Reduction formula for point group D3h



Characters for molecular motions
Motion E 2C3 (z) 3C'2 h (xy) 2S3 3v
Cartesian 3N 24 0 0 0 0 4
Translation 3 0 -1 1 -2 1
Rotation 3 0 -1 -1 2 -1
Vibration 18 0 2 0 0 4



Decomposition into Irreducible representations
Motion A'1 A'2 E' A''1 A''2 E'' Total
Cartesian 3N 3 1 4 1 3 4 16
Translation 0 0 1 0 1 0 2
Rotation 0 1 0 0 0 1 2
Vibration 3 0 3 1 2 3 12



Molecule Parameter
Number of Atoms (N) 8
Number of internal coordinates 18
Number of independant internal coordinates 3
Number of vibrational modes 12





Force field analysis


Allowed / forbidden vibronational transitions
Operator A'1 A'2 E' A''1 A''2 E'' Total
Linear (IR) 3 0 3 1 2 3 5 / 7
Quadratic (Raman) 3 0 3 1 2 3 9 / 3
IR + Raman - 0 3 1 - - 3 / 1



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2C3 (z) 3C'2 h (xy) 2S3 3v
linear 1 18 0 2 0 0 4
quadratic 2 171 0 11 9 0 17
cubic 3 1.140 6 20 0 0 48
quartic 4 5.985 0 65 45 0 133
quintic 5 26.334 0 110 0 0 308
sextic 6 100.947 21 275 165 3 693


Decomposition into Irreducible representations
Force field Tensor
Order
A'1 A'2 E' A''1 A''2 E''
linear 1 3 0 3 1 2 3
quadratic 2 22 8 30 12 15 27
cubic 3 113 79 189 89 103 189
quartic 4 552 453 1.005 478 512 990
quintic 5 2.299 2.090 4.389 2.145 2.244 4.389
sextic 6 8.672 8.188 16.848 8.297 8.506 16.794


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