Reduction formula for point group D2



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x)
Cartesian 3N 48 0 0 0
Translation 3 -1 -1 -1
Rotation 3 -1 -1 -1
Vibration 42 2 2 2



Decomposition into Irreducible representations
Motion A B1 B2 B3 Total
Cartesian 3N 12 12 12 12 48
Translation 0 1 1 1 3
Rotation 0 1 1 1 3
Vibration 12 10 10 10 42



Molecule Parameter
Number of Atoms (N) 16
Number of internal coordinates 42
Number of independant internal coordinates 12
Number of vibrational modes 42





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B1 B2 B3 Total
Linear (IR) 12 10 10 10 30 / 12
Quadratic (Raman) 12 10 10 10 42 / 0
IR + Raman - 10 10 10 30 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) C2 (y) C2 (x)
linear 1 42 2 2 2
quadratic 2 903 23 23 23
cubic 3 13.244 44 44 44
quartic 4 148.995 275 275 275
quintic 5 1.370.754 506 506 506
sextic 6 10.737.573 2.277 2.277 2.277


Decomposition into Irreducible representations
Force field Tensor
Order
A B1 B2 B3
linear 1 12 10 10 10
quadratic 2 243 220 220 220
cubic 3 3.344 3.300 3.300 3.300
quartic 4 37.455 37.180 37.180 37.180
quintic 5 343.068 342.562 342.562 342.562
sextic 6 2.686.101 2.683.824 2.683.824 2.683.824


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