Reduction formula for point group D3h



Characters of input representation
E 2C3 (z) 3C'2 h (xy) 2S3 3v
12 0 0 4 -2 4



Decomposition into Irreducible representations
A'1 A'2 E' A''1 A''2 E'' Total
2 0 3 0 2 1 8





Force field analysis


Allowed / forbidden vibronational transitions
Operator A'1 A'2 E' A''1 A''2 E'' Total
Linear (IR) 2 0 3 0 2 1 5 / 3
Quadratic (Raman) 2 0 3 0 2 1 6 / 2
IR + Raman - 0 3 0 - - 3 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2C3 (z) 3C'2 h (xy) 2S3 3v
linear 1 12 0 0 4 -2 4
quadratic 2 78 0 6 14 2 14
cubic 3 364 4 0 36 0 36
quartic 4 1.365 0 21 85 -2 85
quintic 5 4.368 0 0 176 2 176
sextic 6 12.376 10 56 344 2 344


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A'1 A'2 E' A''1 A''2 E''
linear 1 2 0 3 0 2 1
quadratic 2 13 3 15 3 7 11
cubic 3 43 25 66 19 37 54
quartic 4 147 94 242 91 123 213
quintic 5 423 335 757 305 393 699
sextic 6 1.162 962 2.118 932 1.076 2.004


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