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 12
Translation 3 0 -1 1 -2 1
Rotation 3 0 -1 -1 2 -1
Vibration 318 0 2 24 0 12



Decomposition into Irreducible representations
Motion A'1 A'2 E' A''1 A''2 E'' Total
Cartesian 3N 32 26 58 22 28 50 216
Translation 0 0 1 0 1 0 2
Rotation 0 1 0 0 0 1 2
Vibration 32 25 57 22 27 49 212



Molecule Parameter
Number of Atoms (N) 108
Number of internal coordinates 318
Number of independant internal coordinates 32
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) 32 25 57 22 27 49 84 / 128
Quadratic (Raman) 32 25 57 22 27 49 138 / 74
IR + Raman - 25 57 22 - - 57 / 47



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 12
quadratic 2 50.721 0 161 447 0 231
cubic 3 5.410.240 106 320 6.128 8 2.200
quartic 4 434.171.760 0 13.040 72.528 0 25.080
quintic 5 27.960.661.344 0 25.760 741.552 0 201.432
sextic 6 1.505.215.602.352 5.671 708.400 6.858.544 85 1.748.824


Decomposition into Irreducible representations
Force field Tensor
Order
A'1 A'2 E' A''1 A''2 E''
linear 1 32 25 57 22 27 49
quadratic 2 4.362 4.166 8.528 4.172 4.207 8.379
cubic 3 452.013 450.753 902.709 449.889 450.829 900.669
quartic 4 36.196.554 36.177.494 72.374.048 36.171.926 36.177.946 72.349.872
quintic 5 2.330.173.706 2.330.060.110 4.660.233.816 2.329.949.398 2.330.037.234 4.659.986.632
sextic 6 125.435.820.340 125.434.591.728 250.870.409.190 125.433.802.809 125.434.323.021 250.868.123.037


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