Reduction formula for point group D2



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x)
Cartesian 3N 24 0 0 0
Translation 3 -1 -1 -1
Rotation 3 -1 -1 -1
Vibration 18 2 2 2



Decomposition into Irreducible representations
Motion A B1 B2 B3 Total
Cartesian 3N 6 6 6 6 24
Translation 0 1 1 1 3
Rotation 0 1 1 1 3
Vibration 6 4 4 4 18



Molecule Parameter
Number of Atoms (N) 8
Number of internal coordinates 18
Number of independant internal coordinates 6
Number of vibrational modes 18





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B1 B2 B3 Total
Linear (IR) 6 4 4 4 12 / 6
Quadratic (Raman) 6 4 4 4 18 / 0
IR + Raman - 4 4 4 12 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) C2 (y) C2 (x)
linear 1 18 2 2 2
quadratic 2 171 11 11 11
cubic 3 1.140 20 20 20
quartic 4 5.985 65 65 65
quintic 5 26.334 110 110 110
sextic 6 100.947 275 275 275


Decomposition into Irreducible representations
Force field Tensor
Order
A B1 B2 B3
linear 1 6 4 4 4
quadratic 2 51 40 40 40
cubic 3 300 280 280 280
quartic 4 1.545 1.480 1.480 1.480
quintic 5 6.666 6.556 6.556 6.556
sextic 6 25.443 25.168 25.168 25.168


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