Reduction formula for point group D2



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x)
Cartesian 3N 12 0 0 0
Translation 3 -1 -1 -1
Rotation 3 -1 -1 -1
Vibration 6 2 2 2



Decomposition into Irreducible representations
Motion A B1 B2 B3 Total
Cartesian 3N 3 3 3 3 12
Translation 0 1 1 1 3
Rotation 0 1 1 1 3
Vibration 3 1 1 1 6



Molecule Parameter
Number of Atoms (N) 4
Number of internal coordinates 6
Number of independant internal coordinates 3
Number of vibrational modes 6





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B1 B2 B3 Total
Linear (IR) 3 1 1 1 3 / 3
Quadratic (Raman) 3 1 1 1 6 / 0
IR + Raman - 1 1 1 3 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) C2 (y) C2 (x)
linear 1 6 2 2 2
quadratic 2 21 5 5 5
cubic 3 56 8 8 8
quartic 4 126 14 14 14
quintic 5 252 20 20 20
sextic 6 462 30 30 30


Decomposition into Irreducible representations
Force field Tensor
Order
A B1 B2 B3
linear 1 3 1 1 1
quadratic 2 9 4 4 4
cubic 3 20 12 12 12
quartic 4 42 28 28 28
quintic 5 78 58 58 58
sextic 6 138 108 108 108


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