Reduction formula for point group D3h



Characters for molecular motions
Motion E 2C3 (z) 3C'2 h (xy) 2S3 3v
Cartesian 3N 18 0 -2 4 -2 4
Translation (x,y,z) 3 0 -1 1 -2 1
Rotation (Rx,Ry,Rz) 3 0 -1 -1 2 -1
Vibration 12 0 0 4 -2 4



Decomposition into Irreducible representations
Motion A'1 A'2 E' A''1 A''2 E'' Total
Cartesian 3N 2 1 4 0 3 2 12
Translation (x,y,z) 0 0 1 0 1 0 2
Rotation (Rx,Ry,Rz) 0 1 0 0 0 1 2
Vibration 2 0 3 0 2 1 8



Molecule Parameter
Number of Atoms (N) 6
Number of internal coordinates 12
Number of independant internal coordinates 2
Number of vibrational modes 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 Constructor University Bremen

Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement