Reduction formula for point group D2



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x)
Cartesian 3N 21 -3 -1 -1
Translation 3 -1 -1 -1
Rotation 3 -1 -1 -1
Vibration 15 -1 1 1



Decomposition into Irreducible representations
Motion A B1 B2 B3 Total
Cartesian 3N 4 5 6 6 21
Translation 0 1 1 1 3
Rotation 0 1 1 1 3
Vibration 4 3 4 4 15



Molecule Parameter
Number of Atoms (N) 7
Number of internal coordinates 15
Number of independant internal coordinates 4
Number of vibrational modes 15





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B1 B2 B3 Total
Linear (IR) 4 3 4 4 11 / 4
Quadratic (Raman) 4 3 4 4 15 / 0
IR + Raman - 3 4 4 11 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) C2 (y) C2 (x)
linear 1 15 -1 1 1
quadratic 2 120 8 8 8
cubic 3 680 -8 8 8
quartic 4 3.060 36 36 36
quintic 5 11.628 -36 36 36
sextic 6 38.760 120 120 120


Decomposition into Irreducible representations
Force field Tensor
Order
A B1 B2 B3
linear 1 4 3 4 4
quadratic 2 36 28 28 28
cubic 3 172 164 172 172
quartic 4 792 756 756 756
quintic 5 2.916 2.880 2.916 2.916
sextic 6 9.780 9.660 9.660 9.660


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