Reduction formula for point group D2



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x)
Cartesian 3N 9 -3 -1 -1
Translation (x,y,z) 3 -1 -1 -1
Rotation (Rx,Ry)* 2 -2 0 0
Vibration 4 0 0 0
* Linear molecule


Decomposition into Irreducible representations
Motion A B1 B2 B3 Total
Cartesian 3N 1 2 3 3 9
Translation (x,y,z) 0 1 1 1 3
Rotation (Rx,Ry)* 0 0 1 1 2
Vibration 1 1 1 1 4
* Linear molecule


Molecule Parameter
Number of Atoms (N) 3
Number of internal coordinates 4
Number of independant internal coordinates 1
Number of vibrational modes 4





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B1 B2 B3 Total
Linear (IR) 1 1 1 1 3 / 1
Quadratic (Raman) 1 1 1 1 4 / 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 4 0 0 0
quadratic 2 10 2 2 2
cubic 3 20 0 0 0
quartic 4 35 3 3 3
quintic 5 56 0 0 0
sextic 6 84 4 4 4


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A B1 B2 B3
linear 1 1 1 1 1
quadratic 2 4 2 2 2
cubic 3 5 5 5 5
quartic 4 11 8 8 8
quintic 5 14 14 14 14
sextic 6 24 20 20 20


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