Reduction formula for point group D2



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x)
Cartesian 3N 72 0 0 0
Translation 3 -1 -1 -1
Rotation 3 -1 -1 -1
Vibration 66 2 2 2



Decomposition into Irreducible representations
Motion A B1 B2 B3 Total
Cartesian 3N 18 18 18 18 72
Translation 0 1 1 1 3
Rotation 0 1 1 1 3
Vibration 18 16 16 16 66



Molecule Parameter
Number of Atoms (N) 24
Number of internal coordinates 66
Number of independant internal coordinates 18
Number of vibrational modes 66





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B1 B2 B3 Total
Linear (IR) 18 16 16 16 48 / 18
Quadratic (Raman) 18 16 16 16 66 / 0
IR + Raman - 16 16 16 48 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) C2 (y) C2 (x)
linear 1 66 2 2 2
quadratic 2 2.211 35 35 35
cubic 3 50.116 68 68 68
quartic 4 864.501 629 629 629
quintic 5 12.103.014 1.190 1.190 1.190
sextic 6 143.218.999 7.735 7.735 7.735


Decomposition into Irreducible representations
Force field Tensor
Order
A B1 B2 B3
linear 1 18 16 16 16
quadratic 2 579 544 544 544
cubic 3 12.580 12.512 12.512 12.512
quartic 4 216.597 215.968 215.968 215.968
quintic 5 3.026.646 3.025.456 3.025.456 3.025.456
sextic 6 35.810.551 35.802.816 35.802.816 35.802.816


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