Reduction formula for point group D3h



Characters for molecular motions
Motion E 2C3 (z) 3C'2 h (xy) 2S3 3v
Cartesian 3N 36 0 0 12 0 0
Translation 3 0 -1 1 -2 1
Rotation 3 0 -1 -1 2 -1
Vibration 30 0 2 12 0 0



Decomposition into Irreducible representations
Motion A'1 A'2 E' A''1 A''2 E'' Total
Cartesian 3N 4 4 8 2 2 4 24
Translation 0 0 1 0 1 0 2
Rotation 0 1 0 0 0 1 2
Vibration 4 3 7 2 1 3 20



Molecule Parameter
Number of Atoms (N) 12
Number of internal coordinates 30
Number of independant internal coordinates 4
Number of vibrational modes 20





Force field analysis


Allowed / forbidden vibronational transitions
Operator A'1 A'2 E' A''1 A''2 E'' Total
Linear (IR) 4 3 7 2 1 3 8 / 12
Quadratic (Raman) 4 3 7 2 1 3 14 / 6
IR + Raman - 3 7 2 - - 7 / 5



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2C3 (z) 3C'2 h (xy) 2S3 3v
linear 1 30 0 2 12 0 0
quadratic 2 465 0 17 87 0 15
cubic 3 4.960 10 32 472 4 0
quartic 4 40.920 0 152 2.112 0 120
quintic 5 278.256 0 272 8.184 0 0
sextic 6 1.623.160 55 952 28.336 13 680


Decomposition into Irreducible representations
Force field Tensor
Order
A'1 A'2 E' A''1 A''2 E''
linear 1 4 3 7 2 1 3
quadratic 2 54 38 92 32 31 63
cubic 3 463 447 903 383 367 747
quartic 4 3.654 3.518 7.172 3.242 3.226 6.468
quintic 5 23.938 23.802 47.740 22.574 22.438 45.012
sextic 6 138.044 137.228 275.238 132.977 132.841 265.797


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