Reduction formula for point group D2



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x)
Cartesian 3N 60 0 0 0
Translation 3 -1 -1 -1
Rotation 3 -1 -1 -1
Vibration 54 2 2 2



Decomposition into Irreducible representations
Motion A B1 B2 B3 Total
Cartesian 3N 15 15 15 15 60
Translation 0 1 1 1 3
Rotation 0 1 1 1 3
Vibration 15 13 13 13 54



Molecule Parameter
Number of Atoms (N) 20
Number of internal coordinates 54
Number of independant internal coordinates 15
Number of vibrational modes 54





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B1 B2 B3 Total
Linear (IR) 15 13 13 13 39 / 15
Quadratic (Raman) 15 13 13 13 54 / 0
IR + Raman - 13 13 13 39 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) C2 (y) C2 (x)
linear 1 54 2 2 2
quadratic 2 1.485 29 29 29
cubic 3 27.720 56 56 56
quartic 4 395.010 434 434 434
quintic 5 4.582.116 812 812 812
sextic 6 45.057.474 4.466 4.466 4.466


Decomposition into Irreducible representations
Force field Tensor
Order
A B1 B2 B3
linear 1 15 13 13 13
quadratic 2 393 364 364 364
cubic 3 6.972 6.916 6.916 6.916
quartic 4 99.078 98.644 98.644 98.644
quintic 5 1.146.138 1.145.326 1.145.326 1.145.326
sextic 6 11.267.718 11.263.252 11.263.252 11.263.252


Literature




Character tables for chemically important point groups Character table for point group D2 Jacobs University Bremen

Last update Mai, 23rd 2018 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement