Reduction formula for point group D3h



Characters for molecular motions
Motion E 2C3 (z) 3C'2 h (xy) 2S3 3v
Cartesian 3N 36 0 -4 12 0 4
Translation 3 0 -1 1 -2 1
Rotation 3 0 -1 -1 2 -1
Vibration 30 0 -2 12 0 4



Decomposition into Irreducible representations
Motion A'1 A'2 E' A''1 A''2 E'' Total
Cartesian 3N 4 4 8 0 4 4 24
Translation 0 0 1 0 1 0 2
Rotation 0 1 0 0 0 1 2
Vibration 4 3 7 0 3 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 0 3 3 10 / 10
Quadratic (Raman) 4 3 7 0 3 3 14 / 6
IR + Raman - 3 7 0 - - 7 / 3



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 4
quadratic 2 465 0 17 87 0 23
cubic 3 4.960 10 -32 472 4 72
quartic 4 40.920 0 152 2.112 0 256
quintic 5 278.256 0 -272 8.184 0 680
sextic 6 1.623.160 55 952 28.336 13 1.904


Decomposition into Irreducible representations
Force field Tensor
Order
A'1 A'2 E' A''1 A''2 E''
linear 1 4 3 7 0 3 3
quadratic 2 56 36 92 30 33 63
cubic 3 465 445 903 349 401 747
quartic 4 3.688 3.484 7.172 3.208 3.260 6.468
quintic 5 23.972 23.768 47.740 22.268 22.744 45.012
sextic 6 138.350 136.922 275.238 132.671 133.147 265.797


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