Reduction formula for point group D2



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x)
Cartesian 3N 6 -2 0 0
Translation (x,y,z) 3 -1 -1 -1
Rotation (Rx,Ry)* 2 -2 0 0
Vibration 1 1 1 1
* Linear molecule


Decomposition into Irreducible representations
Motion A B1 B2 B3 Total
Cartesian 3N 1 1 2 2 6
Translation (x,y,z) 0 1 1 1 3
Rotation (Rx,Ry)* 0 0 1 1 2
Vibration 1 0 0 0 1
* Linear molecule


Molecule Parameter
Number of Atoms (N) 2
Number of internal coordinates 1
Number of independant internal coordinates 1
Number of vibrational modes 1





Force field analysis


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



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) C2 (y) C2 (x)
linear 1 1 1 1 1
quadratic 2 1 1 1 1
cubic 3 1 1 1 1
quartic 4 1 1 1 1
quintic 5 1 1 1 1
sextic 6 1 1 1 1


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A B1 B2 B3
linear 1 1 0 0 0
quadratic 2 1 0 0 0
cubic 3 1 0 0 0
quartic 4 1 0 0 0
quintic 5 1 0 0 0
sextic 6 1 0 0 0


Literature




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

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