Reduction formula for point group D2



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x)
Cartesian 3N 36 0 0 0
Translation 3 -1 -1 -1
Rotation 3 -1 -1 -1
Vibration 30 2 2 2



Decomposition into Irreducible representations
Motion A B1 B2 B3 Total
Cartesian 3N 9 9 9 9 36
Translation 0 1 1 1 3
Rotation 0 1 1 1 3
Vibration 9 7 7 7 30



Molecule Parameter
Number of Atoms (N) 12
Number of internal coordinates 30
Number of independant internal coordinates 9
Number of vibrational modes 30





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B1 B2 B3 Total
Linear (IR) 9 7 7 7 21 / 9
Quadratic (Raman) 9 7 7 7 30 / 0
IR + Raman - 7 7 7 21 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) C2 (y) C2 (x)
linear 1 30 2 2 2
quadratic 2 465 17 17 17
cubic 3 4.960 32 32 32
quartic 4 40.920 152 152 152
quintic 5 278.256 272 272 272
sextic 6 1.623.160 952 952 952


Decomposition into Irreducible representations
Force field Tensor
Order
A B1 B2 B3
linear 1 9 7 7 7
quadratic 2 129 112 112 112
cubic 3 1.264 1.232 1.232 1.232
quartic 4 10.344 10.192 10.192 10.192
quintic 5 69.768 69.496 69.496 69.496
sextic 6 406.504 405.552 405.552 405.552


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