 36.173.696 36.176.176 72.349.872
quintic 5 2.330.152.376 2.330.081.440 4.660.233.816 2.329.970.728 2.330.015.904 4.659.986.632
sextic 6 125.435.663.338 125.434.748.730 250.870.409.190 125.433.959.811 125.434.166.019 250.868.123.037


Literature




Character tables for chemically important point groups Character table for point group D3h Jacobs University Bremen

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