Reduction formula for point group D3h



Characters for molecular motions
Motion E 2C3 (z) 3C'2 h (xy) 2S3 3v
Cartesian 3N 12 0 -2 4 -2 2
Translation (x,y,z) 3 0 -1 1 -2 1
Rotation (Rx,Ry,Rz) 3 0 -1 -1 2 -1
Vibration 6 0 0 4 -2 2



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



Molecule Parameter
Number of Atoms (N) 4
Number of internal coordinates 6
Number of independant internal coordinates 1
Number of vibrational modes 4





Force field analysis


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



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2C3 (z) 3C'2 h (xy) 2S3 3v
linear 1 6 0 0 4 -2 2
quadratic 2 21 0 3 11 2 5
cubic 3 56 2 0 24 0 8
quartic 4 126 0 6 46 -2 14
quintic 5 252 0 0 80 2 20
sextic 6 462 3 10 130 1 30


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 1 0 2 0 1 0
quadratic 2 5 1 5 0 1 2
cubic 3 9 5 13 1 5 5
quartic 4 19 9 29 5 9 13
quintic 5 33 23 55 9 19 29
sextic 6 60 40 98 23 33 55


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